diff --git a/.github/dlsmt.sh b/.github/dlsmt.sh
new file mode 100755
index 0000000..f741a67
--- /dev/null
+++ b/.github/dlsmt.sh
@@ -0,0 +1,73 @@
+# No shebang!
+
+## Weigl's little helper to download SMT-solvers.
+# SPDX-License-Identifier: GPL-2.0-or-later
+
+# This script is meant to be executed inside an Github Action to download the SMT-solver.
+# It uses the Github cli tool "gh", which allows an easy access to the releases of a
+# repository, and to download it artifacts.
+#
+# This script will always the latest uploaded artifact.
+#
+#
+# For performance, you should consider caching. This script skips downloading if files are present.
+
+
+## Github workflow commands
+# Please have a look at https://docs.github.com/en/actions/using-workflows/workflow-commands-for-github-actions
+# which explains a lot of workflow commands and special files in Github Actions.
+
+
+## TODO
+# It would be nice to convert it into a real! Github action, which can also exploit
+# the API library of Github. A manual/tutorial is here:
+#
+# https://docs.github.com/en/actions/creating-actions/developing-a-third-party-cli-action
+
+mkdir smt-solvers
+cd smt-solvers
+
+
+#################################################
+echo "::group::{install z3}"
+echo "Check for Z3, if present skip installation"
+
+if readlink -f */bin/z3; then
+ echo "::notice::{Z3 found. Caching works! Skip installation}"
+else
+ echo "Download Z3"
+ wget 'https://github.com/Z3Prover/z3/releases/download/z3-4.12.2/z3-4.12.2-x64-glibc-2.31.zip'
+ unzip -n z3*.zip
+ rm z3-*.zip
+fi
+
+Z3=$(readlink -f */bin/z3)
+chmod u+x $Z3
+echo "Z3 added to path: $Z3"
+echo $(dirname $Z3) >> $GITHUB_PATH
+
+echo "::endgroup::"
+#################################################
+
+#################################################
+echo "::group::{install cvc5}"
+if -f cvc5-Linux; then
+ echo "::notice::{Z3 found. Caching works! Skip installation}"
+else
+ echo "Install CVC5"
+ gh release download --skip-existing -p 'cvc5-Linux' -R cvc5/cvc5
+fi
+
+CVC5=$(readlink -f cvc5-Linux)
+echo "CVC5 installed and added to path: CVC5"
+chmod u+x $CVC5
+echo $(dirname $CVC5) >> $GITHUB_PATH
+
+echo "::endgroup::"
+#################################################
+
+echo "::group::{check installation/versions}"
+$Z3 -version
+
+$CVC5 --version
+echo "::endgroup::"
\ No newline at end of file
diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 269ba31..f3b598e 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -1,51 +1,45 @@
-name: Broad Release Tests
+name: Proof Replay
-on:
- workflow_dispatch:
- push:
- branches: ["main", "master"]
- schedule:
- - cron: '0 5 * * 1' # every monday morning
+on: [ push ]
permissions:
- checks: write
+ checks: write
jobs:
- unit-tests:
- strategy:
- fail-fast: false
- matrix:
- os: [macos-latest, ubuntu-latest, windows-latest]
- java: [8,11,17,21]
- continue-on-error: false
- runs-on: ${{ matrix.os }}
- env:
- GH_TOKEN: ${{ github.token }}
- steps:
- - uses: actions/checkout@v3
- - name: Set up JDK ${{ matrix.java }}
- uses: actions/setup-java@v3
- with:
- java-version: ${{ matrix.java }}
- distribution: 'corretto'
+ compile_and_test:
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@v3
+ - name: Set up JDK 21
+ uses: actions/setup-java@v3
+ with:
+ java-version: 21
+ distribution: 'corretto'
+ - name: Build with Gradle
+ uses: gradle/gradle-build-action@v2.4.2
+ with:
+ arguments: --continue assemble check
- - name: Build with Gradle
- uses: gradle/gradle-build-action@v2.4.2
- with:
- arguments: --continue test
+ replay-proofs:
+ strategy:
+ fail-fast: false
+ matrix:
+ # target: [ check-overflow-methods, check-overflow-constructors, check-methods, check-constructors ]
+ # Reduce checks until overflow is fixed
+ target: [ check-methods, check-constructors ]
+ runs-on: ubuntu-latest
+ env:
+ GH_TOKEN: ${{ github.token }}
- - name: Verify with KeY
- uses: gradle/gradle-build-action@v2.4.2
- with:
- arguments: --continue checkAll
-
-
- - name: Upload test results
- uses: actions/upload-artifact@v3.1.1
- if: success() || failure()
- with:
- name: test-results-${{ matrix.os }}
- path: |
- **/build/test-results/*/*.xml
- **/build/reports/
- !**/jacocoTestReport.xml
+ steps:
+ - uses: actions/checkout@v3
+ - name: Set up JDK 21
+ uses: actions/setup-java@v3
+ with:
+ java-version: 21
+ distribution: 'corretto'
+ - name: Install SMT-Solvers
+ run: .github/dlsmt.sh
+ shell: bash
+ - name: "Verify with KeY ${{ matrix.target }}"
+ run: make ${{ matrix.target }}
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..29fd787
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,50 @@
+KEY_JAR=tools/key-2.11.0-exe.jar
+KEY_OVERFLOW_JAR=tools/key-2.11.0-o-exe.jar
+CI_TOOL=tools/citool-1.4.0-mini.jar
+
+checkCommand=java -Dlogback.configurationFile=./gradle/disablelogging.xml -Dkey.contractOrder="contract-order.txt" -cp "$(KEY_JAR):$(CI_TOOL)" de.uka.ilkd.key.CheckerKt --no-auto-mode --proof-path src/main/key
+
+checkOverflowCommand=java -Dlogback.configurationFile=./gradle/disablelogging.xml -Dkey.contractOrder="contract-order.txt" -cp "$(KEY_OVERFLOW_JAR):$(CI_TOOL)" de.uka.ilkd.key.CheckerKt -v --no-auto-mode --proof-path src/main/key-overflow
+
+default:
+ @echo Available targets:
+ @sed -n 's/^\([a-zA-Z_-]\+\):.*/ \1/p' Makefile
+
+proofSettings:
+ mkdir -p $${HOME}/.key
+ cp proofIndependentSettings.props $${HOME}/.key
+
+run:
+ @echo Consider loading one of the following files:
+ @find -iname "project*.key"
+ java -Dkey.contractOrder="contract-order.txt" -jar $(KEY_JAR)
+
+compile:
+ find -name "*.java" > sources.txt
+ javac @sources.txt
+
+constr-src:
+ rm -rf src/main/java-constr
+ cp -r src/main/java src/main/java-constr
+ sed -i 's/no_state int bucketStart/int bucketStart/' src/main/java-constr/de/wiesler/BucketPointers.java
+ sed -i 's/no_state int bucketSize/int bucketSize/' src/main/java-constr/de/wiesler/BucketPointers.java
+
+constr-overflow-src:
+ rm -rf src/main/java-constr-overflow
+ cp -r src/main/java src/main/java-constr-overflow
+ sed -i 's/no_state int bucketStart/int bucketStart/' src/main/java-constr-overflow/de/wiesler/BucketPointers.java
+ sed -i 's/no_state int bucketSize/int bucketSize/' src/main/java-constr-overflow/de/wiesler/BucketPointers.java
+
+check: check-methods check-constructors check-overflow-methods check-overflow-constructors
+
+check-methods: proofSettings
+ $(checkCommand) --forbid-contracts-file "contracts/ignore.txt" --forbid-contracts-file "contracts/constructors.txt" -s statistics-methods.json src/main/key/project.key
+
+check-constructors: constr-src
+ $(checkCommand) --contracts-file contracts/constructors.txt -s statistics-constructors.json src/main/key/project-constr.key
+
+check-overflow-methods:
+ $(checkOverflowCommand) --contracts-file "contracts/overflow.txt" --forbid-contracts-file "contracts/constructors.txt" -s statistics-overflow-methods.json src/main/key-overflow/project.key
+
+check-overflow-constructors: constr-overflow-src
+ $(checkOverflowCommand) --contracts-file "contracts/constructors.txt" -s statistics-overflow-constructors.json src/main/key-overflow/project-constr.key
diff --git a/README.md b/README.md
index e777c99..ff796c6 100644
--- a/README.md
+++ b/README.md
@@ -1,22 +1,159 @@
-# Formal Specification and Verification of a Java Implementation of In-Place Super Scalar Sample Sort
+# A Formally Verified Efficient Sorting Routine For Java
-This is the verified code and all proof files.
+This repostiory contains a sorting routine for Java programs that
+combines two important properties that a decent algorithm should have: [2]
+1. The implementation is competitively efficient.
+2. The implementation is correct in all possible application cases.
-The code in [`src`](src) is based on [this](https://github.com/jwiesler/ips4o) Rust rewrite of the [original paper implementation](https://github.com/ips4o/ips4o).
+The first point is shown empirically by benchmarking (see Section 5 of
+[2] and the [Sascha Witt's
+repository](https://github.com/SaschaWitt/ips4o-java-benchmark)). The
+correctness of the implementation has been formally proven using the
+[deductive verification engine KeY](https://www.key-project.org) with
+which Java programs can be verified against a formal specification
+using the [Java Modeling Language
+(JML)](https://www.cs.ucf.edu/~leavens/JML/index.shtml).
-The proofs are located in [`proofs`](proofs) and can be loaded using the KeY binaries in [`tools`](tools).
-The [`contracts`](contracts) folder contains listing of subsets of all contracts used for filtering.
-The proof statistics can be found in [`statistics`](statistics).
+You can use the algorithm in your Java programs by declaring a
+maven/gradle dependency in your project (s. below).
+## In-Place Super Scalar Sample Sort
+
+The sorting algorithm [1] implemented in this project is a Java
+implementation of in-place super scalar sample sort (ips4o), an award
+winning highly efficient sorting routine that was algorithmically
+engineered to make use of CPU features like caching, predictive
+execution or SIMD.
+
+The [source code](src/main/java) is based on [this Rust
+rewrite](https://github.com/jwiesler/ips4o) of the [original paper
+implementation](https://github.com/ips4o/ips4o).
+
+The source code comprises approximately 900 lines of code. The JML
+specification that annotates the Java code (in comments) adds another
+2500 lines to the sources.
+
+## Using ips4o in your project
+
+You can use the following [maven coordinates](todo) to use `ips4o` in your JVM projects.
+
+
+```groovy
+dependencies {
+ implementation("org.key-project.ips4o:ips4o-verify:1.0")
+}
+```
+
+```xml
+
+ org.key-project.ips4o
+ ips4o-verify
+ 1.0
+
+```
+
+## Verified Properties
+
+In this case study, the following properties of the Java ips4o implementation
+have been specified and successfully verified:
+1. **Sorting Property:** The array is sorted after the method invocation.
+2. **Permutation Property:** The content of the input array after sorting is a permutation of the initial content.
+3. **Exception Safety:** No uncaught exceptions are thrown.
+4. **Memory Safety:** The implementation does not modify any previously allocated memory location except the entries of the input array.
+5. **Termination:** Every method invocation terminates.
+6. **Absence of Overflows:** During the execution of the method, no integer operation will overflow or underflow.
+
+The top-level specification of the sorting routine reads as follows:
+```
+/*@ public normal_behaviour
+ @ requires values.length <= Buffers.MAX_LEN;
+ @
+ @ ensures \dl_seqPerm(\dl_array2seq(values), \old(\dl_array2seq(values)));
+ @ ensures Functions.isSortedSlice(values, 0, values.length);
+ @
+ @ assignable values[*];
+ @*/
+public static void sort(int[] values) { ... }
+```
+
+This repository contains the verified code incl. the specification and all proof files.
## Usage
-You can either run the respective KeY binaries in [`tools`](tools) or take some inspiration from the [`justfile`](justfile).
-Make sure to pass `-Dkey.contractOrder=""` to java such that the contract order file is loaded.
+### Compilation
+
+In order to compile the sources invoke
+```
+./gradlew compileJava
+```
+
+In order to obtain a jar file with the binary class files of the implementation invoke
+```
+./gradlew jar
+```
+and find the jar file in `./build/libs/ips4o-verify-1.0.jar`.
+
+### Verification
+
+In order to check / redo the proofs, you can load the interactive interface of KeY using
+```
+make run
+```
+
+To check whether all proofs can be replpayed, invoke
+```
+make check
+```
+This may take some time (possible hours).
+
+You find the respective KeY binaries in the directory
+[`tools`](tools). The [`Makefile`](Makefile) gives you hints on how to
+execute the checker.
+
+The proofs are located in [`proofs`](proofs) and can be loaded using
+the KeY binaries in [`tools`](tools).
+
+The [`contracts`](contracts) folder contains listing of subsets of all
+contracts used for filtering. The proof statistics can be found in
+[`statistics`](statistics).
+
+
+Make sure to pass `-Dkey.contractOrder=""`
+to java such that the contract order file is loaded.
## Caveats
-* Overflow proofs and annotations can be found on the branch `overflow`. They have to be loaded using the second KeY binary [`key-2.11.0-o-exe.jar`](tools/key-2.11.0-o-exe.jar).
-* To run proofs in [`contracts/constructors.txt`](contracts/constructors.txt) the `no_state` modifier on `BucketPointers::bucketStart` and `BucketPointers::bucketSize` has to be removed. Both methods are only `no_state` when using the final heap which has a soundness problem with constructors. There is currently no nicer way to do this in KeY automatically.
+
+* The overflow proofs have been conducted after the other proofs. The
+ annotated sources can be found under
+ [`src/main/java-overflow`](src/main/java-overflow). In them most
+ artifacts are assumed without proving them (using the `_free`) since
+ they have been shown in the original proof obligations. They have
+ to be loaded using the second KeY binary
+ [`key-2.11.0-o-exe.jar`](tools/key-2.11.0-o-exe.jar).
+
+* To run proofs in
+ [`contracts/constructors.txt`](contracts/constructors.txt) the
+ `no_state` modifier on `BucketPointers::bucketStart` and
+ `BucketPointers::bucketSize` has to be removed. Both methods are
+ only `no_state` when using the final heap which has a soundness
+ problem with constructors. There is currently no nicer way to do
+ this in KeY automatically. The Makefile takes care of this
+ adaptation.
+
* The methods `Tree::classify`, `Tree::classify_all` as well as `Tree::build` were left out as future work.
+
* To run the code use the `bench` branch which has the proper fallback sorting algorithm not commented out.
+
* The sampling function `Functions::select_n` is left empty and should probably be implemented.
+
+## Publications
+
+1. Axtmann, M., Ferizovic, D., Sanders, P., Witt, S.: [*Engineering
+in-place (shared- memory) sorting
+algorithms*](https://dl.acm.org/doi/full/10.1145/3505286). ACM
+Transaction on Parallel Computing 9(1), 2:1– 2:62 (2022), see also
+[github.com/ips4o](https://github.com/ips4o). Conference version in
+ESA 2017
+
+2. B. Beckert, P. Sanders, M. Ulbrich, J. Wiesler, and S. Witt:
+ *Formally Verifying an Efficient Sorter*. arxiv
diff --git a/build.gradle.kts b/build.gradle.kts
index a6d94fe..dbd16c7 100644
--- a/build.gradle.kts
+++ b/build.gradle.kts
@@ -108,84 +108,4 @@ nexusPublishing {
// If you get the error "java.net.SocketTimeoutException: timeout", these lines will help.
connectTimeout = Duration.ofMinutes(3)
clientTimeout = Duration.ofMinutes(3)
-}
-
-// verification
-
-val keyClasspath: Configuration = configurations.create("key")
-val keyClasspathOverflow: Configuration = configurations.create("keyoverflow")
-dependencies {
- keyClasspath(files("tools/key-2.11.0-exe.jar", "tools/citool-1.4.0-mini.jar"))
- keyClasspathOverflow(files("tools/key-2.11.0-o-exe.jar", "tools/citool-1.4.0-mini.jar"))
-}
-
-val mainClassName = "de.uka.ilkd.key.CheckerKt"
-
-fun JavaExec.checkCommand() {
- mainClass = "de.uka.ilkd.key.CheckerKt"
- classpath = keyClasspath
- systemProperty("key.contractOrder", "contract-order.txt")
- args("--verbose", "--no-auto-mode", "--proof-path", "src/main/key/", "src/main/key/project.key")
- group = "key"
- tasks.named("check").get().dependsOn(this)
-}
-
-fun JavaExec.checkOverflowCommand() {
- mainClass = "de.uka.ilkd.key.CheckerKt"
- systemProperty("key.contractOrder", "contract-order.txt")
- args("-v", "--no-auto-mode", "--proof-path", "proofs-overflow/", "src/main/key/project.key")
- classpath = keyClasspathOverflow
- group = "key"
- tasks.named("check").get().dependsOn(this)
-}
-
-tasks.create("run") {
- mainClass = "de.uka.ilkd.key.core.Main"
- classpath = files("tools/key-2.11.0-exe.jar", "tools/citool-1.4.0-mini.jar")
- systemProperty("key.contractOrder", "contract-order.txt")
-}
-
-tasks.create("checkAll") {
- checkCommand()
- args("--forbid-contracts-file", "contracts/ignore.txt", "-s", "statistics.json")
-}
-
-tasks.create("checkMethods") {
- checkCommand()
- args(
- "--forbid-contracts-file", "contracts/ignore.txt", "-s", "statistics-methods.json",
- "--forbid-contracts-file", "contracts/constructors.txt"
- )
-}
-
-tasks.create("checkConstructors") {
- checkCommand()
- args("--contracts-file", "contracts/constructors.txt", "-s", "statistics-constructors.json")
-}
-
-tasks.create("checkClassTarget")
-{
- checkCommand()
- args(
- "--forbid-contracts",
- "-file",
- "contracts/ignore.txt",
- "--contracts-filter",
- """^de.wiesler.{{target}}[.*""",
- "-s",
- "statistics.json"
- )
-}
-
-tasks.create("checkOverflowMethods") {
- checkOverflowCommand()
- args(
- "--contracts-file", "contracts/overflow.txt", "--forbid-contracts-file", "contracts/constructors.txt",
- "-s", "statistics-overflow-methods.json"
- )
-}
-
-tasks.create("checkOverflowConstructors") {
- checkOverflowCommand()
- args("--contracts-file", "contracts/constructors.txt", "-s", "statistics-overflow-constructors.json")
-}
+}
\ No newline at end of file
diff --git a/contract-order.txt b/contract-order.txt
index f4f088d..e794972 100644
--- a/contract-order.txt
+++ b/contract-order.txt
@@ -109,6 +109,7 @@ de.wiesler.Partition[de.wiesler.Partition::bucketCountsToTotalCount([I,int,int,[
de.wiesler.SampleParameters[de.wiesler.SampleParameters::isValidForLen(int)].JML model_behavior operation contract.0
+de.wiesler.Sorter[de.wiesler.Sorter::seqUpd(\seq,int,int)].JML model_behavior operation contract.0
de.wiesler.Sorter[de.wiesler.Sorter::allBucketsInRangeSorted([I,int,int,[I,int,int,int)].JML model_behavior operation contract.0
de.wiesler.Sorter[de.wiesler.Sorter::allBucketsPartitioned([I,int,int,[I,int)].JML model_behavior operation contract.0
de.wiesler.Sorter[de.wiesler.Sorter::allBucketsPartitionedLemma(de.wiesler.Classifier,[I,int,int,[I)].JML model_behavior operation contract.0
@@ -227,6 +228,7 @@ de.wiesler.Classifier[de.wiesler.Classifier::classify_locally_batched([I,int,int
de.wiesler.Classifier[de.wiesler.Classifier::classify_locally([I,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+de.wiesler.Sorter[de.wiesler.Sorter::insertion_sort([I,int,int)].JML normal_behavior operation contract.0
de.wiesler.Sorter[de.wiesler.Sorter::fallback_sort([I,int,int)].JML normal_behavior operation contract.0
de.wiesler.Sorter[de.wiesler.Sorter::base_case_sort([I,int,int)].JML normal_behavior operation contract.0
diff --git a/gradle/disablelogging.xml b/gradle/disablelogging.xml
new file mode 100644
index 0000000..ce4ce39
--- /dev/null
+++ b/gradle/disablelogging.xml
@@ -0,0 +1,13 @@
+
+
+
+
+
+ [%date{HH:mm:ss.SSS}] %highlight(%-5level) %cyan(%logger{0}) - %msg%ex%n
+
+
+
+
+
+
+
diff --git a/justfile b/justfile
deleted file mode 100644
index ec68a4e..0000000
--- a/justfile
+++ /dev/null
@@ -1,34 +0,0 @@
-KEY_JAR := "tools/key-2.11.0-exe.jar"
-KEY_OVERFLOW_JAR := "tools/key-2.11.0-o-exe.jar"
-CI_TOOL := "tools/citool-1.4.0-mini.jar"
-
-checkCommand := 'java -Dkey.contractOrder="contract-order.txt" -cp "' + KEY_JAR + ';' + CI_TOOL + '" de.uka.ilkd.key.CheckerKt --no-auto-mode --proof-path proofs/ project.key'
-checkOverflowCommand := 'java -Dkey.contractOrder="contract-order.txt" -cp "' + KEY_OVERFLOW_JAR + ';' + CI_TOOL + '" de.uka.ilkd.key.CheckerKt -v --no-auto-mode --proof-path proofs-overflow/ project.key'
-
-default:
- @just --list
-
-run:
- java -Dkey.contractOrder="contract-order.txt" -jar {{KEY_JAR}}
-
-compile:
- find -name "*.java" > sources.txt
- javac @sources.txt
-
-check:
- {{checkCommand}} --forbid-contracts-file "contracts/ignore.txt" -s statistics.json
-
-check-methods:
- {{checkCommand}} --forbid-contracts-file "contracts/ignore.txt" --forbid-contracts-file "contracts/constructors.txt" -s statistics-methods.json
-
-check-constructors:
- {{checkCommand}} --contracts-file contracts/constructors.txt -s statistics-constructors.json
-
-check-class target:
- {{checkCommand}} --forbid-contracts-file "contracts/ignore.txt" --contracts-filter "^de\.wiesler\.{{target}}\[.*" -s statistics.json
-
-check-overflow-methods:
- {{checkOverflowCommand}} --contracts-file "contracts/overflow.txt" --forbid-contracts-file "contracts/constructors.txt" -s statistics-overflow-methods.json
-
-check-overflow-constructors:
- {{checkOverflowCommand}} --contracts-file "contracts/constructors.txt" -s statistics-overflow-constructors.json
diff --git a/loc.sh b/loc.sh
deleted file mode 100644
index 9b36d09..0000000
--- a/loc.sh
+++ /dev/null
@@ -1,6 +0,0 @@
-for f in src/de/wiesler/*.java; do
- spec=$(cat "$f" | egrep "@" | egrep -v "@\s*$" | egrep -v "@ //" | wc -l)
- code=$(cat "$f" | egrep -v "(@|^\s+$)" | wc -l)
- base=$(basename $f)
- echo "$base,$code,$spec"
-done
diff --git a/los.csv b/los.csv
deleted file mode 100644
index 22ab0a7..0000000
--- a/los.csv
+++ /dev/null
@@ -1,15 +0,0 @@
-BMC.java,13,0
-BucketPointers.java,48,441
-Buffers.java,44,175
-Classifier.java,123,481
-Cleanup.java,102,181
-Constants.java,45,16
-Functions.java,43,149
-Increment.java,9,6
-Partition.java,30,73
-PartitionResult.java,9,4
-Permute.java,130,413
-SampleParameters.java,42,28
-Sorter.java,93,382
-Storage.java,24,57
-Tree.java,34,97
diff --git a/proofIndependentSettings.props b/proofIndependentSettings.props
new file mode 100644
index 0000000..502b524
--- /dev/null
+++ b/proofIndependentSettings.props
@@ -0,0 +1,72 @@
+#Proof-Independent-Settings-File. Generated Fri Oct 27 16:18:59 CEST 2023
+#Fri Oct 27 16:18:59 CEST 2023
+[General]UseJML=true
+[SMTSettings]solverParametersV1CVC4=\#beg--no-print-success -m --interactive --lang smt2\#end
+[View][Heatmap]maxAge=5
+[View]SequentViewTooltips=true
+[General]RightClickMacros=true
+[View]HideIntermediateProofsteps=false
+[SMTSettings]solverCommandZ3\ FP=\#begz3\#end
+[View][Heatmap]newest=true
+[View]ShowWholeTaclet=false
+[View]SourceViewTooltips=true
+[View]showUninstantiatedTaclet=true
+[View][Heatmap]sf=true
+[SMTSettings]objectBound=3
+[View]HighlightOrigin=true
+[General]DnDDirectionSensitive=true
+[SMTSettings]solverParametersV1Z3=\#beg-in -smt2\#end
+[View]UseSystemLookAndFeel=false
+[View]ShowLoadExamplesDialog=true
+[SMTSettings]fieldBound=3
+[SMTSettings]SolverTimeout=20000
+[View]UseUnicodeSymbols=false
+[View]SyntaxHighlighting=true
+[View]hideInteractiveGoals=false
+[Extensions]disabled=
+[SMTSettings]intBound=3
+[General]StupidMode=true
+[SMTSettings]solverParametersV1Z3\ FP=\#beg-in -smt2\#end
+[SMTSettings]timeoutZ3\ FP=-1
+[SMTSettings]solverCommandZ3_CE=\#begz3\#end
+[SMTSettings]solverCommandZ3\ (Legacy\ Translation)=\#begz3\#end
+[SMTSettings]solverParametersV1CVC4\ (Legacy\ Translation)=\#beg--no-print-success -m --interactive --lang smt2\#end
+[View]ConfirmExit=true
+[SMTSettings]ActiveSolver=\#begZ3\#end
+[View]clutterRules=add_eq,add_greatereq,add_lesseq,add_non_neq_square,apply_eq_monomialseqTermCut,boxToDiamond,case_distinction_l,case_distinction_r,commute_and_2,commute_or_2,cut_direct_l,cut_direct_r,divIncreasingNeg,divIncreasingPos,divide_equation,divide_geq,equal_add_one,geq_add_one,instAll,instEx,jdivAddMultDenom,jmodAltZero,jmodDivisble,jmodUnique1,jmodeUnique2,jmodjmod,leq_add_one,less_is_total,less_zero_is_total,local_cut,polySimp_addOrder,polySimp_expand,pullOut,typeStatic
+[SMTSettings]solverCommandINVISMT=\#beginvismt\#end
+[View]HideClosedSubtrees=false
+[View]FontIndex=2
+[SMTSettings]solverParametersV1Z3_CE=\#beg-in -smt2\#end
+[SMTSettings]checkForSupport=true
+[View]uiFontSizeFactor=1.0
+[View]HideAutomodeProofsteps=false
+[View][Heatmap]enabled=false
+[SMTSettings]solverParametersV1Z3\ (Legacy\ Translation)=\#beg-in -smt2\#end
+[View]clutterRuleSets=inEqSimp_commute,inEqSimp_expand,inEqSimp_nonLin,inEqSimp_nonLin_divide,inEqSimp_special_nonLin,notHumanReadable,obsolete,polySimp_directEquations,polySimp_normalise,pullOutQuantifierAll,pullOutQuantifierEx
+[General]AutoSavePeriod=0
+[SMTSettings]solverCommandZ3=\#begz3\#end
+[General]EnsureSourceConsistency=true
+[SMTSettings]locsetBound=3
+[SMTSettings]solverCommandCVC4=\#begcvc4\#end
+[SMTSettings]pathForSMTTranslation=\#beg\#end
+[SMTSettings]timeoutZ3_CE=-1
+[View]notifyLoadBehaviour=false
+[View]folderBookmarks=/home/mattias
+[View]PrettySyntax=true
+[SMTSettings]solverCommandCVC4\ (Legacy\ Translation)=\#begcvc4\#end
+[SMTSettings]timeoutZ3\ (Legacy\ Translation)=-1
+[SMTSettings]maxConcurrentProcesses=2
+[SMTSettings]timeoutCVC4\ (Legacy\ Translation)=-1
+[SMTSettings]showSMTResDialog=false
+[SMTSettings]solverParametersV1INVISMT=\#beg-in\#end
+[SMTSettings]timeoutCVC4=-1
+[SMTSettings]timeoutINVISMT=-1
+[SMTSettings]modeOfProgressDialog=0
+[SMTSettings]pathForTacletTranslation=\#beg\#end
+[View]MaxTooltipLines=40
+[SMTSettings]timeoutZ3=-1
+[LemmaGenerator]showDialogWhenUsingTacletsAsAxioms=true
+[View]HidePackagePrefix=false
+[LemmaGenerator]showDialogWhenAddingAxioms=true
+[SMTSettings]heapBound=3
diff --git a/src/main/java/de/wiesler/BMC.java b/src/main/java-overflow/de/wiesler/BMC.java
similarity index 100%
rename from src/main/java/de/wiesler/BMC.java
rename to src/main/java-overflow/de/wiesler/BMC.java
diff --git a/src/main/java-overflow/de/wiesler/BucketPointers.java b/src/main/java-overflow/de/wiesler/BucketPointers.java
new file mode 100644
index 0000000..c30dcb8
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/BucketPointers.java
@@ -0,0 +1,587 @@
+package de.wiesler;
+
+public final class BucketPointers {
+ // 2 * n integer (read, write)
+ private /*@ spec_public @*/ final int[] buffer;
+
+ //@ ghost final int num_buckets;
+ //@ ghost final \seq bucket_starts;
+ //@ ghost final int first_empty_position;
+
+ //@ public instance invariant_free 0 <= 2 * this.num_buckets <= this.buffer.length;
+ //@ public instance invariant_free 0 <= this.first_empty_position <= (int) this.bucket_starts[num_buckets] <= Buffers.MAX_LEN && Buffers.isBlockAligned(this.first_empty_position);
+ //@ public instance invariant_free this.bucket_starts.length == this.num_buckets + 1;
+ //@ public instance invariant_free (int) this.bucket_starts[0] == 0 && Functions.isSortedSeqTransitive(this.bucket_starts);
+ //@ public instance invariant_free (\forall int b; 0 <= b < this.num_buckets; this.isValidBucketPointer(b));
+ //@ accessible \inv: this.buffer[*];
+
+ /*@ model_behaviour
+ @ requires true;
+ @ model boolean isValidBucketPointer(int bucket) {
+ @ return this.bucketStart(bucket) <= this.buffer[2 * bucket] <= this.bucketStart(bucket + 1) &&
+ @ this.bucketStart(bucket) <= this.buffer[2 * bucket + 1] <= this.bucketStart(bucket + 1) &&
+ @ (this.bucketStart(bucket) == this.buffer[2 * bucket] || this.buffer[2 * bucket] <= this.first_empty_position) &&
+ @ Buffers.isBlockAligned(this.buffer[2 * bucket]) &&
+ @ Buffers.isBlockAligned(this.buffer[2 * bucket + 1]);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket <= this.num_buckets;
+ @ requires \invariant_for(this);
+ @
+ @ ensures_free 0 <= \result <= this.bucketStart(this.num_buckets) <= Buffers.MAX_LEN;
+ @ ensures_free Buffers.isBlockAligned(\result);
+ @ ensures_free bucket < this.num_buckets ==> \result <= this.bucketStart(bucket + 1);
+ @ ensures_free 0 < bucket <= this.num_buckets ==> this.bucketStart(bucket - 1) <= \result;
+ @
+ @ // final only no_state
+ @ model int bucketStart(int bucket) {
+ @ return Buffers.blockAligned((int) this.bucket_starts[bucket]);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ requires \invariant_for(this);
+ @
+ @ ensures_free \result >= 0;
+ @ ensures_free Buffers.isBlockAligned(\result);
+ @
+ @ // final only no_state
+ @ model int bucketSize(int bucket) {
+ @ return this.bucketStart(bucket + 1) - this.bucketStart(bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @
+ @ ensures_free 0 <= this.bucketStart(bucket) <= \result <= this.bucketStart(bucket + 1) <= this.bucketStart(this.num_buckets);
+ @ ensures_free \result <= this.first_empty_position || \result == this.bucketStart(bucket);
+ @ ensures_free this.first_empty_position <= this.bucketStart(this.num_buckets);
+ @ ensures_free Buffers.isBlockAligned(\result);
+ @
+ @ accessible this.buffer[2 * bucket];
+ @ model int lastReadOf(int bucket) {
+ @ return this.buffer[2 * bucket];
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @
+ @ ensures_free 0 <= this.bucketStart(bucket) <= \result <= this.bucketStart(bucket + 1) <= this.bucketStart(this.num_buckets);
+ @ ensures_free Buffers.isBlockAligned(\result);
+ @
+ @ accessible this.buffer[2 * bucket + 1];
+ @ model int nextWriteOf(int bucket) {
+ @ return this.buffer[2 * bucket + 1];
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @
+ @ accessible this.buffer[2 * bucket + 1];
+ @ model int writtenCountOfBucket(int bucket) {
+ @ return this.nextWriteOf(bucket) - this.bucketStart(bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @
+ @ accessible this.buffer[2 * bucket + 1];
+ @ model int remainingWriteCountOfBucket(int bucket) {
+ @ return this.bucketStart(bucket + 1) - this.nextWriteOf(bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @
+ @ ensures_free \result >= 0;
+ @ ensures_free Buffers.isBlockAligned(\result);
+ @
+ @ accessible this.buffer[2 * bucket], this.buffer[2 * bucket + 1];
+ @ model int toReadCountOfBucket(int bucket) {
+ @ return this.nextWriteOf(bucket) < this.lastReadOf(bucket) ? this.lastReadOf(bucket) - this.nextWriteOf(bucket) : 0;
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ requires overflow.length == Buffers.BUFFER_SIZE;
+ @ requires \invariant_for(classifier);
+ @
+ @ accessible values[begin + this.bucketStart(bucket) .. begin + this.nextWriteOf(bucket) - 1], overflow[*], this.buffer[2 * bucket + 1], classifier.sorted_splitters[*], classifier.tree.tree[*];
+ @ model boolean writtenElementsOfBucketClassified(Classifier classifier, int[] values, int begin, int end, int[] overflow, int bucket) {
+ @ return end - begin < this.nextWriteOf(bucket) && Buffers.BUFFER_SIZE <= this.writtenCountOfBucket(bucket) ?
+ @ classifier.isClassOfSlice(values, begin + this.bucketStart(bucket), begin + this.nextWriteOf(bucket) - Buffers.BUFFER_SIZE, bucket) &&
+ @ classifier.isClassOfSlice(overflow, 0, Buffers.BUFFER_SIZE, bucket) :
+ @ classifier.isClassOfSlice(values, begin + this.bucketStart(bucket), begin + this.nextWriteOf(bucket), bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ requires \invariant_for(classifier);
+ @
+ @ accessible values[begin + this.nextWriteOf(bucket) .. begin + this.lastReadOf(bucket) - 1], this.buffer[2 * bucket..2 * bucket + 1], classifier.sorted_splitters[*], classifier.tree.tree[*];
+ @ model boolean elementsToReadOfBucketBlockClassified(Classifier classifier, int[] values, int begin, int end, int bucket) {
+ @ return this.nextWriteOf(bucket) < this.lastReadOf(bucket) ==> classifier.isClassifiedBlocksRange(values, begin + this.nextWriteOf(bucket), begin + this.lastReadOf(bucket));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ requires overflow.length == Buffers.BUFFER_SIZE;
+ @
+ @ accessible values[begin + this.bucketStart(bucket) .. begin + this.nextWriteOf(bucket) - 1], overflow[*], this.buffer[2 * bucket + 1];
+ @ model int writtenElementsOfBucketCountElement(int[] values, int begin, int end, int[] overflow, int bucket, int element) {
+ @ return end - begin < this.nextWriteOf(bucket) && Buffers.BUFFER_SIZE <= this.writtenCountOfBucket(bucket) ?
+ @ Functions.countElement(values, begin + this.bucketStart(bucket), begin + this.nextWriteOf(bucket) - Buffers.BUFFER_SIZE, element) +
+ @ Functions.countElement(overflow, 0, Buffers.BUFFER_SIZE, element) :
+ @ Functions.countElement(values, begin + this.bucketStart(bucket), begin + this.nextWriteOf(bucket), element);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @
+ @ accessible values[begin + this.nextWriteOf(bucket) .. begin + this.lastReadOf(bucket) - 1], this.buffer[2 * bucket..2 * bucket + 1];
+ @ model int elementsToReadOfBucketCountElement(int[] values, int begin, int end, int bucket, int element) {
+ @ return Functions.countElement(values, begin + this.nextWriteOf(bucket), begin + this.lastReadOf(bucket), element);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires overflow.length == Buffers.BUFFER_SIZE;
+ @
+ @ model int countElement(int[] values, int begin, int end, int[] overflow, int element) {
+ @ return this.elementsToReadCountElement(values, begin, end, element) +
+ @ this.writtenElementsCountElement(values, begin, end, overflow, element);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires overflow.length == Buffers.BUFFER_SIZE;
+ @
+ @ model int writtenElementsCountElement(int[] values, int begin, int end, int[] overflow, int element) {
+ @ return (\sum int b; 0 <= b < this.num_buckets;
+ @ this.writtenElementsOfBucketCountElement(values, begin, end, overflow, b, element)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= split_bucket < this.num_buckets;
+ @ requires begin + this.bucketStart(split_bucket) <= begin + this.nextWriteOf(split_bucket) - Buffers.BUFFER_SIZE <= begin + this.nextWriteOf(split_bucket);
+ @ ensures_free \result;
+ @ model boolean writtenElementsCountElementSplitBucket(int[] values, int begin, int end, int[] overflow, int split_bucket) {
+ @ return (\forall int element; true;
+ @ this.writtenElementsCountElement(values, begin, end, overflow, element) ==
+ @ (\sum int b; 0 <= b < this.num_buckets;
+ @ (b == split_bucket) ?
+ @ Functions.countElement(values, begin + this.bucketStart(split_bucket), begin + this.nextWriteOf(split_bucket) - Buffers.BUFFER_SIZE, element) :
+ @ this.writtenElementsOfBucketCountElement(values, begin, end, overflow, b, element)
+ @ ) +
+ @ (end - begin < this.nextWriteOf(split_bucket) && Buffers.BUFFER_SIZE <= this.writtenCountOfBucket(split_bucket) ?
+ @ Functions.countElement(overflow, 0, Buffers.BUFFER_SIZE, element) :
+ @ Functions.countElement(values, begin + this.nextWriteOf(split_bucket) - Buffers.BUFFER_SIZE, begin + this.nextWriteOf(split_bucket), element))
+ @ );
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires true;
+ @
+ @ model int elementsToReadCountElement(int[] values, int begin, int end, int element) {
+ @ return (\sum int b; 0 <= b < this.num_buckets;
+ @ this.elementsToReadOfBucketCountElement(values, begin, end, b, element)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= split_bucket < this.num_buckets;
+ @ requires begin + this.nextWriteOf(split_bucket) <= mid <= begin + this.lastReadOf(split_bucket);
+ @ ensures_free \result;
+ @ model boolean elementsToReadCountElementSplitBucket(int[] values, int begin, int mid, int end, int split_bucket, boolean pullout_first) {
+ @ return (\forall int element; true;
+ @ this.elementsToReadCountElement(values, begin, end, element) ==
+ @ (\sum int b; 0 <= b < this.num_buckets; (b == split_bucket) ?
+ @ (pullout_first ?
+ @ Functions.countElement(values, mid, begin + this.lastReadOf(b), element) :
+ @ Functions.countElement(values, begin + this.nextWriteOf(b), mid, element)
+ @ ) :
+ @ this.elementsToReadOfBucketCountElement(values, begin, end, b, element)) +
+ @ (pullout_first ?
+ @ Functions.countElement(values, begin + this.nextWriteOf(split_bucket), mid, element) :
+ @ Functions.countElement(values, mid, begin + this.lastReadOf(split_bucket), element)
+ @ )
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires this.num_buckets == classifier.num_buckets;
+ @ requires \invariant_for(classifier);
+ @ ensures_free \result >= 0;
+ @ accessible values[begin + this.nextWriteOf(bucket) .. begin + this.lastReadOf(bucket) - 1], this.buffer[2 * bucket..2 * bucket + 1], classifier.sorted_splitters[*], classifier.tree.tree[*];
+ @ model int elementsToReadOfBucketCountClassEq(Classifier classifier, int[] values, int begin, int end, int bucket, int cls) {
+ @ return classifier.countClassOfSliceEq(values, begin + this.nextWriteOf(bucket), begin + this.lastReadOf(bucket), cls);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ requires 0 <= begin <= end <= values.length;
+ @ ensures_free \result >= 0;
+ @ model int elementsToReadCountClassEq(Classifier classifier, int[] values, int begin, int end, int bucket) {
+ @ return (\sum int b; 0 <= b < this.num_buckets;
+ @ this.elementsToReadOfBucketCountClassEq(classifier, values, begin, end, b, bucket)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= split_bucket < this.num_buckets;
+ @ requires this.num_buckets == classifier.num_buckets;
+ @ requires begin + this.nextWriteOf(split_bucket) <= mid <= begin + this.lastReadOf(split_bucket);
+ @ ensures_free \result;
+ @ model boolean elementsToReadCountClassEqSplitBucket(Classifier classifier, int[] values, int begin, int mid, int end, int split_bucket, boolean pullout_first) {
+ @ return (\forall int bucket; 0 <= bucket < this.num_buckets;
+ @ this.elementsToReadCountClassEq(classifier, values, begin, end, bucket) ==
+ @ (\sum int b; 0 <= b < this.num_buckets; (b == split_bucket) ?
+ @ (pullout_first ?
+ @ classifier.countClassOfSliceEq(values, mid, begin + this.lastReadOf(b), bucket) :
+ @ classifier.countClassOfSliceEq(values, begin + this.nextWriteOf(b), mid, bucket)
+ @ ) :
+ @ this.elementsToReadOfBucketCountClassEq(classifier, values, begin, end, b, bucket)) +
+ @ (pullout_first ?
+ @ classifier.countClassOfSliceEq(values, begin + this.nextWriteOf(split_bucket), mid, bucket) :
+ @ classifier.countClassOfSliceEq(values, mid, begin + this.lastReadOf(split_bucket), bucket)
+ @ )
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ ensures_free \result;
+ @ model boolean disjointBucketsLemma(int bucket) {
+ @ return (\forall int b; 0 <= b < this.num_buckets && b != bucket;
+ @ (b < bucket ==> this.bucketStart(b + 1) <= this.bucketStart(bucket)) &&
+ @ (b > bucket ==> this.bucketStart(bucket + 1) <= this.bucketStart(b))
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end;
+ @ requires end - begin == (int) this.bucket_starts[num_buckets];
+ @ ensures_free \result;
+ @ model boolean overflowBucketCharacteristic(int begin, int end) {
+ @ return (\forall int b; 0 <= b < this.num_buckets;
+ @ end - begin < this.nextWriteOf(b) && Buffers.BUFFER_SIZE <= this.writtenCountOfBucket(b) ==>
+ @ this.bucketStart(b) < end - begin &&
+ @ this.nextWriteOf(b) == this.bucketStart(b + 1) &&
+ @ this.bucketStart(b + 1) == this.bucketStart(this.num_buckets)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end;
+ @ requires 0 <= bucket < this.num_buckets;
+ @ requires end - begin == (int) this.bucket_starts[num_buckets];
+ @ requires end - begin < this.nextWriteOf(bucket) && Buffers.BUFFER_SIZE <= this.writtenCountOfBucket(bucket);
+ @ requires this.disjointBucketsLemma(bucket);
+ @ requires this.overflowBucketCharacteristic(begin, end);
+ @ ensures_free \result;
+ @ model boolean overflowBucketUniqueLemma(int begin, int end, int bucket) {
+ @ return (\forall int b; 0 <= b < this.num_buckets && b != bucket;
+ @ // Show that nextWriteOf(bucket) == bucketStart(bucket) == bucketStart(num_buckets)
+ @ // b > bucket: writtenCountOfBucket can't be > 0 since nextWriteOf(b) <= bucketStart(num_buckets)
+ @ // b < bucket: bucketStart(bucket) <= end - begin
+ @ !(end - begin < this.nextWriteOf(b) && Buffers.BUFFER_SIZE <= this.writtenCountOfBucket(b))
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ requires begin + this.bucketStart(bucket) <= subBegin <= subEnd <= begin + this.bucketStart(bucket + 1);
+ @ requires this.disjointBucketsLemma(bucket);
+ @ ensures_free \result;
+ @ model boolean disjointBucketsAreaLemma(int[] values, int begin, int end, int bucket, int subBegin, int subEnd) {
+ @ return (\forall int b; 0 <= b < this.num_buckets && b != bucket;
+ @ \disjoint(\dl_arrayRange(values, begin + this.bucketStart(b), begin + this.nextWriteOf(b) - 1), \dl_arrayRange(values, subBegin, subEnd - 1)) &&
+ @ \disjoint(\dl_arrayRange(values, begin + this.nextWriteOf(b), begin + this.lastReadOf(b) - 1), \dl_arrayRange(values, subBegin, subEnd - 1))
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires start <= read <= stop;
+ @ static model no_state boolean readIsMaximal(int start, int read, int stop, int first_empty_position) {
+ @ return read == (first_empty_position <= start ? start : (stop <= first_empty_position ? stop : first_empty_position));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @
+ @ accessible this.buffer[2 * bucket..2 * bucket + 1];
+ @ model boolean isAtInitialBucketState(int bucket) {
+ @ return this.writtenCountOfBucket(bucket) == 0 &&
+ @ BucketPointers.readIsMaximal(this.bucketStart(bucket), this.lastReadOf(bucket), this.bucketStart(bucket + 1), this.first_empty_position);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @
+ @ model boolean isAtInitialState() {
+ @ return (\forall int b; 0 <= b < this.num_buckets;
+ @ this.isAtInitialBucketState(b)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires end - begin == (int) this.bucket_starts[num_buckets];
+ @ requires this.isAtInitialState();
+ @ requires classifier.isClassifiedBlocksRange(values, begin, begin + this.first_empty_position);
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean initialReadAreasBlockClassified(Classifier classifier, int[] values, int begin, int end) {
+ @ return (\forall int b; 0 <= b < this.num_buckets; this.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires end - begin == (int) this.bucket_starts[num_buckets];
+ @ requires this.isAtInitialState();
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean initialReadAreasCountLemma(int[] values, int begin, int end) {
+ @ return (\forall int iv; 0 <= iv <= this.num_buckets;
+ @ (\forall int element; true;
+ @ Functions.countElement(values, begin, begin + (this.bucketStart(iv) < first_empty_position ? this.bucketStart(iv) : first_empty_position), element) ==
+ @ (\sum int b; 0 <= b < iv; this.elementsToReadOfBucketCountElement(values, begin, end, b, element))
+ @ )
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires this.initialReadAreasCountLemma(values, begin, end);
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean initialReadAreasCount(int[] values, int begin, int end) {
+ @ return (\forall int element; true;
+ @ Functions.countElement(values, begin, begin + first_empty_position, element) ==
+ @ this.elementsToReadCountElement(values, begin, end, element)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires end - begin == (int) this.bucket_starts[num_buckets];
+ @ requires this.isAtInitialState();
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean initialReadAreasCountBucketElementsLemma(Classifier classifier, int[] values, int begin, int end) {
+ @ return (\forall int iv; 0 <= iv <= this.num_buckets;
+ @ (\forall int bucket; 0 <= bucket < this.num_buckets;
+ @ classifier.countClassOfSliceEq(values, begin, begin + (this.bucketStart(iv) < first_empty_position ? this.bucketStart(iv) : first_empty_position), bucket) ==
+ @ (\sum int b; 0 <= b < iv; this.elementsToReadOfBucketCountClassEq(classifier, values, begin, end, b, bucket))
+ @ )
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires this.initialReadAreasCountBucketElementsLemma(classifier, values, begin, end);
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean initialReadAreasCountBucketElements(Classifier classifier, int[] values, int begin, int end) {
+ @ return (\forall int bucket; 0 <= bucket < this.num_buckets;
+ @ classifier.countClassOfSliceEq(values, begin, begin + first_empty_position, bucket) ==
+ @ this.elementsToReadCountClassEq(classifier, values, begin, end, bucket)
+ @ );
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires_free 0 <= start <= stop <= Buffers.MAX_LEN;
+ @ ensures_free \result;
+ @ static model no_state boolean alignedBoundariesKeepEnoughSpace(int start, int stop) {
+ @ return stop - start - Buffers.bufferSizeForBucketLen(stop - start) <= Buffers.blockAligned(stop) - Buffers.blockAligned(start);
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free Functions.isSortedSliceTransitive(bucket_starts, 0, num_buckets + 1);
+ @ requires_free num_buckets + 1 <= bucket_starts.length;
+ @ requires_free bucket_starts[num_buckets] <= Buffers.MAX_LEN;
+ @ requires_free bucket_starts[0] == 0;
+ @ requires_free 0 <= 2 * num_buckets <= buffer.length;
+ @ requires_free 0 <= first_empty_position <= bucket_starts[num_buckets];
+ @ requires_free Buffers.isBlockAligned(first_empty_position);
+ @ requires_free \disjoint(bucket_starts[*], buffer[*]);
+ @
+ @ ensures_free this.num_buckets == num_buckets && this.buffer == buffer && this.first_empty_position == first_empty_position;
+ @ ensures_free bucket_starts[num_buckets] == (int) this.bucket_starts[num_buckets];
+ @ ensures_free this.isAtInitialState();
+ @ ensures_free (\forall int b; 0 <= b < num_buckets;
+ @ // enough space to write everything except the buffer content
+ @ bucket_starts[b + 1] - bucket_starts[b] - Buffers.bufferSizeForBucketLen(bucket_starts[b + 1] - bucket_starts[b]) <= this.bucketSize(b)
+ @ );
+ @ ensures_free (\forall int b; 0 <= b <= num_buckets; this.bucketStart(b) == Buffers.blockAligned(bucket_starts[b]));
+ @
+ @ assignable_free buffer[0..2 * num_buckets - 1];
+ @*/
+ public BucketPointers(final int[] bucket_starts, final int num_buckets, final int first_empty_position, final int[] buffer) {
+ //@ set this.num_buckets = num_buckets;
+ //@ set this.first_empty_position = first_empty_position;
+ //@ set this.bucket_starts = \dl_seq_def_workaround(0, num_buckets + 1, bucket_starts);
+
+ /*@ assume
+ @ (\forall int b; 0 <= b <= num_buckets; this.bucketStart(b) == Buffers.blockAligned(bucket_starts[b])) &&
+ @ Functions.isSortedSeqTransitive(this.bucket_starts);
+ @*/
+
+ this.buffer = buffer;
+
+ /*@ loop_invariant_free 0 <= bucket && bucket <= num_buckets;
+ @ loop_invariant_free (\forall int b; 0 <= b < bucket;
+ @ this.isValidBucketPointer(b) &&
+ @ this.isAtInitialBucketState(b) &&
+ @ bucket_starts[b + 1] - bucket_starts[b] - Buffers.bufferSizeForBucketLen(bucket_starts[b + 1] - bucket_starts[b]) <= this.bucketSize(b)
+ @ );
+ @
+ @ decreases num_buckets - bucket;
+ @
+ @ assignable_free this.buffer[0..2 * num_buckets - 1];
+ @*/
+ for (int bucket = 0; bucket < num_buckets; ++bucket) {
+ //@ assume 0 <= bucket_starts[bucket] <= bucket_starts[bucket + 1] <= bucket_starts[num_buckets];
+ int start = Buffers.align_to_next_block(bucket_starts[bucket]);
+ int stop = Buffers.align_to_next_block(bucket_starts[bucket + 1]);
+ //@ assume start == this.bucketStart(bucket) && stop == this.bucketStart(bucket + 1) && start <= stop;
+ int read = -1;
+
+ /*@ normal_behaviour
+ @ ensures_free start <= read <= stop;
+ @ ensures_free Buffers.isBlockAligned(read);
+ @ ensures_free BucketPointers.readIsMaximal(start, read, stop, this.first_empty_position);
+ @
+ @ assignable_free \strictly_nothing;
+ @*/
+ {
+ if (first_empty_position <= start) {
+ read = start;
+ } else if (stop <= first_empty_position) {
+ read = stop;
+ } else {
+ read = first_empty_position;
+ }
+ }
+
+ this.buffer[2 * bucket] = read;
+ this.buffer[2 * bucket + 1] = start;
+
+ //@ assume BucketPointers.alignedBoundariesKeepEnoughSpace(bucket_starts[bucket], bucket_starts[bucket + 1]);
+ }
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= bucket < this.num_buckets;
+ @
+ @ ensures_free \result == this.nextWriteOf(bucket);
+ @ ensures_free \result == this.writtenCountOfBucket(bucket) + this.bucketStart(bucket);
+ @
+ @ assignable_free \strictly_nothing;
+ @*/
+ public int write(int bucket) {
+ final int write_pos = 2 * bucket + 1;
+ return this.buffer[write_pos];
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= bucket < this.num_buckets;
+ @ requires_free this.bucketSize(bucket) >= this.writtenCountOfBucket(bucket) + Buffers.BUFFER_SIZE;
+ @
+ @ ensures_free \old(this.nextWriteOf(bucket)) + Buffers.BUFFER_SIZE == this.nextWriteOf(bucket);
+ @ ensures_free \old(this.remainingWriteCountOfBucket(bucket)) == this.remainingWriteCountOfBucket(bucket) + Buffers.BUFFER_SIZE;
+ @ ensures_free \old(this.writtenCountOfBucket(bucket)) + Buffers.BUFFER_SIZE == this.writtenCountOfBucket(bucket);
+ @ ensures_free this.lastReadOf(bucket) == \old(this.lastReadOf(bucket));
+ @ // read count either decreased or stayed 0
+ @ ensures_free \old(this.toReadCountOfBucket(bucket)) >= Buffers.BUFFER_SIZE ?
+ @ this.toReadCountOfBucket(bucket) < \old(this.toReadCountOfBucket(bucket)) :
+ @ this.toReadCountOfBucket(bucket) == 0;
+ @
+ @ ensures_free \result.position == \old(this.nextWriteOf(bucket));
+ @ ensures_free \result.occupied <==> \old(this.toReadCountOfBucket(bucket)) >= Buffers.BUFFER_SIZE;
+ @
+ @ assignable_free this.buffer[2 * bucket + 1];
+ @*/
+ public Increment increment_write(int bucket) {
+ final int read_pos = 2 * bucket;
+ final int write_pos = 2 * bucket + 1;
+ final int write = this.buffer[write_pos];
+ this.buffer[write_pos] += Buffers.BUFFER_SIZE;
+ return new Increment(this.buffer[read_pos] > write, write);
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= bucket < this.num_buckets;
+ @
+ @ ensures_free \result <==> this.toReadCountOfBucket(bucket) >= Buffers.BUFFER_SIZE;
+ @
+ @ assignable_free \strictly_nothing;
+ @*/
+ public boolean hasRemainingRead(int bucket) {
+ final int read_pos = 2 * bucket;
+ final int write_pos = 2 * bucket + 1;
+ int read = this.buffer[read_pos];
+ final int write = this.buffer[write_pos];
+ return read > write;
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= bucket < this.num_buckets;
+ @ requires_free this.toReadCountOfBucket(bucket) != 0;
+ @
+ @ ensures_free \result == this.lastReadOf(bucket);
+ @
+ @ ensures_free this.toReadCountOfBucket(bucket) + Buffers.BUFFER_SIZE == \old(this.toReadCountOfBucket(bucket));
+ @ ensures_free \old(this.lastReadOf(bucket)) == this.lastReadOf(bucket) + Buffers.BUFFER_SIZE;
+ @ // ensures (\forall int b; 0 <= b < this.num_buckets && b != bucket; this.toReadCountOfBucket(b) == \old(this.toReadCountOfBucket(b)));
+ @ // ensures (\forall int b; 0 <= b < this.num_buckets; this.writtenCountOfBucket(b) == \old(this.writtenCountOfBucket(b)));
+ @
+ @ assignable_free this.buffer[2 * bucket];
+ @*/
+ public int decrement_read(int bucket) {
+ final int read_pos = 2 * bucket;
+ int read = this.buffer[read_pos];
+ read -= Buffers.BUFFER_SIZE;
+ this.buffer[read_pos] = read;
+ return read;
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Buffers.java b/src/main/java-overflow/de/wiesler/Buffers.java
new file mode 100644
index 0000000..4a9a40c
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Buffers.java
@@ -0,0 +1,283 @@
+package de.wiesler;
+
+public final class Buffers {
+ public static final int BUFFER_SIZE = 1024 / 4;
+ public static final int MAX_INT = 0x7FFFFFFF;
+ public static final int MAX_LEN = MAX_INT - BUFFER_SIZE + 1;
+
+ /*@ public model_behaviour
+ @ requires 0 <= len;
+ @
+ @ ensures_free 0 <= \result <= BUFFER_SIZE;
+ @
+ @ // A remainder modulo BUFFER_SIZE that is never 0 for nonempty buckets
+ @ static no_state model int bufferSizeForBucketLen(int len) {
+ @ return (len >= Buffers.BUFFER_SIZE && len % Buffers.BUFFER_SIZE == 0) ?
+ @ Buffers.BUFFER_SIZE : (len % Buffers.BUFFER_SIZE);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= value <= MAX_LEN;
+ @
+ @ // checked by exhaustive search below
+ @ ensures_free Buffers.isBlockAligned(\result);
+ @ ensures_free \result >= value;
+ @ ensures_free \result - value < BUFFER_SIZE;
+ @
+ @ static no_state model int blockAligned(int value) {
+ @ return (value + BUFFER_SIZE - 1) & (-BUFFER_SIZE);
+ @ }
+ @*/
+
+ private static boolean testBlockAlignedContract(int value, int result) {
+ return
+ result % BUFFER_SIZE == 0 &&
+ result >= value &&
+ result - value < BUFFER_SIZE;
+ }
+
+ /*@ public model_behaviour
+ @ requires value >= 0;
+ @
+ @ static no_state model boolean isBlockAligned(int value) {
+ @ return value % BUFFER_SIZE == 0;
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= i;
+ @ requires 0 <= j;
+ @ requires isBlockAligned(i) && isBlockAligned(j);
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean isBlockAlignedAdd(int i, int j) {
+ @ return isBlockAligned(i + j);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= j <= i;
+ @ requires isBlockAligned(i) && isBlockAligned(j);
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean isBlockAlignedSub(int i, int j) {
+ @ return isBlockAligned(i - j);
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= offset <= MAX_LEN;
+ @
+ @ ensures_free \result == blockAligned(offset);
+ @
+ @ assignable_free \strictly_nothing;
+ @*/
+ public static int align_to_next_block(int offset) {
+ return (offset + BUFFER_SIZE - 1) & (-BUFFER_SIZE);
+ }
+
+ public static void testContracts(int i) {
+ if (0 <= i && i <= MAX_LEN && !testBlockAlignedContract(i, align_to_next_block(i))) {
+ throw new Error("blockAligned contract fails for " + i);
+ }
+ }
+
+ private /*@ spec_public @*/ final int[] buffer;
+ private /*@ spec_public @*/ final int[] indices;
+ //@ ghost final int num_buckets;
+
+ /*@ public model_behaviour
+ @ requires true;
+ @
+ @ ensures_free \result ==> this.count() == 0;
+ @ ensures_free \result ==> (\forall int element; true; this.countElement(element) == 0);
+ @ model boolean isEmpty() {
+ @ return (\forall int b; 0 <= b < this.num_buckets; this.bufferLen(b) == 0);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @ ensures_free 0 <= \result <= BUFFER_SIZE;
+ @ accessible this.indices[bucket];
+ @ model int bufferLen(int bucket) {
+ @ return this.indices[bucket];
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @ accessible this.buffer[bucket * BUFFER_SIZE + offset];
+ @ model int bufferElement(int bucket, int offset) {
+ @ return this.buffer[bucket * BUFFER_SIZE + offset];
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @
+ @ accessible this.indices[0..this.num_buckets - 1];
+ @ model int count() {
+ @ return (\sum int b; 0 <= b < this.num_buckets; this.bufferLen(b));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires \invariant_for(classifier);
+ @ requires classifier.num_buckets == this.num_buckets;
+ @
+ @ accessible this.indices[0..this.num_buckets - 1], this.buffer[0..Buffers.BUFFER_SIZE * this.num_buckets - 1], classifier.sorted_splitters[*], classifier.tree.tree[*];
+ @ model boolean isClassifiedWith(Classifier classifier) {
+ @ return (\forall
+ @ int b;
+ @ 0 <= b < this.num_buckets;
+ @ classifier.isClassOfSlice(this.buffer, b * BUFFER_SIZE, b * BUFFER_SIZE + this.bufferLen(b), b)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @
+ @ model int countElementInBucket(int bucket, int element) {
+ @ return Functions.countElement(this.buffer, bucket * BUFFER_SIZE, bucket * BUFFER_SIZE + this.bufferLen(bucket), element);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @
+ @ accessible this.indices[0..this.num_buckets - 1], this.buffer[0..Buffers.BUFFER_SIZE * this.num_buckets - 1];
+ @ model int countElement(int element) {
+ @ return (\sum int b; 0 <= b < this.num_buckets; this.countElementInBucket(b, element));
+ @ }
+ @*/
+
+ /*@
+ @ invariant_free this.buffer != this.indices;
+ @ invariant_free this.buffer.length == Buffers.BUFFER_SIZE * Constants.MAX_BUCKETS;
+ @ invariant_free this.indices.length == Constants.MAX_BUCKETS;
+ @ invariant_free 0 <= this.num_buckets <= Constants.MAX_BUCKETS;
+ @ invariant_free (\forall int b; 0 <= b && b < this.num_buckets; 0 <= this.indices[b] && this.indices[b] <= BUFFER_SIZE);
+ @
+ @ accessible \inv: this.indices[*];
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free buffer != indices;
+ @ requires_free buffer.length == Buffers.BUFFER_SIZE * Constants.MAX_BUCKETS;
+ @ requires_free indices.length == Constants.MAX_BUCKETS;
+ @ requires_free 0 <= num_buckets <= Constants.MAX_BUCKETS;
+ @
+ @ ensures_free this.num_buckets == num_buckets;
+ @ ensures_free this.buffer == buffer;
+ @ ensures_free this.indices == indices;
+ @ ensures_free this.isEmpty();
+ @
+ @ assignable_free indices[0..num_buckets - 1];
+ @*/
+ public Buffers(int[] buffer, int[] indices, int num_buckets) {
+ this.buffer = buffer;
+ this.indices = indices;
+ //@ set this.num_buckets = num_buckets;
+
+ Functions.fill(this.indices, 0, num_buckets, 0);
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= bucket && bucket < this.num_buckets;
+ @
+ @ requires_free this.bufferLen(bucket) != BUFFER_SIZE;
+ @
+ @ ensures_free this.bufferLen(bucket) == \old(this.bufferLen(bucket)) + 1;
+ @ ensures_free this.bufferElement(bucket, \old(this.bufferLen(bucket))) == value;
+ @ ensures_free this.count() == \old(this.count()) + 1;
+ @
+ @ ensures_free (\forall int element; true; this.countElement(element) == \old(this.countElement(element)) + (element == value ? 1 : 0));
+ @
+ @ assignable_free this.indices[bucket];
+ @ assignable_free this.buffer[bucket * BUFFER_SIZE + this.bufferLen(bucket)];
+ @*/
+ public void push(int bucket, int value) {
+ /*@ normal_behaviour
+ @ assignable \nothing;
+ @*/
+ {
+ value = value;
+ }
+ int buffer_offset = bucket * BUFFER_SIZE;
+ int index = this.indices[bucket];
+ this.buffer[buffer_offset + index] = value;
+ this.indices[bucket] = index + 1;
+ //@ assume Functions.countElementSplit(this.buffer, bucket * BUFFER_SIZE, bucket * BUFFER_SIZE + index, bucket * BUFFER_SIZE + index + 1);
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= bucket < this.num_buckets;
+ @ requires_free \disjoint(values[*], this.buffer[*], this.indices[*]);
+ @ requires_free this.bufferLen(bucket) == BUFFER_SIZE;
+ @ requires_free 0 <= write <= end <= values.length;
+ @ requires_free end - write >= BUFFER_SIZE;
+ @
+ @ ensures_free this.bufferLen(bucket) == 0;
+ @ ensures_free (\forall int i; 0 <= i && i < BUFFER_SIZE; values[write + i] == \old(this.buffer[bucket * BUFFER_SIZE + i]));
+ @ ensures_free (\forall int element; true;
+ @ \old(this.countElement(element)) ==
+ @ Functions.countElement(values, write, write + BUFFER_SIZE, element) +
+ @ this.countElement(element)
+ @ );
+ @ ensures_free this.count() == \old(this.count()) - BUFFER_SIZE;
+ @
+ @ assignable_free this.indices[bucket];
+ @ assignable_free values[write..write + BUFFER_SIZE - 1];
+ @*/
+ public void flush(int bucket, int[] values, int write, int end) {
+ int buffer_offset = bucket * BUFFER_SIZE;
+ Functions.copy_nonoverlapping(this.buffer, buffer_offset, values, write, BUFFER_SIZE);
+ this.indices[bucket] = 0;
+ //@ assume (\forall int element; true; \old(this.countElementInBucket(bucket, element)) == Functions.countElement(values, write, write + BUFFER_SIZE, element));
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= bucket && bucket < this.num_buckets;
+ @ requires_free \disjoint(values[*], this.buffer[*], this.indices[*]);
+ @
+ @ requires_free 0 <= head_start <= head_start + head_len <= values.length;
+ @ requires_free 0 <= tail_start <= tail_start + tail_len <= values.length;
+ @
+ @ requires_free head_len + tail_len == this.bufferLen(bucket);
+ @ // Don't overlap
+ @ requires_free \disjoint(values[head_start..(head_start + head_len - 1)], values[tail_start..(tail_start + tail_len - 1)]);
+ @
+ @ ensures_free (\forall int i; 0 <= i && i < head_len; values[head_start + i] == \old(this.bufferElement(bucket, i)));
+ @ ensures_free (\forall int i; 0 <= i && i < tail_len; values[tail_start + i] == \old(this.bufferElement(bucket, head_len + i)));
+ @
+ @ ensures_free (\forall int element; true;
+ @ Functions.countElement(values, head_start, head_start + head_len, element) +
+ @ Functions.countElement(values, tail_start, tail_start + tail_len, element) ==
+ @ \old(this.countElementInBucket(bucket, element))
+ @ );
+ @
+ @ assignable_free values[head_start..(head_start + head_len - 1)];
+ @ assignable_free values[tail_start..(tail_start + tail_len - 1)];
+ @*/
+ public void distribute(int bucket, int[] values, int head_start, int head_len, int tail_start, int tail_len) {
+ //@ assume head_len + tail_len == this.indices[bucket];
+ int offset = bucket * BUFFER_SIZE;
+ //@ assume Functions.countElementSplit(this.buffer, offset, offset + head_len, offset + head_len + tail_len);
+ Functions.copy_nonoverlapping(this.buffer, offset, values, head_start, head_len);
+ Functions.copy_nonoverlapping(this.buffer, offset + head_len, values, tail_start, tail_len);
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= bucket < this.num_buckets;
+ @ ensures_free \result == this.bufferLen(bucket);
+ @ assignable_free \strictly_nothing;
+ @*/
+ public int len(int bucket) {
+ return this.indices[bucket];
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Classifier.java b/src/main/java-overflow/de/wiesler/Classifier.java
new file mode 100644
index 0000000..22c68b9
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Classifier.java
@@ -0,0 +1,759 @@
+package de.wiesler;
+
+public final class Classifier {
+ public static final int STORAGE_SIZE = (1 << Constants.LOG_MAX_BUCKETS);
+
+ private /*@ spec_public @*/ final Tree tree;
+ private /*@ spec_public @*/ final int num_buckets;
+ private /*@ spec_public @*/ final int[] sorted_splitters;
+ private /*@ spec_public @*/ final boolean equal_buckets;
+
+ /*@ invariant_free 2 <= this.num_buckets <= Constants.MAX_BUCKETS;
+ @ invariant_free this.num_buckets == (this.equal_buckets ? 2 * this.tree.num_buckets : this.tree.num_buckets);
+ @ invariant_free this.tree.sorted_splitters == this.sorted_splitters;
+ @ invariant_free Functions.isSortedSliceTransitive(this.sorted_splitters, 0, this.tree.num_buckets);
+ @ invariant_free this.sorted_splitters[this.tree.num_buckets - 1] == this.sorted_splitters[this.tree.num_buckets - 2];
+ @ invariant_free \invariant_for(this.tree);
+ @
+ @ accessible \inv: this.sorted_splitters[*], this.tree.tree[*];
+ @*/
+
+ // This is a wrapper around classify not to be expanded in partition.
+ /*@ public model_behaviour
+ @ ensures_free 0 <= \result < this.num_buckets;
+ @ ensures_free this.isClassifiedAs(value, \result);
+ @ accessible this.sorted_splitters[*], this.tree.tree[*];
+ @ model int classOf(int value) {
+ @ return this.classify(value);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ accessible this.sorted_splitters[*], this.tree.tree[*], values[begin..end - 1];
+ @ model boolean isClassOfSlice(int[] values, int begin, int end, int bucket) {
+ @ return (\forall
+ @ int i;
+ @ begin <= i < end;
+ @ this.classOf(values[i]) == bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires begin <= mid <= end;
+ @
+ @ ensures_free \result;
+ @
+ @ // Verified
+ @ model boolean isClassOfSliceSplit(int[] values, int begin, int mid, int end, int bucket) {
+ @ return this.isClassOfSlice(values, begin, end, bucket) <==>
+ @ this.isClassOfSlice(values, begin, mid, bucket) && this.isClassOfSlice(values, mid, end, bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires this.isClassOfSlice(src, srcPos, srcPos + length, bucket);
+ @ requires (\forall int i; 0 <= i && i < length; dest[destPos + i] == src[srcPos + i]);
+ @
+ @ ensures_free \result;
+ @
+ @ // Verified
+ @ model boolean isClassOfSliceCopy(int[] src, int srcPos, int[] dest, int destPos, int length, int bucket) {
+ @ return this.isClassOfSlice(dest, destPos, destPos + length, bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ accessible values[begin..end - 1], this.sorted_splitters[*], this.tree.tree[*];
+ @ model int countClassOfSliceEq(int[] values, int begin, int end, int bucket) {
+ @ return (\num_of
+ @ int i;
+ @ begin <= i < end;
+ @ this.classOf(values[i]) == bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires this.isClassOfSlice(values, begin, end, bucket);
+ @ requires begin <= end;
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean countClassOfSliceEqLemma(int[] values, int begin, int end, int bucket) {
+ @ return (\forall int b; 0 <= b < this.num_buckets;
+ @ this.countClassOfSliceEq(values, begin, end, b) ==
+ @ (b == bucket ? end - begin : 0)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ accessible this.sorted_splitters[*], this.tree.tree[*], values[begin..end - 1];
+ @ model boolean isClassifiedBlock(int[] values, int begin, int end) {
+ @ return (\exists int bucket; 0 <= bucket < this.num_buckets; this.isClassOfSlice(values, begin, end, bucket));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires this.isClassifiedBlock(values, begin, end);
+ @ requires this.classOf(values[begin]) == bucket;
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean classOfClassifiedBlockFromFirst(int[] values, int begin, int end, int bucket) {
+ @ return this.isClassOfSlice(values, begin, end, bucket);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires Buffers.isBlockAligned(end - begin);
+ @ accessible this.sorted_splitters[*], this.tree.tree[*], values[begin..end - 1];
+ @ model boolean isClassifiedBlocksRange(int[] values, int begin, int end) {
+ @ return (\forall
+ @ int block;
+ @ 0 <= block && block < (end - begin) / Buffers.BUFFER_SIZE;
+ @ this.isClassifiedBlock(values, begin + block * Buffers.BUFFER_SIZE, begin + (block + 1) * Buffers.BUFFER_SIZE)
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires begin <= mid <= end;
+ @ requires Buffers.isBlockAligned(end - begin);
+ @ requires Buffers.isBlockAligned(mid - begin);
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean isClassifiedBlocksRangeSplit(int[] values, int begin, int mid, int end) {
+ @ return this.isClassifiedBlocksRange(values, begin, end) <==>
+ @ this.isClassifiedBlocksRange(values, begin, mid) && this.isClassifiedBlocksRange(values, mid, end);
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free tree != sorted_splitters;
+ @ requires_free 1 <= log_buckets <= Constants.LOG_MAX_BUCKETS;
+ @ requires_free 0 <= (1 << log_buckets) <= sorted_splitters.length;
+ @ requires_free Functions.isSortedSliceTransitive(sorted_splitters, 0, 1 << log_buckets);
+ @ requires_free (1 << log_buckets) <= tree.length;
+ @ requires_free sorted_splitters[(1 << log_buckets) - 1] == sorted_splitters[(1 << log_buckets) - 2];
+ @
+ @ ensures_free this.tree.tree == tree && this.sorted_splitters == sorted_splitters;
+ @ ensures_free this.tree.log_buckets == log_buckets && this.equal_buckets == equal_buckets && this.num_buckets == (equal_buckets ? 2 * (1 << log_buckets) : (1 << log_buckets));
+ @
+ @ assignable_free tree[*];
+ @*/
+ public Classifier(int[] sorted_splitters, int[] tree, int log_buckets, boolean equal_buckets) {
+ int num_buckets = 1 << log_buckets;
+ //@ assume 2 <= num_buckets <= (1 << Constants.LOG_MAX_BUCKETS);
+
+ int num_splitters = num_buckets - 1;
+ //@ assume (sorted_splitters[num_splitters] == sorted_splitters[num_splitters - 1]);
+
+ this.tree = new Tree(sorted_splitters, tree, log_buckets);
+ //@ assume this.tree.log_buckets == log_buckets;
+ //@ assume sorted_splitters[num_splitters] == sorted_splitters[num_splitters - 1];
+ this.sorted_splitters = sorted_splitters;
+ /*@ normal_behaviour
+ @ ensures_free this.num_buckets == (equal_buckets ? 2 * num_buckets : num_buckets);
+ @ assignable_free this.num_buckets;
+ @*/
+ {
+ this.num_buckets = equal_buckets ? 2 * num_buckets : num_buckets;
+ }
+ this.equal_buckets = equal_buckets;
+ }
+
+ /*@ public model_behaviour
+ @ requires this.tree.classOfFirstSplitters();
+ @ ensures_free \result;
+ @
+ @ model boolean classOfFirstSplitters() {
+ @ return this.classOf(this.sorted_splitters[0]) != this.classOf(this.sorted_splitters[1]);
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= num_splitters <= splitters.length;
+ @ requires_free (\forall
+ @ int j;
+ @ 0 <= j < num_splitters - 1;
+ @ splitters[j] < splitters[j + 1]
+ @ );
+ @ requires_free \disjoint(splitters[*], tree[*]);
+ @
+ @ requires_free 2 <= num_splitters && num_splitters <= num_buckets - 1;
+ @ requires_free 2 <= num_buckets && num_buckets <= (1 << Constants.LOG_MAX_BUCKETS);
+ @ requires_free splitters.length == Classifier.STORAGE_SIZE;
+ @ requires_free tree.length == Classifier.STORAGE_SIZE;
+ @
+ @ ensures_free \fresh(\result);
+ @ ensures_free \invariant_free_for(\result);
+ @ ensures \invariant_for(\result);
+ @ ensures_free \result.sorted_splitters == splitters && \result.tree.tree == tree;
+ @ ensures_free \result.num_buckets % 2 == 0;
+ @ ensures_free splitters[0] == \old(splitters[0]) && splitters[1] == \old(splitters[1]);
+ @ ensures_free \result.classOf(splitters[0]) != \result.classOf(splitters[1]);
+ @
+ @ assignable_free splitters[*], tree[*];
+ @*/
+ public static Classifier from_sorted_samples(
+ int[] splitters,
+ int[] tree,
+ int num_splitters,
+ int num_buckets
+ ) {
+ // Check for duplicate splitters
+ boolean use_equal_buckets = (num_buckets - 1 - num_splitters) >= Constants.EQUAL_BUCKETS_THRESHOLD;
+
+ // Fill the array to the next power of two
+ int log_buckets = Constants.log2(num_splitters) + 1;
+ // Cut for result >= Constants.LOG_MAX_BUCKETS, lower bound
+ //@ assume log_buckets <= Constants.LOG_MAX_BUCKETS;
+ int actual_num_buckets = 1 << log_buckets;
+ //@ assume actual_num_buckets <= splitters.length && num_splitters < actual_num_buckets;
+
+ /*@ loop_invariant_free num_splitters <= i && i <= actual_num_buckets;
+ @
+ @ loop_invariant_free (\forall
+ @ int j;
+ @ 0 <= j < num_splitters;
+ @ // It is unchanged
+ @ splitters[j] == \old(splitters[j])
+ @ );
+ @ loop_invariant_free (\forall int j; num_splitters <= j < i; splitters[j] == splitters[num_splitters - 1]);
+ @ loop_invariant_free 0 <= i <= splitters.length;
+ @ loop_invariant_free Functions.isSortedSlice(splitters, 0, i);
+ @
+ @ decreases actual_num_buckets - i;
+ @ assignable_free splitters[num_splitters..actual_num_buckets - 1];
+ @*/
+ for (int i = num_splitters; i < actual_num_buckets; ++i) {
+ splitters[i] = splitters[num_splitters - 1];
+ }
+
+ Classifier classifier = new Classifier(splitters, tree, log_buckets, use_equal_buckets);
+ //@ assume classifier.classOfFirstSplitters();
+ return classifier;
+ }
+
+ /*@ public normal_behaviour
+ @ ensures_free \result == this.num_buckets;
+ @ assignable_free \strictly_nothing;
+ @*/
+ public int num_buckets() {
+ return this.num_buckets;
+ }
+
+ /*@ public normal_behaviour
+ @ ensures_free \result == this.equal_buckets;
+ @ assignable_free \strictly_nothing;
+ @*/
+ public boolean equal_buckets() {
+ return this.equal_buckets;
+ }
+
+ /*@ public model_behaviour
+ @ requires true;
+ @
+ @ model boolean isClassifiedAs(int value, int bucket) {
+ @ return this.equal_buckets ?
+ @ ((bucket % 2 == 0 || bucket == this.num_buckets - 1) ?
+ @ ((0 < bucket ==> this.sorted_splitters[bucket / 2 - 1] < value) &&
+ @ (bucket < this.num_buckets - 1 ==> value < this.sorted_splitters[bucket / 2])) :
+ @ (this.sorted_splitters[bucket / 2] == value &&
+ @ // elements land in equality buckets iff the non equality bucket actually allows elements
+ @ (0 < bucket / 2 ==> this.sorted_splitters[bucket / 2 - 1] < value))) :
+ @ ((0 < bucket ==> this.sorted_splitters[bucket - 1] < value) &&
+ @ (bucket < this.num_buckets - 1 ==> value <= this.sorted_splitters[bucket]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @
+ @ ensures_free \result;
+ @
+ @ model boolean classOfTrans() {
+ @ return (\forall int i, j, classI, classJ; 0 <= classI < classJ < this.num_buckets;
+ @ this.isClassifiedAs(i, classI) && this.isClassifiedAs(j, classJ) ==> i < j
+ @ );
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free \dl_inInt(value);
+ @ ensures_free 0 <= \result < this.num_buckets;
+ @ ensures_free this.isClassifiedAs(value, \result);
+ @
+ @ // Needed to bring this method to logic
+ @ ensures_free \result == this.classify(value);
+ @
+ @ assignable_free \strictly_nothing;
+ @
+ @ accessible this.sorted_splitters[*], this.tree.tree[*];
+ @*/
+ public int classify(int value) {
+ /*@ normal_behaviour
+ @ assignable \nothing;
+ @*/
+ {
+ value = value;
+ }
+ int index = this.tree.classify(value);
+ int bucket;
+ if (this.equal_buckets) {
+ int bucket_index = index - this.num_buckets / 2;
+ boolean equal_to_splitter = !Constants.cmp(value, this.sorted_splitters[bucket_index]);
+ bucket = 2 * index + Constants.toInt(equal_to_splitter) - this.num_buckets;
+ } else {
+ bucket = index - this.num_buckets;
+ }
+ return bucket;
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin == indices.length;
+ @ requires_free \disjoint(values[*], indices[*], this.tree.tree[*], this.sorted_splitters[*]);
+ @
+ @ ensures_free (\forall int i; 0 <= i && i < indices.length; this.classOf(values[begin + i]) == indices[i]);
+ @
+ @ assignable_free indices[*];
+ @*/
+ public void classify_all(int[] values, int begin, int end, int[] indices) {
+ this.tree.classify_all(values, begin, end, indices);
+ if (this.equal_buckets) {
+ /*@ loop_invariant_free 0 <= i <= indices.length;
+ @ loop_invariant_free (\forall int j; 0 <= j < i; this.classify(values[begin + j]) == indices[j]);
+ @ loop_invariant_free (\forall int j; i <= j < indices.length; this.tree.classify(values[begin + j]) == indices[j]);
+ @ loop_invariant_free \invariant_for(this) && \invariant_for(this.tree);
+ @
+ @ decreases indices.length - i;
+ @ assignable_free indices[*];
+ @*/
+ for (int i = 0; i < indices.length; ++i) {
+ final int value = values[begin + i];
+ //@ assume \dl_inInt(value);
+ final int index = indices[i];
+ //@ assert this.tree.num_buckets <= index < 2 * this.tree.num_buckets;
+ //@ assume 0 <= (index - this.num_buckets / 2) < this.sorted_splitters.length;
+ final int bucket = index - this.num_buckets / 2;
+ final boolean equal_to_splitter = !Constants.cmp(value, this.sorted_splitters[bucket]);
+ indices[i] = 2 * index + Constants.toInt(equal_to_splitter) - this.num_buckets;
+ }
+ } else {
+ /*@ loop_invariant_free 0 <= i <= indices.length;
+ @ loop_invariant_free (\forall int j; 0 <= j < i; this.classify(values[begin + j]) == indices[j]);
+ @ loop_invariant_free (\forall int j; i <= j < indices.length; this.tree.classify(values[begin + j]) == indices[j]);
+ @ loop_invariant_free \invariant_for(this) && \invariant_for(this.tree);
+ @
+ @ decreases indices.length - i;
+ @ assignable_free indices[*];
+ @*/
+ for (int i = 0; i < indices.length; ++i) {
+ //@ assume \dl_inInt(values[begin + i]);
+ indices[i] -= this.num_buckets;
+ }
+ }
+ }
+
+ /*@ model_behaviour
+ @ requires bucket_starts.length >= this.num_buckets;
+ @ accessible this.sorted_splitters[*];
+ @ accessible this.tree.tree[*];
+ @ accessible values[begin..write - 1];
+ @ accessible bucket_starts[0..this.num_buckets];
+ @ model boolean allElementsCounted(int[] values, int begin, int write, int[] bucket_starts) {
+ @ return
+ @ (\forall int b; 0 <= b && b < this.num_buckets; bucket_starts[b] == this.countClassOfSliceEq(values, begin, write, b)) &&
+ @ (\sum int b; 0 <= b < this.num_buckets; bucket_starts[b]) == write - begin;
+ @ }
+ @*/
+
+ public static final int BATCH_SIZE = 16;
+
+ /*@ model_behaviour
+ @ requires \invariant_for(buffers);
+ @
+ @ requires bucket_starts.length >= this.num_buckets;
+ @ requires buffers.num_buckets == this.num_buckets;
+ @ requires Buffers.isBlockAligned(write - begin);
+ @ accessible
+ @ this.sorted_splitters[*], this.tree.tree[*],
+ @ values[begin..write - 1],
+ @ bucket_starts[0..this.num_buckets],
+ @ buffers.indices[0..this.num_buckets - 1],
+ @ buffers.buffer[0..Buffers.BUFFER_SIZE * this.num_buckets - 1];
+ @ model boolean isClassifiedUntil(int[] values, int begin, int write, int i, int[] bucket_starts, Buffers buffers) {
+ @ return this.allElementsCounted(values, begin, write, bucket_starts) &&
+ @ isClassifiedBlocksRange(values, begin, write) &&
+ @ buffers.isClassifiedWith(this) &&
+ @ (\forall int b; 0 <= b < this.num_buckets; isValidBufferLen(buffers.bufferLen(b), bucket_starts[b])) &&
+ @ buffers.count() == i - write;
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires \invariant_for(buffers);
+ @ ensures_free \result >= 0;
+ @
+ @ accessible values[begin..write - 1];
+ @ accessible values[read..end - 1];
+ @ accessible buffers.indices[0..buffers.num_buckets - 1], buffers.buffer[0..Buffers.BUFFER_SIZE * buffers.num_buckets - 1];
+ @ model static int countElement(int[] values, int begin, int write, int read, int end, Buffers buffers, int element) {
+ @ return
+ @ // element in [begin,write)
+ @ Functions.countElement(values, begin, write, element) +
+ @ // element in [read,end)
+ @ Functions.countElement(values, read, end, element) +
+ @ // element in all buffers
+ @ buffers.countElement(element);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires 0 <= len <= Buffers.BUFFER_SIZE;
+ @
+ @ ensures_free \result ==> Buffers.bufferSizeForBucketLen(len + writtenElements) == len;
+ @ static model no_state boolean isValidBufferLen(int len, int writtenElements) {
+ @ return
+ @ 0 <= writtenElements &&
+ @ Buffers.isBlockAligned(writtenElements) &&
+ @ (0 < writtenElements ==> len != 0);
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free \invariant_free_for(buffers);
+ @
+ @ requires_free bucket_starts.length >= this.num_buckets + 1;
+ @ requires_free \disjoint(values[*], bucket_starts[*], buffers.buffer[*], buffers.indices[*], this.sorted_splitters[*], this.tree.tree[*], indices[*]);
+ @ requires_free buffers.num_buckets == this.num_buckets;
+ @
+ @ requires_free 0 <= begin <= end <= values.length;
+ @
+ @ requires_free begin <= write <= i && i + indices.length <= end;
+ @ requires_free Buffers.isBlockAligned(write - begin);
+ @ requires_free (i - begin) % BATCH_SIZE == 0;
+ @ requires_free indices.length <= BATCH_SIZE;
+ @
+ @ requires_free (\forall int j; 0 <= j < indices.length; this.classOf(values[i + j]) == indices[j]);
+ @
+ @ requires_free this.isClassifiedUntil(values, begin, write, i, bucket_starts, buffers);
+ @
+ @ ensures_free \invariant_free_for(buffers) && \invariant_free_for(this);
+ @ ensures \invariant_for(buffers) && \invariant_for(this);
+ @
+ @ ensures_free write <= \result && \result <= i && Buffers.isBlockAligned(\result - begin);
+ @ ensures_free this.isClassifiedUntil(values, begin, \result, i + indices.length, bucket_starts, buffers);
+ @
+ @ ensures_free (\forall int element; true;
+ @ \old(Classifier.countElement(values, begin, write, i, end, buffers, element)) ==
+ @ Classifier.countElement(values, begin, \result, i + indices.length, end, buffers, element)
+ @ );
+ @
+ @ // Bucket starts
+ @
+ @ assignable_free values[write..i - 1];
+ @ assignable_free bucket_starts[0..this.num_buckets - 1];
+ @ assignable_free buffers.indices[0..this.num_buckets - 1], buffers.buffer[0..Buffers.BUFFER_SIZE * this.num_buckets - 1];
+ @*/
+ private int finish_batch(int[] indices, int[] values, int begin, int write, int i, int end, int[] bucket_starts, Buffers buffers) {
+ //@ ghost int old_write = write;
+ /*@ loop_invariant_free 0 <= j && j <= indices.length;
+ @
+ @ loop_invariant_free \old(write) <= write && write <= i;
+ @ loop_invariant_free Buffers.isBlockAligned(write - begin);
+ @
+ @ loop_invariant_free this.isClassifiedUntil(values, begin, write, i + j, bucket_starts, buffers);
+ @
+ @ loop_invariant_free (\forall int element; true;
+ @ \old(Classifier.countElement(values, begin, old_write, i, end, buffers, element)) ==
+ @ Classifier.countElement(values, begin, write, i + j, end, buffers, element)
+ @ );
+ @
+ @ loop_invariant_free \invariant_for(buffers) && \invariant_for(this);
+ @
+ @ decreases indices.length - j;
+ @
+ @ assignable_free buffers.indices[0..this.num_buckets - 1], buffers.buffer[0..Buffers.BUFFER_SIZE * this.num_buckets - 1];
+ @ assignable_free values[old_write..i - 1];
+ @ assignable_free bucket_starts[0..this.num_buckets - 1];
+ @*/
+ for (int j = 0; j < indices.length; ++j) {
+ //@ ghost \dl_Heap heapAtLoopBodyBegin = \dl_heap();
+
+ int bucket = indices[j];
+ int value = values[i + j];
+
+ //@ assume this.classOf(value) == bucket;
+ //@ assume 0 <= bucket < this.num_buckets;
+
+ /*@ public normal_behaviour
+ @ ensures_free buffers.bufferLen(bucket) != Buffers.BUFFER_SIZE;
+ @
+ @ ensures_free \old(write) <= write && write <= i;
+ @ ensures_free Buffers.isBlockAligned(write - begin);
+ @
+ @ ensures_free this.allElementsCounted(values, begin, write, bucket_starts) &&
+ @ isClassifiedBlocksRange(values, begin, write) &&
+ @ buffers.isClassifiedWith(this) &&
+ @ buffers.count() == i + j - write;
+ @
+ @ ensures_free (\forall int b; 0 <= b < this.num_buckets;
+ @ isValidBufferLen(buffers.bufferLen(b) + (b == bucket ? 1 : 0), bucket_starts[b])
+ @ );
+ @
+ @ ensures_free (\forall int element; true;
+ @ \old(Classifier.countElement(values, begin, old_write, i, end, buffers, element)) ==
+ @ Classifier.countElement(values, begin, write, i + j, end, buffers, element)
+ @ );
+ @
+ @ ensures_free \invariant_free_for(buffers) && \invariant_free_for(this);
+ @ ensures \invariant_for(buffers) && \invariant_for(this);
+ @
+ @ assignable_free buffers.indices[bucket];
+ @ assignable_free values[old_write..i - 1];
+ @ assignable_free bucket_starts[bucket];
+ @*/
+ {
+ if (buffers.len(bucket) == Buffers.BUFFER_SIZE) {
+ // Use element lower bound
+ /*@ assume write + 256 <= i &&
+ @ Buffers.isBlockAlignedAdd(write - begin, Buffers.BUFFER_SIZE) &&
+ @ Buffers.isBlockAlignedAdd(bucket_starts[bucket], Buffers.BUFFER_SIZE);
+ @*/
+
+ // This was moved ahead to remove heap modifications after flush, changes nothing in the algorithm
+ bucket_starts[bucket] += Buffers.BUFFER_SIZE;
+
+ buffers.flush(bucket, values, write, i);
+
+ /*@ assume
+ @ \invariant_for(this) &&
+ @ Buffers.isBlockAligned(write + Buffers.BUFFER_SIZE - begin) &&
+ @ Buffers.isBlockAligned(bucket_starts[bucket]);
+ @*/
+
+ // Split off the written part
+ /*@ assume
+ @ this.isClassifiedBlocksRangeSplit(values, begin, write, write + Buffers.BUFFER_SIZE) &&
+ @ this.isClassOfSliceCopy(buffers.buffer, bucket * Buffers.BUFFER_SIZE, values, write, Buffers.BUFFER_SIZE, bucket) &&
+ @ Functions.countElementSplit(values, begin, write, write + Buffers.BUFFER_SIZE);
+ @*/
+ //@ assume this.isClassOfSlice(values, write, write + Buffers.BUFFER_SIZE, bucket);
+ //@ assume this.countClassOfSliceEqLemma(values, write, write + Buffers.BUFFER_SIZE, bucket);
+ /*@ assume (\forall int b; 0 <= b && b < this.num_buckets;
+ @ \at(this.countClassOfSliceEq(values, begin, write, b), heapAtLoopBodyBegin) + (b == bucket ? Buffers.BUFFER_SIZE : 0) ==
+ @ this.countClassOfSliceEq(values, begin, write + Buffers.BUFFER_SIZE, b)
+ @ );
+ @*/
+
+ /*@ assume (\sum int b; 0 <= b < this.num_buckets; bucket_starts[b]) ==
+ @ (\sum int b; 0 <= b < this.num_buckets; \at(bucket_starts[b], heapAtLoopBodyBegin)) + Buffers.BUFFER_SIZE;
+ @*/
+
+ write += Buffers.BUFFER_SIZE;
+ }
+ }
+ //@ assume \dl_inInt(value);
+ buffers.push(bucket, value);
+ //@ assume \invariant_for(this) && Functions.countElementSplit(values, i + j, i + j + 1, end);
+ // permutation property: elements in [begin,write) stayed the same, split first in [read,end), split on element = value
+ }
+
+ return write;
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free \invariant_free_for(buffers);
+ @
+ @ requires_free bucket_starts.length >= this.num_buckets + 1;
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free (\forall int b; 0 <= b < this.num_buckets; bucket_starts[b] == 0);
+ @ requires_free buffers.isEmpty();
+ @ requires_free \disjoint(values[*], bucket_starts[*], buffers.buffer[*], buffers.indices[*], this.sorted_splitters[*], this.tree.tree[*]);
+ @ requires_free buffers.num_buckets == this.num_buckets;
+ @
+ @ ensures_free \invariant_free_for(buffers);
+ @ ensures \invariant_for(buffers);
+ @
+ @ // classifies until end - (end - begin) % BATCH_SIZE
+ @
+ @ ensures_free begin <= \result && \result <= (end - (end - begin) % BATCH_SIZE) && Buffers.isBlockAligned(\result - begin);
+ @ ensures_free this.isClassifiedUntil(values, begin, \result, end - (end - begin) % BATCH_SIZE, bucket_starts, buffers);
+ @ ensures_free (\forall int element; true;
+ @ \old(Classifier.countElement(values, begin, begin, begin, end, buffers, element)) ==
+ @ Classifier.countElement(values, begin, \result, end - (end - begin) % BATCH_SIZE, end, buffers, element)
+ @ );
+ @
+ @ assignable_free values[begin..end - (end - begin) % BATCH_SIZE - 1];
+ @ assignable_free bucket_starts[0..this.num_buckets - 1];
+ @ assignable_free buffers.indices[0..this.num_buckets - 1], buffers.buffer[0..Buffers.BUFFER_SIZE * this.num_buckets - 1];
+ @*/
+ public int classify_locally_batched(int[] values, int begin, int end, int[] bucket_starts, Buffers buffers) {
+ int write = begin;
+ int i = begin;
+
+ /*@ assume
+ @ this.isClassifiedUntil(values, begin, write, i, bucket_starts, buffers) &&
+ @ (\forall int element; true;
+ @ \old(Classifier.countElement(values, begin, begin, begin, end, buffers, element)) ==
+ @ Classifier.countElement(values, begin, write, i, end, buffers, element)
+ @ );
+ @*/
+ if (end - begin >= BATCH_SIZE) {
+ int cutoff = end - BATCH_SIZE;
+ final int[] indices = new int[BATCH_SIZE];
+ //@ assume \disjoint(values[*], bucket_starts[*], buffers.buffer[*], buffers.indices[*], this.sorted_splitters[*], this.tree.tree[*], indices[*]);
+
+ /*@ loop_invariant_free begin <= i && i <= end - (end - begin) % BATCH_SIZE;
+ @
+ @ loop_invariant_free begin <= write && write <= i;
+ @ loop_invariant_free (i - begin) % BATCH_SIZE == 0;
+ @ loop_invariant_free Buffers.isBlockAligned(write - begin);
+ @
+ @ // Bucket starts contain all elements in values[..write]
+ @ loop_invariant_free this.isClassifiedUntil(values, begin, write, i, bucket_starts, buffers);
+ @
+ @ loop_invariant_free (\forall int element; true;
+ @ \old(Classifier.countElement(values, begin, begin, begin, end, buffers, element)) ==
+ @ Classifier.countElement(values, begin, write, i, end, buffers, element)
+ @ );
+ @
+ @ loop_invariant_free \invariant_for(buffers) && \invariant_for(this);
+ @
+ @ decreases end - i;
+ @
+ @ assignable_free buffers.indices[0..this.num_buckets - 1], buffers.buffer[0..Buffers.BUFFER_SIZE * this.num_buckets - 1];
+ @ assignable_free values[begin..end - (end - begin) % BATCH_SIZE - 1];
+ @ assignable_free bucket_starts[0..this.num_buckets - 1];
+ @ assignable_free indices[*];
+ @*/
+ while (i <= cutoff) {
+ this.classify_all(values, i, i + BATCH_SIZE, indices);
+
+ write = this.finish_batch(indices, values, begin, write, i, end, bucket_starts, buffers);
+
+ i += BATCH_SIZE;
+ }
+ //@ assume i == end - (end - begin) % BATCH_SIZE;
+ }
+
+ return write;
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free \invariant_free_for(buffers);
+ @
+ @ requires_free bucket_starts.length >= this.num_buckets + 1;
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free \disjoint(values[*], bucket_starts[*], buffers.buffer[*], buffers.indices[*], this.sorted_splitters[*], this.tree.tree[*]);
+ @ requires_free buffers.num_buckets == this.num_buckets;
+ @ requires_free this.isClassifiedUntil(values, begin, write, end, bucket_starts, buffers);
+ @ requires_free begin <= write <= end;
+ @ requires_free Buffers.isBlockAligned(write - begin);
+ @
+ @ ensures_free Functions.isValidBucketStarts(bucket_starts, this.num_buckets) && bucket_starts[this.num_buckets] == end - begin;
+ @ ensures_free (\forall int b; 0 <= b < this.num_buckets;
+ @ bucket_starts[b + 1] - bucket_starts[b] ==
+ @ \old(this.countClassOfSliceEq(values, begin, write, b)) + \old(buffers.bufferLen(b))
+ @ );
+ @
+ @ assignable_free bucket_starts[0..this.num_buckets];
+ @*/
+ public void calculate_bucket_starts(int[] values, int begin, int write, int end, int[] bucket_starts, Buffers buffers) {
+ // bucket_starts contains the bucket counts without buffer contents
+ // Calculate bucket starts
+ int sum = 0;
+
+ /*@ loop_invariant_free 0 <= j <= this.num_buckets;
+ @ loop_invariant_free 0 < j ==> bucket_starts[j - 1] <= sum && bucket_starts[0] == 0;
+ @ loop_invariant_free sum == (\sum int b; 0 <= b < j;
+ @ \old(this.countClassOfSliceEq(values, begin, write, b)) + \old(buffers.bufferLen(b))
+ @ );
+ @ loop_invariant_free Functions.isSortedSlice(bucket_starts, 0, j);
+ @ loop_invariant_free (\forall int b; j <= b < this.num_buckets; bucket_starts[b] == \old(this.countClassOfSliceEq(values, begin, write, b)));
+ @ loop_invariant_free (\forall int b; 0 <= b < j;
+ @ (b + 1 == j ? sum : bucket_starts[b + 1]) - bucket_starts[b] ==
+ @ \old(this.countClassOfSliceEq(values, begin, write, b)) + \old(buffers.bufferLen(b))
+ @ );
+ @
+ @ decreases this.num_buckets - j;
+ @
+ @ assignable_free bucket_starts[0..this.num_buckets];
+ @*/
+ for (int j = 0; j < this.num_buckets; ++j) {
+ //@ assume \invariant_for(buffers);
+ /*@ assume
+ @ bucket_starts[j] == \old(this.countClassOfSliceEq(values, begin, write, j)) &&
+ @ buffers.bufferLen(j) == \old(buffers.bufferLen(j));
+ @*/
+ // Add the partially filled buffers
+ int size = bucket_starts[j] + buffers.len(j);
+
+ // Exclusive prefix sum
+ bucket_starts[j] = sum;
+ sum += size;
+ //@ assume size >= 0;
+ }
+ bucket_starts[this.num_buckets] = sum;
+
+ //@ assume sum == end - begin && Functions.isSortedSlice(bucket_starts, 0, this.num_buckets + 1);
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free \invariant_free_for(buffers);
+ @
+ @ requires_free bucket_starts.length >= this.num_buckets + 1;
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free (\forall int b; 0 <= b < this.num_buckets; bucket_starts[b] == 0);
+ @ requires_free buffers.isEmpty();
+ @ requires_free \disjoint(values[*], bucket_starts[*], buffers.buffer[*], buffers.indices[*], this.sorted_splitters[*], this.tree.tree[*]);
+ @ requires_free buffers.num_buckets == this.num_buckets;
+ @
+ @ ensures_free begin <= \result && \result <= end && Buffers.isBlockAligned(\result - begin);
+ @ ensures_free this.isClassifiedBlocksRange(values, begin, \result);
+ @ ensures_free buffers.isClassifiedWith(this);
+ @ ensures_free Functions.isValidBucketStarts(bucket_starts, this.num_buckets) && bucket_starts[this.num_buckets] == end - begin;
+ @
+ @ ensures_free (\forall int b; 0 <= b < this.num_buckets;
+ @ // Bucket starts contains the bucket counts
+ @ bucket_starts[b + 1] - bucket_starts[b] ==
+ @ buffers.bufferLen(b) + this.countClassOfSliceEq(values, begin, \result, b) &&
+ @ // Buffer len is correct for the bucket size
+ @ buffers.bufferLen(b) == Buffers.bufferSizeForBucketLen(bucket_starts[b + 1] - bucket_starts[b])
+ @ );
+ @ ensures_free (\forall int element; true;
+ @ \old(Functions.countElement(values, begin, end, element)) ==
+ @ Functions.countElement(values, begin, \result, element) +
+ @ buffers.countElement(element)
+ @ );
+ @ ensures_free \invariant_free_for(buffers);
+ @ ensures \invariant_for(buffers);
+ @
+ @ // All values are either in a buffer or in values[..\result]
+ @ // Bucket starts
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free bucket_starts[0..this.num_buckets];
+ @ assignable_free buffers.indices[0..this.num_buckets - 1], buffers.buffer[0..Buffers.BUFFER_SIZE * this.num_buckets - 1];
+ @*/
+ public int classify_locally(int[] values, int begin, int end, int[] bucket_starts, Buffers buffers) {
+ /*@ assume (\forall int element; true;
+ @ Functions.countElement(values, begin, end, element) ==
+ @ Classifier.countElement(values, begin, begin, begin, end, buffers, element)
+ @ );
+ @*/
+ int write = this.classify_locally_batched(values, begin, end, bucket_starts, buffers);
+ int i = end - (end - begin) % BATCH_SIZE;
+ //@ assume end - i >= 0;
+ int[] indices = new int[end - i];
+ //@ assume \disjoint(values[*], bucket_starts[*], buffers.buffer[*], buffers.indices[*], this.sorted_splitters[*], this.tree.tree[*], indices[*]);
+ this.classify_all(values, i, end, indices);
+ write = this.finish_batch(indices, values, begin, write, i, end, bucket_starts, buffers);
+
+ this.calculate_bucket_starts(values, begin, write, end, bucket_starts, buffers);
+ return write;
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Cleanup.java b/src/main/java-overflow/de/wiesler/Cleanup.java
new file mode 100644
index 0000000..ed460fe
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Cleanup.java
@@ -0,0 +1,335 @@
+package de.wiesler;
+
+public final class Cleanup {
+ /*@ public model_behaviour
+ @ requires \invariant_for(classifier);
+ @
+ @ accessible values[begin + bucket_begin..begin + bucket_end - 1], classifier.sorted_splitters[*], classifier.tree.tree[*];
+ @
+ @ static model boolean cleanedUpSlice(int[] values, int begin, int end, int bucket_begin, int bucket_end, Classifier classifier, int bucket) {
+ @ return classifier.isClassOfSlice(values, begin + bucket_begin, begin + bucket_end, bucket) &&
+ @ Sorter.smallBucketIsSorted(values, begin, end, bucket_begin, bucket_end);
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free Functions.isValidBucketStarts(bucket_starts, classifier.num_buckets);
+ @ requires_free bucket_starts[classifier.num_buckets] == end - begin;
+ @ requires_free classifier.num_buckets == buffers.num_buckets && classifier.num_buckets == bucket_pointers.num_buckets;
+ @ requires_free \invariant_free_for(buffers) && \invariant_free_for(bucket_pointers) && \invariant_free_for(classifier);
+ @ requires \invariant_for(buffers) && \invariant_for(bucket_pointers) && \invariant_for(classifier);
+ @
+ @ requires_free \disjoint(values[*], bucket_starts[*], overflow[*], bucket_pointers.buffer[*], buffers.indices[*], buffers.buffer[*], classifier.sorted_splitters[*], classifier.tree.tree[*]);
+ @ requires_free overflow.length == Buffers.BUFFER_SIZE;
+ @
+ @ requires_free (\forall int b; 0 <= b <= classifier.num_buckets;
+ @ bucket_pointers.bucketStart(b) == Buffers.blockAligned(bucket_starts[b])
+ @ );
+ @ requires_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ classifier.isClassOfSlice(buffers.buffer, b * Buffers.BUFFER_SIZE, b * Buffers.BUFFER_SIZE + buffers.bufferLen(b), b) &&
+ @ // All elements are read
+ @ bucket_pointers.toReadCountOfBucket(b) == 0 &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b) &&
+ @ // Remaining elements: bucket size == buffer length + written elements
+ @ bucket_starts[b + 1] - bucket_starts[b] == buffers.bufferLen(b) + bucket_pointers.writtenCountOfBucket(b) &&
+ @ buffers.bufferLen(b) == Buffers.bufferSizeForBucketLen(bucket_starts[b + 1] - bucket_starts[b])
+ @ );
+ @
+ @ ensures_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ classifier.isClassOfSlice(values, begin + bucket_starts[b], begin + bucket_starts[b + 1], b) &&
+ @ Sorter.smallBucketIsSorted(values, begin, end, bucket_starts[b], bucket_starts[b + 1])
+ @ );
+ @
+ @ // Permutation property
+ @ ensures_free (\forall int element; true;
+ @ \old(bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element)) +
+ @ \old(buffers.countElement(element)) ==
+ @ Functions.countElement(values, begin, end, element)
+ @ );
+ @
+ @ assignable_free values[begin..end - 1];
+ @*/
+ public static void cleanup(
+ final int[] values,
+ final int begin,
+ final int end,
+ final Buffers buffers,
+ final int[] bucket_starts,
+ final BucketPointers bucket_pointers,
+ final Classifier classifier,
+ final int[] overflow
+ ) {
+ //@ ghost \dl_Heap heapOld = \dl_heap();
+ final int num_buckets = classifier.num_buckets();
+ final boolean is_last_level = end - begin <= Constants.SINGLE_LEVEL_THRESHOLD;
+
+ /*@ loop_invariant_free 0 <= bucket <= num_buckets;
+ @ loop_invariant_free (\forall int b; 0 <= b < bucket;
+ @ cleanedUpSlice(values, begin, end, \old(bucket_starts[b]), \old(bucket_starts[b + 1]), classifier, b)
+ @ );
+ @
+ @ loop_invariant_free (\forall int element; true;
+ @ (\sum int b; 0 <= b < bucket; \old(bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, b, element))) +
+ @ (\sum int b; 0 <= b < bucket; \old(buffers.countElementInBucket(b, element))) ==
+ @ Functions.countElement(values, begin, begin + \old(bucket_starts[bucket]), element)
+ @ );
+ @
+ @ loop_invariant_free (\forall int b; bucket <= b < classifier.num_buckets;
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b) &&
+ @ (\forall int element; true;
+ @ \old(bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, b, element)) ==
+ @ bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, b, element) &&
+ @ \old(buffers.countElementInBucket(b, element)) ==
+ @ buffers.countElementInBucket(b, element))
+ @ );
+ @
+ @ loop_invariant_free \invariant_for(classifier) && \invariant_for(bucket_pointers) && \invariant_for(buffers);
+ @
+ @ assignable_free values[begin..end - 1];
+ @
+ @ decreases num_buckets - bucket;
+ @*/
+ for (int bucket = 0; bucket < num_buckets; ++bucket) {
+ //@ assert \old(Functions.bucketStartsOrdering(bucket_starts, num_buckets, bucket));
+ final int relative_start = bucket_starts[bucket];
+ final int relative_stop = bucket_starts[bucket + 1];
+ final int relative_write = bucket_pointers.write(bucket);
+ //@ assert \dl_inInt(begin + relative_start) && \dl_inInt(begin + relative_stop);
+ final int start = begin + relative_start;
+ final int stop = begin + relative_stop;
+ final int write = begin + relative_write;
+
+ /*@ assume 0 <= bucket_starts[bucket] <= bucket_starts[bucket + 1] <= bucket_starts[num_buckets] &&
+ @ Buffers.blockAligned(bucket_starts[num_buckets]) == bucket_pointers.bucketStart(num_buckets);
+ @*/
+
+ //@ assert \dl_inInt(begin + bucket_pointers.bucketStart(bucket)) && \dl_inInt(begin + bucket_pointers.bucketStart(bucket + 1));
+
+ /*@ normal_behaviour
+ @ ensures_free classifier.isClassOfSlice(values, start, stop, bucket);
+ @ ensures_free (\forall int element; true;
+ @ \at(bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, bucket, element), heapOld) +
+ @ \at(buffers.countElementInBucket(bucket, element), heapOld) ==
+ @ Functions.countElement(values, start, stop, element)
+ @ );
+ @
+ @ assignable_free values[start..stop - 1];
+ @*/
+ {
+ /*@ assume relative_write == \old(bucket_pointers.nextWriteOf(bucket)) &&
+ @ Buffers.blockAligned(bucket_starts[bucket]) == bucket_pointers.bucketStart(bucket) &&
+ @ Buffers.blockAligned(bucket_starts[bucket + 1]) == bucket_pointers.bucketStart(bucket + 1);
+ @*/
+ //@ assume Buffers.blockAligned(bucket_starts[bucket]) <= relative_write <= Buffers.blockAligned(bucket_starts[bucket + 1]);
+
+ final int head_start = start;
+ int head_stop = -1;
+
+ int tail_start = -1;
+ final int tail_stop = stop;
+
+ /*@ normal_behaviour
+ @ requires_free begin <= start <= stop <= end;
+ @
+ @ ensures_free \invariant_free_for(classifier) && \invariant_free_for(bucket_pointers);
+ @ ensures \invariant_for(classifier) && \invariant_for(bucket_pointers);
+ @
+ @ ensures_free start <= head_start <= head_stop <= tail_start <= tail_stop <= stop <= end <= values.length;
+ @ ensures_free tail_start - head_stop == \at(bucket_pointers.writtenCountOfBucket(bucket), heapOld);
+ @ ensures_free classifier.isClassOfSlice(values, head_stop, tail_start, bucket);
+ @ ensures_free (\forall int element; true;
+ @ Functions.countElement(values, head_stop, tail_start, element) ==
+ @ \at(bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, bucket, element), heapOld)
+ @ );
+ @
+ @ assignable_free values[start..stop - 1];
+ @*/
+ {
+ // Overflow happened:
+ // - block was written at least once
+ // - write was out of bounds
+
+ if (relative_stop - relative_start <= Buffers.BUFFER_SIZE) {
+ // Nothing written
+ // Valid: use precondition and split on the buffer length
+ //@ assume \old(bucket_pointers.writtenCountOfBucket(bucket)) == 0;
+ //@ assume (\forall int element; true; \old(bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, bucket, element)) == 0);
+
+ // Bucket is at most one block large => head is the full block, no tail
+ head_stop = stop;
+ tail_start = stop;
+ // verified
+ } else {
+ final int aligned_relative_start = Buffers.align_to_next_block(relative_start);
+ //@ assume aligned_relative_start == Buffers.blockAligned(relative_start);
+ //@ assume aligned_relative_start == bucket_pointers.bucketStart(bucket);
+ head_stop = begin + aligned_relative_start;
+
+ // Valid: use precondition and observer dependency
+ //@ assume head_start <= head_stop <= tail_stop;
+
+ if (stop < write) {
+ // Final block has been written
+ // Write pointer must be at aligned end of bucket
+
+ // Valid: use contract from nextWrite and blockAlign
+ //@ assume relative_write == Buffers.blockAligned(relative_stop);
+
+ if (end < write) {
+ // Overflow: write is out of bounds, content is in overflow
+
+ tail_start = write - Buffers.BUFFER_SIZE;
+
+ // Valid: Use contract of blockAligned
+ //@ assume head_start <= head_stop <= tail_start <= tail_stop;
+
+ int tail_len = tail_stop - tail_start;
+
+ // There must be space for all elements
+ // Valid: Precondition and observer
+ //@ assume Buffers.BUFFER_SIZE + buffers.bufferLen(bucket) == (tail_stop - tail_start) + (head_stop - head_start);
+
+ // Fill tail
+ Functions.copy_nonoverlapping(overflow, 0, values, tail_start, tail_len);
+
+ // Write remaining elements to end of head
+ int head_elements = Buffers.BUFFER_SIZE - tail_len;
+ head_stop -= head_elements;
+ Functions.copy_nonoverlapping(overflow, tail_len, values, head_stop, head_elements);
+
+ //@ assume \invariant_for(classifier) && \invariant_for(bucket_pointers);
+
+ /*@ assume
+ @ classifier.isClassOfSlice(overflow, 0, Buffers.BUFFER_SIZE, bucket) &&
+ @ // Follows from writtenElementsOfBucketClassified
+ @ classifier.isClassOfSlice(values, head_stop + head_elements, tail_start, bucket) &&
+ @ classifier.isClassOfSliceSplit(overflow, 0, tail_len, Buffers.BUFFER_SIZE, bucket) &&
+ @ classifier.isClassOfSliceSplit(values, head_stop, head_stop + head_elements, tail_start, bucket) &&
+ @ classifier.isClassOfSliceSplit(values, head_stop, tail_start, tail_stop, bucket);
+ @*/
+ /*@ assume
+ @ classifier.isClassOfSliceCopy(overflow, 0, values, tail_start, tail_len, bucket) &&
+ @ classifier.isClassOfSliceCopy(overflow, tail_len, values, head_stop, head_elements, bucket);
+ @*/
+
+ /*@ assume (\forall int element; true;
+ @ \old(bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, bucket, element)) ==
+ @ Functions.countElement(values, head_stop + head_elements, tail_start, element) +
+ @ Functions.countElement(overflow, 0, Buffers.BUFFER_SIZE, element)
+ @ );
+ @*/
+
+ /*@ assume
+ @ // Split overflow buffer
+ @ Functions.countElementSplit(overflow, 0, tail_len, Buffers.BUFFER_SIZE) &&
+ @ // Split off tail
+ @ Functions.countElementSplit(values, head_stop, tail_start, tail_stop) &&
+ @ // Split off head
+ @ Functions.countElementSplit(values, head_stop, head_stop + head_elements, tail_start);
+ @*/
+
+ tail_start = tail_stop;
+ // rest verified
+ } else {
+ // Normal overflow: write is in bounds and content is after the end of the bucket
+ int overflow_len = write - stop;
+
+ //@ assume head_start <= head_stop <= stop <= stop + overflow_len <= end;
+
+ // Must fit, no other empty space left
+ // Follows from precondition and lots of observers
+ //@ assume overflow_len + buffers.bufferLen(bucket) == head_stop - head_start;
+ // Follows from previous and buffer length >= 0
+ //@ assume head_start <= head_stop - overflow_len;
+
+ // Write overflow of last block to [head_stop - overflow_len..head_stop)
+ head_stop -= overflow_len;
+
+ Functions.copy_nonoverlapping(values, stop, values, head_stop, overflow_len);
+
+ //@ assume \invariant_for(classifier) && \invariant_for(bucket_pointers);
+
+ //@ assume classifier.isClassOfSlice(values, head_stop + overflow_len, write, bucket);
+ //@ assume classifier.isClassOfSliceSplit(values, head_stop + overflow_len, stop, write, bucket);
+ //@ assume classifier.isClassOfSliceCopy(values, stop, values, head_stop, overflow_len, bucket);
+ //@ assume classifier.isClassOfSliceSplit(values, head_stop, head_stop + overflow_len, stop, bucket);
+
+ /*@ assume (\forall int element; true;
+ @ \old(bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, bucket, element)) ==
+ @ Functions.countElement(values, begin + bucket_pointers.bucketStart(bucket), begin + \old(bucket_pointers.nextWriteOf(bucket)), element)
+ @ );
+ @*/
+ //@ assume Functions.countElementSplit(values, head_stop + overflow_len, stop, write);
+ //@ assume Functions.countElementSplit(values, head_stop, head_stop + overflow_len, stop);
+
+ // Tail is empty
+ tail_start = tail_stop;
+ // rest verified (all the dependency contracts)
+ }
+ } else {
+ // No overflow, write <= stop
+ tail_start = write;
+
+ // verified: use equality
+ }
+ }
+
+ //@ assume \invariant_for(classifier) && \invariant_for(bucket_pointers);
+ }
+
+ int head_len = head_stop - head_start;
+ int tail_len = tail_stop - tail_start;
+ //@ assume buffers.bufferLen(bucket) == head_len + tail_len;
+ // Write remaining elements from buffer to head and tail
+ buffers.distribute(
+ bucket,
+ values,
+ head_start,
+ head_len,
+ tail_start,
+ tail_len
+ );
+ /*@ assume Functions.countElementSplit(values, head_start, head_stop, tail_stop) &&
+ @ Functions.countElementSplit(values, head_stop, tail_start, tail_stop) &&
+ @ buffers.bufferLen(bucket) == head_len + tail_len &&
+ @ \invariant_for(classifier);
+ @*/
+ //@ ghost int bucketOffset = bucket * Buffers.BUFFER_SIZE;
+ /*@ assume
+ @ classifier.isClassOfSlice(buffers.buffer, bucketOffset, bucketOffset + buffers.bufferLen(bucket), bucket) &&
+ @ classifier.isClassOfSliceSplit(buffers.buffer, bucketOffset, bucketOffset + head_len, bucketOffset + buffers.bufferLen(bucket), bucket);
+ @*/
+ /*@ assume
+ @ classifier.isClassOfSliceCopy(buffers.buffer, bucketOffset, values, head_start, head_len, bucket) &&
+ @ classifier.isClassOfSliceCopy(buffers.buffer, bucketOffset + head_len, values, tail_start, tail_len, bucket) &&
+ @ classifier.isClassOfSliceSplit(values, head_start, head_stop, tail_stop, bucket) &&
+ @ classifier.isClassOfSliceSplit(values, head_stop, tail_start, tail_stop, bucket);
+ @*/
+ }
+
+ /*@ normal_behaviour
+ @ ensures_free cleanedUpSlice(values, begin, end, \at(bucket_starts[bucket], heapOld), \at(bucket_starts[bucket + 1], heapOld), classifier, bucket);
+ @ ensures_free (\forall int element; true;
+ @ \at(bucket_pointers.writtenElementsOfBucketCountElement(values, begin, end, overflow, bucket, element), heapOld) +
+ @ \at(buffers.countElementInBucket(bucket, element), heapOld) ==
+ @ Functions.countElement(values, start, stop, element)
+ @ );
+ @
+ @ assignable_free values[start..stop - 1];
+ @*/
+ {}
+
+ /*@ assume \invariant_for(classifier) && \invariant_for(bucket_pointers) && \invariant_for(buffers) &&
+ @ Functions.countElementSplit(values, begin, begin + \old(bucket_starts[bucket]), begin + \old(bucket_starts[bucket + 1])) &&
+ @ (\forall int b; 0 <= b < num_buckets && b != bucket;
+ @ (b < bucket ==> 0 <= \old(bucket_starts[b]) <= \old(bucket_starts[b + 1]) <= \old(bucket_starts[bucket])) &&
+ @ (b > bucket ==> \old(bucket_starts[bucket + 1]) <= \old(bucket_starts[b]) <= \old(bucket_starts[b + 1]) <= \old(bucket_starts[num_buckets]) &&
+ @ \old(bucket_starts[b]) <= bucket_pointers.bucketStart(b)
+ @ ));
+ @*/
+ }
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Constants.java b/src/main/java-overflow/de/wiesler/Constants.java
new file mode 100644
index 0000000..01bbbf0
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Constants.java
@@ -0,0 +1,70 @@
+package de.wiesler;
+
+public final class Constants {
+ public static final int BASE_CASE_SIZE = 32;
+ public static final int ACTUAL_BASE_CASE_SIZE = 4 * BASE_CASE_SIZE;
+ public static final int LOG_MAX_BUCKETS = 8;
+ public static final int MAX_BUCKETS = 1 << (LOG_MAX_BUCKETS + 1);
+ public static final int SINGLE_LEVEL_THRESHOLD = BASE_CASE_SIZE * (1 << LOG_MAX_BUCKETS);
+ public static final int TWO_LEVEL_THRESHOLD = SINGLE_LEVEL_THRESHOLD * (1 << LOG_MAX_BUCKETS);
+ public static final int EQUAL_BUCKETS_THRESHOLD = 5;
+
+ /*@ public model_behaviour
+ @ requires n > 0;
+ @ static no_state model boolean isLog2Of(int n, int log) {
+ @ return log >= 0 &&
+ @ log <= 30 &&
+ @ (1 << log) <= n &&
+ @ (log != 30 ==> n < (1 << (log + 1)));
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free n > 0;
+ @
+ @ ensures_free isLog2Of(n, \result);
+ @
+ @ assignable_free \strictly_nothing;
+ @*/
+ public static int log2(int n) {
+ int log = 0;
+ if ((n & 0xffff0000) != 0) {
+ n >>>= 16;
+ log = 16;
+ }
+ if (n >= 256) {
+ n >>>= 8;
+ log += 8;
+ }
+ if (n >= 16) {
+ n >>>= 4;
+ log += 4;
+ }
+ if (n >= 4) {
+ n >>>= 2;
+ log += 2;
+ }
+ return log + (n >>> 1);
+ }
+
+ private static boolean testLogContract(int n, int log) {
+ return log >= 0 &&
+ log <= 30 &&
+ (1 << log) <= n &&
+ (log == 30 || n < (1 << (log + 1)));
+ }
+
+ public static void testContracts(int i) {
+ if (i > 0 && !testLogContract(i, log2(i))) {
+ throw new Error("log2 contract fails for " + i);
+ }
+ }
+
+ public static /*@ strictly_pure */ int toInt(boolean b) {
+ return b ? 1 : 0;
+ }
+
+ public static /*@ strictly_pure */ boolean cmp(int a, int b) {
+ return a < b;
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Functions.java b/src/main/java-overflow/de/wiesler/Functions.java
new file mode 100644
index 0000000..c801669
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Functions.java
@@ -0,0 +1,233 @@
+package de.wiesler;
+
+public final class Functions {
+ /*@ public model_behaviour
+ @ accessible values[begin..end - 1];
+ @
+ @ static model int countElement(int[] values, int begin, int end, int element) {
+ @ return (\num_of int i; begin <= i < end; values[i] == element);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires begin <= mid <= end;
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean countElementSplit(int[] values, int begin, int mid, int end) {
+ @ return (\forall int element; true; countElement(values, begin, end, element) == countElement(values, begin, mid, element) + countElement(values, mid, end, element));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ ensures_free \result ==> Functions.isSortedSliceTransitive(values, begin, end);
+ @
+ @ accessible values[begin..end - 1];
+ @ static model boolean isSortedSlice(int[] values, int begin, int end) {
+ @ return (\forall int i; begin <= i && i < end - 1; values[i] <= values[i + 1]);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ ensures_free \result ==> Functions.isSortedSlice(values, begin, end);
+ @
+ @ accessible values[begin..end - 1];
+ @
+ @ static model boolean isSortedSliceTransitive(int[] values, int begin, int end) {
+ @ return
+ @ (\forall int i; begin <= i < end;
+ @ (\forall int j; i <= j < end; values[i] <= values[j]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ ensures_free \result;
+ @ static model boolean isSortedSeqTransitiveFromSlice(int[] values, int begin, int end) {
+ @ return isSortedSliceTransitive(values, begin, end) ==> isSortedSeqTransitive(\dl_seq_def_workaround(begin, end, values));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @ static no_state model boolean isSortedSeqTransitive(\seq values) {
+ @ return
+ @ (\forall int i; 0 <= i < values.length;
+ @ (\forall int j; i <= j < values.length; (int) values[i] <= (int) values[j]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ accessible bucket_starts[0..num_buckets];
+ @ static model boolean isValidBucketStarts(int[] bucket_starts, int num_buckets) {
+ @ return 2 <= num_buckets &&
+ @ num_buckets + 1 <= bucket_starts.length &&
+ @ isSortedSliceTransitive(bucket_starts, 0, num_buckets + 1) &&
+ @ bucket_starts[0] == 0;
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free 1 <= num_samples && num_samples <= end - begin;
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @
+ @ assignable_free values[begin..end - 1];
+ @*/
+ public static void select_n(int[] values, int begin, int end, int num_samples) {}
+
+ /*@ public normal_behaviour
+ @ ensures_free \result == ((a >= b) ? a : b);
+ @ assignable_free \strictly_nothing;
+ @*/
+ public static int max(int a, int b) {
+ return (a >= b) ? a : b;
+ }
+
+ /*@ public normal_behaviour
+ @ ensures_free \result == ((a <= b) ? a : b);
+ @ assignable_free \strictly_nothing;
+ @*/
+ public static int min(int a, int b) {
+ return (a <= b) ? a : b;
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @
+ @ ensures_free (\forall int i; begin <= i < end; values[i] == value);
+ @
+ @ assignable_free values[begin..end - 1];
+ @*/
+ public static void fill(int[] values, int begin, int end, int value) {
+ /*@ loop_invariant_free begin <= i <= end;
+ @ loop_invariant_free (\forall int j; begin <= j < i; values[j] == value);
+ @ assignable_free values[begin..end - 1];
+ @ decreases end - i;
+ @*/
+ for (int i = begin; i < end; i++) {
+ values[i] = value;
+ }
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= length;
+ @ requires_free 0 <= srcPos && srcPos + length <= src.length;
+ @ requires_free 0 <= destPos && destPos + length <= dest.length;
+ @ requires_free \disjoint(src[srcPos..srcPos + length - 1], dest[destPos..destPos + length - 1]);
+ @
+ @ ensures_free (\forall int i; 0 <= i && i < length; dest[destPos + i] == src[srcPos + i]);
+ @ // ensures \dl_seq_def_workaround(destPos, destPos + length, dest) == \dl_seq_def_workaround(srcPos, srcPos + length, src);
+ @ ensures_free (\forall int element; true;
+ @ countElement(dest, destPos, destPos + length, element) == countElement(src, srcPos, srcPos + length, element)
+ @ );
+ @
+ @ assignable_free dest[destPos..destPos + length - 1];
+ @*/
+ public static void copy_nonoverlapping(int[] src, int srcPos, int[] dest, int destPos, int length) {
+ /*@ loop_invariant_free 0 <= i <= length;
+ @ loop_invariant_free (\forall int j; 0 <= j < i; dest[destPos + j] == src[srcPos + j]);
+ @
+ @ decreases length - i;
+ @
+ @ assignable_free dest[destPos..destPos + length - 1];
+ @*/
+ for (int i = 0; i < length; ++i) {
+ dest[destPos + i] = src[srcPos + i];
+ }
+ // System.arraycopy(src, srcPos, dest, destPos, length);
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free Functions.isSortedSlice(values, begin, end);
+ @ requires_free \disjoint(target[*], values[*]);
+ @
+ @ requires_free target.length >= count;
+ @
+ @ requires_free count > 0;
+ @ requires_free step > 0;
+ @ requires_free begin + count * step - 1 < end;
+ @
+ @ ensures_free (\forall
+ @ int i;
+ @ 0 <= i < \result;
+ @ // It is from the source array
+ @ (\exists int j; begin <= j < end; values[j] == target[i])
+ @ );
+ @ ensures_free (\forall
+ @ int i;
+ @ 0 <= i < \result;
+ @ // It is unique in the target array (or: strictly ascending)
+ @ (i < \result - 1 ==> target[i] < target[i + 1])
+ @ );
+ @ ensures_free 1 <= \result <= count;
+ @
+ @ assignable_free target[0..count - 1];
+ @*/
+ public static int copy_unique(
+ int[] values,
+ int begin,
+ int end,
+ int count,
+ int step,
+ int[] target
+ ) {
+ int offset = begin + step - 1;
+ //@ assume offset < end;
+ target[0] = values[offset];
+ int target_offset = 1;
+ offset += step;
+
+ /*@
+ @ loop_invariant_free 1 <= i && i <= count;
+ @ loop_invariant_free 1 <= target_offset && target_offset <= i;
+ @
+ @ loop_invariant_free begin <= offset;
+ @ loop_invariant_free offset == begin + (step * (i + 1)) - 1;
+ @ loop_invariant_free i < count ==> offset < end;
+ @
+ @ loop_invariant_free (\forall
+ @ int j;
+ @ 0 <= j < target_offset;
+ @ // It is from the source array
+ @ (\exists int k; begin <= k < end; values[k] == target[j])
+ @ );
+ @ loop_invariant_free (\forall
+ @ int j;
+ @ 0 <= j < target_offset - 1;
+ @ // It is unique in the target array (or: strictly ascending)
+ @ target[j] < target[j + 1]
+ @ );
+ @
+ @ decreases count - i;
+ @ assignable_free target[1..count - 1];
+ @*/
+ for (int i = 1; i < count; ++i) {
+ // multiply both sides by step, this can't be proven automatically
+ //@ assume i + 2 <= count ==> (i + 2) * step <= count * step;
+ if (Constants.cmp(target[target_offset - 1], values[offset])) {
+ target[target_offset] = values[offset];
+ target_offset += 1;
+ }
+ offset += step;
+ }
+
+ return target_offset;
+ }
+
+ /*@ public model_behaviour
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets);
+ @ requires 0 <= bucket < num_buckets;
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean bucketStartsOrdering(int[] bucket_starts, int num_buckets, int bucket) {
+ @ return 0 <= bucket_starts[bucket] <= bucket_starts[bucket + 1] <= bucket_starts[num_buckets] &&
+ @ (\forall int b; 0 <= b < num_buckets && b != bucket;
+ @ (b < bucket ==> 0 <= bucket_starts[b] <= bucket_starts[b + 1] <= bucket_starts[bucket]) &&
+ @ (b > bucket ==> bucket_starts[bucket + 1] <= bucket_starts[b] <= bucket_starts[b + 1] <= bucket_starts[num_buckets])
+ @ );
+ @ }
+ @*/
+}
diff --git a/src/main/java-overflow/de/wiesler/Increment.java b/src/main/java-overflow/de/wiesler/Increment.java
new file mode 100644
index 0000000..e1ad783
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Increment.java
@@ -0,0 +1,17 @@
+package de.wiesler;
+
+public final class Increment {
+ public final boolean occupied;
+ public final int position;
+
+ /*@ public normal_behaviour
+ @ requires_free true;
+ @ ensures_free this.occupied == occupied;
+ @ ensures_free this.position == position;
+ @ assignable_free \nothing;
+ @*/
+ public Increment(boolean occupied, int position) {
+ this.occupied = occupied;
+ this.position = position;
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Partition.java b/src/main/java-overflow/de/wiesler/Partition.java
new file mode 100644
index 0000000..2b70ebb
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Partition.java
@@ -0,0 +1,117 @@
+package de.wiesler;
+
+public final class Partition {
+ /*@ public model_behaviour
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets);
+ @ requires 0 <= begin <= end <= values.length;
+ @
+ @ ensures_free \result;
+ @ static model boolean bucketCountsToTotalCount(int[] values, int begin, int end, int[] bucket_starts, int num_buckets) {
+ @ return (\forall int bucket; 0 <= bucket <= num_buckets;
+ @ (\forall int element; true;
+ @ (\sum int b; 0 <= b < bucket; Functions.countElement(values, begin + bucket_starts[b], begin + bucket_starts[b + 1], element)) ==
+ @ Functions.countElement(values, begin, begin + bucket_starts[bucket], element)
+ @ )
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @ static model boolean allBucketsClassified(int[] values, int begin, int end, Classifier classifier, int[] bucket_starts) {
+ @ return (\forall int b; 0 <= b < classifier.num_buckets;
+ @ classifier.isClassOfSlice(values, begin + bucket_starts[b], begin + bucket_starts[b + 1], b)
+ @ );
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free bucket_starts.length == Constants.MAX_BUCKETS + 1;
+ @ requires_free (\forall int b; 0 <= b < bucket_starts.length; bucket_starts[b] == 0);
+ @ requires_free end - begin > Constants.ACTUAL_BASE_CASE_SIZE;
+ @ requires_free \invariant_free_for(storage) && \invariant_free_for(classifier);
+ @ requires \invariant_for(storage) && \invariant_for(classifier);
+ @
+ @ requires_free \disjoint(
+ @ values[*],
+ @ bucket_starts[*],
+ @ classifier.tree.tree[*],
+ @ classifier.sorted_splitters[*],
+ @ storage.bucket_pointers[*],
+ @ storage.buffers_buffer[*],
+ @ storage.buffers_indices[*],
+ @ storage.swap_1[*],
+ @ storage.swap_2[*],
+ @ storage.overflow[*]
+ @ );
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free Functions.isValidBucketStarts(bucket_starts, classifier.num_buckets);
+ @ ensures_free bucket_starts[classifier.num_buckets] == end - begin;
+ @ ensures_free allBucketsClassified(values, begin, end, classifier, bucket_starts);
+ @ ensures_free Sorter.smallBucketsInRangeSorted(values, begin, end, bucket_starts, classifier.num_buckets, 0, classifier.num_buckets);
+ @ ensures_free \invariant_free_for(storage) && \invariant_free_for(classifier);
+ @ ensures \invariant_for(storage) && \invariant_for(classifier);
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free bucket_starts[*];
+ @ assignable_free storage.bucket_pointers[*];
+ @ assignable_free storage.buffers_buffer[*];
+ @ assignable_free storage.buffers_indices[*];
+ @ assignable_free storage.swap_1[*];
+ @ assignable_free storage.swap_2[*];
+ @ assignable_free storage.overflow[*];
+ @*/
+ public static void partition(
+ int[] values,
+ int begin,
+ int end,
+ int[] bucket_starts,
+ Classifier classifier,
+ Storage storage
+ ) {
+ Buffers buffers = new Buffers(storage.buffers_buffer, storage.buffers_indices, classifier.num_buckets());
+ int first_empty_position = classifier.classify_locally(values, begin, end, bucket_starts, buffers);
+ //@ ghost \dl_Heap heapAfterClassify = \dl_heap();
+
+ BucketPointers bucket_pointers = new BucketPointers(
+ bucket_starts,
+ classifier.num_buckets(),
+ first_empty_position - begin,
+ storage.bucket_pointers
+ );
+
+ /*@ assume
+ @ \invariant_for(classifier) &&
+ @ Buffers.blockAligned(end - begin) == bucket_pointers.bucketStart(bucket_pointers.num_buckets);
+ @*/
+ /*@ assume
+ @ bucket_pointers.initialReadAreasCount(values, begin, end) &&
+ @ bucket_pointers.initialReadAreasBlockClassified(classifier, values, begin, end) &&
+ @ bucket_pointers.initialReadAreasCountBucketElements(classifier, values, begin, end);
+ @*/
+ /*@ assume (\forall int b; 0 <= b < classifier.num_buckets;
+ @ \at(classifier.countClassOfSliceEq(values, begin, first_empty_position, b), heapAfterClassify) ==
+ @ bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b)
+ @ );
+ @*/
+
+ int[] overflow = storage.overflow;
+ Permute.permute(values, begin, end, classifier, bucket_pointers, storage.swap_1, storage.swap_2, overflow);
+
+ Cleanup.cleanup(values,
+ begin,
+ end,
+ buffers,
+ bucket_starts,
+ bucket_pointers,
+ classifier,
+ overflow);
+
+ //@ assume Functions.isValidBucketStarts(bucket_starts, classifier.num_buckets);
+ //@ assume Partition.bucketCountsToTotalCount(values, begin, end, bucket_starts, classifier.num_buckets);
+ //@ assume (\forall int element; true; Functions.countElement(values, begin, end, element) == \old(Functions.countElement(values, begin, end, element)));
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/PartitionResult.java b/src/main/java-overflow/de/wiesler/PartitionResult.java
new file mode 100644
index 0000000..e450ff7
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/PartitionResult.java
@@ -0,0 +1,16 @@
+package de.wiesler;
+
+public final class PartitionResult {
+ public final int num_buckets;
+ public final boolean equal_buckets;
+
+ /*@ public normal_behaviour
+ @ ensures_free this.num_buckets == num_buckets && this.equal_buckets == equal_buckets;
+ @
+ @ assignable_free \nothing;
+ @*/
+ public PartitionResult(int num_buckets, boolean equal_buckets) {
+ this.num_buckets = num_buckets;
+ this.equal_buckets = equal_buckets;
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Permute.java b/src/main/java-overflow/de/wiesler/Permute.java
new file mode 100644
index 0000000..06e5c35
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Permute.java
@@ -0,0 +1,637 @@
+package de.wiesler;
+
+public final class Permute {
+ // Places the block in current_swap into target_bucket
+ // Might skip blocks in current_swap if they are occupied and already in the right bucket
+ //
+ // If the target is occupied it is copied to other_swap and current_swap is placed in its position => result >= 0 && result == new_target
+ // Else it is placed there or in the overflow buffer => result == -1
+ //
+ // Permutation between:
+ // * the occupied area of each bucket
+ // * the written area of each bucket
+ // * current_swap
+ // * overflow if written
+ // and
+ // * the new occupied area of each bucket
+ // * the new written area of each bucket
+ // * other_swap
+ // * overflow if written now or before
+ /*@ public normal_behaviour
+ @ requires_free \invariant_free_for(bucket_pointers);
+ @ requires \invariant_for(bucket_pointers);
+ @ requires_free \invariant_free_for(classifier);
+ @ requires \invariant_for(classifier);
+ @ requires_free classifier.num_buckets == bucket_pointers.num_buckets;
+ @ requires_free current_swap.length == Buffers.BUFFER_SIZE && other_swap.length == Buffers.BUFFER_SIZE && overflow.length == Buffers.BUFFER_SIZE;
+ @
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free 0 <= target_bucket < classifier.num_buckets;
+ @ requires_free (int) bucket_pointers.bucket_starts[classifier.num_buckets] == end - begin;
+ @ requires_free bucket_pointers.first_empty_position <= end - begin;
+ @
+ @ requires_free \disjoint(values[*], current_swap[*], other_swap[*], overflow[*], bucket_pointers.buffer[*], classifier.sorted_splitters[*], classifier.tree.tree[*]);
+ @
+ @ // The buffer is classified as target_bucket
+ @ requires_free classifier.isClassOfSlice(current_swap, 0, Buffers.BUFFER_SIZE, target_bucket);
+ @
+ @ requires_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ // Enough space for bucket elements
+ @ countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0)
+ @ <= bucket_pointers.bucketSize(b) &&
+ @ bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b) &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b)
+ @ );
+ @
+ @ ensures_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ // Count of bucket elements is maintained
+ @ countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) +
+ @ (b == \result ? Buffers.BUFFER_SIZE : 0) ==
+ @ (\old(countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier)) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0)) &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b) &&
+ @ bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b) &&
+ @ // only decreases elements to read
+ @ bucket_pointers.toReadCountOfBucket(b) <= \old(bucket_pointers.toReadCountOfBucket(b))
+ @ );
+ @
+ @ ensures_free bucket_pointers.remainingWriteCountOfBucket(target_bucket) < \old(bucket_pointers.remainingWriteCountOfBucket(target_bucket));
+ @
+ @ ensures_free \result != -1 ==>
+ @ classifier.isClassOfSlice(other_swap, 0, Buffers.BUFFER_SIZE, \result) &&
+ @ 0 <= \result < classifier.num_buckets;
+ @
+ @ ensures_free (\forall int element; true;
+ @ bucket_pointers.countElement(values, begin, end, overflow, element) +
+ @ (\result != -1 ? Functions.countElement(other_swap, 0, Buffers.BUFFER_SIZE, element) : 0) ==
+ @ \old(bucket_pointers.countElement(values, begin, end, overflow, element)) +
+ @ \old(Functions.countElement(current_swap, 0, Buffers.BUFFER_SIZE, element))
+ @ );
+ @
+ @ ensures_free \invariant_free_for(bucket_pointers) && \invariant_free_for(classifier);
+ @ ensures \invariant_for(bucket_pointers) && \invariant_for(classifier);
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free bucket_pointers.buffer[2 * target_bucket + 1];
+ @ assignable_free other_swap[*], overflow[*];
+ @*/
+ private static int swap_block(
+ int target_bucket,
+ int[] values,
+ int begin,
+ int end,
+ Classifier classifier,
+ BucketPointers bucket_pointers,
+ int[] current_swap,
+ int[] other_swap,
+ int[] overflow
+ ) {
+ //@ assume bucket_pointers.bucketStart(classifier.num_buckets) == Buffers.blockAligned(end - begin) && bucket_pointers.disjointBucketsLemma(target_bucket);
+
+ /*@ loop_invariant_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) ==
+ @ \old(countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier))
+ @ );
+ @
+ @ // current_swap isn't changed, we need to maintain only countElement
+ @ loop_invariant_free (\forall int element; true;
+ @ bucket_pointers.countElement(values, begin, end, overflow, element) ==
+ @ \old(bucket_pointers.countElement(values, begin, end, overflow, element))
+ @ );
+ @
+ @ loop_invariant_free bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, target_bucket);
+ @ // All written elements are classified as b
+ @ loop_invariant_free bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, target_bucket);
+ @ loop_invariant_free bucket_pointers.toReadCountOfBucket(target_bucket) <= \old(bucket_pointers.toReadCountOfBucket(target_bucket));
+ @ loop_invariant_free bucket_pointers.remainingWriteCountOfBucket(target_bucket) <= \old(bucket_pointers.remainingWriteCountOfBucket(target_bucket));
+ @
+ @ loop_invariant_free \invariant_for(bucket_pointers) && \invariant_for(classifier);
+ @
+ @ assignable_free bucket_pointers.buffer[2 * target_bucket + 1];
+ @
+ @ decreases bucket_pointers.remainingWriteCountOfBucket(target_bucket);
+ @*/
+ while (true) {
+ //@ ghost \dl_Heap heapAtLoopBodyBegin = \dl_heap();
+
+ //@ assume bucket_pointers.writtenCountOfBucket(target_bucket) + Buffers.BUFFER_SIZE <= bucket_pointers.bucketSize(target_bucket);
+ Increment increment = bucket_pointers.increment_write(target_bucket);
+ boolean occupied = increment.occupied;
+ int write = begin + increment.position;
+
+ /*@ assume
+ @ Buffers.isBlockAligned(increment.position) &&
+ @ begin <= write <= end &&
+ @ bucket_pointers.lastReadOf(target_bucket) == \at(bucket_pointers.lastReadOf(target_bucket), heapAtLoopBodyBegin);
+ @*/
+
+ /*@ assume
+ @ \old(bucket_pointers.disjointBucketsAreaLemma(values, begin, end, target_bucket, write, write + Buffers.BUFFER_SIZE)) &&
+ @ \at(bucket_pointers.disjointBucketsAreaLemma(values, begin, end, target_bucket, write, write + Buffers.BUFFER_SIZE), heapAtLoopBodyBegin);
+ @*/
+
+ if (occupied) {
+ // Follows from contract of lastReadOf and definition of toReadCount
+ // other case is start == read which contradicts start <= write < read
+ //@ assume \at(bucket_pointers.lastReadOf(target_bucket), heapAtLoopBodyBegin) - \at(bucket_pointers.nextWriteOf(target_bucket), heapAtLoopBodyBegin) >= Buffers.BUFFER_SIZE;
+ /*@ assume \at(bucket_pointers.elementsToReadCountClassEqSplitBucket(
+ @ classifier,
+ @ values,
+ @ begin,
+ @ begin + bucket_pointers.nextWriteOf(target_bucket) + Buffers.BUFFER_SIZE,
+ @ end,
+ @ target_bucket,
+ @ true
+ @ ), heapAtLoopBodyBegin) &&
+ @ \at(bucket_pointers.elementsToReadCountElementSplitBucket(
+ @ values,
+ @ begin,
+ @ begin + bucket_pointers.nextWriteOf(target_bucket) + Buffers.BUFFER_SIZE,
+ @ end,
+ @ target_bucket,
+ @ true
+ @ ), heapAtLoopBodyBegin) &&
+ @ Buffers.isBlockAlignedSub(bucket_pointers.lastReadOf(target_bucket), \at(bucket_pointers.nextWriteOf(target_bucket), heapAtLoopBodyBegin));
+ @*/
+ //@ assume write + Buffers.BUFFER_SIZE <= end && Buffers.isBlockAligned(bucket_pointers.lastReadOf(target_bucket) - \at(bucket_pointers.nextWriteOf(target_bucket), heapAtLoopBodyBegin));
+
+ //@ assume \dl_inInt(values[write]);
+ int new_target = classifier.classify(values[write]);
+ //@ assume classifier.isClassifiedBlocksRange(values, write, begin + bucket_pointers.lastReadOf(target_bucket));
+ //@ assume classifier.isClassifiedBlocksRangeSplit(values, write, write + Buffers.BUFFER_SIZE, begin + bucket_pointers.lastReadOf(target_bucket));
+ //@ assume classifier.classOfClassifiedBlockFromFirst(values, write, write + Buffers.BUFFER_SIZE, new_target);
+ //@ assume classifier.classOfClassifiedBlockFromFirst(values, write, write + Buffers.BUFFER_SIZE, new_target);
+ //@ assume \at(classifier.countClassOfSliceEqLemma(values, write, write + Buffers.BUFFER_SIZE, new_target), heapAtLoopBodyBegin);
+
+ //@ assume bucket_pointers.toReadCountOfBucket(target_bucket) <= \old(bucket_pointers.toReadCountOfBucket(target_bucket));
+ //@ assume bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, target_bucket);
+
+ // Todo disjointness of the ranges
+ // Write area is disjoint from all other read and write areas
+
+ // Swap only if this block is not already in the right bucket
+ if (new_target != target_bucket) {
+ //@ ghost \dl_Heap heapBeforeWrite = \dl_heap();
+
+ // Copy to other swap
+ Functions.copy_nonoverlapping(values, write, other_swap, 0, Buffers.BUFFER_SIZE);
+ //@ assume \invariant_for(classifier);
+ //@ assume classifier.isClassOfSliceCopy(values, write, other_swap, 0, Buffers.BUFFER_SIZE, new_target);
+
+ // Copy in current swap
+ Functions.copy_nonoverlapping(current_swap, 0, values, write, Buffers.BUFFER_SIZE);
+
+ /*@ assume
+ @ \invariant_for(classifier) &&
+ @ \invariant_for(bucket_pointers) &&
+ @ bucket_pointers.lastReadOf(target_bucket) == \at(bucket_pointers.lastReadOf(target_bucket), heapBeforeWrite) &&
+ @ bucket_pointers.nextWriteOf(target_bucket) == \at(bucket_pointers.nextWriteOf(target_bucket), heapBeforeWrite);
+ @*/
+
+ //@ assume classifier.isClassOfSliceCopy(current_swap, 0, values, write, Buffers.BUFFER_SIZE, target_bucket);
+
+ /*@ assume
+ @ classifier.isClassOfSliceSplit(
+ @ values,
+ @ begin + bucket_pointers.bucketStart(target_bucket),
+ @ write,
+ @ write + Buffers.BUFFER_SIZE,
+ @ target_bucket
+ @ ) &&
+ @ bucket_pointers.writtenElementsCountElementSplitBucket(values, begin, end, overflow, target_bucket);
+ @*/
+
+ /*@ assume (\forall int b; 0 <= b < classifier.num_buckets;
+ @ bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b) +
+ @ (b == new_target ? Buffers.BUFFER_SIZE : 0) ==
+ @ \at(bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b), heapAtLoopBodyBegin) &&
+ @ bucket_pointers.writtenCountOfBucket(b) ==
+ @ \at(bucket_pointers.writtenCountOfBucket(b), heapAtLoopBodyBegin) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0)
+ @ );
+ @*/
+
+ /*@ assume (\forall int element; true;
+ @ bucket_pointers.elementsToReadCountElement(values, begin, end, element) +
+ @ Functions.countElement(other_swap, 0, Buffers.BUFFER_SIZE, element) ==
+ @ \at(bucket_pointers.elementsToReadCountElement(values, begin, end, element), heapAtLoopBodyBegin) &&
+ @ bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element) ==
+ @ \at(bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element), heapAtLoopBodyBegin) +
+ @ \old(Functions.countElement(current_swap, 0, Buffers.BUFFER_SIZE, element))
+ @ );
+ @*/
+ return new_target;
+ }
+
+ /*@ assume
+ @ classifier.isClassOfSliceSplit(
+ @ values,
+ @ begin + bucket_pointers.bucketStart(target_bucket),
+ @ write,
+ @ write + Buffers.BUFFER_SIZE,
+ @ target_bucket
+ @ ) &&
+ @ bucket_pointers.writtenElementsCountElementSplitBucket(values, begin, end, overflow, target_bucket);
+ @*/
+
+ /*@ assume (\forall int b; 0 <= b < classifier.num_buckets;
+ @ bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0) ==
+ @ \at(bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b), heapAtLoopBodyBegin) &&
+ @ bucket_pointers.writtenCountOfBucket(b) == \at(bucket_pointers.writtenCountOfBucket(b), heapAtLoopBodyBegin) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0)
+ @ );
+ @*/
+
+ /*@ assume (\forall int element; true;
+ @ bucket_pointers.elementsToReadCountElement(values, begin, end, element) +
+ @ Functions.countElement(values, write, write + Buffers.BUFFER_SIZE, element) ==
+ @ \at(bucket_pointers.elementsToReadCountElement(values, begin, end, element), heapAtLoopBodyBegin) &&
+ @ bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element) ==
+ @ \at(bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element), heapAtLoopBodyBegin) +
+ @ Functions.countElement(values, write, write + Buffers.BUFFER_SIZE, element)
+ @ );
+ @*/
+ {}
+ } else {
+ // Destination block is empty
+ // Read area is empty
+ //@ ghost \dl_Heap heapBeforeWrite = \dl_heap();
+
+ /*@ normal_behaviour
+ @ ensures_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b)
+ @ );
+ @ ensures_free (\forall int element; true;
+ @ bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element) ==
+ @ \at(bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element), heapAtLoopBodyBegin) +
+ @ \old(Functions.countElement(current_swap, 0, Buffers.BUFFER_SIZE, element))
+ @ );
+ @ ensures_free \invariant_free_for(classifier) && \invariant_free_for(bucket_pointers);
+ @ ensures \invariant_for(classifier) && \invariant_for(bucket_pointers);
+ @ assignable_free values[write..write + (write + Buffers.BUFFER_SIZE <= end ? Buffers.BUFFER_SIZE - 1 : 0)], overflow[*];
+ @*/
+ {
+ if (end < write + Buffers.BUFFER_SIZE) {
+ //@ assume write + Buffers.BUFFER_SIZE == begin + Buffers.blockAligned(end - begin);
+ // Out-of-bounds; write to overflow buffer instead
+ Functions.copy_nonoverlapping(current_swap, 0, overflow, 0, Buffers.BUFFER_SIZE);
+ //@ assume \invariant_for(classifier) && \invariant_for(bucket_pointers);
+ //@ assume bucket_pointers.nextWriteOf(target_bucket) == \at(bucket_pointers.nextWriteOf(target_bucket), heapBeforeWrite);
+ // writtenCount >= 256 follows from increment_write
+ //@ assume classifier.isClassOfSliceCopy(current_swap, 0, overflow, 0, Buffers.BUFFER_SIZE, target_bucket);
+ //@ assume bucket_pointers.overflowBucketUniqueLemma(begin, end, target_bucket);
+ // TODO show that this can't be happening for all other buckets (by disjointness)
+ {}
+ } else {
+ // Write block
+ Functions.copy_nonoverlapping(current_swap, 0, values, write, Buffers.BUFFER_SIZE);
+ //@ assume \invariant_for(classifier) && \invariant_for(bucket_pointers);
+ //@ assume bucket_pointers.nextWriteOf(target_bucket) == \at(bucket_pointers.nextWriteOf(target_bucket), heapBeforeWrite);
+ //@ assume classifier.isClassOfSliceCopy(current_swap, 0, values, write, Buffers.BUFFER_SIZE, target_bucket);
+ /*@ assume classifier.isClassOfSliceSplit(
+ @ values,
+ @ begin + bucket_pointers.bucketStart(target_bucket),
+ @ write,
+ @ write + Buffers.BUFFER_SIZE,
+ @ target_bucket
+ @ );
+ @*/
+ }
+
+ //@ assume bucket_pointers.writtenElementsCountElementSplitBucket(values, begin, end, overflow, target_bucket);
+ }
+ /*@ assume
+ @ bucket_pointers.lastReadOf(target_bucket) == \at(bucket_pointers.lastReadOf(target_bucket), heapBeforeWrite) &&
+ @ bucket_pointers.nextWriteOf(target_bucket) == \at(bucket_pointers.nextWriteOf(target_bucket), heapBeforeWrite);
+ @*/
+
+ /*@ assume (\forall int b; 0 <= b < classifier.num_buckets;
+ @ bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b) ==
+ @ \at(bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b), heapAtLoopBodyBegin) &&
+ @ bucket_pointers.writtenCountOfBucket(b) == \at(bucket_pointers.writtenCountOfBucket(b), heapAtLoopBodyBegin) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0)
+ @ );
+ @*/
+
+ /*@ assume (\forall int element; true;
+ @ bucket_pointers.elementsToReadCountElement(values, begin, end, element) ==
+ @ \at(bucket_pointers.elementsToReadCountElement(values, begin, end, element), heapAtLoopBodyBegin)
+ @ );
+ @*/
+
+ return -1;
+ }
+ }
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free \invariant_free_for(bucket_pointers);
+ @ requires \invariant_for(bucket_pointers);
+ @ requires_free \invariant_free_for(classifier);
+ @ requires \invariant_for(classifier);
+ @ requires_free classifier.num_buckets == bucket_pointers.num_buckets;
+ @ requires_free swap_1.length == Buffers.BUFFER_SIZE && swap_2.length == Buffers.BUFFER_SIZE && overflow.length == Buffers.BUFFER_SIZE;
+ @ requires_free \disjoint(values[*], swap_1[*], swap_2[*], overflow[*], bucket_pointers.buffer[*], classifier.sorted_splitters[*], classifier.tree.tree[*]);
+ @
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free 0 <= target_bucket < classifier.num_buckets;
+ @ requires_free (int) bucket_pointers.bucket_starts[classifier.num_buckets] == end - begin;
+ @ requires_free bucket_pointers.first_empty_position <= end - begin;
+ @
+ @ // swap_1 is classified as target_bucket
+ @ requires_free classifier.isClassOfSlice(swap_1, 0, Buffers.BUFFER_SIZE, target_bucket);
+ @ requires_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0)
+ @ <= bucket_pointers.bucketSize(b) &&
+ @ bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b) &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b)
+ @ );
+ @
+ @ ensures_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ (countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) ==
+ @ (\old(countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier)) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0))) &&
+ @ bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b) &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b)
+ @ );
+ @ // only decreases elements to read
+ @ ensures_free (\forall int b; 0 <= b < classifier.num_buckets; bucket_pointers.toReadCountOfBucket(b) <= \old(bucket_pointers.toReadCountOfBucket(b)));
+ @
+ @ ensures_free (\forall int element; true;
+ @ bucket_pointers.countElement(values, begin, end, overflow, element) ==
+ @ \old(
+ @ bucket_pointers.countElement(values, begin, end, overflow, element) +
+ @ Functions.countElement(swap_1, 0, Buffers.BUFFER_SIZE, element))
+ @ );
+ @
+ @ ensures_free \invariant_free_for(bucket_pointers) && \invariant_free_for(classifier);
+ @ ensures \invariant_for(bucket_pointers) && \invariant_for(classifier);
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free bucket_pointers.buffer[*];
+ @ assignable_free swap_1[*], swap_2[*], overflow[*];
+ @*/
+ private static void place_block(
+ int target_bucket,
+ final int[] values,
+ final int begin,
+ final int end,
+ final Classifier classifier,
+ final BucketPointers bucket_pointers,
+ final int[] swap_1,
+ final int[] swap_2,
+ final int[] overflow
+ ) {
+ //@ ghost int first_target_bucket = target_bucket;
+ boolean first_is_current_swap = true;
+
+ /*@ loop_invariant_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ // The old countBucketElementsEverywhere is missing the BUFFER_SIZE elements of first_target_bucket that were in swap_1
+ @ // The current countBucketElementsEverywhere is missing the BUFFER_SIZE elements of target_bucket that are in swap_1
+ @ countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) +
+ @ (b == target_bucket ? Buffers.BUFFER_SIZE : 0) ==
+ @ (\old(countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier)) +
+ @ (b == first_target_bucket ? Buffers.BUFFER_SIZE : 0)) &&
+ @ bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b) &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b)
+ @ );
+ @ loop_invariant_free 0 <= target_bucket < classifier.num_buckets;
+ @ // The buffer is classified as target_bucket
+ @ loop_invariant_free classifier.isClassOfSlice(first_is_current_swap ? swap_1 : swap_2, 0, Buffers.BUFFER_SIZE, target_bucket);
+ @ // only decreases elements to read
+ @ loop_invariant_free (\forall int b; 0 <= b < classifier.num_buckets; bucket_pointers.toReadCountOfBucket(b) <= \old(bucket_pointers.toReadCountOfBucket(b)));
+ @ loop_invariant_free \invariant_for(bucket_pointers) && \invariant_for(classifier);
+ @
+ @ loop_invariant_free (\forall int element; true;
+ @ bucket_pointers.countElement(values, begin, end, overflow, element) +
+ @ Functions.countElement(first_is_current_swap ? swap_1 : swap_2, 0, Buffers.BUFFER_SIZE, element) ==
+ @ \old(bucket_pointers.countElement(values, begin, end, overflow, element)) +
+ @ \old(Functions.countElement(swap_1, 0, Buffers.BUFFER_SIZE, element))
+ @ );
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free bucket_pointers.buffer[*];
+ @ assignable_free swap_1[*], swap_2[*], overflow[*];
+ @
+ @ decreases (\sum int b; 0 <= b < classifier.num_buckets; bucket_pointers.remainingWriteCountOfBucket(b));
+ @*/
+ while (true) {
+ int new_target = swap_block(
+ target_bucket,
+ values,
+ begin,
+ end,
+ classifier,
+ bucket_pointers,
+ first_is_current_swap ? swap_1 : swap_2,
+ first_is_current_swap ? swap_2 : swap_1,
+ overflow
+ );
+ if (new_target == -1) {
+ break;
+ }
+ first_is_current_swap = !first_is_current_swap;
+ target_bucket = new_target;
+ }
+ }
+
+ /*@ model_behaviour
+ @ requires_free 0 <= bucket < bucket_pointers.num_buckets;
+ @ requires_free bucket_pointers.num_buckets == classifier.num_buckets;
+ @ static model int countBucketElementsEverywhere(int[] values, int begin, int end, int bucket, BucketPointers bucket_pointers, Classifier classifier) {
+ @ return bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, bucket) + bucket_pointers.writtenCountOfBucket(bucket);
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free \invariant_free_for(bucket_pointers);
+ @ requires \invariant_for(bucket_pointers);
+ @ requires_free \invariant_free_for(classifier);
+ @ requires \invariant_for(classifier);
+ @ requires_free classifier.num_buckets == bucket_pointers.num_buckets;
+ @ requires_free swap_1.length == Buffers.BUFFER_SIZE && swap_2.length == Buffers.BUFFER_SIZE && overflow.length == Buffers.BUFFER_SIZE;
+ @ requires_free \disjoint(values[*], swap_1[*], swap_2[*], overflow[*], classifier.sorted_splitters[*], classifier.tree.tree[*], bucket_pointers.buffer[*]);
+ @
+ @ // requires (int) bucket_pointers.aligned_bucket_starts[0] == 0 && (int) bucket_pointers.aligned_bucket_starts[classifier.num_buckets] == Buffers.blockAligned(end - begin);
+ @
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free (int) bucket_pointers.bucket_starts[classifier.num_buckets] == end - begin;
+ @ requires_free bucket_pointers.first_empty_position <= end - begin;
+ @ requires_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b) <= bucket_pointers.bucketSize(b) &&
+ @ bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b) &&
+ @ bucket_pointers.writtenCountOfBucket(b) == 0
+ @ );
+ @
+ @ ensures_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ // Blocks are maintained
+ @ bucket_pointers.writtenCountOfBucket(b) ==
+ @ \old(bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b)) &&
+ @ // All elements are read
+ @ bucket_pointers.toReadCountOfBucket(b) == 0 &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b)
+ @ );
+ @
+ @ ensures_free (\forall int element; true;
+ @ bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element) ==
+ @ \old(bucket_pointers.elementsToReadCountElement(values, begin, end, element))
+ @ );
+ @
+ @ ensures_free \invariant_free_for(bucket_pointers) && \invariant_free_for(classifier);
+ @ ensures \invariant_for(bucket_pointers) && \invariant_for(classifier);
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free bucket_pointers.buffer[*];
+ @ assignable_free swap_1[*], swap_2[*], overflow[*];
+ @*/
+ public static void permute(
+ final int[] values,
+ final int begin,
+ final int end,
+ final Classifier classifier,
+ final BucketPointers bucket_pointers,
+ final int[] swap_1,
+ final int[] swap_2,
+ final int[] overflow
+ ) {
+ //@ assume bucket_pointers.bucketStart(classifier.num_buckets) == Buffers.blockAligned(end - begin);
+ final int num_buckets = classifier.num_buckets();
+
+ /*@ loop_invariant_free 0 <= bucket <= num_buckets;
+ @ loop_invariant_free \invariant_for(bucket_pointers) && \invariant_for(classifier);
+ @
+ @ loop_invariant_free (\forall int b; 0 <= b < bucket; bucket_pointers.toReadCountOfBucket(b) == 0);
+ @ loop_invariant_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ // Blocks are maintained
+ @ countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) ==
+ @ \old(bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b)) &&
+ @ bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b) &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b)
+ @ );
+ @ loop_invariant_free (\forall int element; true;
+ @ bucket_pointers.countElement(values, begin, end, overflow, element) ==
+ @ \old(bucket_pointers.elementsToReadCountElement(values, begin, end, element))
+ @ );
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free bucket_pointers.buffer[*];
+ @ assignable_free swap_1[*], swap_2[*], overflow[*];
+ @
+ @ decreases num_buckets - bucket;
+ @*/
+ for (int bucket = 0; bucket < num_buckets; ++bucket) {
+ /*@ loop_invariant_free \invariant_for(bucket_pointers) && \invariant_for(classifier);
+ @
+ @ loop_invariant_free (\forall int b; 0 <= b < bucket; bucket_pointers.toReadCountOfBucket(b) == 0);
+ @ loop_invariant_free (\forall int b; 0 <= b < classifier.num_buckets;
+ @ // Blocks are maintained
+ @ countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) ==
+ @ \old(bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b)) &&
+ @ bucket_pointers.elementsToReadOfBucketBlockClassified(classifier, values, begin, end, b) &&
+ @ // All written elements are classified as b
+ @ bucket_pointers.writtenElementsOfBucketClassified(classifier, values, begin, end, overflow, b)
+ @ );
+ @ loop_invariant_free (\forall int element; true;
+ @ bucket_pointers.countElement(values, begin, end, overflow, element) ==
+ @ \old(bucket_pointers.elementsToReadCountElement(values, begin, end, element))
+ @ );
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free bucket_pointers.buffer[*];
+ @ assignable_free swap_1[*], swap_2[*], overflow[*];
+ @
+ @ decreases bucket_pointers.toReadCountOfBucket(bucket);
+ @*/
+ while (bucket_pointers.hasRemainingRead(bucket)) {
+ //@ ghost \dl_Heap heapAtLoopBegin = \dl_heap();
+
+ /*@ assume
+ @ bucket_pointers.elementsToReadCountClassEqSplitBucket(classifier, values, begin, begin + bucket_pointers.lastReadOf(bucket) - Buffers.BUFFER_SIZE, end, bucket, false) &&
+ @ bucket_pointers.elementsToReadCountElementSplitBucket(values, begin, begin + bucket_pointers.lastReadOf(bucket) - Buffers.BUFFER_SIZE, end, bucket, false);
+ @*/
+ int read = bucket_pointers.decrement_read(bucket);
+
+ //@ assume begin + read + Buffers.BUFFER_SIZE <= end;
+
+ Functions.copy_nonoverlapping(values, begin + read, swap_1, 0, Buffers.BUFFER_SIZE);
+ //@ assume \invariant_for(classifier) && \invariant_for(bucket_pointers);
+ /*@ assume bucket_pointers.lastReadOf(bucket) == read &&
+ @ bucket_pointers.nextWriteOf(bucket) == \at(bucket_pointers.nextWriteOf(bucket), heapAtLoopBegin);
+ @*/
+ /*@ assume bucket_pointers.nextWriteOf(bucket) <= read &&
+ @ bucket_pointers.toReadCountOfBucket(bucket) < \at(bucket_pointers.toReadCountOfBucket(bucket), heapAtLoopBegin);
+ @*/
+ //@ assume Buffers.isBlockAlignedSub(read, bucket_pointers.nextWriteOf(bucket));
+ //@ assume Buffers.isBlockAligned(read - bucket_pointers.nextWriteOf(bucket));
+ //@ assume Buffers.isBlockAlignedAdd(read - bucket_pointers.nextWriteOf(bucket), Buffers.BUFFER_SIZE);
+ //@ assume Buffers.isBlockAligned(read + Buffers.BUFFER_SIZE - bucket_pointers.nextWriteOf(bucket));
+
+ //@ assume classifier.isClassifiedBlocksRange(values, begin + bucket_pointers.nextWriteOf(bucket), begin + read + Buffers.BUFFER_SIZE);
+ //@ assume classifier.isClassifiedBlocksRangeSplit(values, begin + bucket_pointers.nextWriteOf(bucket), begin + read, begin + read + Buffers.BUFFER_SIZE);
+ //@ assume classifier.isClassifiedBlock(values, begin + read, begin + read + Buffers.BUFFER_SIZE);
+ int first_value = swap_1[0];
+ //@ assume \dl_inInt(first_value);
+ int target_bucket = classifier.classify(first_value);
+ //@ assume classifier.classOfClassifiedBlockFromFirst(values, begin + read, begin + read + Buffers.BUFFER_SIZE, target_bucket);
+ /*@ assume
+ @ classifier.isClassOfSlice(values, begin + read, begin + read + Buffers.BUFFER_SIZE, target_bucket) &&
+ @ classifier.isClassOfSliceCopy(values, begin + read, swap_1, 0, Buffers.BUFFER_SIZE, target_bucket);
+ @*/
+ //@ assume classifier.countClassOfSliceEqLemma(values, begin + read, begin + read + Buffers.BUFFER_SIZE, target_bucket);
+
+ /*@ assume (\forall int b; 0 <= b < classifier.num_buckets;
+ @ bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b) + (b == target_bucket ? Buffers.BUFFER_SIZE : 0) ==
+ @ \at(bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b), heapAtLoopBegin) &&
+ @ bucket_pointers.writtenCountOfBucket(b) == \at(bucket_pointers.writtenCountOfBucket(b), heapAtLoopBegin)
+ @ );
+ @*/
+
+ /*@ assume (\forall int b; 0 <= b < classifier.num_buckets;
+ @ countBucketElementsEverywhere(values, begin, end, b, bucket_pointers, classifier) + (b == target_bucket ? Buffers.BUFFER_SIZE : 0) ==
+ @ \old(bucket_pointers.elementsToReadCountClassEq(classifier, values, begin, end, b))
+ @ );
+ @*/
+
+ /*@ assume (\forall int element; true;
+ @ bucket_pointers.elementsToReadCountElement(values, begin, end, element) +
+ @ Functions.countElement(swap_1, 0, Buffers.BUFFER_SIZE, element) ==
+ @ \at(bucket_pointers.elementsToReadCountElement(values, begin, end, element), heapAtLoopBegin) &&
+ @ bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element) ==
+ @ \at(bucket_pointers.writtenElementsCountElement(values, begin, end, overflow, element), heapAtLoopBegin)
+ @ );
+ @*/
+ /*@ assume (\forall int element; true;
+ @ bucket_pointers.countElement(values, begin, end, overflow, element) +
+ @ Functions.countElement(swap_1, 0, Buffers.BUFFER_SIZE, element) ==
+ @ \old(bucket_pointers.elementsToReadCountElement(values, begin, end, element))
+ @ );
+ @*/
+
+ place_block(
+ target_bucket,
+ values,
+ begin,
+ end,
+ classifier,
+ bucket_pointers,
+ swap_1,
+ swap_2,
+ overflow
+ );
+ }
+ }
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/SampleParameters.java b/src/main/java-overflow/de/wiesler/SampleParameters.java
new file mode 100644
index 0000000..e36e7af
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/SampleParameters.java
@@ -0,0 +1,90 @@
+package de.wiesler;
+
+public final class SampleParameters {
+ public final int num_samples;
+ public final int num_buckets;
+ public final int step;
+
+ /*@ public normal_behaviour
+ @ requires_free n >= Constants.BASE_CASE_SIZE;
+ @
+ @ assignable_free \strictly_nothing;
+ @*/
+ public static int log_buckets(int n) {
+ if (n <= Constants.SINGLE_LEVEL_THRESHOLD) {
+ // Only one more level until the base case, reduce the number of buckets
+ return Functions.max(1, Constants.log2(n / Constants.BASE_CASE_SIZE));
+ } else if (n <= Constants.TWO_LEVEL_THRESHOLD) {
+ // Only two more levels until we reach the base case, split the buckets
+ // evenly
+ return Functions.max(1, (Constants.log2(n / Constants.BASE_CASE_SIZE) + 1) / 2);
+ } else {
+ // Use the maximum number of buckets
+ return Constants.LOG_MAX_BUCKETS;
+ }
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free n >= Constants.BASE_CASE_SIZE;
+ @
+ @ assignable_free \strictly_nothing;
+ @*/
+ public static int oversampling_factor(int n) {
+ return Constants.log2(n) / 5;
+ }
+
+ /*@ public model_behaviour
+ @ requires true;
+ @ accessible \nothing;
+ @ model boolean isValidForLen(int n) {
+ @ return
+ @ 3 <= this.num_samples <= n / 2 &&
+ @ // This states the same as the previous line but is somehow hard to deduce
+ @ this.num_samples < n &&
+ @ 1 <= this.step &&
+ @ 2 <= this.num_buckets <= 1 << Constants.LOG_MAX_BUCKETS &&
+ @ this.num_buckets % 2 == 0 &&
+ @ // there are enough samples to perform num_buckets selections with the given step size
+ @ this.step * this.num_buckets - 1 <= this.num_samples;
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @ accessible \nothing;
+ @ model boolean isInInt() {
+ @ return
+ @ \dl_inInt(this.num_samples) &&
+ @ \dl_inInt(this.step) &&
+ @ \dl_inInt(this.num_buckets);
+ @ }
+ @*/
+
+ private static boolean isValidForLen(SampleParameters p, int n) {
+ return
+ 3 <= p.num_samples && p.num_samples <= n / 2 &&
+ p.num_samples < n &&
+ 1 <= p.step &&
+ 2 <= p.num_buckets && p.num_buckets <= 1 << Constants.LOG_MAX_BUCKETS &&
+ p.num_buckets % 2 == 0 &&
+ p.step * p.num_buckets - 1 <= p.num_samples;
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free n >= Constants.ACTUAL_BASE_CASE_SIZE;
+ @ ensures_free this.isValidForLen(n) && this.isInInt();
+ @ assignable_free \nothing;
+ @*/
+ public SampleParameters(int n) {
+ int log_buckets = log_buckets(n);
+ this.num_buckets = 1 << log_buckets;
+ this.step = Functions.max(1, oversampling_factor(n));
+ this.num_samples = step * num_buckets - 1;
+ }
+
+ public static void testContracts(int i) {
+ if (i >= Constants.ACTUAL_BASE_CASE_SIZE && !isValidForLen(new SampleParameters(i), i)) {
+ throw new Error("SampleParameters contract fails for " + i);
+ }
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Sorter.java b/src/main/java-overflow/de/wiesler/Sorter.java
new file mode 100644
index 0000000..3c0b84d
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Sorter.java
@@ -0,0 +1,646 @@
+package de.wiesler;
+
+public final class Sorter {
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free Constants.ACTUAL_BASE_CASE_SIZE < end - begin <= Buffers.MAX_LEN;
+ @ requires_free \invariant_free_for(storage);
+ @ requires_free \disjoint(storage.allArrays, values[*]);
+ @ requires \invariant_for(storage);
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free \result.isValidForLen(end - begin);
+ @ ensures_free Functions.isSortedSlice(values, begin, begin + \result.num_samples);
+ @ ensures_free \invariant_free_for(storage);
+ @ ensures_free \fresh(\result);
+ @ ensures \invariant_for(storage);
+ @ ensures \result.isInInt();
+ @
+ @ // Calls sort directly => +0
+ @ measured_by end - begin, 0;
+ @
+ @ assignable_free storage.allArrays;
+ @ assignable_free values[begin..end - 1];
+ @*/
+ private static SampleParameters sample(int[] values, int begin, int end, Storage storage) {
+ SampleParameters parameters = new SampleParameters(end - begin);
+ /*@ normal_behaviour
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ measured_by end - begin, 0;
+ @ assignable_free \strictly_nothing;
+ @*/
+ {;;}
+
+ Functions.select_n(values, begin, end, parameters.num_samples);
+ /*@ normal_behaviour
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ measured_by end - begin, 0;
+ @ assignable_free \strictly_nothing;
+ @*/
+ {;;}
+ //@ ghost \seq before_sort = \dl_seq_def_workaround(begin, end, values);
+ sort(values, begin, begin + parameters.num_samples, storage);
+ /*@ normal_behaviour
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), before_sort);
+ @ measured_by end - begin, 0;
+ @ assignable_free \strictly_nothing;
+ @*/
+ {;;}
+
+ return parameters;
+ }
+
+ /*@ public model_behaviour
+ @ requires true;
+ @
+ @ static model boolean isBucketPartitioned(int[] values, int begin, int end, int bucket_begin, int bucket_end) {
+ @ return // for all bucket elements
+ @ (\forall
+ @ int i;
+ @ begin + bucket_begin <= i < begin + bucket_end;
+ @ // all subsequent elements are bigger
+ @ (\forall int j; begin + bucket_end <= j < end; values[i] < values[j])
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets) && end - begin == bucket_starts[num_buckets];
+ @
+ @ // accessible values[begin..end - 1], bucket_starts[0..num_buckets + 1];
+ @
+ @ static model boolean allBucketsPartitioned(int[] values, int begin, int end, int[] bucket_starts, int num_buckets) {
+ @ return (\forall int b; 0 <= b < num_buckets; Sorter.isBucketPartitioned(values, begin, end, bucket_starts[b], bucket_starts[b + 1]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires \invariant_for(classifier);
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires nonEmptyBucketsLemma(classifier, values, begin, end, bucket_starts);
+ @ requires classifier.classOfTrans();
+ @ requires Functions.isValidBucketStarts(bucket_starts, classifier.num_buckets) && end - begin == bucket_starts[classifier.num_buckets];
+ @ requires Partition.allBucketsClassified(values, begin, end, classifier, bucket_starts);
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean allBucketsPartitionedLemma(Classifier classifier, int[] values, int begin, int end, int[] bucket_starts) {
+ @ return allBucketsPartitioned(values, begin, end, bucket_starts, classifier.num_buckets);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires 0 <= lower && lower <= upper && upper <= num_buckets;
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets) && end - begin == bucket_starts[num_buckets];
+ @
+ @ // accessible values[begin..end - 1], bucket_starts[0..num_buckets + 1];
+ @
+ @ static model boolean allBucketsInRangeSorted(int[] values, int begin, int end, int[] bucket_starts, int num_buckets, int lower, int upper) {
+ @ return (\forall int b; lower <= b < upper; Functions.isSortedSlice(values, begin + bucket_starts[b], begin + bucket_starts[b + 1]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ accessible values[begin..end - 1];
+ @
+ @ static model boolean isEqualityBucket(int[] values, int begin, int end) {
+ @ return
+ @ (\forall int i; begin <= i < end - 1; values[i] == values[i + 1]);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires 0 <= lower && lower <= upper && upper <= num_buckets;
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets) && end - begin == bucket_starts[num_buckets];
+ @
+ @ // accessible values[begin..end - 1], bucket_starts[lower..upper];
+ @
+ @ static model boolean equalityBucketsInRange(int[] values, int begin, int end, int[] bucket_starts, int num_buckets, int lower, int upper) {
+ @ return
+ @ (\forall int b;
+ @ lower <= b < upper && b % 2 == 1;
+ @ Sorter.isEqualityBucket(values, begin + bucket_starts[b], begin + bucket_starts[b + 1]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires \invariant_for(classifier);
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires Functions.isValidBucketStarts(bucket_starts, classifier.num_buckets) && end - begin == bucket_starts[classifier.num_buckets];
+ @ requires Partition.allBucketsClassified(values, begin, end, classifier, bucket_starts);
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean equalityBucketsLemma(Classifier classifier, int[] values, int begin, int end, int[] bucket_starts) {
+ @ return classifier.equal_buckets ==>
+ @ Sorter.equalityBucketsInRange(values, begin, end, bucket_starts, classifier.num_buckets, 1, classifier.num_buckets - 1);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires true;
+ @ static model boolean smallBucketIsSorted(int[] values, int begin, int end, int bucket_begin, int bucket_end) {
+ @ return true;
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires 0 <= lower <= upper <= num_buckets;
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets) && end - begin == bucket_starts[num_buckets];
+ @ // accessible values[begin..end - 1], bucket_starts[lower..upper];
+ @
+ @ static model boolean smallBucketsInRangeSorted(int[] values, int begin, int end, int[] bucket_starts, int num_buckets, int lower, int upper) {
+ @ return (\forall int b; lower <= b < upper; Sorter.smallBucketIsSorted(values, begin, end, bucket_starts[b], bucket_starts[b + 1]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets) && len == bucket_starts[num_buckets];
+ @
+ @ accessible bucket_starts[0..num_buckets];
+ @
+ @ static model boolean notAllValuesInOneBucket(int[] bucket_starts, int num_buckets, int len) {
+ @ return (\forall int b; 0 <= b < num_buckets; bucket_starts[b + 1] - bucket_starts[b] < len);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets);
+ @ requires bucket_starts[num_buckets] == end - begin;
+ @
+ @ // Buckets are partitioned
+ @ requires Sorter.allBucketsPartitioned(values, begin, end, bucket_starts, num_buckets);
+ @
+ @ // Buckets are sorted
+ @ requires Sorter.allBucketsInRangeSorted(values, begin, end, bucket_starts, num_buckets, 0, num_buckets);
+ @
+ @ requires bucketIndexFromOffset(bucket_starts, num_buckets, end - begin);
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean sortednessFromPartitionSorted(int[] values, int begin, int end, int[] bucket_starts, int num_buckets) {
+ @ return Functions.isSortedSlice(values, begin, end);
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets);
+ @ requires bucket_starts[num_buckets] == len;
+ @
+ @ ensures_free \result;
+ @ // ( nv >= 0
+ @ // -> nv <= num_buckets & i_0 < bucket_starts[nv]
+ @ // -> \exists int b; (0 <= b & b < nv & bucket_starts[b] <= i_0 & i_0 < bucket_starts[b + 1]))
+ @
+ @ static model boolean bucketIndexFromOffset(int[] bucket_starts, int num_buckets, int len) {
+ @ return (\forall int i; 0 <= i < len; (\exists int b; 0 <= b < num_buckets; bucket_starts[b] <= i < bucket_starts[b + 1]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires \invariant_for(classifier);
+ @ requires Functions.isValidBucketStarts(bucket_starts, classifier.num_buckets) && end - begin == bucket_starts[classifier.num_buckets];
+ @ requires bucketIndexFromOffset(bucket_starts, classifier.num_buckets, end - begin);
+ @ requires Partition.allBucketsClassified(values, begin, end, classifier, bucket_starts);
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean nonEmptyBucketsLemma(Classifier classifier, int[] values, int begin, int end, int[] bucket_starts) {
+ @ return (\forall int i; begin <= i < end;
+ @ bucket_starts[classifier.classOf(values[i])] <= i - begin < bucket_starts[classifier.classOf(values[i]) + 1]
+ @ );
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires Functions.isValidBucketStarts(bucket_starts, num_buckets) && len == bucket_starts[num_buckets];
+ @ requires (\forall int b; 0 <= b < num_buckets;
+ @ (\exists int c; 0 <= c < num_buckets && b != c; bucket_starts[c] < bucket_starts[c + 1])
+ @ );
+ @
+ @ ensures_free \result;
+ @
+ @ static model boolean notAllValuesInOneBucketLemma(int[] bucket_starts, int num_buckets, int len) {
+ @ return notAllValuesInOneBucket(bucket_starts, num_buckets, len);
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free bucket_starts.length == Constants.MAX_BUCKETS + 1;
+ @ requires_free (\forall int b; 0 <= b < bucket_starts.length; bucket_starts[b] == 0);
+ @ requires_free end - begin > Constants.ACTUAL_BASE_CASE_SIZE;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free \invariant_free_for(storage);
+ @ requires \invariant_for(storage);
+ @
+ @ requires_free \disjoint(values[*], bucket_starts[*], storage.allArrays);
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free \result != null ==>
+ @ \result.num_buckets % 2 == 0 &&
+ @ Functions.isValidBucketStarts(bucket_starts, \result.num_buckets) &&
+ @ bucket_starts[\result.num_buckets] == end - begin &&
+ @ // Buckets are partitioned
+ @ Sorter.allBucketsPartitioned(values, begin, end, bucket_starts, \result.num_buckets) &&
+ @ // Small buckets are sorted
+ @ Sorter.smallBucketsInRangeSorted(values, begin, end, bucket_starts, \result.num_buckets, 0, \result.num_buckets) &&
+ @ // Equality buckets at odd indices except the last bucket
+ @ (\result.equal_buckets ==> Sorter.equalityBucketsInRange(values, begin, end, bucket_starts, \result.num_buckets, 1, \result.num_buckets - 1)) &&
+ @ Sorter.notAllValuesInOneBucket(bucket_starts, \result.num_buckets, end - begin);
+ @ ensures_free \invariant_free_for(storage);
+ @ ensures \invariant_for(storage);
+ @
+ @ // Calls sample which has +0 => +1
+ @ measured_by end - begin, 1;
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free storage.allArrays;
+ @ assignable_free bucket_starts[*];
+ @*/
+ private static /*@ nullable */ PartitionResult partition(
+ int[] values,
+ int begin,
+ int end,
+ int[] bucket_starts,
+ Storage storage
+ ) {
+ /*@ normal_behaviour
+ @ ensures_free \disjoint(
+ @ values[*],
+ @ bucket_starts[*],
+ @ storage.tree[*],
+ @ storage.splitters[*],
+ @ storage.bucket_pointers[*],
+ @ storage.buffers_buffer[*],
+ @ storage.buffers_indices[*],
+ @ storage.swap_1[*],
+ @ storage.swap_2[*],
+ @ storage.overflow[*]
+ @ );
+ @
+ @ assignable_free \strictly_nothing;
+ @
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+
+ //@ ghost \seq oldValues = \dl_seq_def_workaround(begin, end, values);
+
+ final SampleParameters sample = sample(values, begin, end, storage);
+ final int num_samples = sample.num_samples;
+ final int num_buckets = sample.num_buckets;
+ final int step = sample.step;
+ final int[] splitters = storage.splitters;
+
+ //@ ghost \seq before_copy_unique = \dl_seq_def_workaround(begin, end, values);
+
+ // Select num_buckets - 1 splitters
+ final int num_splitters = Functions.copy_unique(values, begin, begin + num_samples, num_buckets - 1, step, splitters);
+
+ //@ ghost \seq before_from_sorted_samples = \dl_seq_def_workaround(begin, end, values);
+ /*@ normal_behaviour
+ @ ensures_free before_from_sorted_samples == before_copy_unique;
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+ /*@ normal_behaviour
+ @ ensures_free \dl_seqPerm(before_from_sorted_samples, oldValues);
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+
+ if (num_splitters <= 1) {
+ return null;
+ }
+
+ // >= 2 unique splitters, therefore >= 3 buckets and >= 2 nonempty buckets
+ final Classifier classifier = Classifier.from_sorted_samples(splitters, storage.tree, num_splitters, num_buckets);
+
+ // Create this first, classifier is immutable and this removes heap mutations after partition
+ final PartitionResult r = new PartitionResult(classifier.num_buckets(), classifier.equal_buckets());
+
+ //@ ghost \seq valuesBeforePartition = \dl_seq_def_workaround(begin, end, values);
+ /*@ normal_behaviour
+ @ ensures_free valuesBeforePartition == before_from_sorted_samples;
+ @ ensures_free \invariant_free_for(classifier);
+ @ ensures \invariant_for(classifier);
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+ /*@ normal_behaviour
+ @ ensures_free \dl_seqPerm(valuesBeforePartition, oldValues);
+ @ ensures_free (\exists int i; begin <= i < end; (\exists int j; begin <= j < end; classifier.classOf(values[i]) != classifier.classOf(values[j])));
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+ Partition.partition(values, begin, end, bucket_starts, classifier, storage);
+
+ //@ ghost \seq valuesAfterPartition = \dl_seq_def_workaround(begin, end, values);
+ /*@ normal_behaviour
+ @ ensures_free bucketIndexFromOffset(bucket_starts, classifier.num_buckets, end - begin);
+ @ ensures_free (\exists int i; 0 <= i < valuesAfterPartition.length;
+ @ (\exists int j; 0 <= j < valuesAfterPartition.length;
+ @ classifier.classOf((int) valuesAfterPartition[i]) != classifier.classOf((int) valuesAfterPartition[j]))
+ @ );
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+
+ /*@ normal_behaviour
+ @ ensures_free (\exists int i; begin <= i < end; (\exists int j; begin <= j < end; classifier.classOf(values[i]) != classifier.classOf(values[j])));
+ @ ensures_free nonEmptyBucketsLemma(classifier, values, begin, end, bucket_starts);
+ @ ensures_free equalityBucketsLemma(classifier, values, begin, end, bucket_starts);
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+
+ /*@ normal_behaviour
+ @ ensures_free notAllValuesInOneBucketLemma(bucket_starts, classifier.num_buckets, end - begin);
+ @ ensures_free allBucketsPartitionedLemma(classifier, values, begin, end, bucket_starts);
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+
+ // assignable: apply eq of allArrays
+
+ return r;
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free 0 <= bucket && bucket < num_buckets;
+ @ requires_free Functions.isValidBucketStarts(bucket_starts, num_buckets) && bucket_starts[num_buckets] == end - begin;
+ @ requires_free Sorter.allBucketsInRangeSorted(values, begin, end, bucket_starts, num_buckets, 0, bucket);
+ @
+ @ // Stays partitioned
+ @ requires_free Sorter.allBucketsPartitioned(values, begin, end, bucket_starts, num_buckets);
+ @ // All subsequent buckets keep the sorting property
+ @ requires_free Sorter.smallBucketsInRangeSorted(values, begin, end, bucket_starts, num_buckets, bucket, num_buckets);
+ @ // Equality buckets
+ @ requires_free equal_buckets ==>
+ @ (bucket % 2 == 0 || bucket == num_buckets - 1) &&
+ @ // starting at the next bucket, ending before the last bucket
+ @ Sorter.equalityBucketsInRange(values, begin, end, bucket_starts, num_buckets, bucket + 1, num_buckets - 1);
+ @ requires_free Sorter.notAllValuesInOneBucket(bucket_starts, num_buckets, end - begin);
+ @ requires_free \disjoint(storage.allArrays, values[*], bucket_starts[*]);
+ @ requires_free \invariant_free_for(storage);
+ @ requires \invariant_for(storage);
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @
+ @ // Previous stay sorted, current is now sorted
+ @ ensures_free Sorter.allBucketsInRangeSorted(values, begin, end, bucket_starts, num_buckets, 0, bucket + 1);
+ @ // Stays partitioned
+ @ ensures_free Sorter.allBucketsPartitioned(values, begin, end, bucket_starts, num_buckets);
+ @ // All subsequent buckets keep the sorting property
+ @ ensures_free Sorter.smallBucketsInRangeSorted(values, begin, end, bucket_starts, num_buckets, bucket + 1, num_buckets);
+ @ // Equality buckets at odd indices except the last bucket
+ @ ensures_free equal_buckets ==>
+ @ Sorter.equalityBucketsInRange(values, begin, end, bucket_starts, num_buckets, bucket + 1, num_buckets - 1);
+ @ ensures_free \invariant_free_for(storage);
+ @ ensures \invariant_for(storage);
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free storage.allArrays;
+ @
+ @ measured_by end - begin, 1;
+ @*/
+ private static void sample_sort_recurse_on(int[] values, int begin, int end, Storage storage, int[] bucket_starts, int num_buckets, boolean equal_buckets, int bucket) {
+ int inner_begin = begin + bucket_starts[bucket];
+ int inner_end = begin + bucket_starts[bucket + 1];
+
+ /*@ normal_behaviour
+ @ ensures_free Functions.bucketStartsOrdering(bucket_starts, num_buckets, bucket);
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+ /*@ normal_behaviour
+ @ ensures_free 0 <= bucket_starts[bucket] <= bucket_starts[bucket + 1] <= bucket_starts[num_buckets] &&
+ @ (\forall int b; 0 <= b < num_buckets && b != bucket;
+ @ (b < bucket ==> 0 <= bucket_starts[b] <= bucket_starts[b + 1] <= bucket_starts[bucket]) &&
+ @ (b > bucket ==> bucket_starts[bucket + 1] <= bucket_starts[b] <= bucket_starts[b + 1] <= bucket_starts[num_buckets]));
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+ /*@ normal_behaviour
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin + bucket_starts[bucket], inner_end, values), \old(\dl_seq_def_workaround(begin + bucket_starts[bucket], begin + bucket_starts[bucket + 1], values)));
+ @ ensures_free Functions.isSortedSlice(values, begin + bucket_starts[bucket], inner_end);
+ @ assignable_free values[inner_begin..inner_end - 1], storage.allArrays;
+ @ measured_by end - begin, 1;
+ @*/
+ {
+ if (inner_end - inner_begin > Constants.ACTUAL_BASE_CASE_SIZE) {
+ sample_sort(values, inner_begin, inner_end, storage);
+ } else {
+ base_case_sort(values, inner_begin, inner_end);
+ }
+ }
+ /*@ normal_behaviour
+ @ ensures_free \dl_seq_def_workaround(begin, inner_begin, values) == \old(\dl_seq_def_workaround(begin, begin + bucket_starts[bucket], values));
+ @ ensures_free \dl_seq_def_workaround(inner_end, end, values) == \old(\dl_seq_def_workaround(begin + bucket_starts[bucket + 1], end, values));
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+ /*@ normal_behaviour
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, inner_begin, values), \old(\dl_seq_def_workaround(begin, begin + bucket_starts[bucket], values)));
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(inner_end, end, values), \old(\dl_seq_def_workaround(begin + bucket_starts[bucket + 1], end, values)));
+ @ assignable_free \strictly_nothing;
+ @ measured_by end - begin, 1;
+ @*/
+ {;;}
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin > Constants.ACTUAL_BASE_CASE_SIZE;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free \invariant_free_for(storage);
+ @ requires \invariant_for(storage);
+ @ requires_free \disjoint(storage.allArrays, values[*]);
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free Functions.isSortedSlice(values, begin, end);
+ @ ensures_free \invariant_free_for(storage);
+ @ ensures \invariant_for(storage);
+ @
+ @ // partition has +1, sample_sort_recurse +0 => +2
+ @ measured_by end - begin, 2;
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free storage.allArrays;
+ @*/
+ private static void sample_sort(int[] values, int begin, int end, Storage storage) {
+ int[] bucket_starts = Storage.createArray(Constants.MAX_BUCKETS + 1);
+
+ /*@ normal_behaviour
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free \disjoint(\all_fields(values), \all_fields(bucket_starts), storage.allArrays);
+ @ ensures_free \disjoint(storage.*, storage.allArrays);
+ @
+ @ assignable_free \strictly_nothing;
+ @
+ @ measured_by end - begin, 2;
+ @*/
+ {;;}
+
+ PartitionResult partition = partition(values, begin, end, bucket_starts, storage);
+
+ if (partition == null) {
+ fallback_sort(values, begin, end);
+ return;
+ }
+
+ int num_buckets = partition.num_buckets;
+ boolean equal_buckets = partition.equal_buckets;
+
+ /*@ normal_behaviour
+ @ // this is needed in many places and harder to deduce
+ @ requires_free \disjoint(\all_fields(values), \all_fields(bucket_starts), storage.allArrays, storage.*);
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free Sorter.allBucketsInRangeSorted(values, begin, end, bucket_starts, num_buckets, 0, num_buckets);
+ @ ensures_free Sorter.allBucketsPartitioned(values, begin, end, bucket_starts, num_buckets);
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free storage.allArrays;
+ @
+ @ measured_by end - begin, 2;
+ @*/
+ {
+ /*@ loop_invariant_free 0 <= bucket && bucket <= num_buckets;
+ @ loop_invariant_free equal_buckets ==> bucket % 2 == 0;
+ @ loop_invariant_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @
+ @ loop_invariant_free Sorter.allBucketsInRangeSorted(values, begin, end, bucket_starts, num_buckets, 0, bucket < num_buckets || !equal_buckets ? bucket : num_buckets - 1);
+ @ // Stays partitioned
+ @ loop_invariant_free Sorter.allBucketsPartitioned(values, begin, end, bucket_starts, num_buckets);
+ @ // All subsequent buckets keep the small sorted property (especially the last one if equal_buckets)
+ @ loop_invariant_free Sorter.smallBucketsInRangeSorted(values, begin, end, bucket_starts, num_buckets, bucket < num_buckets || !equal_buckets ? bucket : num_buckets - 1, num_buckets);
+ @ loop_invariant_free equal_buckets ==>
+ @ bucket % 2 == 0 && bucket != num_buckets - 1 &&
+ @ // starting at the next bucket, ending before the last bucket
+ @ Sorter.equalityBucketsInRange(values, begin, end, bucket_starts, num_buckets, bucket + 1, num_buckets - 1);
+ @
+ @ decreases num_buckets - bucket;
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free storage.allArrays;
+ @*/
+ for (int bucket = 0; bucket < num_buckets; bucket += 1 + Constants.toInt(equal_buckets)) {
+ sample_sort_recurse_on(values, begin, end, storage, bucket_starts, num_buckets, equal_buckets, bucket);
+ }
+
+ if (equal_buckets) {
+ sample_sort_recurse_on(values, begin, end, storage, bucket_starts, num_buckets, equal_buckets, num_buckets - 1);
+ }
+ }
+
+ /*@ normal_behaviour
+ @ ensures_free sortednessFromPartitionSorted(values, begin, end, bucket_starts, num_buckets);
+ @
+ @ assignable_free \strictly_nothing;
+ @
+ @ measured_by end - begin, 2;
+ @*/
+ {;;}
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free (\forall int element; true;
+ @ Functions.countElement(values, begin, end, element) ==
+ @ \old(Functions.countElement(values, begin, end, element))
+ @ );
+ @ ensures_free Functions.isSortedSlice(values, begin, end);
+ @
+ @ assignable_free values[begin..end - 1];
+ @*/
+ public static void fallback_sort(int[] values, int begin, int end) {
+ // insertion_sort(values, begin, end);
+ }
+
+ public static void insertion_sort(int[] values, int begin, int end) {
+ if (end - begin < 2) return;
+
+ for (++begin; begin < end; ++begin) {
+ int value = values[begin];
+ int hole = begin;
+ for (int i = begin - 1; i > 0 && value < values[i]; --i) {
+ values[hole] = values[i];
+ hole = i;
+ }
+ values[hole] = value;
+ }
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free Functions.isSortedSlice(values, begin, end);
+ @
+ @ assignable_free values[begin..end - 1];
+ @*/
+ private static void base_case_sort(int[] values, int begin, int end) {
+ fallback_sort(values, begin, end);
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free end - begin <= Buffers.MAX_LEN;
+ @ requires_free \invariant_free_for(storage);
+ @ requires \invariant_for(storage);
+ @ requires_free \disjoint(storage.allArrays, values[*]);
+ @
+ @ ensures_free \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @ ensures_free Functions.isSortedSlice(values, begin, end);
+ @ ensures_free \invariant_free_for(storage);
+ @ ensures \invariant_for(storage);
+ @
+ @ // sample_sort has +2 => +3
+ @ measured_by end - begin, 3;
+ @
+ @ assignable_free values[begin..end - 1];
+ @ assignable_free storage.allArrays;
+ @*/
+ public static void sort(int[] values, int begin, int end, Storage storage) {
+ if (end - begin <= Constants.ACTUAL_BASE_CASE_SIZE) {
+ base_case_sort(values, begin, end);
+ } else {
+ sample_sort(values, begin, end, storage);
+ }
+ }
+
+ /*@ public normal_behaviour
+ @ requires_free values.length <= Buffers.MAX_LEN;
+ @
+ @ ensures_free \dl_seqPerm(\dl_array2seq(values), \old(\dl_array2seq(values)));
+ @ ensures_free Functions.isSortedSlice(values, 0, values.length);
+ @
+ @ assignable_free values[*];
+ @*/
+ public static void sort(int[] values) {
+ Storage storage = new Storage();
+ //@ assume \disjoint(storage.allArrays, values);
+ sort(values, 0, values.length, storage);
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Storage.java b/src/main/java-overflow/de/wiesler/Storage.java
new file mode 100644
index 0000000..dc958f5
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Storage.java
@@ -0,0 +1,90 @@
+package de.wiesler;
+
+public final class Storage {
+ /*@ public normal_behaviour
+ @ requires_free length >= 0;
+ @ ensures_free \result.length == length;
+ @ ensures_free \fresh(\result);
+ @ ensures_free (\forall int i; 0 <= i < length; \result[i] == 0);
+ @ assignable_free \nothing;
+ @*/
+ static int[] createArray(int length) {
+ return new int[length];
+ }
+
+ final int[] tree;
+ final int[] splitters;
+ final int[] bucket_pointers;
+ final int[] buffers_buffer;
+ final int[] buffers_indices;
+ final int[] swap_1;
+ final int[] swap_2;
+ final int[] overflow;
+
+ //@ ghost final \locset allArrays;
+
+ /*@ public instance invariant_free this.tree.length == Classifier.STORAGE_SIZE &&
+ @ this.splitters.length == Classifier.STORAGE_SIZE &&
+ @ this.bucket_pointers.length == 2 * Constants.MAX_BUCKETS &&
+ @ this.buffers_buffer.length == Buffers.BUFFER_SIZE * Constants.MAX_BUCKETS &&
+ @ this.buffers_indices.length == Constants.MAX_BUCKETS &&
+ @ this.swap_1.length == Buffers.BUFFER_SIZE &&
+ @ this.swap_2.length == Buffers.BUFFER_SIZE &&
+ @ this.overflow.length == Buffers.BUFFER_SIZE;
+ @*/
+
+ /*@ public instance invariant_free this.allArrays == \set_union(
+ @ \set_union(
+ @ \set_union(
+ @ \all_fields(tree),
+ @ \all_fields(splitters)
+ @ ),
+ @ \set_union(
+ @ \all_fields(bucket_pointers),
+ @ \all_fields(buffers_buffer)
+ @ )
+ @ ),
+ @ \set_union(
+ @ \set_union(
+ @ \all_fields(buffers_indices),
+ @ \all_fields(swap_1)
+ @ ),
+ @ \set_union(
+ @ \all_fields(swap_2),
+ @ \all_fields(overflow)
+ @ )
+ @ )
+ @ );
+ @*/
+
+ /*@ public instance invariant_free \disjoint(
+ @ \all_fields(tree),
+ @ \all_fields(splitters),
+ @ \all_fields(bucket_pointers),
+ @ \all_fields(buffers_buffer),
+ @ \all_fields(buffers_indices),
+ @ \all_fields(swap_1),
+ @ \all_fields(swap_2),
+ @ \all_fields(overflow)
+ @ );
+ @*/
+
+ //@ accessible \inv: this.*;
+
+ /*@ public normal_behaviour
+ @ ensures_free \fresh(this.allArrays);
+ @ assignable_free \nothing;
+ @*/
+ public Storage() {
+ this.splitters = createArray(Classifier.STORAGE_SIZE);
+ this.tree = createArray(Classifier.STORAGE_SIZE);
+ this.bucket_pointers = createArray(2 * Constants.MAX_BUCKETS);
+ this.buffers_buffer = createArray(Buffers.BUFFER_SIZE * Constants.MAX_BUCKETS);
+ this.buffers_indices = createArray(Constants.MAX_BUCKETS);
+ this.swap_1 = createArray(Buffers.BUFFER_SIZE);
+ this.swap_2 = createArray(Buffers.BUFFER_SIZE);
+ this.overflow = createArray(Buffers.BUFFER_SIZE);
+
+ //@ set this.allArrays = \set_union(\set_union(\set_union(\all_fields(tree), \all_fields(splitters)), \set_union(\all_fields(bucket_pointers), \all_fields(buffers_buffer))), \set_union(\set_union(\all_fields(buffers_indices), \all_fields(swap_1)), \set_union(\all_fields(swap_2), \all_fields(overflow))));
+ }
+}
diff --git a/src/main/java-overflow/de/wiesler/Tree.java b/src/main/java-overflow/de/wiesler/Tree.java
new file mode 100644
index 0000000..6d5783d
--- /dev/null
+++ b/src/main/java-overflow/de/wiesler/Tree.java
@@ -0,0 +1,442 @@
+package de.wiesler;
+
+public final class Tree {
+ private /*@ spec_public @*/ final int[] tree;
+ private /*@ spec_public @*/ final int log_buckets;
+ //@ ghost final int num_buckets;
+ //@ ghost final int[] sorted_splitters;
+
+ /*@ public invariant 1 <= this.log_buckets <= Constants.LOG_MAX_BUCKETS;
+ @ public invariant this.num_buckets == (1 << this.log_buckets);
+ @ public invariant 2 <= this.num_buckets <= this.tree.length;
+ @ public invariant this.num_buckets <= this.sorted_splitters.length;
+ @ public invariant Functions.isSortedSliceTransitive(this.sorted_splitters, 0, this.num_buckets - 1);
+ @
+ @ invariant (\forall int i; 1 <= i < this.num_buckets; 1 <= Tree.pi(i, this.log_buckets) < this.num_buckets);
+ @ invariant (\forall int i; 1 <= i < this.num_buckets; this.tree[i] == this.sorted_splitters[Tree.pi(i, this.log_buckets) - 1]);
+ @
+ @ accessible \inv: this.tree[*], this.sorted_splitters[*];
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires_free 1 <= log_buckets <= Constants.LOG_MAX_BUCKETS;
+ @ requires_free 0 <= (1 << log_buckets) <= sorted_splitters.length;
+ @ requires_free Functions.isSortedSliceTransitive(sorted_splitters, 0, (1 << log_buckets) - 1);
+ @ requires_free (1 << log_buckets) <= tree.length;
+ @ requires_free \disjoint(sorted_splitters[*], tree[*]);
+ @
+ @ ensures_free this.log_buckets == log_buckets;
+ @ ensures_free this.tree == tree;
+ @ ensures_free this.sorted_splitters == sorted_splitters;
+ @
+ @ assignable_free tree[*];
+ @*/
+ public Tree(int[] sorted_splitters, int[] tree, int log_buckets) {
+ //@ set num_buckets = 1 << log_buckets;
+ //@ set this.sorted_splitters = sorted_splitters;
+ final int num_buckets = 1 << log_buckets;
+ final int num_splitters = num_buckets - 1;
+
+ //@ assume 2 <= num_buckets <= tree.length;
+
+ this.log_buckets = log_buckets;
+ this.tree = tree;
+ this.build(sorted_splitters);
+ //@ assert (1 << this.log_buckets) == \dl_pow(2, this.log_buckets);
+ //@ assert (\forall int i; 1 <= i < this.num_buckets; Tree.piInRangeLower(i, log_buckets) && Tree.piInRangeUpper(i, log_buckets));
+ }
+
+ /*@ public normal_behaviour
+ @ requires this.tree != null && sorted_splitters != null;
+ @ requires \disjoint(sorted_splitters[*], this.tree[*]);
+ @ requires this.num_buckets <= sorted_splitters.length;
+ @ requires 1 <= this.log_buckets <= Constants.LOG_MAX_BUCKETS;
+ @ requires 2 <= this.num_buckets <= tree.length;
+ @ requires this.num_buckets == (1 << this.log_buckets);
+ @ requires Functions.isSortedSliceTransitive(sorted_splitters, 0, (1 << this.log_buckets) - 1);
+ @
+ @ ensures (\forall int i; 1 <= i < this.num_buckets; this.tree[i] == sorted_splitters[Tree.pi(i, this.log_buckets) - 1]);
+ @
+ @ assignable this.tree[*];
+ @*/
+ /*@ helper */ void build(int[] sorted_splitters) {
+ //@ assert 1 <= \dl_pow(2, this.log_buckets) <= \dl_pow(2, 6);
+ //@ assert (1 << this.log_buckets) == \dl_pow(2, this.log_buckets);
+ int num_buckets = 1 << this.log_buckets;
+ //@ assert this.num_buckets == num_buckets;
+
+ int tree_offset = 1;
+ int offset = num_buckets;
+ /*@ loop_invariant 0 <= l <= this.log_buckets;
+ @ loop_invariant tree_offset == \dl_pow(2, l);
+ @ loop_invariant offset == \dl_pow(2, this.log_buckets - l);
+ @ loop_invariant (\forall int i; 1 <= i < tree_offset;
+ @ this.tree[i] == sorted_splitters[Tree.pi(i, this.log_buckets) - 1]
+ @ );
+ @
+ @ decreases this.log_buckets - l;
+ @ assignable this.tree[*];
+ @*/
+ for (int l = 0; l < this.log_buckets; ++l) {
+ final int step = offset;
+ offset /= 2;
+
+ //@ assert step == \dl_pow(2, this.log_buckets - l);
+ //@ assert offset == \dl_pow(2, this.log_buckets - l - 1);
+ //@ assert step == offset * 2;
+ //@ assert 1 <= offset < num_buckets;
+ //@ assert \dl_pow(2, l + 1) <= num_buckets;
+
+ //@ ghost int tree_start_offset = tree_offset;
+
+ //@ assert \dl_pow(2, l + 1) - \dl_pow(2, l) == \dl_pow(2, l);
+ //@ assert step * \dl_pow(2, l) == \dl_pow(2, this.log_buckets);
+ //@ assert offset - 1 + step * \dl_pow(2, l) >= num_buckets;
+ //@ assert offset - 1 + step * (\dl_pow(2, l) - 1) < num_buckets;
+
+ /*@ loop_invariant offset - 1 <= o < step + num_buckets;
+ @ loop_invariant o == offset - 1 + step * (tree_offset - tree_start_offset);
+ @ loop_invariant \dl_pow(2, l) <= tree_offset <= \dl_pow(2, l + 1);
+ @ loop_invariant (\forall int i; 1 <= i < tree_offset;
+ @ this.tree[i] == sorted_splitters[Tree.pi(i, this.log_buckets) - 1]
+ @ );
+ @
+ @ decreases step + num_buckets - o;
+ @ assignable this.tree[*];
+ @*/
+ for (int o = offset - 1; o < num_buckets; o += step) {
+ //@ assert \dl_log(2, tree_offset) == l;
+ //@ assert Tree.pi(tree_offset, this.log_buckets) - 1 == o;
+ this.tree[tree_offset] = sorted_splitters[o];
+ tree_offset += 1;
+ }
+
+ //@ assert tree_offset == \dl_pow(2, l + 1);
+ }
+ }
+
+ /*@ model_behaviour
+ @ requires true;
+ @ static no_state model int pi(int b, int log_buckets) {
+ @ return (2 * (b - \dl_pow(2, \dl_log(2, b))) + 1) * \dl_pow(2, log_buckets - 1 - \dl_log(2, b));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires 0 <= bucket < this.num_buckets;
+ @
+ @ model boolean isClassifiedAs(int value, int bucket) {
+ @ return ((0 < bucket ==> this.sorted_splitters[bucket - 1] < value) &&
+ @ (bucket < this.num_buckets - 1 ==> value <= this.sorted_splitters[bucket]));
+ @ }
+ @*/
+
+ /*@ public model_behaviour
+ @ requires this.sorted_splitters[0] < this.sorted_splitters[1];
+ @ ensures_free \result;
+ @
+ @ model boolean classOfFirstSplitters() {
+ @ return this.classify(this.sorted_splitters[0]) != this.classify(this.sorted_splitters[1]);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires b >= 1;
+ @ ensures \result;
+ @ // Provable using powLogMore2
+ @ static model boolean piLemmaUpperBound(int b) {
+ @ return 2 * (b - \dl_pow(2, \dl_log(2, b))) + 1 < \dl_pow(2, \dl_log(2, b) + 1);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires 1 <= b < \dl_pow(2, log_buckets);
+ @ requires 1 <= log_buckets;
+ @ ensures \result;
+ @ static model boolean piInRangeLower(int b, int log_buckets) {
+ @ return 1 <= Tree.pi(b, log_buckets);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires 1 <= b < \dl_pow(2, log_buckets);
+ @ requires 1 <= log_buckets;
+ @ requires Tree.piLemmaUpperBound(b);
+ @ ensures \result;
+ @ static model boolean piInRangeUpper(int b, int log_buckets) {
+ @ return Tree.pi(b, log_buckets) < \dl_pow(2, log_buckets);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires 1 <= b < \dl_pow(2, log_buckets - 1);
+ @ requires 1 <= log_buckets;
+ @ ensures \result;
+ @ static model boolean piLemmaLeft(int b, int log_buckets) {
+ @ return Tree.pi(b, log_buckets) - Tree.pi(2 * b, log_buckets) == \dl_pow(2, log_buckets - 2 - \dl_log(2, b));
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires 1 <= b < \dl_pow(2, log_buckets - 1);
+ @ requires 1 <= log_buckets;
+ @ ensures \result;
+ @ static model boolean piLemmaRight(int b, int log_buckets) {
+ @ return Tree.pi(2 * b + 1, log_buckets) - Tree.pi(b, log_buckets) == \dl_pow(2, log_buckets - 2 - \dl_log(2, b));
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires 1 <= b < \dl_pow(2, log_buckets - 1);
+ @ requires 1 <= log_buckets;
+ @ ensures \result;
+ @ static model boolean piLemma(int b, int log_buckets) {
+ @ return Tree.piLemmaLeft(b, log_buckets) && Tree.piLemmaRight(b, log_buckets);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires log_buckets >= 1;
+ @ ensures \result;
+ @ static model boolean piOf1(int log_buckets) {
+ @ return Tree.pi(1, log_buckets) == \dl_pow(2, log_buckets) - \dl_pow(2, log_buckets) / 2;
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires true;
+ @ accessible this.sorted_splitters[*];
+ @ model boolean binarySearchInvariant(int b, int d, int value) {
+ @ return d - 1 <= b <= this.num_buckets - 1 &&
+ @ (b - d == -1 || this.sorted_splitters[b - d] < value) &&
+ @ (b == this.num_buckets - 1 || value <= this.sorted_splitters[b]);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires this.binarySearchInvariant(b, d, value);
+ @ requires 0 <= l < this.log_buckets;
+ @ requires d == \dl_pow(2, this.log_buckets - l);
+ @ ensures \result;
+ @
+ @ model boolean binarySearchInvariantLemma(int b, int d, int value, int l) {
+ @ return this.binarySearchInvariant(this.sorted_splitters[b - d / 2] < value ? b : b - d / 2, d / 2, value);
+ @ }
+ @*/
+
+ /*@ model_behaviour
+ @ requires true;
+ @ // final only no_state
+ @ model boolean treeSearchInvariant(int b, int l, int b_bin, int d_bin) {
+ @ return \dl_pow(2, l) <= b < \dl_pow(2, l + 1) &&
+ @ \dl_log(2, b) == l &&
+ @ (l < this.log_buckets ==> b_bin - d_bin / 2 == Tree.pi(b, this.log_buckets) - 1) &&
+ @ (l == this.log_buckets ==> b_bin == b - \dl_pow(2, this.log_buckets));
+ @ }
+ @*/
+
+ /*@ normal_behaviour
+ @ requires this.binarySearchInvariant(b_bin, d_bin, value);
+ @ requires treeSearchInvariant(b, l, b_bin, d_bin);
+ @ requires 0 <= l < this.log_buckets;
+ @ requires d_bin == \dl_pow(2, this.log_buckets - l);
+ @ requires this.num_buckets == \dl_pow(2, this.log_buckets);
+ @ ensures treeSearchInvariant(2 * b + (this.tree[b] < value ? 1 : 0), l + 1, this.sorted_splitters[b_bin - d_bin / 2] < value ? b_bin : b_bin - d_bin / 2, d_bin / 2);
+ @ ensures \result;
+ @ assignable \strictly_nothing;
+ @*/
+ boolean treeSearchInvariantLemmaImpl(int b, int l, int b_bin, int d_bin, int value) {
+ //@ assert 1 <= \dl_pow(2, l);
+ //@ assert \dl_pow(2, l + 1) == 2 * \dl_pow(2, l);
+ //@ assert \dl_pow(2, l + 2) == 2 * \dl_pow(2, l + 1);
+ //@ assert \dl_pow(2, l + 1) <= \dl_pow(2, this.log_buckets);
+ //@ assert this.sorted_splitters[b_bin - d_bin / 2] == this.tree[b];
+ //@ assert \dl_log(2, 2 * b + (this.tree[b] < value ? 1 : 0)) == l + 1;
+ if (l < this.log_buckets - 1) {
+ //@ assert \dl_pow(2, l + 1) <= \dl_pow(2, this.log_buckets - 1);
+ //@ assert Tree.piLemma(b, this.log_buckets);
+ /*@ assert Tree.pi(2 * b + (this.tree[b] < value ? 1 : 0), this.log_buckets) - Tree.pi(b, this.log_buckets) == (
+ @ this.tree[b] < value ? (\dl_pow(2, this.log_buckets - 2 - \dl_log(2, b))) : -(\dl_pow(2, this.log_buckets - 2 - \dl_log(2, b)))
+ @ );
+ @*/
+ //@ assert \dl_pow(2, this.log_buckets - 2 - \dl_log(2, b)) == d_bin / 2 / 2;
+ }
+ return true;
+ }
+
+ /*@ model_behaviour
+ @ requires this.binarySearchInvariant(b_bin, d_bin, value);
+ @ requires treeSearchInvariant(b, l, b_bin, d_bin);
+ @ requires 0 <= l < this.log_buckets;
+ @ requires d_bin == \dl_pow(2, this.log_buckets - l);
+ @ requires this.num_buckets == \dl_pow(2, this.log_buckets);
+ @ ensures \result ==> treeSearchInvariant(2 * b + (this.tree[b] < value ? 1 : 0), l + 1, this.sorted_splitters[b_bin - d_bin / 2] < value ? b_bin : b_bin - d_bin / 2, d_bin / 2);
+ @ ensures \result;
+ @
+ @ model boolean treeSearchInvariantLemma(int b, int l, int b_bin, int d_bin, int value) {
+ @ return treeSearchInvariantLemmaImpl(b, l, b_bin, d_bin, value);
+ @ }
+ @*/
+
+ /*@ normal_behaviour
+ @ requires_free \dl_inInt(value);
+ @ ensures_free this.num_buckets <= \result < 2 * this.num_buckets;
+ @
+ @ ensures_free this.isClassifiedAs(value, \result - this.num_buckets);
+ @
+ @ // Needed to bring this method to logic
+ @ ensures_free \result == this.classify(value);
+ @
+ @ assignable_free \strictly_nothing;
+ @
+ @ accessible this.tree[*], this.sorted_splitters[*];
+ @*/
+ int classify(int value) {
+ //@ assert \dl_pow(2, 1) <= \dl_pow(2, this.log_buckets) <= \dl_pow(2, Constants.LOG_MAX_BUCKETS);
+ //@ assert \dl_pow(2, this.log_buckets) == this.num_buckets;
+ //@ ghost int b_bin = this.num_buckets - 1;
+ //@ ghost int d_bin = this.num_buckets;
+ int b = 1;
+
+ //@ assert Tree.piOf1(this.log_buckets);
+
+ /*@ loop_invariant 0 <= l && l <= this.log_buckets;
+ @ loop_invariant d_bin == \dl_pow(2, this.log_buckets - l);
+ @
+ @ // Ghost binary search
+ @ loop_invariant this.binarySearchInvariant(b_bin, d_bin, value);
+ @ loop_invariant this.treeSearchInvariant(b, l, b_bin, d_bin);
+ @
+ @ decreases this.log_buckets - l;
+ @ assignable \strictly_nothing;
+ @*/
+ for (int l = 0; l < this.log_buckets; ++l) {
+ //@ assert treeSearchInvariantLemma(b, l, b_bin, d_bin, value);
+ //@ assert this.binarySearchInvariantLemma(b_bin, d_bin, value, l);
+ //@ assert treeSearchInvariant(2 * b + (this.tree[b] < value ? 1 : 0), l + 1, this.sorted_splitters[b_bin - d_bin / 2] < value ? b_bin : b_bin - d_bin / 2, d_bin / 2);
+ //@ assert this.binarySearchInvariant(this.sorted_splitters[b_bin - d_bin / 2] < value ? b_bin : b_bin - d_bin / 2, d_bin / 2, value);
+
+ //@ assert (d_bin / 2) * 2 == d_bin;
+ //@ set d_bin = d_bin / 2;
+ //@ assert 0 <= \dl_pow(2, this.log_buckets - l) <= \dl_pow(2, this.log_buckets);
+ //@ assert 0 <= b_bin - d_bin < this.num_buckets;
+ //@ assert \dl_pow(2, l + 1) <= \dl_pow(2, this.log_buckets);
+ //@ assert 0 <= b < this.num_buckets;
+ //@ assert d_bin == \dl_pow(2, this.log_buckets - l - 1);
+ //@ assert \dl_inInt(l + 1);
+ //@ assert \dl_inInt(2 * b + (this.tree[b] < value ? 1 : 0));
+ //@ set b_bin = this.sorted_splitters[b_bin - d_bin] < value ? b_bin : b_bin - d_bin;
+ b = 2 * b + (this.tree[b] < value ? 1 : 0);
+ }
+ return b;
+ }
+
+ /*@ normal_behaviour
+ @ requires_free 0 <= begin <= end <= values.length;
+ @ requires_free indices.length == end - begin;
+ @ requires_free \disjoint(values[*], indices[*], this.tree[*], this.sorted_splitters[*]);
+ @
+ @ ensures_free (\forall int i; 0 <= i < indices.length; this.num_buckets <= indices[i] < 2 * this.num_buckets);
+ @ // Needed to bring this method to logic
+ @ ensures_free (\forall int i; 0 <= i < indices.length; indices[i] == this.classify(values[begin + i]));
+ @
+ @ assignable_free indices[*];
+ @*/
+ void classify_all(int[] values, int begin, int end, int[] indices) {
+ Functions.fill(indices, 0, indices.length, 1);
+
+ //@ assert \dl_pow(2, 1) <= \dl_pow(2, this.log_buckets) <= \dl_pow(2, Constants.LOG_MAX_BUCKETS);
+ //@ assert \dl_pow(2, this.log_buckets) == this.num_buckets;
+ //@ ghost int[] b_bins = new int[indices.length];
+ //@ ghost int d_bin = this.num_buckets;
+
+ //@ assert Tree.piOf1(this.log_buckets);
+
+ /*@ loop_invariant 0 <= o <= indices.length;
+ @
+ @ // Ghost binary search
+ @ loop_invariant (\forall int j; 0 <= j < o;
+ @ b_bins[j] == this.num_buckets - 1
+ @ );
+ @
+ @ decreases indices.length - o;
+ @ assignable b_bins[*];
+ @*/
+ for (int o = 0; o < indices.length; ++o) {
+ //@ set b_bins[o] = this.num_buckets - 1;
+ }
+
+ /*@ loop_invariant 0 <= l && l <= this.log_buckets;
+ @ loop_invariant d_bin == \dl_pow(2, this.log_buckets - l);
+ @
+ @ // Ghost binary search
+ @ loop_invariant (\forall int i; 0 <= i < indices.length;
+ @ this.binarySearchInvariant(b_bins[i], d_bin, values[begin + i]) &&
+ @ this.treeSearchInvariant(indices[i], l, b_bins[i], d_bin)
+ @ );
+ @
+ @ decreases this.log_buckets - l;
+ @ assignable b_bins[*], indices[*];
+ @*/
+ for (int l = 0; l < this.log_buckets; ++l) {
+ //@ assert (d_bin / 2) * 2 == d_bin;
+ //@ set d_bin = d_bin / 2;
+
+ //@ assert \dl_pow(2, l + 1) == 2 * \dl_pow(2, l) && \dl_pow(2, l + 2) == 2 * \dl_pow(2, l + 1);
+
+ /*@ loop_invariant 0 <= j && j <= indices.length;
+ @
+ @ loop_invariant (\forall int i; 0 <= i < j;
+ @ this.binarySearchInvariant(b_bins[i], d_bin, values[begin + i]) &&
+ @ this.treeSearchInvariant(indices[i], l + 1, b_bins[i], d_bin)
+ @ );
+ @
+ @ loop_invariant (\forall int i; j <= i < indices.length;
+ @ this.binarySearchInvariant(b_bins[i], 2 * d_bin, values[begin + i]) &&
+ @ this.treeSearchInvariant(indices[i], l, b_bins[i], 2 * d_bin)
+ @ );
+ @
+ @ decreases indices.length - j;
+ @ assignable b_bins[*], indices[*];
+ @*/
+ for (int j = 0; j < indices.length; ++j) {
+ //@ assert indices != b_bins && values != b_bins;
+ //@ assert this.sorted_splitters != b_bins && this.tree != b_bins;
+
+ /*@ normal_behaviour
+ @ ensures this.binarySearchInvariant(b_bins[j], d_bin, values[begin + j]) &&
+ @ this.treeSearchInvariant(indices[j], l + 1, b_bins[j], d_bin);
+ @ assignable b_bins[j], indices[j];
+ @*/
+ {
+ int value = values[begin + j];
+ int b = indices[j];
+
+ //@ ghost int b_bin = b_bins[j];
+ /*@ assert this.binarySearchInvariant(b_bin, 2 * d_bin, value) &&
+ @ this.treeSearchInvariant(b, l, b_bin, 2 * d_bin);
+ @*/
+
+ //@ assert treeSearchInvariantLemma(b, l, b_bin, 2 * d_bin, value);
+ //@ assert \invariant_for(this);
+ //@ assert this.binarySearchInvariantLemma(b_bin, 2 * d_bin, value, l);
+ //@ assert treeSearchInvariant(2 * b + (this.tree[b] < value ? 1 : 0), l + 1, this.sorted_splitters[b_bin - d_bin] < value ? b_bin : b_bin - d_bin, d_bin);
+ //@ assert this.binarySearchInvariant(this.sorted_splitters[b_bin - d_bin] < value ? b_bin : b_bin - d_bin, d_bin, value);
+
+ //@ assert 0 <= \dl_pow(2, this.log_buckets - l) <= \dl_pow(2, this.log_buckets);
+ //@ assert 0 <= b_bin - d_bin < this.num_buckets;
+ //@ assert \dl_pow(2, l + 1) <= \dl_pow(2, this.log_buckets);
+ //@ assert 0 <= b < this.num_buckets;
+ //@ assert d_bin == \dl_pow(2, this.log_buckets - l - 1);
+ //@ assert \dl_inInt(l + 1);
+ //@ assert \dl_inInt(2 * b + (this.tree[b] < value ? 1 : 0));
+ //@ set b_bins[j] = this.sorted_splitters[b_bin - d_bin] < value ? b_bin : b_bin - d_bin;
+ indices[j] = 2 * b + (this.tree[b] < value ? 1 : 0);
+ }
+ {;;}
+ }
+ }
+
+ //@ assert d_bin == 1;
+ }
+}
diff --git a/src/main/java/de/wiesler/Cleanup.java b/src/main/java/de/wiesler/Cleanup.java
index 53c944a..50ec32c 100644
--- a/src/main/java/de/wiesler/Cleanup.java
+++ b/src/main/java/de/wiesler/Cleanup.java
@@ -315,7 +315,16 @@ public static void cleanup(
@
@ assignable values[start..stop - 1];
@*/
- {}
+ {
+ if (stop - start <= Constants.ACTUAL_BASE_CASE_SIZE || is_last_level) {
+ //@ ghost \seq bucketValuesBeforeSort = \dl_seq_def_workaround(start, stop, values);
+ // seqPerm(seq, seq2)
+ // forall i in seq2; f(i) ==> forall i in seq; f(i)
+ Sorter.fallback_sort(values, start, stop);
+ //@ ghost \seq bucketValuesAfterSort = \dl_seq_def_workaround(start, stop, values);
+ //@ assert (\forall int i; 0 <= i < bucketValuesAfterSort.length; classifier.classOf((int)bucketValuesAfterSort[i]) == bucket);
+ }
+ }
/*@ assert \invariant_for(classifier) && \invariant_for(bucket_pointers) && \invariant_for(buffers) &&
@ Functions.countElementSplit(values, begin, begin + \old(bucket_starts[bucket]), begin + \old(bucket_starts[bucket + 1])) &&
diff --git a/src/main/java/de/wiesler/Sorter.java b/src/main/java/de/wiesler/Sorter.java
index 04276f9..a842c27 100644
--- a/src/main/java/de/wiesler/Sorter.java
+++ b/src/main/java/de/wiesler/Sorter.java
@@ -565,19 +565,63 @@ private static void sample_sort(int[] values, int begin, int end, Storage storag
@ assignable values[begin..end - 1];
@*/
public static void fallback_sort(int[] values, int begin, int end) {
- // insertion_sort(values, begin, end);
+ insertion_sort(values, begin, end);
}
+ /*@ model_behaviour
+ @ requires 0 <= idx < seq.length;
+ @ ensures (\forall int x; 0 <= x < seq.length;
+ @ \result[x] == (x == idx ? value : seq[x]));
+ @ ensures \result.length == seq.length;
+ @ static no_state model \seq seqUpd(\seq seq, int idx, int value) {
+ @ return \seq_concat(\seq_concat(
+ @ \seq_sub(seq, 0, idx),
+ @ \seq_singleton(value)),
+ @ \seq_sub(seq, idx+1, seq.length));
+ @ }
+ @*/
+
+ /*@ public normal_behaviour
+ @ requires 0 <= begin <= end <= values.length;
+ @
+ @ ensures \dl_seqPerm(\dl_seq_def_workaround(begin, end, values), \old(\dl_seq_def_workaround(begin, end, values)));
+ @
+ @ ensures Functions.isSortedSlice(values, begin, end);
+ @
+ @ assignable values[begin..end - 1];
+ @*/
public static void insertion_sort(int[] values, int begin, int end) {
if (end - begin < 2) return;
+ int k = begin + 1;
- for (++begin; begin < end; ++begin) {
- int value = values[begin];
- int hole = begin;
- for (int i = begin - 1; i > 0 && value < values[i]; --i) {
+ /*@ loop_invariant \dl_seqPerm(\dl_seq_def_workaround(begin, end, values),
+ @ \old(\dl_seq_def_workaround(begin, end, values)));
+ @ loop_invariant begin < k <= end;
+ @ loop_invariant (\forall int x; k <= x < end; values[x] == \old(values[x]));
+ @ loop_invariant Functions.isSortedSlice(values, begin, k);
+ @ assignable values[begin..end - 1];
+ @ decreases end - k;
+ @*/
+ for (; k < end; ++k) {
+ int value = values[k];
+ int hole = k;
+
+ /*@ loop_invariant hole == i + 1;
+ @ loop_invariant begin-1 <= i < k;
+ @ loop_invariant i == k - 1 || Functions.isSortedSlice(values, begin, k+1);
+ @ loop_invariant Functions.isSortedSlice(values, begin, k);
+ @ loop_invariant \dl_seqPerm(
+ @ seqUpd(\dl_seq_def_workaround(begin, end, values), hole - begin, value),
+ @ \old(\dl_seq_def_workaround(begin, end, values)));
+ @ loop_invariant value <= values[hole];
+ @ assignable values[begin..k];
+ @ decreases i + 1;
+ */
+ for(int i = k - 1; i >= begin && value < values[i]; i--) {
values[hole] = values[i];
hole = i;
}
+
values[hole] = value;
}
}
diff --git a/src/main/java/de/wiesler/de.wiesler.Sorter(de.wiesler.Sorter__insertion_sort((I,int,int)).JML normal_behavior operation contract.0.proof b/src/main/java/de/wiesler/de.wiesler.Sorter(de.wiesler.Sorter__insertion_sort((I,int,int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..6d8dfe5
--- /dev/null
+++ b/src/main/java/de/wiesler/de.wiesler.Sorter(de.wiesler.Sorter__insertion_sort((I,int,int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,8039 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Tue Oct 24 17:46:35 CEST 2023
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:off , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsIgnoringOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:off , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_INVARIANT
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=7000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource ".";
+
+\proofObligation "#Proof Obligation Settings
+#Tue Oct 24 17:46:35 CEST 2023
+contract=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:insertion_sort([I,int,int)].JML normal_behavior operation contract.0
+name=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:insertion_sort([I,int,int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
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+
+(autoModeTime "98267")
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+ (rule "qeq_literals" (formula "22") (term "0"))
+ (builtin "One Step Simplification" (formula "22"))
+ (rule "false_right" (formula "22"))
+ (rule "inEqSimp_exactShadow3" (formula "4") (ifseqformula "5"))
+ (rule "polySimp_mulComm0" (formula "4") (term "0,0"))
+ (rule "polySimp_addAssoc" (formula "4") (term "0"))
+ (rule "polySimp_addComm0" (formula "4") (term "0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "4"))
+ (rule "polySimp_mulComm0" (formula "4") (term "1"))
+ (rule "polySimp_rightDist" (formula "4") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "4") (term "1,1"))
+ (rule "mul_literals" (formula "4") (term "0,1"))
+ (rule "polySimp_elimOne" (formula "4") (term "1,1"))
+ (rule "inEqSimp_subsumption1" (formula "7") (ifseqformula "4"))
+ (rule "inEqSimp_homoInEq0" (formula "7") (term "0"))
+ (rule "polySimp_mulComm0" (formula "7") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "7") (term "1,0,0"))
+ (rule "mul_literals" (formula "7") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "7") (term "0,0"))
+ (rule "polySimp_addComm1" (formula "7") (term "0,0,0"))
+ (rule "add_literals" (formula "7") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "7") (term "0,0"))
+ (rule "add_literals" (formula "7") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "7") (term "1,0,0"))
+ (rule "add_literals" (formula "7") (term "0,0"))
+ (rule "qeq_literals" (formula "7") (term "0"))
+ (builtin "One Step Simplification" (formula "7"))
+ (rule "true_left" (formula "7"))
+ (rule "inEqSimp_exactShadow3" (formula "4") (ifseqformula "7"))
+ (rule "polySimp_rightDist" (formula "4") (term "0,0"))
+ (rule "mul_literals" (formula "4") (term "0,0,0"))
+ (rule "polySimp_addAssoc" (formula "4") (term "0"))
+ (rule "polySimp_addComm1" (formula "4") (term "0,0"))
+ (rule "add_literals" (formula "4") (term "0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "4"))
+ (rule "polySimp_mulComm0" (formula "4") (term "1"))
+ (rule "polySimp_rightDist" (formula "4") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "4") (term "1,1"))
+ (rule "mul_literals" (formula "4") (term "0,1"))
+ (rule "polySimp_elimOne" (formula "4") (term "1,1"))
+ (rule "inEqSimp_subsumption1" (formula "2") (ifseqformula "4"))
+ (rule "inEqSimp_homoInEq0" (formula "2") (term "0"))
+ (rule "polySimp_mulComm0" (formula "2") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "2") (term "1,0,0"))
+ (rule "mul_literals" (formula "2") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "2") (term "0,0"))
+ (rule "polySimp_addComm1" (formula "2") (term "0,0,0"))
+ (rule "add_literals" (formula "2") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "2") (term "0,0"))
+ (rule "add_literals" (formula "2") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "2") (term "1,0,0"))
+ (rule "add_literals" (formula "2") (term "0,0"))
+ (rule "qeq_literals" (formula "2") (term "0"))
+ (builtin "One Step Simplification" (formula "2"))
+ (rule "true_left" (formula "2"))
+ (rule "all_pull_out3" (formula "15") (term "0"))
+ (rule "shift_paren_or" (formula "15") (term "0,0"))
+ (rule "shift_paren_or" (formula "15") (term "0,0,0"))
+ (rule "allLeft" (formula "20") (inst "t=i_1_0"))
+ (rule "replaceKnownSelect_taclet110000120011_11" (formula "20") (term "1,1"))
+ (rule "replaceKnownSelect_taclet110000120011_14" (formula "20") (term "0,1"))
+ (rule "replaceKnownAuxiliaryConstant_taclet110000120011_12" (formula "20") (term "1,1"))
+ (rule "replaceKnownAuxiliaryConstant_taclet110000120011_15" (formula "20") (term "0,1"))
+ (rule "inEqSimp_contradInEq0" (formula "20") (term "1,0") (ifseqformula "6"))
+ (rule "inEqSimp_homoInEq1" (formula "20") (term "0,1,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "20") (term "1,0,0,1,0"))
+ (rule "mul_literals" (formula "20") (term "0,1,0,0,1,0"))
+ (rule "polySimp_addAssoc" (formula "20") (term "0,0,1,0"))
+ (rule "polySimp_addComm1" (formula "20") (term "0,0,0,1,0"))
+ (rule "add_literals" (formula "20") (term "0,0,0,0,1,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "20") (term "0,0,1,0"))
+ (rule "add_literals" (formula "20") (term "1,1,0,0,1,0"))
+ (rule "times_zero_1" (formula "20") (term "1,0,0,1,0"))
+ (rule "add_literals" (formula "20") (term "0,0,1,0"))
+ (rule "leq_literals" (formula "20") (term "0,1,0"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "inEqSimp_contradInEq1" (formula "20") (term "0") (ifseqformula "5"))
+ (rule "inEqSimp_homoInEq1" (formula "20") (term "0,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "20") (term "1,0,0,0"))
+ (rule "mul_literals" (formula "20") (term "0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "20") (term "0,0,0"))
+ (rule "polySimp_addComm0" (formula "20") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "20") (term "0,0,0"))
+ (rule "add_literals" (formula "20") (term "1,1,0,0,0"))
+ (rule "times_zero_1" (formula "20") (term "1,0,0,0"))
+ (rule "add_literals" (formula "20") (term "0,0,0"))
+ (rule "leq_literals" (formula "20") (term "0,0"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "inEqSimp_contradInEq0" (formula "20") (ifseqformula "1"))
+ (rule "andLeft" (formula "20"))
+ (rule "inEqSimp_homoInEq1" (formula "20"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "20") (term "1,0"))
+ (rule "mul_literals" (formula "20") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "20") (term "0"))
+ (rule "polySimp_addComm0" (formula "20") (term "0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "20") (term "0"))
+ (rule "add_literals" (formula "20") (term "1,1,0"))
+ (rule "times_zero_1" (formula "20") (term "1,0"))
+ (rule "add_literals" (formula "20") (term "0"))
+ (rule "leq_literals" (formula "20"))
+ (rule "closeFalse" (formula "20"))
+ )
+ )
+ )
+ )
+ (branch "Case 2"
+ (rule "allRight" (formula "29") (inst "sk=f_0"))
+ (rule "allRight" (formula "29") (inst "sk=o_0"))
+ (rule "orRight" (formula "29"))
+ (rule "orRight" (formula "29"))
+ (rule "selectOfStore" (formula "31") (term "1"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "castDel" (formula "31") (term "1,1"))
+ (rule "selectOfAnon" (formula "31") (term "2,1"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "elementOfArrayRange" (formula "31") (term "0,0,0,2,1") (inst "iv=iv"))
+ (rule "selectOfAnon" (formula "31") (term "2,2,1"))
+ (builtin "One Step Simplification" (formula "31") (ifInst "" (formula "30")))
+ (rule "elementOfArrayRange" (formula "31") (term "0,0,2,2,1") (inst "iv=iv"))
+ (builtin "SMTRule")
+ )
+ )
+ (branch "Case 2"
+ (builtin "SMTRule")
+ )
+ )
+ (branch "Null Reference (_values = null)"
+ (builtin "One Step Simplification" (formula "30"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "29")))
+ (rule "closeFalse" (formula "1"))
+ )
+ (branch "Index Out of Bounds (_values != null, but hole Out of Bounds!)"
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "29")))
+ (builtin "One Step Simplification" (formula "30"))
+ (builtin "SMTRule")
+ )
+ )
+ (branch "Null Reference (_values = null)"
+ (builtin "One Step Simplification" (formula "27"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "26")))
+ (rule "closeFalse" (formula "1"))
+ )
+ (branch "Index Out of Bounds (_values != null, but i Out of Bounds!)"
+ (builtin "One Step Simplification" (formula "27"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "26")))
+ (builtin "SMTRule")
+ )
+ )
+ )
+ )
+ (branch "Null Reference (_values = null)"
+ (builtin "One Step Simplification" (formula "16"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "15")))
+ (rule "closeFalse" (formula "1"))
+ )
+ (branch "Index Out of Bounds (_values != null, but k Out of Bounds!)"
+ (builtin "One Step Simplification" (formula "16"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "15")))
+ (builtin "SMTRule")
+ )
+ )
+ (branch "if x_2 false"
+ (builtin "One Step Simplification" (formula "16"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "closeFalse" (formula "1"))
+ )
+ )
+ (branch "Use Case"
+ (builtin "One Step Simplification" (formula "11"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "translateJavaSubInt" (formula "11") (term "2,1,0,1,1,0"))
+ (rule "translateJavaSubInt" (formula "8") (term "2,1,0,0,1"))
+ (rule "andLeft" (formula "8"))
+ (rule "andLeft" (formula "8"))
+ (rule "polySimp_elimSub" (formula "13") (term "2,1,0,1,1,0"))
+ (rule "mul_literals" (formula "13") (term "1,2,1,0,1,1,0"))
+ (rule "polySimp_elimSub" (formula "10") (term "2,1,0,0"))
+ (rule "mul_literals" (formula "10") (term "1,2,1,0,0"))
+ (rule "polySimp_addComm0" (formula "13") (term "2,1,0,1,1,0"))
+ (rule "polySimp_addComm0" (formula "10") (term "2,1,0,0"))
+ (rule "variableDeclarationAssign" (formula "13") (term "1"))
+ (rule "variableDeclaration" (formula "13") (term "1") (newnames "b_1"))
+ (rule "less_than_comparison_simple" (formula "13") (term "1"))
+ (builtin "One Step Simplification" (formula "13"))
+ (rule "methodCallEmpty" (formula "13") (term "1"))
+ (rule "emptyModality" (formula "13") (term "1"))
+ (builtin "One Step Simplification" (formula "13"))
+ (rule "impRight" (formula "13"))
+ (rule "notLeft" (formula "1"))
+ (rule "methodCallEmpty" (formula "14") (term "1"))
+ (rule "tryEmpty" (formula "14") (term "1"))
+ (rule "emptyModality" (formula "14") (term "1"))
+ (rule "andRight" (formula "14"))
+ (branch "Case 1"
+ (rule "andRight" (formula "14"))
+ (branch "Case 1"
+ (builtin "One Step Simplification" (formula "14"))
+ (builtin "SMTRule")
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "14"))
+ (rule "closeTrue" (formula "14"))
+ )
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "14"))
+ (rule "allRight" (formula "14") (inst "sk=f_0"))
+ (rule "allRight" (formula "14") (inst "sk=o_0"))
+ (rule "orRight" (formula "14"))
+ (rule "orRight" (formula "14"))
+ (rule "selectOfAnon" (formula "16") (term "1"))
+ (builtin "One Step Simplification" (formula "16") (ifInst "" (formula "15")))
+ (rule "elementOfArrayRange" (formula "16") (term "0,0,1") (inst "iv=iv"))
+ (builtin "SMTRule")
+ )
+ )
+)
+)
+}
diff --git a/src/main/java/de/wiesler/notes.tmp b/src/main/java/de/wiesler/notes.tmp
new file mode 100644
index 0000000..1695e56
--- /dev/null
+++ b/src/main/java/de/wiesler/notes.tmp
@@ -0,0 +1,43 @@
+
+
+sp(su(cur),old)
+
+before = su(cur)
+
+su(cur') = swap(before, i, hole)
+
+---------------
+
+sp(su(cur'), old)
+
+
+sp(swap(before, i, hole), old)
+
+
+cut: sp(swap(before, i, hole), before)
+
+
+
+
+
+
+1 2 4 5 3
+
+1 2 4 5 5
+ 3
+
+1 2 4 4 5
+ 3
+ ^ hole
+ ^ i
+
+ ^ hole
+ ^ i
+
+1 2 4 3 5
+
+
+
+upd(S, hole, value)
+
+
diff --git a/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__BucketPointers((I,int,int,(I)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__BucketPointers((I,int,int,(I)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..562a43c
--- /dev/null
+++ b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__BucketPointers((I,int,int,(I)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,4908 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Sun Jun 05 15:23:19 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:onHeap , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Sun Jun 05 15:23:19 CEST 2022
+contract=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:BucketPointers([I,int,int,[I)].JML normal_behavior operation contract.0
+name=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:BucketPointers([I,int,int,[I)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "2" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "14944")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "4"))
+(rule "notLeft" (formula "4"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "9"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "12"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "15"))
+(rule "andLeft" (formula "16"))
+(rule "andLeft" (formula "15"))
+(rule "translateJavaAddInt" (formula "9") (term "3,0"))
+(rule "translateJavaAddInt" (formula "10") (term "0"))
+(rule "translateJavaMulInt" (formula "13") (term "1"))
+(rule "translateJavaMulInt" (formula "14") (term "0"))
+(rule "replace_known_right" (formula "7") (term "0") (ifseqformula "19"))
+ (builtin "One Step Simplification" (formula "7"))
+(rule "replace_known_right" (formula "2") (term "0") (ifseqformula "20"))
+ (builtin "One Step Simplification" (formula "2"))
+(rule "polySimp_mulComm0" (formula "13") (term "1"))
+(rule "polySimp_mulComm0" (formula "14") (term "0"))
+(rule "polySimp_addComm0" (formula "9") (term "3,0"))
+(rule "polySimp_addComm0" (formula "10") (term "0"))
+(rule "disjointDefinition" (formula "18"))
+ (builtin "One Step Simplification" (formula "18"))
+(rule "notLeft" (formula "18"))
+(rule "eqSymm" (formula "18"))
+(rule "inEqSimp_commuteLeq" (formula "6"))
+(rule "inEqSimp_commuteLeq" (formula "4"))
+(rule "inEqSimp_commuteLeq" (formula "15"))
+(rule "inEqSimp_commuteLeq" (formula "16"))
+(rule "inEqSimp_commuteLeq" (formula "13"))
+(rule "inEqSimp_commuteLeq" (formula "14"))
+(rule "inEqSimp_commuteLeq" (formula "10"))
+(rule "assignment" (formula "21") (term "1"))
+ (builtin "One Step Simplification" (formula "21"))
+(rule "variableDeclarationAssign" (formula "21") (term "1"))
+(rule "variableDeclaration" (formula "21") (term "1") (newnames "self_25"))
+(rule "arrayLengthIsAShort" (formula "14") (term "0"))
+(rule "expand_inShort" (formula "14"))
+(rule "replace_short_MIN" (formula "14") (term "0,1"))
+(rule "replace_short_MAX" (formula "14") (term "1,0"))
+(rule "andLeft" (formula "14"))
+(rule "inEqSimp_commuteLeq" (formula "15"))
+(rule "arrayLengthNotNegative" (formula "16") (term "0"))
+(rule "arrayLengthNotNegative" (formula "10") (term "0"))
+(rule "arrayLengthIsAShort" (formula "11") (term "0"))
+(rule "expand_inShort" (formula "11"))
+(rule "replace_short_MAX" (formula "11") (term "1,0"))
+(rule "replace_short_MIN" (formula "11") (term "0,1"))
+(rule "andLeft" (formula "11"))
+(rule "inEqSimp_commuteLeq" (formula "12"))
+(rule "staticMethodCallStaticWithAssignmentViaTypereference" (formula "27") (term "1") (inst "#v0=b"))
+(rule "variableDeclaration" (formula "27") (term "1") (newnames "b"))
+(rule "methodBodyExpand" (formula "27") (term "1") (newnames "heapBefore_,savedHeapBefore_"))
+ (builtin "One Step Simplification" (formula "27"))
+(rule "variableDeclaration" (formula "27") (term "1") (newnames "__NEW__"))
+(rule "staticMethodCallStaticWithAssignmentViaTypereference" (formula "27") (term "1") (inst "#v0=b_1"))
+(rule "variableDeclaration" (formula "27") (term "1") (newnames "b_1"))
+(rule "allocateInstance" (formula "27"))
+ (builtin "One Step Simplification" (formula "28"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "2")))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "1"))
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+ (rule "elimGcdLeq_antec" (formula "21") (inst "elimGcdRightDiv=Z(7(0(6(8(8(3(8(#))))))))") (inst "elimGcdLeftDiv=l_0") (inst "elimGcd=Z(6(5(2(#))))"))
+ (rule "leq_literals" (formula "21") (term "0,0"))
+ (builtin "One Step Simplification" (formula "21"))
+ (rule "neg_literal" (formula "21") (term "0,0,0,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "21") (term "1,0,0,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "21") (term "1,0,0"))
+ (rule "mul_literals" (formula "21") (term "1,0,0,0,0,0"))
+ (rule "polySimp_addLiterals" (formula "21") (term "0,0,0,0"))
+ (rule "add_zero_right" (formula "21") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "21") (term "0,0"))
+ (rule "add_literals" (formula "21") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "21") (term "1,0,0"))
+ (rule "add_zero_right" (formula "21") (term "0,0"))
+ (rule "qeq_literals" (formula "21") (term "0"))
+ (builtin "One Step Simplification" (formula "21"))
+ (rule "elimGcdGeq_antec" (formula "20") (inst "elimGcdRightDiv=Z(0(#))") (inst "elimGcdLeftDiv=l_0") (inst "elimGcd=Z(6(5(2(#))))"))
+ (rule "polySimp_mulLiterals" (formula "20") (term "1,0,1,0"))
+ (rule "leq_literals" (formula "20") (term "0,0"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "times_zero_1" (formula "20") (term "1,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "20") (term "0,0,0,0,0"))
+ (rule "add_zero_right" (formula "20") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "20") (term "0,0"))
+ (rule "add_literals" (formula "20") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "20") (term "1,0,0"))
+ (rule "add_zero_right" (formula "20") (term "0,0"))
+ (rule "leq_literals" (formula "20") (term "0"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "inEqSimp_exactShadow3" (formula "22") (ifseqformula "14"))
+ (rule "polySimp_mulAssoc" (formula "22") (term "0,0"))
+ (rule "polySimp_mulComm0" (formula "22") (term "0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "22") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "22") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "22"))
+ (rule "polySimp_mulLiterals" (formula "22") (term "0"))
+ (rule "inEqSimp_subsumption4" (formula "22") (ifseqformula "21"))
+ (rule "greater_literals" (formula "22") (term "0,0"))
+ (builtin "One Step Simplification" (formula "22"))
+ (rule "mul_literals" (formula "22") (term "0,0"))
+ (rule "leq_literals" (formula "22") (term "0"))
+ (builtin "One Step Simplification" (formula "22"))
+ (rule "true_left" (formula "22"))
+ (rule "nnf_imp2or" (formula "28") (term "0"))
+ (rule "nnf_notAnd" (formula "28") (term "0,0"))
+ (rule "nnf_imp2or" (formula "28") (term "0,1,0"))
+ (rule "nnf_notAnd" (formula "28") (term "0,0,0"))
+ (rule "inEqSimp_notLeq" (formula "28") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "28") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "28") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "28") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "28") (term "1,1,0,0,0"))
+ (rule "mul_literals" (formula "28") (term "0,1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "28") (term "1,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "28") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_notGeq" (formula "28") (term "0,0,0,0"))
+ (rule "times_zero_1" (formula "28") (term "1,0,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "28") (term "0,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "28") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "28") (term "1,0,0,0,0"))
+ (rule "nnf_notAnd" (formula "28") (term "1,0,0"))
+ (rule "inEqSimp_notGeq" (formula "28") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "28") (term "1,0,0,1,1,0,0"))
+ (rule "add_literals" (formula "28") (term "0,0,1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "28") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "28") (term "1,1,1,0,0"))
+ (rule "inEqSimp_notLeq" (formula "28") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "28") (term "1,0,0,0,1,0,0"))
+ (rule "add_literals" (formula "28") (term "0,0,0,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "28") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "28") (term "1,0,1,0,0"))
+ (rule "nnf_notAnd" (formula "28") (term "0,0,1,0"))
+ (rule "nnf_notAnd" (formula "28") (term "0,0,0,1,0"))
+ (rule "inEqSimp_notGeq" (formula "28") (term "0,0,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "28") (term "1,0,0,0,0,0,0,1,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "28") (term "0,0,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "28") (term "1,0,0,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "28") (term "1,0,0,0,0,1,0"))
+ (rule "mul_literals" (formula "28") (term "0,1,0,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "28") (term "1,1,0,0,0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "28") (term "1,1,0,0,0,0,1,0"))
+ (rule "inEqSimp_notLeq" (formula "28") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "28") (term "1,0,0,1,0,0,0,1,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "28") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "28") (term "1,1,0,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "28") (term "1,1,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "28") (term "1,1,1,0,0,0,1,0"))
+ (rule "mul_literals" (formula "28") (term "0,1,1,0,0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "28") (term "1,1,1,0,0,0,1,0"))
+ (rule "nnf_notAnd" (formula "28") (term "1,0,0,1,0"))
+ (rule "inEqSimp_notLeq" (formula "28") (term "0,1,0,0,1,0"))
+ (rule "mul_literals" (formula "28") (term "1,0,0,0,1,0,0,1,0"))
+ (rule "add_literals" (formula "28") (term "0,0,0,1,0,0,1,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "28") (term "0,1,0,0,1,0"))
+ (rule "mul_literals" (formula "28") (term "1,0,1,0,0,1,0"))
+ (rule "inEqSimp_notGeq" (formula "28") (term "1,1,0,0,1,0"))
+ (rule "mul_literals" (formula "28") (term "1,0,0,1,1,0,0,1,0"))
+ (rule "add_literals" (formula "28") (term "0,0,1,1,0,0,1,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "28") (term "1,1,0,0,1,0"))
+ (rule "mul_literals" (formula "28") (term "1,1,1,0,0,1,0"))
+ (rule "Definition_axiom_for_bucketSize_in_de_wiesler_BucketPointers" (formula "3") (term "0,0,0,1,1,1,0"))
+ (rule "translateJavaSubInt" (formula "3") (term "0,0,0,1,1,1,0"))
+ (rule "translateJavaAddInt" (formula "3") (term "2,0,0,0,0,1,1,1,0"))
+ (rule "polySimp_elimSub" (formula "3") (term "0,0,0,1,1,1,0"))
+ (rule "polySimp_mulComm0" (formula "3") (term "0,0,1,1,1,0"))
+ (rule "polySimp_addComm0" (formula "3") (term "1,0,0,1,1,1,0"))
+ (rule "polySimp_addComm0" (formula "3") (term "2,1,1,0,0,1,1,1,0"))
+ (rule "polySimp_rightDist" (formula "3") (term "0,0,1,1,1,0"))
+ (rule "polySimp_mulAssoc" (formula "3") (term "0,0,0,1,1,1,0"))
+ (rule "polySimp_mulComm0" (formula "3") (term "0,0,0,0,1,1,1,0"))
+ (rule "polySimp_mulLiterals" (formula "3") (term "0,0,0,1,1,1,0"))
+ (rule "polySimp_elimOne" (formula "3") (term "0,0,0,1,1,1,0"))
+ (rule "Definition_axiom_for_bucketStart_in_de_wiesler_BucketPointers" (formula "26") (term "1,1,0"))
+ (rule "translateJavaCastInt" (formula "26") (term "0,1,1,0"))
+ (rule "eqSymm" (formula "26") (term "1,0"))
+ (rule "castedGetAny" (formula "26") (term "0,0,1,0"))
+ (rule "eqSymm" (formula "26") (term "1,0"))
+ (rule "pullOutSelect" (formula "26") (term "0,0,1,1,0") (inst "selectSK=de_wiesler_BucketPointers_bucket_starts_1"))
+ (rule "simplifySelectOfStore" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+ (rule "castDel" (formula "26") (term "0"))
+ (rule "applyEqReverse" (formula "27") (term "0,0,1,1,0") (ifseqformula "26"))
+ (rule "hideAuxiliaryEq" (formula "26"))
+ (rule "getOfSeqDefEQ" (formula "26") (term "0,1,1,0") (ifseqformula "27"))
+ (rule "add_zero_right" (formula "26") (term "0,2,0,1,0,1,1,0"))
+ (rule "eqSymm" (formula "26") (term "1,0"))
+ (rule "polySimp_elimSub" (formula "26") (term "1,1,0,0,0,1,0"))
+ (rule "times_zero_2" (formula "26") (term "1,1,1,0,0,0,1,0"))
+ (rule "add_zero_right" (formula "26") (term "1,1,0,0,0,1,0"))
+ (rule "inEqSimp_ltToLeq" (formula "26") (term "1,0,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "26") (term "1,0,0,1,0,0,0,1,0"))
+ (rule "mul_literals" (formula "26") (term "0,1,0,0,1,0,0,0,1,0"))
+ (rule "polySimp_addAssoc" (formula "26") (term "0,0,1,0,0,0,1,0"))
+ (rule "add_literals" (formula "26") (term "0,0,0,1,0,0,0,1,0"))
+ (rule "add_zero_left" (formula "26") (term "0,0,1,0,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "26") (term "0,0,0,0,1,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "26") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "26") (term "1,1,0,0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "26") (term "1,1,0,0,0,1,0"))
+ (rule "Class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "34"))
+ (rule "notRight" (formula "34"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0"))
+ (rule "pullOutSelect" (formula "1") (term "0") (inst "selectSK=de_wiesler_BucketPointers_buffer_1"))
+ (rule "simplifySelectOfAnon" (formula "1"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "32")))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,1,0,0"))
+ (rule "applyEq" (formula "1") (term "1") (ifseqformula "2"))
+ (rule "ifEqualsNull" (formula "1"))
+ (rule "elementOfArrayRange" (formula "1") (term "0,0,0,1") (inst "iv=iv"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "elementOfArrayRange" (formula "1") (term "0,0,0") (inst "iv=iv"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "pullOutSelect" (formula "1") (term "0,0,0,0") (inst "selectSK=java_lang_Object_created__0"))
+ (rule "applyEq" (formula "2") (term "0,0,1") (ifseqformula "1"))
+ (rule "simplifySelectOfCreate" (formula "1"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "33")))
+ (rule "castDel" (formula "1") (term "0"))
+ (rule "applyEqReverse" (formula "2") (term "0,0,0,0") (ifseqformula "1"))
+ (builtin "One Step Simplification" (formula "2"))
+ (rule "andLeft" (formula "2"))
+ (rule "applyEqReverse" (formula "2") (term "0") (ifseqformula "1"))
+ (builtin "One Step Simplification" (formula "2"))
+ (rule "true_left" (formula "2"))
+ (rule "hideAuxiliaryEq" (formula "1"))
+ (rule "pullOutSelect" (formula "1") (term "0") (inst "selectSK=de_wiesler_BucketPointers_buffer_2"))
+ (rule "simplifySelectOfStore" (formula "1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "castDel" (formula "1") (term "0"))
+ (rule "applyEqReverse" (formula "2") (term "0") (ifseqformula "1"))
+ (rule "close" (formula "35") (ifseqformula "2"))
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "1"))
+ (builtin "One Step Simplification" (formula "40"))
+ (rule "closeTrue" (formula "40"))
+ )
+ )
+ (branch "Case 2"
+ (rule "impRight" (formula "39"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "closeFalse" (formula "1"))
+ )
+ )
+ (branch "Null Reference (self_25 = null)"
+ (rule "false_right" (formula "40"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "36")))
+ (rule "closeFalse" (formula "1"))
+ )
+ )
+ )
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__decrement_read(int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__decrement_read(int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..c3c96ba
--- /dev/null
+++ b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__decrement_read(int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,4294 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Sun Jun 05 14:36:20 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Sun Jun 05 14:36:20 CEST 2022
+contract=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:decrement_read(int)].JML normal_behavior operation contract.0
+name=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:decrement_read(int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "13469")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "9"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "10"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "2"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "inEqSimp_commuteLeq" (formula "8"))
+(rule "assignment" (formula "13") (term "1"))
+ (builtin "One Step Simplification" (formula "13"))
+(rule "methodBodyExpand" (formula "13") (term "1") (newnames "heapBefore_decrement_read,savedHeapBefore_decrement_read"))
+ (builtin "One Step Simplification" (formula "13"))
+(rule "variableDeclarationFinalAssign" (formula "13") (term "1"))
+(rule "variableDeclarationFinal" (formula "13") (term "1") (newnames "read_pos"))
+(rule "assignmentMultiplicationInt" (formula "13") (term "1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "13"))
+ (rule "expand_inInt" (formula "13"))
+ (rule "replace_int_MAX" (formula "13") (term "1,0"))
+ (rule "replace_int_MIN" (formula "13") (term "0,1"))
+ (rule "polySimp_mulComm0" (formula "13") (term "1,1"))
+ (rule "polySimp_mulComm0" (formula "13") (term "0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "9"))
+ (rule "polySimp_mulComm0" (formula "9") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "9") (term "0"))
+ (rule "inEqSimp_commuteLeq" (formula "13") (term "1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "9"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "0"))
+ (rule "polySimp_elimOne" (formula "9") (term "0"))
+ (rule "inEqSimp_subsumption1" (formula "5") (ifseqformula "8"))
+ (rule "leq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "true_left" (formula "5"))
+ (rule "inEqSimp_subsumption6" (formula "12") (term "1") (ifseqformula "7"))
+ (rule "times_zero_1" (formula "12") (term "1,1,0,1"))
+ (rule "greater_literals" (formula "12") (term "0,0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "leq_literals" (formula "12") (term "0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "inEqSimp_leqRight" (formula "12"))
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+ (rule "translateJavaAddInt" (formula "3") (term "0,2,0,1,1,0"))
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+ (rule "translateJavaMulInt" (formula "3") (term "0,2,0,1,0"))
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+ (rule "translateJavaMulInt" (formula "3") (term "0,2,1,1,0,0"))
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+ (builtin "One Step Simplification" (formula "4"))
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+ (rule "andLeft" (formula "11"))
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+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "4")) (ifInst "" (formula "12")))
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+ (builtin "One Step Simplification" (formula "3") (ifInst "" (formula "5")) (ifInst "" (formula "13")))
+ (rule "newSym_eq" (formula "3") (inst "l=l_1") (inst "newSymDef=mul(de.wiesler.BucketPointers::toReadCountOfBucket(heap,
+ self,
+ bucket),
+ Z(0(#)))"))
+ (rule "times_zero_1" (formula "3") (term "1,1"))
+ (rule "add_zero_right" (formula "3") (term "1"))
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+ (rule "applyEq" (formula "3") (term "0,0") (ifseqformula "4"))
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+ (rule "leq_literals" (formula "1") (term "0,0"))
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+ int[]::final(self,
+ de.wiesler.BucketPointers::$buffer),
+ arr(add(Z(1(#)),
+ mul(bucket, Z(2(#)))))),
+ add(Z(neglit(1(#))),
+ int::select(heap,
+ int[]::final(self,
+ de.wiesler.BucketPointers::$buffer),
+ arr(mul(bucket, Z(2(#))))))))
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+ int[]::final(self,
+ de.wiesler.BucketPointers::$buffer),
+ arr(mul(bucket, Z(2(#))))),
+ mul(int::select(heap,
+ int[]::final(self,
+ de.wiesler.BucketPointers::$buffer),
+ arr(add(Z(1(#)),
+ mul(bucket,
+ Z(2(#)))))),
+ Z(neglit(1(#))))))
+ \\else (Z(0(#))),
+ Z(0(#)))"))
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+ (rule "leq_literals" (formula "5") (term "0,0"))
+ (builtin "One Step Simplification" (formula "5"))
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+ (rule "leq_literals" (formula "11") (term "0,0,1,1,1"))
+ (builtin "One Step Simplification" (formula "11"))
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+ (rule "leq_literals" (formula "12") (term "0,0,0"))
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+ (rule "polySimp_addComm1" (formula "1") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "1") (term "0,0"))
+ (rule "replace_known_left" (formula "1") (term "0,0") (ifseqformula "9"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "1") (term "0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "0,0"))
+ (rule "polySimp_elimOne" (formula "1") (term "0,0"))
+ (rule "replace_known_left" (formula "1") (term "0") (ifseqformula "10"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "andLeft" (formula "1"))
+ (rule "inEqSimp_strengthen1" (formula "1") (ifseqformula "15"))
+ (rule "add_zero_right" (formula "1") (term "1"))
+ (rule "inEqSimp_contradEq7" (formula "15") (ifseqformula "1"))
+ (rule "times_zero_1" (formula "15") (term "1,0,0"))
+ (rule "add_zero_right" (formula "15") (term "0,0"))
+ (rule "leq_literals" (formula "15") (term "0"))
+ (builtin "One Step Simplification" (formula "15"))
+ (rule "false_right" (formula "15"))
+ (rule "Class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "9"))
+ (rule "notLeft" (formula "9"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "11") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "expand_inInt" (formula "11") (term "1,0,0,1"))
+ (rule "replace_int_MAX" (formula "11") (term "1,0,1,0,0,1"))
+ (rule "replace_int_MIN" (formula "11") (term "0,1,1,0,0,1"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "13"))
+ (rule "translateJavaAddInt" (formula "17") (term "1"))
+ (rule "translateJavaCastInt" (formula "18") (term "0"))
+ (rule "translateJavaMulInt" (formula "12") (term "0"))
+ (rule "translateJavaMulInt" (formula "11") (term "1"))
+ (rule "translateJavaCastInt" (formula "15") (term "0"))
+ (rule "translateJavaCastInt" (formula "14") (term "1"))
+ (rule "polySimp_mulComm0" (formula "12") (term "0"))
+ (rule "polySimp_mulComm0" (formula "11") (term "1"))
+ (rule "polySimp_addComm0" (formula "17") (term "1"))
+ (rule "castedGetAny" (formula "18") (term "0"))
+ (rule "castedGetAny" (formula "15") (term "0"))
+ (rule "castedGetAny" (formula "14") (term "1"))
+ (rule "inEqSimp_ltToLeq" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "13"))
+ (rule "inEqSimp_commuteLeq" (formula "11"))
+ (rule "inEqSimp_commuteLeq" (formula "14"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "20") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "20") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "20") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "20") (term "1,1,1,0,0,0"))
+ (rule "elimGcdGeq_antec" (formula "11") (inst "elimGcd=Z(2(#))") (inst "elimGcdLeftDiv=int::final(self,
+ de.wiesler.BucketPointers::$num_buckets)") (inst "elimGcdRightDiv=Z(0(#))"))
+ (rule "add_zero_right" (formula "11") (term "0,0,0,1,0"))
+ (rule "leq_literals" (formula "11") (term "0,0"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "polySimp_mulLiterals" (formula "11") (term "1,0,0"))
+ (rule "times_zero_1" (formula "11") (term "1,0,0,0,0"))
+ (rule "add_zero_right" (formula "11") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "11") (term "0,0"))
+ (rule "add_literals" (formula "11") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "11") (term "1,0,0"))
+ (rule "add_zero_right" (formula "11") (term "0,0"))
+ (rule "leq_literals" (formula "11") (term "0"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "inEqSimp_exactShadow3" (formula "14") (ifseqformula "15"))
+ (rule "polySimp_mulComm0" (formula "14") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "14") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "14"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "0"))
+ (rule "polySimp_elimOne" (formula "14") (term "0"))
+ (rule "inEqSimp_exactShadow2" (formula "10") (ifseqformula "12"))
+ (rule "greater_literals" (formula "10") (term "0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "polySimp_rightDist" (formula "10") (term "1,0,0"))
+ (rule "mul_literals" (formula "10") (term "0,1,0,0"))
+ (rule "polySimp_rightDist" (formula "10") (term "0,0"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "1,0,0"))
+ (rule "mul_literals" (formula "10") (term "0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "10"))
+ (rule "polySimp_mulComm0" (formula "10") (term "1"))
+ (rule "polySimp_rightDist" (formula "10") (term "1"))
+ (rule "mul_literals" (formula "10") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "1,1"))
+ (rule "inEqSimp_contradInEq0" (formula "10") (ifseqformula "3"))
+ (rule "andLeft" (formula "10"))
+ (rule "inEqSimp_homoInEq1" (formula "10"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "1,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "10") (term "0"))
+ (rule "add_literals" (formula "10") (term "1,1,0"))
+ (rule "times_zero_1" (formula "10") (term "1,0"))
+ (rule "add_literals" (formula "10") (term "0"))
+ (rule "leq_literals" (formula "10"))
+ (rule "closeFalse" (formula "10"))
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__hasRemainingRead(int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__hasRemainingRead(int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..d6ee9cb
--- /dev/null
+++ b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__hasRemainingRead(int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,1746 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Sun Jun 05 14:38:40 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Sun Jun 05 14:38:40 CEST 2022
+contract=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:hasRemainingRead(int)].JML normal_behavior operation contract.0
+name=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:hasRemainingRead(int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "1419")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre_0,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0"))
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+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "2"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "inEqSimp_commuteLeq" (formula "8"))
+(rule "assignment" (formula "12") (term "1"))
+ (builtin "One Step Simplification" (formula "12"))
+(rule "methodBodyExpand" (formula "12") (term "1") (newnames "heapBefore_hasRemainingRead,savedHeapBefore_hasRemainingRead"))
+ (builtin "One Step Simplification" (formula "12"))
+(rule "variableDeclarationFinalAssign" (formula "12") (term "1"))
+(rule "variableDeclarationFinal" (formula "12") (term "1") (newnames "read_pos"))
+(rule "assignmentMultiplicationInt" (formula "12") (term "1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "expand_inInt" (formula "12"))
+ (rule "replace_int_MIN" (formula "12") (term "0,1"))
+ (rule "replace_int_MAX" (formula "12") (term "1,0"))
+ (rule "polySimp_mulComm0" (formula "12") (term "0,0"))
+ (rule "polySimp_mulComm0" (formula "12") (term "1,1"))
+ (rule "inEqSimp_ltToLeq" (formula "9"))
+ (rule "polySimp_mulComm0" (formula "9") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "9") (term "0"))
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+ (rule "inEqSimp_sepNegMonomial0" (formula "9"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "0"))
+ (rule "polySimp_elimOne" (formula "9") (term "0"))
+ (rule "inEqSimp_subsumption6" (formula "12") (term "1") (ifseqformula "8"))
+ (rule "greater_literals" (formula "12") (term "0,0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "times_zero_1" (formula "12") (term "1,0,1"))
+ (rule "leq_literals" (formula "12") (term "0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "inEqSimp_leqRight" (formula "12"))
+ (rule "mul_literals" (formula "1") (term "1,0,0"))
+ (rule "add_literals" (formula "1") (term "0,0"))
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+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "9"))
+ (rule "leq_literals" (formula "6") (term "0"))
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+ (rule "true_left" (formula "6"))
+ (rule "elimGcdGeq_antec" (formula "1") (inst "elimGcdRightDiv=Z(4(2(8(1(4(7(3(7(0(1(#)))))))))))") (inst "elimGcdLeftDiv=bucket") (inst "elimGcd=Z(2(#))"))
+ (rule "leq_literals" (formula "1") (term "0,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,0,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,0"))
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+ (rule "polySimp_addLiterals" (formula "1") (term "0,0,0,0"))
+ (rule "add_zero_right" (formula "1") (term "0,0,0,0"))
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+ (rule "leq_literals" (formula "8") (term "0"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "true_left" (formula "8"))
+ (rule "Class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "7"))
+ (rule "notLeft" (formula "7"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "8") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "expand_inInt" (formula "8") (term "1,0,0,1"))
+ (rule "replace_int_MAX" (formula "8") (term "1,0,1,0,0,1"))
+ (rule "replace_int_MIN" (formula "8") (term "0,1,1,0,0,1"))
+ (rule "andLeft" (formula "8"))
+ (rule "andLeft" (formula "8"))
+ (rule "andLeft" (formula "8"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "8"))
+ (rule "andLeft" (formula "8"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "translateJavaAddInt" (formula "14") (term "1"))
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+ (rule "translateJavaMulInt" (formula "8") (term "1"))
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+ (rule "polySimp_elimOne" (formula "17") (term "1,1,1,0,0,0"))
+ (rule "elimGcdGeq_antec" (formula "8") (inst "elimGcdRightDiv=Z(0(#))") (inst "elimGcdLeftDiv=int::final(self,
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+ (rule "leq_literals" (formula "8") (term "0,0"))
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diff --git a/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__increment_write(int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__increment_write(int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..1d56f95
--- /dev/null
+++ b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__increment_write(int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,8181 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Sun Jun 05 14:40:22 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
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+[SMTSettings]invariantForall=false
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+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Sun Jun 05 14:40:22 CEST 2022
+contract=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:increment_write(int)].JML normal_behavior operation contract.0
+name=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:increment_write(int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "107625")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "9"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "2"))
+(rule "translateJavaAddInt" (formula "10") (term "1"))
+(rule "polySimp_addComm0" (formula "10") (term "1"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "inEqSimp_commuteLeq" (formula "8"))
+(rule "assignment" (formula "13") (term "1"))
+ (builtin "One Step Simplification" (formula "13"))
+(rule "methodBodyExpand" (formula "13") (term "1") (newnames "heapBefore_increment_write,savedHeapBefore_increment_write"))
+ (builtin "One Step Simplification" (formula "13"))
+(rule "variableDeclarationFinalAssign" (formula "13") (term "1"))
+(rule "variableDeclarationFinal" (formula "13") (term "1") (newnames "read_pos"))
+(rule "assignmentMultiplicationInt" (formula "13") (term "1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "13"))
+ (rule "expand_inInt" (formula "13"))
+ (rule "replace_int_MAX" (formula "13") (term "1,0"))
+ (rule "replace_int_MIN" (formula "13") (term "0,1"))
+ (rule "polySimp_mulComm0" (formula "13") (term "1,1"))
+ (rule "polySimp_mulComm0" (formula "13") (term "0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "9"))
+ (rule "polySimp_mulComm0" (formula "9") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "9") (term "0"))
+ (rule "inEqSimp_commuteLeq" (formula "13") (term "1"))
+ (rule "inEqSimp_homoInEq1" (formula "10"))
+ (rule "polySimp_addComm1" (formula "10") (term "0"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "9"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "0"))
+ (rule "polySimp_elimOne" (formula "9") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "10"))
+ (rule "polySimp_mulComm0" (formula "10") (term "1"))
+ (rule "polySimp_rightDist" (formula "10") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "1,1"))
+ (rule "mul_literals" (formula "10") (term "0,1"))
+ (rule "polySimp_elimOne" (formula "10") (term "1,1"))
+ (rule "inEqSimp_subsumption1" (formula "5") (ifseqformula "8"))
+ (rule "leq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "true_left" (formula "5"))
+ (rule "inEqSimp_subsumption6" (formula "12") (term "1") (ifseqformula "7"))
+ (rule "greater_literals" (formula "12") (term "0,0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "times_zero_1" (formula "12") (term "1,0,1"))
+ (rule "leq_literals" (formula "12") (term "0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "inEqSimp_leqRight" (formula "12"))
+ (rule "mul_literals" (formula "1") (term "1,0,0"))
+ (rule "add_literals" (formula "1") (term "0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "1"))
+ (rule "mul_literals" (formula "1") (term "1"))
+ (rule "elimGcdGeq_antec" (formula "1") (inst "elimGcd=Z(2(#))") (inst "elimGcdLeftDiv=bucket") (inst "elimGcdRightDiv=Z(4(2(8(1(4(7(3(7(0(1(#)))))))))))"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,0,0,0,1,0"))
+ (rule "leq_literals" (formula "1") (term "0,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "mul_literals" (formula "1") (term "1,0,0,0,0,0"))
+ (rule "polySimp_addLiterals" (formula "1") (term "0,0,0,0"))
+ (rule "add_zero_right" (formula "1") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "1") (term "0,0"))
+ (rule "add_literals" (formula "1") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "1") (term "1,0,0"))
+ (rule "add_zero_right" (formula "1") (term "0,0"))
+ (rule "leq_literals" (formula "1") (term "0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_subsumption1" (formula "8") (ifseqformula "1"))
+ (rule "leq_literals" (formula "8") (term "0"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "true_left" (formula "8"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "10") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "expand_inInt" (formula "10") (term "1,0,0,1"))
+ (rule "replace_int_MAX" (formula "10") (term "1,0,1,0,0,1"))
+ (rule "replace_int_MIN" (formula "10") (term "0,1,1,0,0,1"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "12"))
+ (rule "andLeft" (formula "12"))
+ (rule "translateJavaCastInt" (formula "17") (term "0"))
+ (rule "translateJavaAddInt" (formula "16") (term "1"))
+ (rule "translateJavaMulInt" (formula "10") (term "1"))
+ (rule "translateJavaMulInt" (formula "11") (term "0"))
+ (rule "translateJavaCastInt" (formula "14") (term "0"))
+ (rule "translateJavaCastInt" (formula "13") (term "1"))
+ (rule "polySimp_mulComm0" (formula "10") (term "1"))
+ (rule "polySimp_mulComm0" (formula "11") (term "0"))
+ (rule "polySimp_addComm0" (formula "16") (term "1"))
+ (rule "castedGetAny" (formula "17") (term "0"))
+ (rule "castedGetAny" (formula "14") (term "0"))
+ (rule "castedGetAny" (formula "13") (term "1"))
+ (rule "inEqSimp_ltToLeq" (formula "19") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "19") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "19") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "19") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "12"))
+ (rule "inEqSimp_commuteLeq" (formula "10"))
+ (rule "inEqSimp_commuteLeq" (formula "13"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "19") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "19") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "19") (term "1,1,0,0,0"))
+ (rule "mul_literals" (formula "19") (term "0,1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "19") (term "1,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "19") (term "1,1,1,0,0,0"))
+ (rule "elimGcdGeq_antec" (formula "10") (inst "elimGcd=Z(2(#))") (inst "elimGcdLeftDiv=int::final(self,
+ de.wiesler.BucketPointers::$num_buckets)") (inst "elimGcdRightDiv=Z(0(#))"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "1,0,1,0"))
+ (rule "add_zero_right" (formula "10") (term "0,0,0,1,0"))
+ (rule "leq_literals" (formula "10") (term "0,0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "times_zero_1" (formula "10") (term "1,0,0,0,0"))
+ (rule "add_zero_right" (formula "10") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "10") (term "0,0"))
+ (rule "add_literals" (formula "10") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "10") (term "1,0,0"))
+ (rule "add_zero_right" (formula "10") (term "0,0"))
+ (rule "leq_literals" (formula "10") (term "0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "inEqSimp_exactShadow3" (formula "13") (ifseqformula "14"))
+ (rule "polySimp_mulComm0" (formula "13") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "13") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "13"))
+ (rule "polySimp_mulLiterals" (formula "13") (term "0"))
+ (rule "polySimp_elimOne" (formula "13") (term "0"))
+ (rule "inEqSimp_exactShadow2" (formula "10") (ifseqformula "11"))
+ (rule "greater_literals" (formula "10") (term "0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "times_zero_1" (formula "10") (term "1,0,0"))
+ (rule "times_zero_1" (formula "10") (term "0,0"))
+ (rule "add_zero_left" (formula "10") (term "0"))
+ (rule "inEqSimp_exactShadow2" (formula "8") (ifseqformula "12"))
+ (rule "greater_literals" (formula "8") (term "0"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "polySimp_rightDist" (formula "8") (term "1,0,0"))
+ (rule "mul_literals" (formula "8") (term "0,1,0,0"))
+ (rule "polySimp_rightDist" (formula "8") (term "0,0"))
+ (rule "polySimp_mulLiterals" (formula "8") (term "1,0,0"))
+ (rule "mul_literals" (formula "8") (term "0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "8"))
+ (rule "polySimp_mulComm0" (formula "8") (term "1"))
+ (rule "polySimp_rightDist" (formula "8") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "8") (term "1,1"))
+ (rule "mul_literals" (formula "8") (term "0,1"))
+ (rule "nnf_imp2or" (formula "22") (term "0"))
+ (rule "nnf_notAnd" (formula "22") (term "0,0"))
+ (rule "nnf_notAnd" (formula "22") (term "0,0,0"))
+ (rule "inEqSimp_notGeq" (formula "22") (term "0,0,0,0"))
+ (rule "times_zero_1" (formula "22") (term "1,0,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "22") (term "0,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "22") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,0,0,0"))
+ (rule "inEqSimp_notLeq" (formula "22") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "22") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "22") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "22") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "22") (term "0,0,0,1,0,0,0"))
+ (rule "add_zero_left" (formula "22") (term "0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "22") (term "1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "22") (term "1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "22") (term "1,1,0,0,0"))
+ (rule "nnf_notAnd" (formula "22") (term "1,0,0"))
+ (rule "inEqSimp_notLeq" (formula "22") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,0,0,1,0,0"))
+ (rule "add_literals" (formula "22") (term "0,0,0,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "22") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,1,0,0"))
+ (rule "inEqSimp_notGeq" (formula "22") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,0,1,1,0,0"))
+ (rule "add_literals" (formula "22") (term "0,0,1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "22") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,1,1,0,0"))
+ (rule "Class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "7"))
+ (rule "notLeft" (formula "7"))
+ (rule "Definition_axiom_for_writtenCountOfBucket_in_de_wiesler_BucketPointers" (formula "9") (term "0"))
+ (rule "translateJavaSubInt" (formula "9") (term "0"))
+ (rule "polySimp_elimSub" (formula "9") (term "0"))
+ (rule "polySimp_addComm0" (formula "9") (term "0"))
+ (rule "inEqSimp_homoInEq0" (formula "9"))
+ (rule "polySimp_mulComm0" (formula "9") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "9") (term "1,0"))
+ (rule "polySimp_mulAssoc" (formula "9") (term "0,1,0"))
+ (rule "polySimp_mulComm0" (formula "9") (term "0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "0,1,0"))
+ (rule "polySimp_elimOne" (formula "9") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "9") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "9"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "0"))
+ (rule "polySimp_elimOne" (formula "9") (term "0"))
+ (rule "Definition_axiom_for_isSortedSeqTransitive_in_de_wiesler_Functions" (formula "20") (term "0") (inst "j=j") (inst "i=i"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "expand_inInt" (formula "20") (term "1,0,0"))
+ (rule "expand_inInt" (formula "20") (term "1,0,0,1,0"))
+ (rule "replace_int_MAX" (formula "20") (term "1,0,1,0,0"))
+ (rule "replace_int_MIN" (formula "20") (term "0,1,1,0,0"))
+ (rule "replace_int_MIN" (formula "20") (term "0,1,1,0,0,1,0"))
+ (rule "replace_int_MAX" (formula "20") (term "1,0,1,0,0,1,0"))
+ (rule "translateJavaCastInt" (formula "20") (term "0,1,0,1,0"))
+ (rule "translateJavaCastInt" (formula "20") (term "1,1,0,1,0"))
+ (rule "castedGetAny" (formula "20") (term "0,1,0,1,0"))
+ (rule "castedGetAny" (formula "20") (term "1,1,0,1,0"))
+ (rule "inEqSimp_ltToLeq" (formula "20") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,1,0,0,0,1,0"))
+ (rule "inEqSimp_ltToLeq" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "0,0,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "1,1,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "1,0,1,0"))
+ (rule "applyEq" (formula "20") (term "0,1,0,0,1,0,0,0,1,0") (ifseqformula "18"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,1,0,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "20") (term "1,0,0,1,0,0,0,1,0"))
+ (rule "mul_literals" (formula "20") (term "0,1,0,0,1,0,0,0,1,0"))
+ (rule "polySimp_addAssoc" (formula "20") (term "0,0,1,0,0,0,1,0"))
+ (rule "add_literals" (formula "20") (term "0,0,0,1,0,0,0,1,0"))
+ (rule "add_zero_left" (formula "20") (term "0,0,1,0,0,0,1,0"))
+ (rule "applyEq" (formula "20") (term "0,1,0,0,1,0,0,0") (ifseqformula "18"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "20") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "20") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "20") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "20") (term "0,0,0,1,0,0,0"))
+ (rule "add_zero_left" (formula "20") (term "0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "20") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "20") (term "1,1,0,0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "20") (term "1,1,0,0,0,1,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "20") (term "1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "20") (term "1,1,0,0,0"))
+ (rule "nnf_imp2or" (formula "20") (term "0"))
+ (rule "nnf_notAnd" (formula "20") (term "0,0"))
+ (rule "nnf_imp2or" (formula "20") (term "0,1,0"))
+ (rule "nnf_notAnd" (formula "20") (term "0,0,0"))
+ (rule "inEqSimp_notGeq" (formula "20") (term "0,0,0,0"))
+ (rule "times_zero_1" (formula "20") (term "1,0,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "20") (term "0,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "20") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "20") (term "1,0,0,0,0"))
+ (rule "inEqSimp_notLeq" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "20") (term "1,1,0,0,0"))
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+ (rule "polySimp_mulLiterals" (formula "19") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "19") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "19") (term "1,1,1,0,0,0"))
+ (rule "elimGcdGeq_antec" (formula "10") (inst "elimGcd=Z(2(#))") (inst "elimGcdLeftDiv=int::final(self,
+ de.wiesler.BucketPointers::$num_buckets)") (inst "elimGcdRightDiv=Z(0(#))"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "1,0,1,0"))
+ (rule "leq_literals" (formula "10") (term "0,0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "add_zero_right" (formula "10") (term "0,0,0,0"))
+ (rule "times_zero_1" (formula "10") (term "1,0,0,0,0"))
+ (rule "add_zero_right" (formula "10") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "10") (term "0,0"))
+ (rule "add_literals" (formula "10") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "10") (term "1,0,0"))
+ (rule "add_zero_right" (formula "10") (term "0,0"))
+ (rule "leq_literals" (formula "10") (term "0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "inEqSimp_exactShadow2" (formula "8") (ifseqformula "11"))
+ (rule "greater_literals" (formula "8") (term "0"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "polySimp_rightDist" (formula "8") (term "1,0,0"))
+ (rule "mul_literals" (formula "8") (term "0,1,0,0"))
+ (rule "polySimp_rightDist" (formula "8") (term "0,0"))
+ (rule "polySimp_mulLiterals" (formula "8") (term "1,0,0"))
+ (rule "mul_literals" (formula "8") (term "0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "8"))
+ (rule "polySimp_mulComm0" (formula "8") (term "1"))
+ (rule "polySimp_rightDist" (formula "8") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "8") (term "1,1"))
+ (rule "mul_literals" (formula "8") (term "0,1"))
+ (rule "inEqSimp_contradInEq1" (formula "1") (ifseqformula "8"))
+ (rule "andLeft" (formula "1"))
+ (rule "inEqSimp_homoInEq1" (formula "1"))
+ (rule "polySimp_mulComm0" (formula "1") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "1") (term "1,0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,1,0"))
+ (rule "mul_literals" (formula "1") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "1") (term "0"))
+ (rule "polySimp_addComm1" (formula "1") (term "0,0"))
+ (rule "add_literals" (formula "1") (term "0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "1") (term "0"))
+ (rule "add_literals" (formula "1") (term "1,1,0"))
+ (rule "times_zero_1" (formula "1") (term "1,0"))
+ (rule "add_literals" (formula "1") (term "0"))
+ (rule "leq_literals" (formula "1"))
+ (rule "closeFalse" (formula "1"))
+ )
+ )
+ (branch "Null Reference (x_arr = null)"
+ (rule "false_right" (formula "14"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_ltToLeq" (formula "10"))
+ (rule "polySimp_mulComm0" (formula "10") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "10") (term "0"))
+ (rule "inEqSimp_homoInEq1" (formula "11"))
+ (rule "polySimp_addComm1" (formula "11") (term "0"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "10"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "0"))
+ (rule "polySimp_elimOne" (formula "10") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "11"))
+ (rule "polySimp_mulComm0" (formula "11") (term "1"))
+ (rule "polySimp_rightDist" (formula "11") (term "1"))
+ (rule "mul_literals" (formula "11") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "11") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "11") (term "1,1"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "9"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "Class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "7"))
+ (rule "notLeft" (formula "7"))
+ (rule "close" (formula "11") (ifseqformula "1"))
+ )
+ (branch "Index Out of Bounds (x_arr != null, but write_pos Out of Bounds!)"
+ (rule "false_right" (formula "14"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "andLeft" (formula "1"))
+ (rule "notLeft" (formula "1"))
+ (rule "inEqSimp_ltToLeq" (formula "10"))
+ (rule "polySimp_mulComm0" (formula "10") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "10") (term "0"))
+ (rule "inEqSimp_ltToLeq" (formula "1") (term "1"))
+ (rule "times_zero_1" (formula "1") (term "1,0,0,1"))
+ (rule "add_zero_right" (formula "1") (term "0,0,1"))
+ (rule "polySimp_addAssoc" (formula "1") (term "0,1"))
+ (rule "add_literals" (formula "1") (term "0,0,1"))
+ (rule "inEqSimp_homoInEq1" (formula "11"))
+ (rule "polySimp_addComm1" (formula "11") (term "0"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "10"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "0"))
+ (rule "polySimp_elimOne" (formula "10") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "1") (term "1"))
+ (rule "mul_literals" (formula "1") (term "1,1"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "11"))
+ (rule "polySimp_mulComm0" (formula "11") (term "1"))
+ (rule "polySimp_rightDist" (formula "11") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "11") (term "1,1"))
+ (rule "mul_literals" (formula "11") (term "0,1"))
+ (rule "polySimp_elimOne" (formula "11") (term "1,1"))
+ (rule "inEqSimp_contradInEq5" (formula "1") (term "1") (ifseqformula "9"))
+ (rule "greater_literals" (formula "1") (term "0,0,1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "times_zero_1" (formula "1") (term "1,0,1"))
+ (rule "qeq_literals" (formula "1") (term "0,1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "9"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "11") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "expand_inInt" (formula "11") (term "1,0,0,1"))
+ (rule "replace_int_MAX" (formula "11") (term "1,0,1,0,0,1"))
+ (rule "replace_int_MIN" (formula "11") (term "0,1,1,0,0,1"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "13"))
+ (rule "translateJavaAddInt" (formula "17") (term "1"))
+ (rule "translateJavaCastInt" (formula "18") (term "0"))
+ (rule "translateJavaMulInt" (formula "12") (term "0"))
+ (rule "translateJavaMulInt" (formula "11") (term "1"))
+ (rule "translateJavaCastInt" (formula "15") (term "0"))
+ (rule "translateJavaCastInt" (formula "14") (term "1"))
+ (rule "polySimp_mulComm0" (formula "12") (term "0"))
+ (rule "polySimp_mulComm0" (formula "11") (term "1"))
+ (rule "polySimp_addComm0" (formula "17") (term "1"))
+ (rule "castedGetAny" (formula "18") (term "0"))
+ (rule "castedGetAny" (formula "15") (term "0"))
+ (rule "castedGetAny" (formula "14") (term "1"))
+ (rule "inEqSimp_ltToLeq" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "13"))
+ (rule "inEqSimp_commuteLeq" (formula "11"))
+ (rule "inEqSimp_commuteLeq" (formula "14"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "20") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "20") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "20") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "20") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "20") (term "1,1,1,0,0,0"))
+ (rule "elimGcdGeq_antec" (formula "11") (inst "elimGcd=Z(2(#))") (inst "elimGcdLeftDiv=int::final(self,
+ de.wiesler.BucketPointers::$num_buckets)") (inst "elimGcdRightDiv=Z(0(#))"))
+ (rule "polySimp_mulLiterals" (formula "11") (term "1,0,1,0"))
+ (rule "add_zero_right" (formula "11") (term "0,0,0,1,0"))
+ (rule "leq_literals" (formula "11") (term "0,0"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "times_zero_1" (formula "11") (term "1,0,0,0,0"))
+ (rule "add_zero_right" (formula "11") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "11") (term "0,0"))
+ (rule "add_literals" (formula "11") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "11") (term "1,0,0"))
+ (rule "add_zero_right" (formula "11") (term "0,0"))
+ (rule "leq_literals" (formula "11") (term "0"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "inEqSimp_exactShadow2" (formula "11") (ifseqformula "12"))
+ (rule "times_zero_1" (formula "11") (term "1,0,0,1"))
+ (rule "greater_literals" (formula "11") (term "0"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "times_zero_1" (formula "11") (term "0,0"))
+ (rule "add_zero_left" (formula "11") (term "0"))
+ (rule "inEqSimp_exactShadow2" (formula "9") (ifseqformula "13"))
+ (rule "greater_literals" (formula "9") (term "0"))
+ (builtin "One Step Simplification" (formula "9"))
+ (rule "polySimp_rightDist" (formula "9") (term "1,0,0"))
+ (rule "mul_literals" (formula "9") (term "0,1,0,0"))
+ (rule "polySimp_rightDist" (formula "9") (term "0,0"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "1,0,0"))
+ (rule "mul_literals" (formula "9") (term "0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "9"))
+ (rule "polySimp_mulComm0" (formula "9") (term "1"))
+ (rule "polySimp_rightDist" (formula "9") (term "1"))
+ (rule "mul_literals" (formula "9") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "1,1"))
+ (rule "inEqSimp_contradInEq0" (formula "9") (ifseqformula "1"))
+ (rule "andLeft" (formula "9"))
+ (rule "inEqSimp_homoInEq1" (formula "9"))
+ (rule "polySimp_mulComm0" (formula "9") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "9") (term "1,0"))
+ (rule "mul_literals" (formula "9") (term "0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "1,1,0"))
+ (rule "polySimp_addAssoc" (formula "9") (term "0"))
+ (rule "polySimp_addComm1" (formula "9") (term "0,0"))
+ (rule "add_literals" (formula "9") (term "0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "9") (term "0"))
+ (rule "add_literals" (formula "9") (term "1,1,0"))
+ (rule "times_zero_1" (formula "9") (term "1,0"))
+ (rule "add_literals" (formula "9") (term "0"))
+ (rule "leq_literals" (formula "9"))
+ (rule "closeFalse" (formula "9"))
+ )
+ )
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__write(int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__write(int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..46a832b
--- /dev/null
+++ b/src/main/key-overflow/BucketPointers/de.wiesler.BucketPointers(de.wiesler.BucketPointers__write(int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,1054 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Sun Jun 05 14:41:09 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Sun Jun 05 14:41:09 CEST 2022
+contract=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:write(int)].JML normal_behavior operation contract.0
+name=de.wiesler.BucketPointers[de.wiesler.BucketPointers\\:\\:write(int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "1546")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "2"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "inEqSimp_commuteLeq" (formula "8"))
+(rule "assignment" (formula "12") (term "1"))
+ (builtin "One Step Simplification" (formula "12"))
+(rule "methodBodyExpand" (formula "12") (term "1") (newnames "heapBefore_write,savedHeapBefore_write"))
+ (builtin "One Step Simplification" (formula "12"))
+(rule "variableDeclarationFinalAssign" (formula "12") (term "1"))
+(rule "variableDeclarationFinal" (formula "12") (term "1") (newnames "write_pos"))
+(rule "compound_addition_1" (formula "12") (term "1") (inst "#v=x"))
+(rule "variableDeclarationAssign" (formula "12") (term "1"))
+(rule "variableDeclaration" (formula "12") (term "1") (newnames "x"))
+(rule "assignmentMultiplicationInt" (formula "12") (term "1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "expand_inInt" (formula "12"))
+ (rule "replace_int_MAX" (formula "12") (term "1,0"))
+ (rule "replace_int_MIN" (formula "12") (term "0,1"))
+ (rule "polySimp_mulComm0" (formula "12") (term "1,1"))
+ (rule "polySimp_mulComm0" (formula "12") (term "0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "9"))
+ (rule "polySimp_mulComm0" (formula "9") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "9") (term "0"))
+ (rule "inEqSimp_commuteLeq" (formula "12") (term "1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "9"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "0"))
+ (rule "polySimp_elimOne" (formula "9") (term "0"))
+ (rule "inEqSimp_subsumption6" (formula "12") (term "1") (ifseqformula "8"))
+ (rule "times_zero_1" (formula "12") (term "1,1,0,1"))
+ (rule "greater_literals" (formula "12") (term "0,0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "leq_literals" (formula "12") (term "0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "inEqSimp_leqRight" (formula "12"))
+ (rule "mul_literals" (formula "1") (term "1,0,0"))
+ (rule "add_literals" (formula "1") (term "0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "1"))
+ (rule "mul_literals" (formula "1") (term "1"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "9"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "elimGcdGeq_antec" (formula "1") (inst "elimGcd=Z(2(#))") (inst "elimGcdLeftDiv=bucket") (inst "elimGcdRightDiv=Z(4(2(8(1(4(7(3(7(0(1(#)))))))))))"))
+ (rule "leq_literals" (formula "1") (term "0,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,0,0,0,0"))
+ (rule "mul_literals" (formula "1") (term "1,0,0,0,0,0"))
+ (rule "polySimp_addLiterals" (formula "1") (term "0,0,0,0"))
+ (rule "add_zero_right" (formula "1") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "1") (term "0,0"))
+ (rule "add_literals" (formula "1") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "1") (term "1,0,0"))
+ (rule "add_zero_right" (formula "1") (term "0,0"))
+ (rule "leq_literals" (formula "1") (term "0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_subsumption1" (formula "8") (ifseqformula "1"))
+ (rule "leq_literals" (formula "8") (term "0"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "true_left" (formula "8"))
+ (rule "Class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "7"))
+ (rule "notLeft" (formula "7"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_BucketPointers" (formula "8") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "8"))
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diff --git a/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__Buffers((I,(I,int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__Buffers((I,(I,int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..fb5b905
--- /dev/null
+++ b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__Buffers((I,(I,int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,108 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Thu Jun 02 20:07:55 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:onHeap , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Thu Jun 02 20:07:55 CEST 2022
+contract=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:Buffers([I,[I,int)].JML normal_behavior operation contract.0
+name=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:Buffers([I,[I,int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "16")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre_0,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "4"))
+(rule "notLeft" (formula "4"))
+(rule "notLeft" (formula "4"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "9"))
+(rule "eqSymm" (formula "11"))
+(rule "translateJavaMulInt" (formula "7") (term "1"))
+(rule "mul_literals" (formula "7") (term "1"))
+(rule "replace_known_right" (formula "3") (term "0") (ifseqformula "12"))
+ (builtin "One Step Simplification" (formula "3"))
+(rule "replace_known_right" (formula "2") (term "0") (ifseqformula "13"))
+ (builtin "One Step Simplification" (formula "2"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "inEqSimp_commuteLeq" (formula "9"))
+(rule "assignment" (formula "14") (term "1"))
+ (builtin "One Step Simplification" (formula "14"))
+(rule "variableDeclarationAssign" (formula "14") (term "1"))
+(rule "variableDeclaration" (formula "14") (term "1") (newnames "self_25"))
+(rule "arrayLengthIsAShort" (formula "7") (term "0"))
+(rule "expand_inShort" (formula "7"))
+(rule "replace_short_MIN" (formula "7") (term "0,1"))
+(rule "replace_short_MAX" (formula "7") (term "1,0"))
+(rule "andLeft" (formula "7"))
+(rule "inEqSimp_commuteLeq" (formula "8"))
+(rule "applyEq" (formula "7") (term "0") (ifseqformula "9"))
+(rule "leq_literals" (formula "7"))
+(rule "closeFalse" (formula "7"))
+)
+}
diff --git a/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__distribute(int,(I,int,int,int,int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__distribute(int,(I,int,int,int,int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..e92e06e
--- /dev/null
+++ b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__distribute(int,(I,int,int,int,int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,2191 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Thu Jun 02 20:21:54 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Thu Jun 02 20:21:54 CEST 2022
+contract=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:distribute(int,[I,int,int,int,int)].JML normal_behavior operation contract.0
+name=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:distribute(int,[I,int,int,int,int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "2411")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre_0,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "0,0,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,0,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,0,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "2"))
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+(rule "andLeft" (formula "12"))
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+(rule "translateJavaAddInt" (formula "23") (term "1"))
+(rule "eqSymm" (formula "28"))
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+(rule "translateJavaAddInt" (formula "29") (term "0,2,0"))
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+(rule "translateJavaAddInt" (formula "29") (term "0,2,1"))
+(rule "replace_known_right" (formula "6") (term "0") (ifseqformula "32"))
+ (builtin "One Step Simplification" (formula "6"))
+(rule "polySimp_elimSub" (formula "29") (term "2,0"))
+(rule "mul_literals" (formula "29") (term "1,2,0"))
+(rule "polySimp_elimSub" (formula "29") (term "2,1"))
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+(rule "polySimp_addComm0" (formula "29") (term "0,2,0"))
+(rule "polySimp_addComm0" (formula "29") (term "0,2,1"))
+(rule "disjointDefinition" (formula "21"))
+ (builtin "One Step Simplification" (formula "21"))
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+ (builtin "One Step Simplification" (formula "19"))
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+(rule "disjointDefinition" (formula "19"))
+ (builtin "One Step Simplification" (formula "19"))
+(rule "notLeft" (formula "19"))
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+(rule "disjointDefinition" (formula "26"))
+(rule "inEqSimp_commuteLeq" (formula "17"))
+(rule "disjointArrayRanges" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "notLeft" (formula "26"))
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+(rule "assignment" (formula "33") (term "1"))
+ (builtin "One Step Simplification" (formula "33"))
+(rule "commute_and" (formula "27") (term "1,1"))
+(rule "cnf_rightDist" (formula "27") (term "1"))
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+(rule "methodBodyExpand" (formula "33") (term "1") (newnames "heapBefore_distribute,savedHeapBefore_distribute"))
+ (builtin "One Step Simplification" (formula "33"))
+ (builtin "Block Contract (Internal)" (formula "33") (newnames "exc_103,heap_Before_BLOCK,savedHeap_Before_BLOCK,o,f"))
+(branch "Validity"
+ (builtin "One Step Simplification" (formula "34"))
+ (builtin "One Step Simplification" (formula "27") (ifInst "" (formula "15")) (ifInst "" (formula "1")) (ifInst "" (formula "32")) (ifInst "" (formula "2")) (ifInst "" (formula "3")))
+ (rule "true_left" (formula "27"))
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+ (rule "methodCallEmpty" (formula "33") (term "1"))
+ (rule "emptyModality" (formula "33") (term "1"))
+ (rule "andRight" (formula "33"))
+ (branch
+ (builtin "One Step Simplification" (formula "33"))
+ (rule "closeTrue" (formula "33"))
+ )
+ (branch
+ (builtin "One Step Simplification" (formula "33"))
+ (rule "closeTrue" (formula "33"))
+ )
+)
+(branch "Precondition"
+ (rule "andRight" (formula "33"))
+ (branch
+ (rule "andRight" (formula "33"))
+ (branch
+ (builtin "One Step Simplification" (formula "33") (ifInst "" (formula "15")))
+ (rule "closeTrue" (formula "33"))
+ )
+ (branch
+ (builtin "One Step Simplification" (formula "33") (ifInst "" (formula "1")))
+ (rule "closeTrue" (formula "33"))
+ )
+ )
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+ (rule "andRight" (formula "33"))
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+ (rule "andRight" (formula "33"))
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+ (builtin "One Step Simplification" (formula "33") (ifInst "" (formula "31")))
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+ )
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+ )
+ )
+ (branch
+ (builtin "One Step Simplification" (formula "33") (ifInst "" (formula "3")))
+ (rule "closeTrue" (formula "33"))
+ )
+ )
+)
+(branch "Usage"
+ (builtin "One Step Simplification" (formula "34"))
+ (builtin "One Step Simplification" (formula "27"))
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+ (rule "times_zero_1" (formula "29") (term "1,0,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "29") (term "0,0,0,0,0,0"))
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+ (rule "andLeft" (formula "23"))
+ (rule "inEqSimp_commuteLeq" (formula "24"))
+ (rule "applyEq" (formula "23") (term "0") (ifseqformula "25"))
+ (rule "leq_literals" (formula "23"))
+ (rule "closeFalse" (formula "23"))
+ )
+ )
+ )
+ )
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__flush(int,(I,int,int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__flush(int,(I,int,int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..0d4e608
--- /dev/null
+++ b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__flush(int,(I,int,int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,1229 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Thu Jun 02 20:22:14 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Thu Jun 02 20:22:14 CEST 2022
+contract=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:flush(int,[I,int,int)].JML normal_behavior operation contract.0
+name=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:flush(int,[I,int,int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "846")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre_0,o,f"))
+(rule "expand_inInt" (formula "1") (term "0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "notLeft" (formula "7"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "9"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "12"))
+(rule "andLeft" (formula "14"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "15"))
+(rule "andLeft" (formula "19"))
+(rule "notLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "19"))
+(rule "andLeft" (formula "21"))
+(rule "andLeft" (formula "19"))
+(rule "translateJavaSubInt" (formula "22") (term "0"))
+(rule "replace_known_right" (formula "6") (term "0") (ifseqformula "25"))
+ (builtin "One Step Simplification" (formula "6"))
+(rule "polySimp_elimSub" (formula "22") (term "0"))
+(rule "disjointDefinition" (formula "17"))
+ (builtin "One Step Simplification" (formula "17"))
+(rule "notLeft" (formula "17"))
+(rule "eqSymm" (formula "23"))
+(rule "disjointDefinition" (formula "15"))
+ (builtin "One Step Simplification" (formula "15"))
+(rule "notLeft" (formula "15"))
+(rule "eqSymm" (formula "22"))
+(rule "disjointDefinition" (formula "15"))
+ (builtin "One Step Simplification" (formula "15"))
+(rule "notLeft" (formula "15"))
+(rule "eqSymm" (formula "21"))
+(rule "inEqSimp_commuteLeq" (formula "13"))
+(rule "inEqSimp_commuteLeq" (formula "10"))
+(rule "inEqSimp_commuteLeq" (formula "8"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "inEqSimp_commuteLeq" (formula "18"))
+(rule "inEqSimp_commuteLeq" (formula "16"))
+(rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodBodyExpand" (formula "26") (term "1") (newnames "heapBefore_flush,savedHeapBefore_flush"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "variableDeclarationAssign" (formula "26") (term "1"))
+(rule "variableDeclaration" (formula "26") (term "1") (newnames "buffer_offset"))
+(rule "assignmentMultiplicationInt" (formula "26") (term "1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "26"))
+ (rule "expand_inInt" (formula "26"))
+ (rule "replace_int_MIN" (formula "26") (term "0,1"))
+ (rule "replace_int_MAX" (formula "26") (term "1,0"))
+ (rule "inEqSimp_ltToLeq" (formula "14"))
+ (rule "polySimp_mulComm0" (formula "14") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "14") (term "0"))
+ (rule "inEqSimp_commuteLeq" (formula "26") (term "1"))
+ (rule "inEqSimp_homoInEq1" (formula "19"))
+ (rule "polySimp_mulComm0" (formula "19") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "19") (term "1,0"))
+ (rule "polySimp_mulLiterals" (formula "19") (term "1,1,0"))
+ (rule "polySimp_elimOne" (formula "19") (term "1,1,0"))
+ (rule "polySimp_mulComm0" (formula "19") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "19") (term "0"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "14"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "0"))
+ (rule "polySimp_elimOne" (formula "14") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "19"))
+ (rule "polySimp_mulComm0" (formula "19") (term "1"))
+ (rule "polySimp_rightDist" (formula "19") (term "1"))
+ (rule "mul_literals" (formula "19") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "19") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "19") (term "1,1"))
+ (rule "inEqSimp_subsumption6" (formula "26") (term "1") (ifseqformula "13"))
+ (rule "times_zero_1" (formula "26") (term "1,1,0,1"))
+ (rule "greater_literals" (formula "26") (term "0,0,1"))
+ (builtin "One Step Simplification" (formula "26"))
+ (rule "leq_literals" (formula "26") (term "0,1"))
+ (builtin "One Step Simplification" (formula "26"))
+ (rule "inEqSimp_leqRight" (formula "26"))
+ (rule "mul_literals" (formula "1") (term "1,0,0"))
+ (rule "add_literals" (formula "1") (term "0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "1"))
+ (rule "mul_literals" (formula "1") (term "1"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "14"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "inEqSimp_subsumption0" (formula "17") (ifseqformula "19"))
+ (rule "inEqSimp_homoInEq0" (formula "17") (term "0"))
+ (rule "polySimp_mulComm0" (formula "17") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "17") (term "1,0,0"))
+ (rule "mul_literals" (formula "17") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "17") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "17") (term "0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "17") (term "0,0"))
+ (rule "add_literals" (formula "17") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "17") (term "1,0,0"))
+ (rule "add_literals" (formula "17") (term "0,0"))
+ (rule "qeq_literals" (formula "17") (term "0"))
+ (builtin "One Step Simplification" (formula "17"))
+ (rule "true_left" (formula "17"))
+ (rule "inEqSimp_subsumption1" (formula "8") (ifseqformula "16"))
+ (rule "leq_literals" (formula "8") (term "0"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "true_left" (formula "8"))
+ (rule "elimGcdGeq_antec" (formula "1") (inst "elimGcdRightDiv=Z(8(0(6(8(8(3(8(#))))))))") (inst "elimGcdLeftDiv=bucket") (inst "elimGcd=Z(6(5(2(#))))"))
+ (rule "mul_literals" (formula "1") (term "0,1,0,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,1,0"))
+ (rule "leq_literals" (formula "1") (term "0,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "mul_literals" (formula "1") (term "1,0,0,0,0,0"))
+ (rule "polySimp_addLiterals" (formula "1") (term "0,0,0,0"))
+ (rule "add_zero_right" (formula "1") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "1") (term "0,0"))
+ (rule "add_literals" (formula "1") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "1") (term "1,0,0"))
+ (rule "add_literals" (formula "1") (term "0,0"))
+ (rule "leq_literals" (formula "1") (term "0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_subsumption1" (formula "12") (ifseqformula "1"))
+ (rule "leq_literals" (formula "12") (term "0"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "true_left" (formula "12"))
+ (rule "inEqSimp_exactShadow3" (formula "14") (ifseqformula "16"))
+ (rule "times_zero_1" (formula "14") (term "0,0"))
+ (rule "add_zero_left" (formula "14") (term "0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "14"))
+ (rule "mul_literals" (formula "14") (term "1"))
+ (rule "inEqSimp_subsumption1" (formula "9") (ifseqformula "14"))
+ (rule "leq_literals" (formula "9") (term "0"))
+ (builtin "One Step Simplification" (formula "9"))
+ (rule "true_left" (formula "9"))
+ (rule "Contract_axiom_for_bufferLen_in_Buffers" (formula "12") (term "0"))
+ (builtin "One Step Simplification" (formula "12") (ifInst "" (formula "10")) (ifInst "" (formula "2")) (ifInst "" (formula "3")) (ifInst "" (formula "22")) (ifInst "" (formula "10")) (ifInst "" (formula "18")))
+ (rule "inEqSimp_ltToLeq" (formula "12") (term "1,0"))
+ (rule "polySimp_mulComm0" (formula "12") (term "1,0,0,1,0"))
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+ (rule "qeq_literals" (formula "12") (term "0,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "applyEq" (formula "12") (term "0,1") (ifseqformula "13"))
+ (rule "leq_literals" (formula "12") (term "1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "true_left" (formula "12"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Buffers" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "notLeft" (formula "11"))
+ (rule "notLeft" (formula "10"))
+ (rule "Definition_axiom_for_bufferLen_in_de_wiesler_Buffers" (formula "11") (term "0"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Buffers" (formula "16") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "16"))
+ (rule "expand_inInt" (formula "16") (term "1,0,0,1"))
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+ (rule "qeq_literals" (formula "9") (term "0"))
+ (builtin "One Step Simplification" (formula "9"))
+ (rule "closeFalse" (formula "9"))
+)
+(branch "Usage"
+ (builtin "One Step Simplification" (formula "26"))
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+ (builtin "One Step Simplification" (formula "26"))
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+ (builtin "One Step Simplification" (formula "26"))
+ (rule "variableDeclarationAssign" (formula "26") (term "1"))
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+ (builtin "One Step Simplification" (formula "26"))
+ (rule "variableDeclarationAssign" (formula "26") (term "1"))
+ (rule "variableDeclaration" (formula "26") (term "1") (newnames "var_4"))
+ (rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+ (builtin "Use Operation Contract" (formula "26") (newnames "heapBefore_copy_nonoverlapping,exc_129,heapAfter_copy_nonoverlapping,anon_heap_copy_nonoverlapping") (contract "de.wiesler.Functions[de.wiesler.Functions::copy_nonoverlapping([I,int,[I,int,int)].JML normal_behavior operation contract.0"))
+ (branch "Post (copy_nonoverlapping)"
+ (builtin "One Step Simplification" (formula "22"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "expand_inInt" (formula "22") (term "1,0,0,0,1,0,1"))
+ (rule "expand_inInt" (formula "22") (term "0,0,1,1,0,1"))
+ (rule "replace_int_MIN" (formula "22") (term "0,1,1,0,0,0,1,0,1"))
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+ (rule "andLeft" (formula "22"))
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+ (rule "andLeft" (formula "23"))
+ (rule "translateJavaSubInt" (formula "22") (term "2,1,0"))
+ (rule "translateJavaAddInt" (formula "23") (term "0,2,0,1,0"))
+ (rule "translateJavaAddInt" (formula "23") (term "0,2,1,1,0"))
+ (rule "translateJavaAddInt" (formula "24") (term "3,1,1,0"))
+ (rule "translateJavaAddInt" (formula "24") (term "3,0,1,0"))
+ (rule "translateJavaAddInt" (formula "22") (term "0,2,1,0"))
+ (rule "eqSymm" (formula "24") (term "1,0"))
+ (rule "polySimp_elimSub" (formula "22") (term "2,1,0"))
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+ (rule "polySimp_addLiterals" (formula "22") (term "2,1,0"))
+ (rule "polySimp_addComm0" (formula "24") (term "3,0,1,0"))
+ (rule "polySimp_addComm0" (formula "24") (term "3,1,1,0"))
+ (rule "polySimp_addComm0" (formula "22") (term "2,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "24") (term "1,0,0"))
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+ (rule "inEqSimp_commuteLeq" (formula "23") (term "1,1,0,0"))
+ (rule "blockEmpty" (formula "31") (term "1"))
+ (rule "eval_order_array_access1" (formula "31") (term "1") (inst "#v0=x_arr"))
+ (rule "variableDeclarationAssign" (formula "31") (term "1"))
+ (rule "variableDeclaration" (formula "31") (term "1") (newnames "x_arr"))
+ (rule "assignment_read_attribute_this_final" (formula "31"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "assignment_to_primitive_array_component" (formula "31"))
+ (branch "Normal Execution (x_arr != null)"
+ (builtin "One Step Simplification" (formula "31"))
+ (builtin "Block Contract (Internal)" (formula "31") (newnames "exc_130,heap_Before_BLOCK,savedHeap_Before_BLOCK,o,f"))
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+ (rule "inEqSimp_homoInEq0" (formula "16") (term "0"))
+ (rule "polySimp_mulComm0" (formula "16") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "16") (term "1,0,0"))
+ (rule "mul_literals" (formula "16") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "16") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "16") (term "0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "16") (term "0,0"))
+ (rule "add_literals" (formula "16") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "16") (term "1,0,0"))
+ (rule "add_zero_right" (formula "16") (term "0,0"))
+ (rule "qeq_literals" (formula "16") (term "0"))
+ (builtin "One Step Simplification" (formula "16"))
+ (rule "true_left" (formula "16"))
+ (rule "inEqSimp_subsumption1" (formula "5") (ifseqformula "12"))
+ (rule "leq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "true_left" (formula "5"))
+ (rule "elimGcdLeq" (formula "23") (term "1,1") (inst "elimGcdRightDiv=Z(7(0(6(8(8(3(8(#))))))))") (inst "elimGcdLeftDiv=bucket") (inst "elimGcd=Z(6(5(2(#))))"))
+ (rule "polySimp_mulLiterals" (formula "23") (term "1,0,1,0,1,1"))
+ (rule "polySimp_mulLiterals" (formula "23") (term "0,0,0,0,1,0,1,1"))
+ (rule "polySimp_mulLiterals" (formula "23") (term "1,0,0,0,0,0,0,1,1"))
+ (rule "sub_literals" (formula "23") (term "0,0,0,0,0,0,0,1,1"))
+ (rule "polySimp_mulLiterals" (formula "23") (term "1,0,0,0,1,1"))
+ (rule "mul_literals" (formula "23") (term "0,0,0,0,1,0,1,1"))
+ (rule "mul_literals" (formula "23") (term "1,0,0,0,0,0,0,1,1"))
+ (rule "add_literals" (formula "23") (term "0,0,0,1,0,1,1"))
+ (rule "polySimp_addLiterals" (formula "23") (term "0,0,0,0,0,1,1"))
+ (rule "add_literals" (formula "23") (term "0,0,0,0,0,1,1"))
+ (rule "add_zero_left" (formula "23") (term "0,0,0,0,1,1"))
+ (rule "polySimp_pullOutFactor0b" (formula "23") (term "0,1,0,1,1"))
+ (rule "add_literals" (formula "23") (term "1,1,0,1,0,1,1"))
+ (rule "times_zero_1" (formula "23") (term "1,0,1,0,1,1"))
+ (rule "add_zero_right" (formula "23") (term "0,1,0,1,1"))
+ (rule "qeq_literals" (formula "23") (term "1,0,1,1"))
+ (builtin "One Step Simplification" (formula "23"))
+ (rule "polySimp_pullOutFactor0" (formula "23") (term "0,0,1,1"))
+ (rule "add_literals" (formula "23") (term "1,0,0,1,1"))
+ (rule "times_zero_1" (formula "23") (term "0,0,1,1"))
+ (rule "leq_literals" (formula "23") (term "0,1,1"))
+ (builtin "One Step Simplification" (formula "23"))
+ (rule "inEqSimp_exactShadow3" (formula "14") (ifseqformula "16"))
+ (rule "times_zero_1" (formula "14") (term "0,0"))
+ (rule "add_zero_left" (formula "14") (term "0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "14"))
+ (rule "mul_literals" (formula "14") (term "1"))
+ (rule "inEqSimp_subsumption1" (formula "8") (ifseqformula "14"))
+ (rule "leq_literals" (formula "8") (term "0"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "true_left" (formula "8"))
+ (rule "Contract_axiom_for_bufferLen_in_Buffers" (formula "12") (term "0"))
+ (builtin "One Step Simplification" (formula "12") (ifInst "" (formula "9")) (ifInst "" (formula "1")) (ifInst "" (formula "2")) (ifInst "" (formula "22")) (ifInst "" (formula "9")) (ifInst "" (formula "18")))
+ (rule "inEqSimp_ltToLeq" (formula "12") (term "1,0"))
+ (rule "polySimp_mulComm0" (formula "12") (term "1,0,0,1,0"))
+ (rule "polySimp_addComm1" (formula "12") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "12") (term "0,0"))
+ (rule "replace_known_left" (formula "12") (term "0,0") (ifseqformula "10"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "inEqSimp_commuteLeq" (formula "12") (term "0,1"))
+ (rule "applyEq" (formula "12") (term "0,1,1") (ifseqformula "13"))
+ (rule "leq_literals" (formula "12") (term "1,1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "applyEq" (formula "12") (term "0,1") (ifseqformula "13"))
+ (rule "qeq_literals" (formula "12") (term "1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "true_left" (formula "12"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Buffers" (formula "17") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "17"))
+ (rule "expand_inInt" (formula "17") (term "1,0,0,1"))
+ (rule "replace_int_MIN" (formula "17") (term "0,1,1,0,0,1"))
+ (rule "replace_int_MAX" (formula "17") (term "1,0,1,0,0,1"))
+ (rule "andLeft" (formula "17"))
+ (rule "andLeft" (formula "17"))
+ (rule "andLeft" (formula "18"))
+ (rule "andLeft" (formula "17"))
+ (rule "andLeft" (formula "17"))
+ (rule "notLeft" (formula "17"))
+ (rule "translateJavaMulInt" (formula "17") (term "1"))
+ (rule "mul_literals" (formula "17") (term "1"))
+ (rule "eqSymm" (formula "22"))
+ (rule "inEqSimp_ltToLeq" (formula "21") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "21") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "19"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "21") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "21") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "21") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "21") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "21") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "21") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_exactShadow3" (formula "11") (ifseqformula "20"))
+ (rule "polySimp_rightDist" (formula "11") (term "0,0"))
+ (rule "mul_literals" (formula "11") (term "0,0,0"))
+ (rule "polySimp_addComm1" (formula "11") (term "0"))
+ (rule "add_literals" (formula "11") (term "0,0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "11"))
+ (rule "polySimp_mulLiterals" (formula "11") (term "0"))
+ (rule "polySimp_elimOne" (formula "11") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "4") (ifseqformula "11"))
+ (rule "leq_literals" (formula "4") (term "0"))
+ (builtin "One Step Simplification" (formula "4"))
+ (rule "true_left" (formula "4"))
+ (rule "inEqSimp_subsumption0" (formula "27") (term "1,1") (ifseqformula "10"))
+ (rule "leq_literals" (formula "27") (term "0,1,1"))
+ (builtin "One Step Simplification" (formula "27"))
+ (rule "nnf_imp2or" (formula "21") (term "0"))
+ (rule "nnf_notAnd" (formula "21") (term "0,0"))
+ (rule "nnf_notAnd" (formula "21") (term "1,0,0"))
+ (rule "inEqSimp_notLeq" (formula "21") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "21") (term "1,0,0,0,1,0,0"))
+ (rule "add_literals" (formula "21") (term "0,0,0,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "21") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "21") (term "1,0,1,0,0"))
+ (rule "inEqSimp_notGeq" (formula "21") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "21") (term "1,0,0,1,1,0,0"))
+ (rule "add_literals" (formula "21") (term "0,0,1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "21") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "21") (term "1,1,1,0,0"))
+ (rule "nnf_notAnd" (formula "21") (term "0,0,0"))
+ (rule "inEqSimp_notGeq" (formula "21") (term "0,0,0,0"))
+ (rule "times_zero_1" (formula "21") (term "1,0,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "21") (term "0,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "21") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "21") (term "1,0,0,0,0"))
+ (rule "inEqSimp_notLeq" (formula "21") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "21") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "21") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "21") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "21") (term "0,0,0,1,0,0,0"))
+ (rule "add_zero_left" (formula "21") (term "0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "21") (term "1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "21") (term "1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "21") (term "1,1,0,0,0"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Buffers" (formula "8"))
+ (rule "andLeft" (formula "8"))
+ (rule "notLeft" (formula "9"))
+ (rule "notLeft" (formula "8"))
+ (rule "replace_known_right" (formula "28") (term "0,1") (ifseqformula "21"))
+ (builtin "One Step Simplification" (formula "28") (ifInst "" (formula "21")))
+ (rule "Definition_axiom_for_bufferLen_in_de_wiesler_Buffers" (formula "11") (term "0"))
+ (rule "commute_or_2" (formula "20") (term "0,0"))
+ (rule "commute_or" (formula "20") (term "1,0,0,0"))
+ (rule "shift_paren_or" (formula "20") (term "0,0,0"))
+ (rule "cnf_rightDist" (formula "20") (term "0"))
+ (rule "distr_forallAnd" (formula "20"))
+ (rule "andLeft" (formula "20"))
+ (rule "commute_or" (formula "21") (term "0"))
+ (rule "commute_or" (formula "20") (term "0,0,0,0"))
+ (rule "inEqSimp_or_subsumption0" (formula "20") (term "0,0,0,0"))
+ (rule "qeq_literals" (formula "20") (term "0,0,0,0,0,0"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "commute_or" (formula "21") (term "0,0,0,0"))
+ (rule "inEqSimp_or_subsumption0" (formula "21") (term "0,0,0,0"))
+ (rule "qeq_literals" (formula "21") (term "0,0,0,0,0,0"))
+ (builtin "One Step Simplification" (formula "21"))
+ (rule "arrayLengthNotNegative" (formula "14") (term "0"))
+ (rule "arrayLengthIsAShort" (formula "15") (term "0"))
+ (rule "expand_inShort" (formula "15"))
+ (rule "replace_short_MAX" (formula "15") (term "1,0"))
+ (rule "replace_short_MIN" (formula "15") (term "0,1"))
+ (rule "andLeft" (formula "15"))
+ (rule "inEqSimp_commuteLeq" (formula "16"))
+ (rule "inEqSimp_subsumption1" (formula "16") (ifseqformula "14"))
+ (rule "leq_literals" (formula "16") (term "0"))
+ (builtin "One Step Simplification" (formula "16"))
+ (rule "true_left" (formula "16"))
+ (rule "inEqSimp_exactShadow3" (formula "16") (ifseqformula "15"))
+ (rule "polySimp_mulComm0" (formula "16") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "16") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "16"))
+ (rule "polySimp_mulLiterals" (formula "16") (term "0"))
+ (rule "polySimp_elimOne" (formula "16") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "6") (ifseqformula "16"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "arrayLengthIsAShort" (formula "19") (term "0"))
+ (rule "expand_inShort" (formula "19"))
+ (rule "replace_short_MAX" (formula "19") (term "1,0"))
+ (rule "replace_short_MIN" (formula "19") (term "0,1"))
+ (rule "andLeft" (formula "19"))
+ (rule "inEqSimp_commuteLeq" (formula "20"))
+ (rule "applyEq" (formula "20") (term "0") (ifseqformula "21"))
+ (rule "qeq_literals" (formula "20"))
+ (rule "true_left" (formula "20"))
+ (rule "applyEq" (formula "19") (term "0") (ifseqformula "20"))
+ (rule "leq_literals" (formula "19"))
+ (rule "true_left" (formula "19"))
+ (rule "arrayLengthNotNegative" (formula "19") (term "0"))
+ (rule "applyEq" (formula "19") (term "0") (ifseqformula "20"))
+ (rule "qeq_literals" (formula "19"))
+ (rule "true_left" (formula "19"))
+ (rule "arrayLengthNotNegative" (formula "18") (term "0"))
+ (rule "applyEq" (formula "18") (term "0") (ifseqformula "19"))
+ (rule "qeq_literals" (formula "18"))
+ (rule "true_left" (formula "18"))
+ (rule "arrayLengthIsAShort" (formula "18") (term "0"))
+ (rule "expand_inShort" (formula "18"))
+ (rule "replace_short_MAX" (formula "18") (term "1,0"))
+ (rule "replace_short_MIN" (formula "18") (term "0,1"))
+ (rule "andLeft" (formula "18"))
+ (rule "inEqSimp_commuteLeq" (formula "19"))
+ (rule "applyEq" (formula "18") (term "0") (ifseqformula "20"))
+ (rule "leq_literals" (formula "18"))
+ (rule "closeFalse" (formula "18"))
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__len(int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__len(int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..a3d71ee
--- /dev/null
+++ b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__len(int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,276 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Thu Jun 02 20:22:34 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Thu Jun 02 20:22:34 CEST 2022
+contract=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:len(int)].JML normal_behavior operation contract.0
+name=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:len(int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "100")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre_0,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "2"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "inEqSimp_commuteLeq" (formula "8"))
+(rule "assignment" (formula "12") (term "1"))
+ (builtin "One Step Simplification" (formula "12"))
+(rule "methodBodyExpand" (formula "12") (term "1") (newnames "heapBefore_len,savedHeapBefore_len"))
+ (builtin "One Step Simplification" (formula "12"))
+(rule "returnUnfold" (formula "12") (term "1") (inst "#v0=x"))
+(rule "variableDeclarationAssign" (formula "12") (term "1"))
+(rule "variableDeclaration" (formula "12") (term "1") (newnames "x"))
+(rule "eval_order_array_access4" (formula "12") (term "1") (inst "#v0=x_arr"))
+(rule "variableDeclarationAssign" (formula "12") (term "1"))
+(rule "variableDeclaration" (formula "12") (term "1") (newnames "x_arr"))
+(rule "assignment_read_attribute_this_final" (formula "12"))
+ (builtin "One Step Simplification" (formula "12"))
+(rule "assignment_array2" (formula "12"))
+(branch "Normal Execution (x_arr != null)"
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "methodCallReturn" (formula "12") (term "1"))
+ (rule "assignment" (formula "12") (term "1"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "methodCallEmpty" (formula "12") (term "1"))
+ (rule "tryEmpty" (formula "12") (term "1"))
+ (rule "emptyModality" (formula "12") (term "1"))
+ (rule "andRight" (formula "12"))
+ (branch "Case 1"
+ (builtin "One Step Simplification" (formula "12") (ifInst "" (formula "7")))
+ (rule "closeTrue" (formula "12"))
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "closeTrue" (formula "12"))
+ )
+)
+(branch "Null Reference (x_arr = null)"
+ (rule "false_right" (formula "13"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_ltToLeq" (formula "10"))
+ (rule "polySimp_mulComm0" (formula "10") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "10") (term "0"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "10"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "0"))
+ (rule "polySimp_elimOne" (formula "10") (term "0"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "9"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Buffers" (formula "10") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "expand_inInt" (formula "10") (term "1,0,0,1"))
+ (rule "replace_int_MAX" (formula "10") (term "1,0,1,0,0,1"))
+ (rule "replace_int_MIN" (formula "10") (term "0,1,1,0,0,1"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "notLeft" (formula "10"))
+ (rule "translateJavaMulInt" (formula "10") (term "1"))
+ (rule "mul_literals" (formula "10") (term "1"))
+ (rule "eqSymm" (formula "15"))
+ (rule "inEqSimp_ltToLeq" (formula "14") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "14") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "12"))
+ (rule "applyEq" (formula "14") (term "1,0,0,1,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "15") (term "0") (ifseqformula "1"))
+ (rule "eqSymm" (formula "15"))
+ (rule "applyEq" (formula "11") (term "0,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "14") (term "1,0,1,1,0") (ifseqformula "1"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "14") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "14") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "14") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "14") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "14") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_exactShadow3" (formula "9") (ifseqformula "13"))
+ (rule "polySimp_rightDist" (formula "9") (term "0,0"))
+ (rule "mul_literals" (formula "9") (term "0,0,0"))
+ (rule "polySimp_addComm1" (formula "9") (term "0"))
+ (rule "add_literals" (formula "9") (term "0,0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "9"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "0"))
+ (rule "polySimp_elimOne" (formula "9") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "5") (ifseqformula "9"))
+ (rule "leq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "true_left" (formula "5"))
+ (rule "nnf_imp2or" (formula "14") (term "0"))
+ (rule "nnf_notAnd" (formula "14") (term "0,0"))
+ (rule "nnf_notAnd" (formula "14") (term "1,0,0"))
+ (rule "inEqSimp_notGeq" (formula "14") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "14") (term "1,0,0,1,1,0,0"))
+ (rule "add_literals" (formula "14") (term "0,0,1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "14") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "14") (term "1,1,1,0,0"))
+ (rule "inEqSimp_notLeq" (formula "14") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "14") (term "1,0,0,0,1,0,0"))
+ (rule "add_literals" (formula "14") (term "0,0,0,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "14") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "14") (term "1,0,1,0,0"))
+ (rule "nnf_notAnd" (formula "14") (term "0,0,0"))
+ (rule "inEqSimp_notLeq" (formula "14") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "14") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "14") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "14") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "14") (term "0,0,0,1,0,0,0"))
+ (rule "add_zero_left" (formula "14") (term "0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "14") (term "1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "14") (term "1,1,0,0,0"))
+ (rule "inEqSimp_notGeq" (formula "14") (term "0,0,0,0"))
+ (rule "times_zero_1" (formula "14") (term "1,0,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "14") (term "0,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "14") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "14") (term "1,0,0,0,0"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Buffers" (formula "6"))
+ (rule "andLeft" (formula "6"))
+ (rule "notLeft" (formula "7"))
+ (rule "close" (formula "15") (ifseqformula "1"))
+)
+(branch "Index Out of Bounds (x_arr != null, but _bucket Out of Bounds!)"
+ (rule "false_right" (formula "13"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "andLeft" (formula "1"))
+ (rule "notLeft" (formula "1"))
+ (rule "inEqSimp_ltToLeq" (formula "10"))
+ (rule "polySimp_mulComm0" (formula "10") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "10") (term "0"))
+ (rule "inEqSimp_ltToLeq" (formula "1") (term "1"))
+ (rule "times_zero_1" (formula "1") (term "1,0,0,1"))
+ (rule "add_zero_right" (formula "1") (term "0,0,1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "10"))
+ (rule "polySimp_mulLiterals" (formula "10") (term "0"))
+ (rule "polySimp_elimOne" (formula "10") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "1") (term "1"))
+ (rule "mul_literals" (formula "1") (term "1,1"))
+ (rule "inEqSimp_contradInEq1" (formula "1") (term "1") (ifseqformula "9"))
+ (rule "qeq_literals" (formula "1") (term "0,1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "9"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Buffers" (formula "10") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "expand_inInt" (formula "10") (term "1,0,0,1"))
+ (rule "replace_int_MAX" (formula "10") (term "1,0,1,0,0,1"))
+ (rule "replace_int_MIN" (formula "10") (term "0,1,1,0,0,1"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "11"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "notLeft" (formula "10"))
+ (rule "translateJavaMulInt" (formula "10") (term "1"))
+ (rule "mul_literals" (formula "10") (term "1"))
+ (rule "eqSymm" (formula "15"))
+ (rule "inEqSimp_ltToLeq" (formula "14") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "14") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "12"))
+ (rule "applyEq" (formula "1") (term "0") (ifseqformula "11"))
+ (rule "inEqSimp_commuteLeq" (formula "1"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "14") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "14") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "14") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "14") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "14") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_subsumption1" (formula "8") (ifseqformula "1"))
+ (rule "leq_literals" (formula "8") (term "0"))
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "true_left" (formula "8"))
+ (rule "inEqSimp_exactShadow3" (formula "8") (ifseqformula "12"))
+ (rule "polySimp_rightDist" (formula "8") (term "0,0"))
+ (rule "mul_literals" (formula "8") (term "0,0,0"))
+ (rule "polySimp_addComm1" (formula "8") (term "0"))
+ (rule "add_literals" (formula "8") (term "0,0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "8"))
+ (rule "polySimp_mulLiterals" (formula "8") (term "0"))
+ (rule "polySimp_elimOne" (formula "8") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "5") (ifseqformula "8"))
+ (rule "leq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "true_left" (formula "5"))
+ (rule "inEqSimp_contradInEq0" (formula "1") (ifseqformula "7"))
+ (rule "qeq_literals" (formula "1") (term "0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "closeFalse" (formula "1"))
+)
+)
+}
diff --git a/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__push(int,int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__push(int,int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..bc1c832
--- /dev/null
+++ b/src/main/key-overflow/Buffers/de.wiesler.Buffers(de.wiesler.Buffers__push(int,int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,1590 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Sun Jun 05 14:42:03 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Sun Jun 05 14:42:03 CEST 2022
+contract=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:push(int,int)].JML normal_behavior operation contract.0
+name=de.wiesler.Buffers[de.wiesler.Buffers\\:\\:push(int,int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "2299")
+
+(branch "dummy ID"
+(rule "eqSymm" (formula "1") (term "1,0,0,1,0,1,1"))
+(rule "assignment" (formula "1") (term "1,1"))
+(rule "methodBodyExpand" (formula "1") (term "1,1,1") (newnames "heapBefore_push,savedHeapBefore_push,_valueBefore_push,_valueBefore_push_0"))
+(rule "assignment" (formula "1") (term "1,1,1,1"))
+(rule "blockEmpty" (formula "1") (term "1,1,1,1,1"))
+(rule "variableDeclarationAssign" (formula "1") (term "1,1,1,1,1"))
+(rule "variableDeclaration" (formula "1") (term "1,1,1,1,1") (newnames "buffer_offset"))
+(rule "assignmentMultiplicationInt" (formula "1") (term "1,1,1,1,1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "expand_inInt" (formula "1") (term "1"))
+ (rule "expand_inInt" (formula "1") (term "0,1,0,0,0"))
+ (rule "expand_inInt" (formula "1") (term "1,1,0,0,0"))
+ (rule "replace_int_MAX" (formula "1") (term "1,0,1"))
+ (rule "replace_int_MIN" (formula "1") (term "0,1,1"))
+ (rule "replace_int_MIN" (formula "1") (term "0,1,0,1,0,0,0"))
+ (rule "replace_int_MAX" (formula "1") (term "1,0,0,1,0,0,0"))
+ (rule "replace_int_MAX" (formula "1") (term "1,0,1,1,0,0,0"))
+ (rule "replace_int_MIN" (formula "1") (term "0,1,1,1,0,0,0"))
+ (rule "impRight" (formula "1"))
+ (rule "andLeft" (formula "1"))
+ (rule "andLeft" (formula "1"))
+ (rule "andLeft" (formula "3"))
+ (rule "andLeft" (formula "1"))
+ (rule "andLeft" (formula "5"))
+ (rule "andLeft" (formula "1"))
+ (rule "andLeft" (formula "3"))
+ (rule "andLeft" (formula "7"))
+ (rule "andLeft" (formula "9"))
+ (rule "andLeft" (formula "1"))
+ (rule "andLeft" (formula "4"))
+ (rule "andLeft" (formula "6"))
+ (rule "notLeft" (formula "12"))
+ (rule "andLeft" (formula "1"))
+ (rule "notLeft" (formula "2"))
+ (rule "inEqSimp_ltToLeq" (formula "11"))
+ (rule "polySimp_mulComm0" (formula "11") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "11") (term "0"))
+ (rule "inEqSimp_commuteLeq" (formula "15") (term "1"))
+ (rule "inEqSimp_commuteLeq" (formula "10"))
+ (rule "inEqSimp_commuteLeq" (formula "5"))
+ (rule "inEqSimp_commuteLeq" (formula "7"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "11"))
+ (rule "polySimp_mulLiterals" (formula "11") (term "0"))
+ (rule "polySimp_elimOne" (formula "11") (term "0"))
+ (rule "inEqSimp_subsumption6" (formula "15") (term "1") (ifseqformula "10"))
+ (rule "times_zero_1" (formula "15") (term "1,1,0,1"))
+ (rule "greater_literals" (formula "15") (term "0,0,1"))
+ (builtin "One Step Simplification" (formula "15"))
+ (rule "leq_literals" (formula "15") (term "0,1"))
+ (builtin "One Step Simplification" (formula "15"))
+ (rule "inEqSimp_leqRight" (formula "15"))
+ (rule "mul_literals" (formula "1") (term "1,0,0"))
+ (rule "add_literals" (formula "1") (term "0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "1"))
+ (rule "mul_literals" (formula "1") (term "1"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "11"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "elimGcdGeq_antec" (formula "1") (inst "elimGcdRightDiv=Z(8(0(6(8(8(3(8(#))))))))") (inst "elimGcdLeftDiv=bucket") (inst "elimGcd=Z(6(5(2(#))))"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0,1,0"))
+ (rule "leq_literals" (formula "1") (term "0,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "mul_literals" (formula "1") (term "1,0,0,0,0,0"))
+ (rule "polySimp_addLiterals" (formula "1") (term "0,0,0,0"))
+ (rule "add_zero_right" (formula "1") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "1") (term "0,0"))
+ (rule "add_literals" (formula "1") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "1") (term "1,0,0"))
+ (rule "add_zero_right" (formula "1") (term "0,0"))
+ (rule "leq_literals" (formula "1") (term "0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_subsumption1" (formula "10") (ifseqformula "1"))
+ (rule "leq_literals" (formula "10") (term "0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "true_left" (formula "10"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Buffers" (formula "9"))
+ (rule "andLeft" (formula "9"))
+ (rule "notLeft" (formula "9"))
+ (rule "notLeft" (formula "9"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Buffers" (formula "10") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "expand_inInt" (formula "10") (term "1,0,0,1"))
+ (rule "replace_int_MAX" (formula "10") (term "1,0,1,0,0,1"))
+ (rule "replace_int_MIN" (formula "10") (term "0,1,1,0,0,1"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "10"))
+ (rule "andLeft" (formula "12"))
+ (rule "andLeft" (formula "10"))
+ (rule "notLeft" (formula "10"))
+ (rule "translateJavaMulInt" (formula "10") (term "1"))
+ (rule "mul_literals" (formula "10") (term "1"))
+ (rule "eqSymm" (formula "15"))
+ (rule "inEqSimp_ltToLeq" (formula "14") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "14") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "14") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "12"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "14") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "14") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "14") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "14") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "14") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_exactShadow3" (formula "9") (ifseqformula "13"))
+ (rule "polySimp_rightDist" (formula "9") (term "0,0"))
+ (rule "mul_literals" (formula "9") (term "0,0,0"))
+ (rule "polySimp_addComm1" (formula "9") (term "0"))
+ (rule "add_literals" (formula "9") (term "0,0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "9"))
+ (rule "polySimp_mulLiterals" (formula "9") (term "0"))
+ (rule "polySimp_elimOne" (formula "9") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "5") (ifseqformula "9"))
+ (rule "leq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "true_left" (formula "5"))
+ (rule "inEqSimp_contradInEq0" (formula "1") (ifseqformula "8"))
+ (rule "qeq_literals" (formula "1") (term "0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "closeFalse" (formula "1"))
+)
+(branch "Usage"
+ (rule "translateJavaMulInt" (formula "1") (term "0,0,1,1,1,1,1"))
+ (rule "polySimp_mulComm0" (formula "1") (term "0,0,1,1,1,1,1"))
+ (rule "variableDeclarationAssign" (formula "1") (term "1,1,1,1,1,1"))
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+ (rule "add_zero_right" (formula "1") (term "0,0,1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "12"))
+ (rule "polySimp_mulLiterals" (formula "12") (term "0"))
+ (rule "polySimp_elimOne" (formula "12") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "1") (term "1"))
+ (rule "mul_literals" (formula "1") (term "1,1"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "11"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "inEqSimp_contradInEq1" (formula "1") (term "1") (ifseqformula "10"))
+ (rule "qeq_literals" (formula "1") (term "0,1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "Contract_axiom_for_bufferLen_in_Buffers" (formula "15") (term "0"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "10")) (ifInst "" (formula "3")) (ifInst "" (formula "4")) (ifInst "" (formula "15")) (ifInst "" (formula "10")) (ifInst "" (formula "13")))
+ (rule "inEqSimp_ltToLeq" (formula "1") (term "1,0"))
+ (rule "polySimp_mulComm0" (formula "1") (term "1,0,0,1,0"))
+ (rule "polySimp_addComm1" (formula "1") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "1") (term "0,1"))
+ (rule "inEqSimp_commuteLeq" (formula "1") (term "0,0"))
+ (rule "replace_known_left" (formula "1") (term "0,0") (ifseqformula "11"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "1") (term "0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "0,0"))
+ (rule "polySimp_elimOne" (formula "1") (term "0,0"))
+ (rule "replace_known_left" (formula "1") (term "0") (ifseqformula "12"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "andLeft" (formula "1"))
+ (rule "inEqSimp_strengthen0" (formula "2") (ifseqformula "17"))
+ (rule "add_literals" (formula "2") (term "1"))
+ (rule "inEqSimp_contradEq3" (formula "17") (ifseqformula "2"))
+ (rule "mul_literals" (formula "17") (term "1,0,0"))
+ (rule "add_literals" (formula "17") (term "0,0"))
+ (rule "qeq_literals" (formula "17") (term "0"))
+ (builtin "One Step Simplification" (formula "17"))
+ (rule "false_right" (formula "17"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Buffers" (formula "11"))
+ (rule "andLeft" (formula "11"))
+ (rule "notLeft" (formula "11"))
+ (rule "notLeft" (formula "11"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Buffers" (formula "13") (inst "b=b"))
+ (builtin "One Step Simplification" (formula "13"))
+ (rule "expand_inInt" (formula "13") (term "1,0,0,1"))
+ (rule "replace_int_MAX" (formula "13") (term "1,0,1,0,0,1"))
+ (rule "replace_int_MIN" (formula "13") (term "0,1,1,0,0,1"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "14"))
+ (rule "andLeft" (formula "13"))
+ (rule "andLeft" (formula "13"))
+ (rule "notLeft" (formula "13"))
+ (rule "translateJavaMulInt" (formula "13") (term "1"))
+ (rule "mul_literals" (formula "13") (term "1"))
+ (rule "eqSymm" (formula "18"))
+ (rule "inEqSimp_ltToLeq" (formula "17") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "17") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "17") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "17") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "17") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "15"))
+ (rule "applyEq" (formula "3") (term "0") (ifseqformula "14"))
+ (rule "inEqSimp_commuteLeq" (formula "3"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "17") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "17") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "17") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "17") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "17") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "17") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_subsumption1" (formula "11") (ifseqformula "3"))
+ (rule "leq_literals" (formula "11") (term "0"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "true_left" (formula "11"))
+ (rule "inEqSimp_exactShadow3" (formula "11") (ifseqformula "15"))
+ (rule "polySimp_rightDist" (formula "11") (term "0,0"))
+ (rule "mul_literals" (formula "11") (term "0,0,0"))
+ (rule "polySimp_addComm1" (formula "11") (term "0"))
+ (rule "add_literals" (formula "11") (term "0,0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "11"))
+ (rule "polySimp_mulLiterals" (formula "11") (term "0"))
+ (rule "polySimp_elimOne" (formula "11") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "7") (ifseqformula "11"))
+ (rule "leq_literals" (formula "7") (term "0"))
+ (builtin "One Step Simplification" (formula "7"))
+ (rule "true_left" (formula "7"))
+ (rule "inEqSimp_contradInEq1" (formula "10") (ifseqformula "3"))
+ (rule "qeq_literals" (formula "10") (term "0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "closeFalse" (formula "10"))
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__Classifier((I,(I,int,boolean)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__Classifier((I,(I,int,boolean)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..564a83e
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__Classifier((I,(I,int,boolean)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,4783 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Apr 17 13:09:06 CEST 2023
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L , finalFields-finalFields\\:onHeap
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Apr 17 13:09:06 CEST 2023
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:Classifier([I,[I,int,boolean)].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:Classifier([I,[I,int,boolean)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "2" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "59596")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "4"))
+(rule "notLeft" (formula "4"))
+(rule "notLeft" (formula "4"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
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+(rule "andLeft" (formula "12"))
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+(rule "translateJavaSubInt" (formula "13") (term "0,2,0"))
+(rule "eqSymm" (formula "13"))
+(rule "replace_known_right" (formula "2") (term "0") (ifseqformula "16"))
+ (builtin "One Step Simplification" (formula "2"))
+(rule "replace_known_right" (formula "3") (term "0") (ifseqformula "15"))
+ (builtin "One Step Simplification" (formula "3"))
+(rule "polySimp_elimSub" (formula "13") (term "0,2,1"))
+(rule "mul_literals" (formula "13") (term "1,0,2,1"))
+(rule "polySimp_elimSub" (formula "13") (term "0,2,0"))
+(rule "mul_literals" (formula "13") (term "1,0,2,0"))
+(rule "polySimp_addComm0" (formula "13") (term "0,2,1"))
+(rule "polySimp_addComm0" (formula "13") (term "0,2,0"))
+(rule "inEqSimp_commuteLeq" (formula "7"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "inEqSimp_commuteLeq" (formula "10"))
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+(rule "inEqSimp_commuteLeq" (formula "12"))
+(rule "assignment" (formula "17") (term "1"))
+ (builtin "One Step Simplification" (formula "17"))
+(rule "variableDeclarationAssign" (formula "17") (term "1"))
+(rule "variableDeclaration" (formula "17") (term "1") (newnames "self_51"))
+(rule "arrayLengthIsAShort" (formula "10") (term "0"))
+(rule "expand_inShort" (formula "10"))
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+(rule "replace_short_MAX" (formula "10") (term "1,0"))
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+(rule "variableDeclaration" (formula "23") (term "1") (newnames "c_1"))
+(rule "methodBodyExpand" (formula "23") (term "1") (newnames "heapBefore_,savedHeapBefore_"))
+ (builtin "One Step Simplification" (formula "23"))
+(rule "variableDeclaration" (formula "23") (term "1") (newnames "__NEW__"))
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+(rule "variableDeclaration" (formula "23") (term "1") (newnames "c_2"))
+(rule "allocateInstance" (formula "23"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "2")))
+ (builtin "One Step Simplification" (formula "24"))
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+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodBodyExpand" (formula "26") (term "1") (newnames "heapBefore_,savedHeapBefore_"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "assignment_write_attribute_this" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodCallWithinClass" (formula "26") (term "1"))
+(rule "methodBodyExpand" (formula "26") (term "1") (newnames "heapBefore_,savedHeapBefore_"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodCallSuper" (formula "26") (term "1"))
+(rule "methodBodyExpand" (formula "26") (term "1") (newnames "heapBefore_,savedHeapBefore_"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodCallEmpty" (formula "26") (term "1"))
+(rule "blockEmpty" (formula "26") (term "1"))
+(rule "assignment_write_attribute_this" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "assignment_write_attribute_this" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "assignment_write_attribute_this" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "assignment_write_attribute_this" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodCallEmpty" (formula "26") (term "1"))
+(rule "blockEmpty" (formula "26") (term "1"))
+(rule "methodCallReturnIgnoreResult" (formula "26") (term "1"))
+(rule "methodCallReturn" (formula "26") (term "1"))
+(rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodCallEmpty" (formula "26") (term "1"))
+(rule "blockEmpty" (formula "26") (term "1"))
+(rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "blockEmpty" (formula "26") (term "1"))
+(rule "variableDeclarationAssign" (formula "26") (term "1"))
+(rule "variableDeclaration" (formula "26") (term "1") (newnames "var"))
+(rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "variableDeclarationAssign" (formula "26") (term "1"))
+(rule "variableDeclaration" (formula "26") (term "1") (newnames "var_1"))
+(rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "variableDeclarationAssign" (formula "26") (term "1"))
+(rule "variableDeclaration" (formula "26") (term "1") (newnames "var_2"))
+(rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "variableDeclarationAssign" (formula "26") (term "1"))
+(rule "variableDeclaration" (formula "26") (term "1") (newnames "var_3"))
+(rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodBodyExpand" (formula "26") (term "1") (newnames "heapBefore_,savedHeapBefore_,num_bucketsBefore_,var_3Before_"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodCallSuper" (formula "26") (term "1"))
+(rule "methodBodyExpand" (formula "26") (term "1") (newnames "heapBefore__0,savedHeapBefore__0"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodCallEmpty" (formula "26") (term "1"))
+(rule "blockEmpty" (formula "26") (term "1"))
+(rule "variableDeclarationAssign" (formula "26") (term "1"))
+(rule "variableDeclaration" (formula "26") (term "1") (newnames "num_buckets"))
+(rule "assignmentShiftLeftInt" (formula "26") (term "1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "26"))
+ (rule "mod_lessDenom" (formula "26") (term "1,1,0") (userinteraction))
+ (rule "ifthenelse_split" (formula "1") (term "1,1") (userinteraction))
+ (branch "32 >= 0 TRUE"
+ (rule "impLeft" (formula "2") (userinteraction))
+ (branch "Case 1"
+ (rule "expand_inInt" (formula "28"))
+ (rule "equal_literals" (formula "22") (term "0"))
+ (builtin "One Step Simplification" (formula "22"))
+ (rule "closeTrue" (formula "22"))
+ )
+ (branch "Case 2"
+ (rule "eqTermCut" (formula "28") (term "0,1,1,0") (inst "s=mod(log_buckets, Z(2(3(#))))") (userinteraction))
+ (branch "Assume log_buckets = log_buckets % 32"
+ (rule "applyEqReverse" (formula "29") (term "1,1,0") (ifseqformula "1") (userinteraction))
+ (rule "cut" (inst "cutFormula=leq(pow(Z(2(#)), log_buckets), pow(Z(2(#)), Z(8(#))))<>") (userinteraction))
+ (branch "CUT: pow(2, log_buckets) <= pow(2, 8) TRUE"
+ (rule "powPositive" (formula "1") (term "0") (userinteraction))
+ (rule "qeq_literals" (formula "4"))
+ (rule "true_left" (formula "4"))
+ (rule "pow_literals" (formula "2") (term "1"))
+ (rule "greater_literals" (formula "1") (term "1,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "expand_inInt" (formula "30"))
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+ (rule "replace_int_MIN" (formula "30") (term "0,1"))
+ (rule "translateJavaShiftLeftInt" (formula "19") (term "3,0"))
+ (rule "translateJavaShiftLeftInt" (formula "23") (term "1"))
+ (rule "translateJavaShiftLeftInt" (formula "14") (term "0"))
+ (rule "eqSymm" (formula "3"))
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+ (rule "polySimp_elimNeg" (formula "37") (term "1,1,0,1,1,1,1,0"))
+ (rule "shiftLeftPositiveShiftDef" (formula "37") (term "2,0,1,1,1,1,0"))
+ (rule "polySimp_elimOneLeft0" (formula "37") (term "2,0,1,1,1,1,0"))
+ (rule "shiftRightPositiveShiftDef" (formula "37") (term "1,0,1,1,1,1,0"))
+ (rule "inEqSimp_ltToLeq" (formula "37") (term "0,0,1,1,1,1,0"))
+ (rule "mul_literals" (formula "37") (term "1,0,0,0,0,1,1,1,1,0"))
+ (rule "add_literals" (formula "37") (term "0,0,0,0,1,1,1,1,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "37") (term "0,0,1,1,1,1,0"))
+ (rule "mul_literals" (formula "37") (term "1,0,0,1,1,1,1,0"))
+ (rule "inEqSimp_contradInEq1" (formula "37") (term "0,0,1,1,1,1,0") (ifseqformula "7"))
+ (rule "qeq_literals" (formula "37") (term "0,0,0,1,1,1,1,0"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "pullOutSelect" (formula "35") (term "0") (inst "selectSK=de_wiesler_Tree_num_buckets_0"))
+ (rule "applyEq" (formula "32") (term "0") (ifseqformula "35"))
+ (rule "applyEq" (formula "33") (term "0") (ifseqformula "35"))
+ (rule "applyEq" (formula "37") (term "1,3,0") (ifseqformula "35"))
+ (rule "applyEq" (formula "34") (term "0") (ifseqformula "35"))
+ (rule "simplifySelectOfAnonEQ" (formula "35") (ifseqformula "24"))
+ (builtin "One Step Simplification" (formula "35") (ifInst "" (formula "47")))
+ (rule "eqSymm" (formula "32"))
+ (rule "applyEqReverse" (formula "33") (term "0") (ifseqformula "32"))
+ (rule "applyEqReverse" (formula "36") (term "0") (ifseqformula "32"))
+ (rule "applyEqReverse" (formula "37") (term "1,3,0") (ifseqformula "32"))
+ (rule "applyEqReverse" (formula "34") (term "0") (ifseqformula "32"))
+ (rule "applyEqReverse" (formula "35") (term "1") (ifseqformula "32"))
+ (rule "hideAuxiliaryEq" (formula "32"))
+ (rule "dismissNonSelectedField" (formula "34") (term "2,0"))
+ (rule "sortsDisjointModuloNull" (formula "34") (term "0,0,0"))
+ (rule "replace_known_right" (formula "34") (term "0,0,0,0") (ifseqformula "46"))
+ (builtin "One Step Simplification" (formula "34") (ifInst "" (formula "50")))
+ (rule "dismissNonSelectedField" (formula "34") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "34") (term "2,0"))
+ (rule "dismissNonSelectedField" (formula "34") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "34") (term "2,0"))
+ (rule "dismissNonSelectedField" (formula "34") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "34") (term "2,0"))
+ (rule "dismissNonSelectedField" (formula "34") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "34") (term "2,0"))
+ (rule "dismissNonSelectedField" (formula "34") (term "0,0,0,0"))
+ (rule "replaceKnownSelect_taclet20121121_9" (formula "34") (term "0,0,0,0"))
+ (rule "replaceKnownAuxiliaryConstant_taclet20121121_10" (formula "34") (term "0,0,0,0"))
+ (rule "replace_known_right" (formula "34") (term "0,0,0") (ifseqformula "45"))
+ (builtin "One Step Simplification" (formula "34"))
+ (rule "inEqSimp_commuteLeq" (formula "35"))
+ (rule "inEqSimp_commuteLeq" (formula "33"))
+ (rule "shiftLeftDef" (formula "37") (term "0,1,1,1,0,0,0"))
+ (rule "polySimp_elimNeg" (formula "37") (term "1,1,0,1,1,1,0,0,0"))
+ (rule "shiftLeftPositiveShiftDef" (formula "37") (term "2,0,1,1,1,0,0,0"))
+ (rule "polySimp_elimOneLeft0" (formula "37") (term "2,0,1,1,1,0,0,0"))
+ (rule "shiftRightPositiveShiftDef" (formula "37") (term "1,0,1,1,1,0,0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "37") (term "0,0,1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "37") (term "1,0,0,0,0,1,1,1,0,0,0"))
+ (rule "add_literals" (formula "37") (term "0,0,0,0,1,1,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "37") (term "0,0,1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "37") (term "1,0,0,1,1,1,0,0,0"))
+ (rule "inEqSimp_contradInEq1" (formula "37") (term "0,0,1,1,1,0,0,0") (ifseqformula "7"))
+ (rule "qeq_literals" (formula "37") (term "0,0,0,1,1,1,0,0,0"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "inEqSimp_exactShadow3" (formula "35") (ifseqformula "9"))
+ (rule "polySimp_mulComm0" (formula "35") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "35") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "35"))
+ (rule "polySimp_mulLiterals" (formula "35") (term "0"))
+ (rule "polySimp_elimOne" (formula "35") (term "0"))
+ (rule "inEqSimp_exactShadow3" (formula "33") (ifseqformula "12"))
+ (rule "polySimp_mulComm0" (formula "33") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "33") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "33"))
+ (rule "polySimp_mulLiterals" (formula "33") (term "0"))
+ (rule "polySimp_elimOne" (formula "33") (term "0"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Classifier" (formula "53"))
+ (rule "dismissNonSelectedField" (formula "53") (term "0,0,1"))
+ (rule "dismissNonSelectedField" (formula "53") (term "0,0,0"))
+ (rule "dismissNonSelectedField" (formula "53") (term "0,0,1"))
+ (rule "dismissNonSelectedField" (formula "53") (term "0,0,0"))
+ (rule "pullOutSelect" (formula "53") (term "0,0,1") (inst "selectSK=de_wiesler_Classifier_sorted_splitters_0"))
+ (rule "simplifySelectOfAnon" (formula "1"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "50")))
+ (rule "elementOfSingleton" (formula "1") (term "0,0,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "ifthenelse_negated" (formula "1") (term "0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "1") (term "0,0") (ifseqformula "25"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "pullOutSelect" (formula "54") (term "0,0,0") (inst "selectSK=de_wiesler_Classifier_tree_1"))
+ (rule "simplifySelectOfAnon" (formula "1"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "51")))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "2,0"))
+ (rule "replaceKnownSelect_taclet20121121_11" (formula "1") (term "2,0"))
+ (rule "replaceKnownAuxiliaryConstant_taclet20121121_12" (formula "1") (term "2,0"))
+ (rule "elementOfSingleton" (formula "1") (term "0,0,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "ifthenelse_negated" (formula "1") (term "0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "1") (term "0,0") (ifseqformula "26"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "dismissNonSelectedField" (formula "1") (term "0,0,0,0"))
+ (rule "pullOutSelect" (formula "2") (term "1,0") (inst "selectSK=de_wiesler_Classifier_sorted_splitters_1"))
+ (rule "simplifySelectOfStore" (formula "2"))
+ (builtin "One Step Simplification" (formula "2"))
+ (rule "castDel" (formula "2") (term "0"))
+ (rule "applyEqReverse" (formula "3") (term "1,0") (ifseqformula "2"))
+ (rule "hideAuxiliaryEq" (formula "2"))
+ (rule "pullOutSelect" (formula "2") (term "0,0,0,0") (inst "selectSK=java_lang_Object_created__2"))
+ (rule "applyEq" (formula "1") (term "0,0,0,0") (ifseqformula "2"))
+ (rule "simplifySelectOfCreate" (formula "2"))
+ (builtin "One Step Simplification" (formula "2") (ifInst "" (formula "52")))
+ (rule "castDel" (formula "2") (term "0"))
+ (rule "applyEqReverse" (formula "3") (term "0,0,0,0") (ifseqformula "2"))
+ (builtin "One Step Simplification" (formula "3"))
+ (rule "applyEqReverse" (formula "1") (term "0,0,0,0") (ifseqformula "2"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "applyEqReverse" (formula "56") (term "0,0,1") (ifseqformula "3"))
+ (rule "applyEqReverse" (formula "56") (term "0,0,0") (ifseqformula "1"))
+ (rule "hideAuxiliaryEq" (formula "2"))
+ (rule "hideAuxiliaryEq" (formula "2"))
+ (rule "hideAuxiliaryEq" (formula "1"))
+ (rule "replace_known_right" (formula "53") (term "0,1") (ifseqformula "52"))
+ (builtin "One Step Simplification" (formula "53") (ifInst "" (formula "47")))
+ (rule "closeTrue" (formula "53"))
+ )
+ (branch "Null Reference (self_51 = null)"
+ (rule "false_right" (formula "48"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "44")))
+ (rule "closeFalse" (formula "1"))
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ (branch "Exceptional Post (Tree)"
+ (builtin "One Step Simplification" (formula "30"))
+ (builtin "One Step Simplification" (formula "24"))
+ (rule "andLeft" (formula "24"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "25") (term "1,0,0") (ifseqformula "24"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "25") (term "1,1,0,0,1,0") (ifseqformula "24"))
+ (rule "andLeft" (formula "25"))
+ (rule "andLeft" (formula "25"))
+ (rule "andLeft" (formula "27"))
+ (rule "andLeft" (formula "25"))
+ (rule "andLeft" (formula "27"))
+ (rule "notLeft" (formula "25"))
+ (rule "close" (formula "30") (ifseqformula "29"))
+ )
+ (branch "Pre (Tree)"
+ (builtin "One Step Simplification" (formula "28") (ifInst "" (formula "27")) (ifInst "" (formula "26")) (ifInst "" (formula "27")) (ifInst "" (formula "26")))
+ (rule "wellFormedStorePrimitive" (formula "28") (term "0,0,0"))
+ (rule "expand_inInt" (formula "28") (term "1"))
+ (rule "replace_int_MAX" (formula "28") (term "1,0,1"))
+ (rule "replace_int_MIN" (formula "28") (term "0,1,1"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0,0"))
+ (rule "dismissNonSelectedField" (formula "28") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "28") (term "1,1"))
+ (rule "inEqSimp_subsumption0" (formula "28") (term "0,1") (ifseqformula "8"))
+ (rule "leq_literals" (formula "28") (term "0,0,1"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "inEqSimp_subsumption1" (formula "28") (term "1") (ifseqformula "7"))
+ (rule "leq_literals" (formula "28") (term "0,1"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "wellFormedStoreObject" (formula "28") (term "0,0"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "wellFormedStorePrimitive" (formula "28") (term "0,0"))
+ (rule "wellFormedStoreObject" (formula "28") (term "0,0"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "wellFormedStorePrimitive" (formula "28") (term "0,0"))
+ (rule "wellFormedCreate" (formula "28") (term "0,0"))
+ (rule "replace_known_left" (formula "28") (term "0,0") (ifseqformula "2"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "pullOutSelect" (formula "28") (term "0,0") (inst "selectSK=java_lang_Object_created__0"))
+ (rule "simplifySelectOfCreate" (formula "1"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "25")))
+ (rule "castDel" (formula "1") (term "1,0"))
+ (rule "sortsDisjointModuloNull" (formula "1") (term "0,0"))
+ (rule "replace_known_right" (formula "1") (term "0,0,0") (ifseqformula "25"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "28")))
+ (rule "applyEqReverse" (formula "29") (term "0,0") (ifseqformula "1"))
+ (rule "hideAuxiliaryEq" (formula "1"))
+ (rule "replace_known_left" (formula "28") (term "0") (ifseqformula "3"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "pullOutSelect" (formula "28") (term "0") (inst "selectSK=java_lang_Object_created__1"))
+ (rule "simplifySelectOfCreate" (formula "1"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "25")))
+ (rule "castDel" (formula "1") (term "1,0"))
+ (rule "sortsDisjointModuloNull" (formula "1") (term "0,0"))
+ (rule "replace_known_right" (formula "1") (term "0,0,0") (ifseqformula "25"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "27")))
+ (rule "applyEqReverse" (formula "29") (term "0") (ifseqformula "1"))
+ (rule "close" (formula "29") (ifseqformula "5"))
+ )
+ )
+ )
+ )
+ )
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__calculate_bucket_starts((I,int,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__calculate_bucket_starts((I,int,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..df3469a
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__calculate_bucket_starts((I,int,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,11518 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Sep 05 21:17:13 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Sep 05 21:17:13 CEST 2022
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:calculate_bucket_starts([I,int,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:calculate_bucket_starts([I,int,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "47502")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "10"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "10"))
+(rule "notLeft" (formula "9"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "notLeft" (formula "12"))
+(rule "notLeft" (formula "11"))
+(rule "andLeft" (formula "14"))
+(rule "andLeft" (formula "13"))
+(rule "notLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "17"))
+(rule "andLeft" (formula "16"))
+(rule "andLeft" (formula "14"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "22"))
+(rule "andLeft" (formula "19"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "25"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "26"))
+(rule "andLeft" (formula "28"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "translateJavaAddInt" (formula "16") (term "1"))
+(rule "eqSymm" (formula "35"))
+(rule "translateJavaSubInt" (formula "39") (term "0,0"))
+(rule "replace_known_right" (formula "12") (term "0") (ifseqformula "43"))
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diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify(int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify(int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..d18bd99
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify(int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,16781 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Apr 17 12:42:40 CEST 2023
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L , finalFields-finalFields\\:immutable
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Apr 17 12:42:40 CEST 2023
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:classify(int)].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:classify(int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "2" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "3" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "142098")
+
+(branch "dummy ID"
+(rule "eqSymm" (formula "1") (term "1,0,0,1,0,1,1") (newnames "heapAtPre,o,f"))
+(rule "assignment" (formula "1") (term "1,1"))
+(rule "methodBodyExpand" (formula "1") (term "1,1,1") (newnames "heapBefore_classify,savedHeapBefore_classify,_valueBefore_classify"))
+(rule "assignment" (formula "1") (term "1,1,1,1"))
+(rule "blockEmpty" (formula "1") (term "1,1,1,1,1"))
+(rule "variableDeclarationAssign" (formula "1") (term "1,1,1,1,1"))
+(rule "variableDeclaration" (formula "1") (term "1,1,1,1,1") (newnames "index_1"))
+ (builtin "One Step Simplification" (formula "1"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "0,1,1,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,0,1,1,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,0,1,1,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "2"))
+(rule "inEqSimp_commuteLeq" (formula "5"))
+(rule "methodCallWithAssignmentUnfoldTarget" (formula "10") (term "1") (inst "#v0=t"))
+(rule "variableDeclaration" (formula "10") (term "1") (newnames "t"))
+(rule "assignment_read_attribute_this_final" (formula "10"))
+ (builtin "One Step Simplification" (formula "10"))
+ (builtin "Use Operation Contract" (formula "10") (newnames "heapBefore_classify_0,result_0,exc_0") (contract "de.wiesler.Tree[de.wiesler.Tree::classify(int)].JML normal_behavior operation contract.0"))
+(branch "Post (classify)"
+ (builtin "One Step Simplification" (formula "9"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "expand_inInt" (formula "9") (term "0,1,0"))
+ (rule "replace_int_MAX" (formula "9") (term "1,0,0,1,0"))
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+ (rule "andLeft" (formula "9"))
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+ (rule "andLeft" (formula "10"))
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+ (rule "assignment" (formula "19") (term "1"))
+ (builtin "One Step Simplification" (formula "19"))
+ (rule "variableDeclaration" (formula "19") (term "1") (newnames "bucket"))
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+ (builtin "One Step Simplification" (formula "19"))
+ (rule "ifElseSplit" (formula "19"))
+ (branch "if x true"
+ (builtin "One Step Simplification" (formula "20"))
+ (builtin "One Step Simplification" (formula "1"))
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+ (rule "variableDeclaration" (formula "20") (term "1") (newnames "bucket_index"))
+ (rule "compound_subtraction_2" (formula "20") (term "1") (inst "#v1=x_1") (inst "#v0=x"))
+ (rule "variableDeclarationAssign" (formula "20") (term "1"))
+ (rule "variableDeclaration" (formula "20") (term "1") (newnames "x_2"))
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+ (rule "variableDeclarationAssign" (formula "20") (term "1"))
+ (rule "variableDeclaration" (formula "20") (term "1") (newnames "x_1"))
+ (rule "compound_division_1" (formula "20") (term "1") (inst "#v=x_3"))
+ (rule "variableDeclarationAssign" (formula "20") (term "1"))
+ (rule "variableDeclaration" (formula "20") (term "1") (newnames "x_3"))
+ (rule "assignment_read_attribute_this_final" (formula "20"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "assignmentDivisionInt" (formula "20"))
+ (branch "Case 1"
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "translateJavaDivInt" (formula "20") (term "0,1,0"))
+ (rule "assignmentSubtractionInt" (formula "20") (term "1"))
+ (branch "Overflow check"
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "expand_inInt" (formula "20"))
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+ (rule "replace_int_MAX" (formula "20") (term "1,0"))
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+ (rule "inEqSimp_sepPosMonomial1" (formula "27") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "27") (term "1,0,1,0,0"))
+ (rule "inEqSimp_notGeq" (formula "27") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "27") (term "1,0,0,1,1,0,0"))
+ (rule "add_literals" (formula "27") (term "0,0,1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "27") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "27") (term "1,1,1,0,0"))
+ (rule "nnf_notAnd" (formula "12") (term "0,0,0"))
+ (rule "inEqSimp_notGeq" (formula "12") (term "0,0,0,0"))
+ (rule "times_zero_1" (formula "12") (term "1,0,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "12") (term "0,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "12") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "12") (term "1,0,0,0,0"))
+ (rule "inEqSimp_notLeq" (formula "12") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "12") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "12") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "12") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "12") (term "0,0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "12") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "12") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "12") (term "1,1,0,0,0"))
+ (rule "mul_literals" (formula "12") (term "0,1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "12") (term "1,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "12") (term "1,1,1,0,0,0"))
+ (rule "nnf_notAnd" (formula "12") (term "1,0,0"))
+ (rule "inEqSimp_notLeq" (formula "12") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "12") (term "1,0,0,0,1,0,0"))
+ (rule "add_literals" (formula "12") (term "0,0,0,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "12") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "12") (term "1,0,1,0,0"))
+ (rule "inEqSimp_notGeq" (formula "12") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "12") (term "1,0,0,1,1,0,0"))
+ (rule "add_literals" (formula "12") (term "0,0,1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "12") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "12") (term "1,1,1,0,0"))
+ (rule "commute_or" (formula "13") (term "1,0,0,1,0"))
+ (rule "commute_or_2" (formula "30") (term "0,0"))
+ (rule "commute_or_2" (formula "28") (term "0,0,1,0"))
+ (rule "commute_or" (formula "13") (term "0,0,0,1,0"))
+ (rule "onlyCreatedObjectsAreReferencedFinal" (formula "36") (term "1,0") (ifseqformula "1") (ifseqformula "2"))
+ (rule "replace_known_right" (formula "1") (term "1") (ifseqformula "37"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "34")))
+ (rule "closeFalse" (formula "1"))
+ )
+)
+(branch "Null reference (t = null)"
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "notRight" (formula "10"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Classifier" (formula "9"))
+ (builtin "One Step Simplification" (formula "9"))
+ (rule "andLeft" (formula "9"))
+ (rule "andLeft" (formula "9"))
+ (rule "andLeft" (formula "9"))
+ (rule "andLeft" (formula "9"))
+ (rule "andLeft" (formula "9"))
+ (rule "andLeft" (formula "9"))
+ (rule "eqSymm" (formula "14"))
+ (rule "eqSymm" (formula "11"))
+ (rule "translateJavaSubInt" (formula "14") (term "0,2,0"))
+ (rule "translateJavaSubInt" (formula "14") (term "0,2,1"))
+ (rule "translateJavaMulInt" (formula "11") (term "1,0"))
+ (rule "polySimp_elimSub" (formula "14") (term "0,2,0"))
+ (rule "mul_literals" (formula "14") (term "1,0,2,0"))
+ (rule "eqSymm" (formula "14"))
+ (rule "polySimp_elimSub" (formula "14") (term "0,2,0"))
+ (rule "mul_literals" (formula "14") (term "1,0,2,0"))
+ (rule "eqSymm" (formula "14"))
+ (rule "polySimp_mulComm0" (formula "11") (term "1,0"))
+ (rule "polySimp_addComm0" (formula "14") (term "0,2,0"))
+ (rule "eqSymm" (formula "14"))
+ (rule "polySimp_addComm0" (formula "14") (term "0,2,0"))
+ (rule "eqSymm" (formula "14"))
+ (rule "inEqSimp_commuteLeq" (formula "9"))
+ (rule "applyEq" (formula "14") (term "0,1,0,2,0") (ifseqformula "1"))
+ (rule "eqSymm" (formula "14"))
+ (rule "applyEq" (formula "11") (term "0,2,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "13") (term "0,3,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "15") (term "1") (ifseqformula "1"))
+ (rule "applyEq" (formula "11") (term "0,0,1,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "12") (term "0,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "14") (term "0,1,0,2,0") (ifseqformula "1"))
+ (rule "eqSymm" (formula "14"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Classifier" (formula "8"))
+ (rule "andLeft" (formula "8"))
+ (rule "notLeft" (formula "8"))
+ (rule "close" (formula "16") (ifseqformula "1"))
+)
+)
+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_all((I,int,int,(I)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_all((I,int,int,(I)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..3bcd54c
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_all((I,int,int,(I)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,26539 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Apr 17 12:44:37 CEST 2023
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L , finalFields-finalFields\\:immutable
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Apr 17 12:44:37 CEST 2023
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:classify_all([I,int,int,[I)].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:classify_all([I,int,int,[I)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "2" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "3" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "4" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "248440")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "8"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "8"))
+(rule "notLeft" (formula "7"))
+(rule "andLeft" (formula "10"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "16"))
+(rule "andLeft" (formula "6"))
+(rule "notLeft" (formula "2"))
+(rule "andLeft" (formula "16"))
+(rule "andLeft" (formula "16"))
+(rule "andLeft" (formula "16"))
+(rule "eqSymm" (formula "15"))
+(rule "translateJavaSubInt" (formula "15") (term "1"))
+(rule "replace_known_right" (formula "4") (term "0") (ifseqformula "24"))
+ (builtin "One Step Simplification" (formula "4"))
+(rule "replace_known_right" (formula "9") (term "0") (ifseqformula "25"))
+ (builtin "One Step Simplification" (formula "9"))
+(rule "polySimp_elimSub" (formula "15") (term "1"))
+(rule "polySimp_addComm0" (formula "15") (term "1"))
+(rule "disjointDefinition" (formula "21"))
+ (builtin "One Step Simplification" (formula "21"))
+(rule "notLeft" (formula "21"))
+(rule "disjointDefinition" (formula "20"))
+ (builtin "One Step Simplification" (formula "20"))
+(rule "notLeft" (formula "20"))
+(rule "eqSymm" (formula "21"))
+(rule "disjointDefinition" (formula "19"))
+ (builtin "One Step Simplification" (formula "19"))
+(rule "notLeft" (formula "19"))
+(rule "eqSymm" (formula "20"))
+(rule "disjointDefinition" (formula "18"))
+ (builtin "One Step Simplification" (formula "18"))
+(rule "notLeft" (formula "18"))
+(rule "eqSymm" (formula "19"))
+(rule "disjointDefinition" (formula "16"))
+ (builtin "One Step Simplification" (formula "16"))
+(rule "notLeft" (formula "16"))
+(rule "disjointDefinition" (formula "16"))
+ (builtin "One Step Simplification" (formula "16"))
+(rule "notLeft" (formula "16"))
+(rule "eqSymm" (formula "17"))
+(rule "inEqSimp_commuteLeq" (formula "14"))
+(rule "inEqSimp_commuteLeq" (formula "13"))
+(rule "inEqSimp_commuteLeq" (formula "12"))
+(rule "inEqSimp_commuteLeq" (formula "8"))
+(rule "inEqSimp_commuteLeq" (formula "6"))
+(rule "assignment" (formula "26") (term "1"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodBodyExpand" (formula "26") (term "1") (newnames "heapBefore_classify_all,savedHeapBefore_classify_all,_beginBefore_classify_all,_endBefore_classify_all,_indicesBefore_classify_all,_valuesBefore_classify_all"))
+ (builtin "One Step Simplification" (formula "26"))
+(rule "methodCallUnfoldTarget" (formula "26") (term "1") (inst "#v0=t"))
+(rule "variableDeclaration" (formula "26") (term "1") (newnames "t"))
+(rule "assignment_read_attribute_this_final" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+ (builtin "Use Operation Contract" (formula "26") (newnames "heapBefore_classify_all_0,exc_25,heapAfter_classify_all,anon_heap_classify_all") (contract "de.wiesler.Tree[de.wiesler.Tree::classify_all([I,int,int,[I)].JML normal_behavior operation contract.0"))
+(branch "Post (classify_all)"
+ (builtin "One Step Simplification" (formula "28"))
+ (builtin "One Step Simplification" (formula "18"))
+ (rule "expand_inInt" (formula "18") (term "1,0,0,0,1,0,1"))
+ (rule "expand_inInt" (formula "18") (term "1,0,0,0,1,1,0,1"))
+ (rule "replace_int_MAX" (formula "18") (term "1,0,1,0,0,0,1,0,1"))
+ (rule "replace_int_MIN" (formula "18") (term "0,1,1,0,0,0,1,0,1"))
+ (rule "replace_int_MAX" (formula "18") (term "1,0,1,0,0,0,1,1,0,1"))
+ (rule "replace_int_MIN" (formula "18") (term "0,1,1,0,0,0,1,1,0,1"))
+ (rule "andLeft" (formula "18"))
+ (rule "andLeft" (formula "19"))
+ (rule "andLeft" (formula "20"))
+ (rule "andLeft" (formula "19"))
+ (rule "andLeft" (formula "19"))
+ (rule "andLeft" (formula "20"))
+ (rule "translateJavaMulInt" (formula "19") (term "1,1,1,0"))
+ (rule "eqSymm" (formula "20") (term "1,0"))
+ (rule "translateJavaAddInt" (formula "20") (term "0,2,2,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "19") (term "1,1,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "19") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "19") (term "0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "19") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "20") (term "0,0,0,0"))
+ (rule "applyEq" (formula "20") (term "1,1,0,0,0") (ifseqformula "15"))
+ (rule "applyEq" (formula "19") (term "1,1,0,0,0") (ifseqformula "15"))
+ (rule "commute_and" (formula "19") (term "1,0"))
+ (rule "commute_and" (formula "19") (term "1,0,0"))
+ (rule "commute_and" (formula "20") (term "1,0,0"))
+ (rule "commute_and" (formula "20") (term "0,0,0"))
+ (rule "commute_and" (formula "19") (term "0,0,0"))
+ (rule "shift_paren_and" (formula "20") (term "0,0"))
+ (rule "commute_and_2" (formula "20") (term "0,0,0"))
+ (rule "shift_paren_and" (formula "19") (term "0,0"))
+ (rule "commute_and_2" (formula "19") (term "0,0,0"))
+ (rule "ifElseUnfold" (formula "33") (term "1") (inst "#boolv=x"))
+ (rule "variableDeclaration" (formula "33") (term "1") (newnames "x"))
+ (rule "assignment_read_attribute_this_final" (formula "33"))
+ (builtin "One Step Simplification" (formula "33"))
+ (rule "arrayLengthIsAShort" (formula "15") (term "0"))
+ (rule "expand_inShort" (formula "15"))
+ (rule "replace_short_MIN" (formula "15") (term "0,1"))
+ (rule "replace_short_MAX" (formula "15") (term "1,0"))
+ (rule "andLeft" (formula "15"))
+ (rule "inEqSimp_commuteLeq" (formula "16"))
+ (rule "applyEq" (formula "16") (term "0") (ifseqformula "17"))
+ (rule "applyEq" (formula "15") (term "0") (ifseqformula "17"))
+ (rule "arrayLengthNotNegative" (formula "17") (term "0"))
+ (rule "applyEq" (formula "17") (term "0") (ifseqformula "18"))
+ (rule "arrayLengthNotNegative" (formula "14") (term "0"))
+ (rule "arrayLengthIsAShort" (formula "15") (term "0"))
+ (rule "expand_inShort" (formula "15"))
+ (rule "replace_short_MAX" (formula "15") (term "1,0"))
+ (rule "replace_short_MIN" (formula "15") (term "0,1"))
+ (rule "andLeft" (formula "15"))
+ (rule "inEqSimp_commuteLeq" (formula "16"))
+ (rule "ifElseSplit" (formula "39"))
+ (branch "if x true"
+ (builtin "One Step Simplification" (formula "40"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "for_to_while" (formula "40") (term "1") (inst "#outerLabel=_label3") (inst "#innerLabel=_label2"))
+ (rule "variableDeclarationAssign" (formula "40") (term "1"))
+ (rule "variableDeclaration" (formula "40") (term "1") (newnames "i"))
+ (rule "assignment" (formula "40") (term "1"))
+ (builtin "One Step Simplification" (formula "40"))
+ (rule "loopScopeInvDia" (formula "40") (term "1") (newnames "i_0,o,f") (inst "#x=x_1") (inst "#variant=x") (inst "#permissionsBefore_LOOP=h_2") (inst "#savedHeapBefore_LOOP=h_1") (inst "#heapBefore_LOOP=h") (inst "anon_permissions_LOOP=anon_permissions_LOOP_0") (inst "anon_savedHeap_LOOP=anon_savedHeap_LOOP_0") (inst "anon_heap_LOOP=anon_heap_LOOP_0"))
+ (branch "Invariant Initially Valid"
+ (rule "closeTrue" (formula "40"))
+ )
+ (branch "Invariant Preserved and Used"
+ (builtin "One Step Simplification" (formula "41"))
+ (rule "expand_inInt" (formula "41") (term "1,0,0,1,0,0,0"))
+ (rule "expand_inInt" (formula "41") (term "1,0,0,1,0,0"))
+ (rule "replace_int_MAX" (formula "41") (term "1,0,1,0,0,1,0,0,0"))
+ (rule "replace_int_MIN" (formula "41") (term "0,1,1,0,0,1,0,0,0"))
+ (rule "replace_int_MAX" (formula "41") (term "1,0,1,0,0,1,0,0"))
+ (rule "replace_int_MIN" (formula "41") (term "0,1,1,0,0,1,0,0"))
+ (rule "impRight" (formula "41"))
+ (rule "andLeft" (formula "1"))
+ (rule "andLeft" (formula "2"))
+ (rule "andLeft" (formula "1"))
+ (rule "andLeft" (formula "1"))
+ (rule "andLeft" (formula "1"))
+ (rule "translateJavaSubInt" (formula "47") (term "0,1,1,0,1"))
+ (rule "translateJavaSubInt" (formula "47") (term "0,1,1,0"))
+ (rule "translateJavaAddInt" (formula "4") (term "0,2,2,0,1,0"))
+ (rule "translateJavaAddInt" (formula "3") (term "0,2,2,0,1,0"))
+ (rule "polySimp_elimSub" (formula "47") (term "0,1,1,0,1"))
+ (rule "polySimp_elimSub" (formula "47") (term "0,1,1,0"))
+ (rule "polySimp_addComm0" (formula "47") (term "0,1,1,0,1"))
+ (rule "polySimp_addComm0" (formula "47") (term "0,1,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "4") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "4") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "3") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "3") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "2"))
+ (rule "inEqSimp_commuteLeq" (formula "1"))
+ (rule "variableDeclaration" (formula "47") (term "1") (newnames "x_1"))
+ (rule "applyEq" (formula "4") (term "1,1,0,0,0") (ifseqformula "29"))
+ (rule "applyEq" (formula "47") (term "1,0,1,1,0") (ifseqformula "29"))
+ (rule "polySimp_addComm0" (formula "47") (term "0,1,1,0"))
+ (rule "applyEq" (formula "2") (term "0") (ifseqformula "29"))
+ (rule "inEqSimp_commuteGeq" (formula "2"))
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+ (rule "commute_or" (formula "23") (term "1,0,0"))
+ (rule "nnf_notAnd" (formula "38") (term "0,0"))
+ (rule "nnf_notAnd" (formula "22") (term "0,0"))
+ (rule "commute_or" (formula "39") (term "1,0,0,1,0"))
+ (rule "nnf_notAnd" (formula "38") (term "0,0,0"))
+ (rule "inEqSimp_notGeq" (formula "38") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "38") (term "1,0,0,0,0,0,0"))
+ (rule "add_zero_right" (formula "38") (term "0,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "38") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "38") (term "1,0,0,0,0"))
+ (rule "inEqSimp_notLeq" (formula "38") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "38") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "38") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "38") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "38") (term "0,0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "38") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "38") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "38") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "38") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "38") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "38") (term "1,1,1,0,0,0"))
+ (rule "nnf_notAnd" (formula "38") (term "1,0,0"))
+ (rule "inEqSimp_notGeq" (formula "38") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "38") (term "1,0,0,1,1,0,0"))
+ (rule "add_literals" (formula "38") (term "0,0,1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "38") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "38") (term "1,1,1,0,0"))
+ (rule "inEqSimp_notLeq" (formula "38") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "38") (term "1,0,0,0,1,0,0"))
+ (rule "add_literals" (formula "38") (term "0,0,0,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "38") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "38") (term "1,0,1,0,0"))
+ (rule "nnf_notAnd" (formula "22") (term "1,0,0"))
+ (rule "inEqSimp_notGeq" (formula "22") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,0,1,1,0,0"))
+ (rule "add_literals" (formula "22") (term "0,0,1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "22") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,1,1,0,0"))
+ (rule "inEqSimp_notLeq" (formula "22") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,0,0,1,0,0"))
+ (rule "add_literals" (formula "22") (term "0,0,0,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "22") (term "0,1,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,1,0,0"))
+ (rule "Definition_axiom_for_isSortedSliceTransitive_in_de_wiesler_Functions" (formula "37") (term "0") (inst "j=j") (inst "i=i"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "expand_inInt" (formula "37") (term "1,0,0,1,0"))
+ (rule "expand_inInt" (formula "37") (term "1,0,0"))
+ (rule "replace_int_MAX" (formula "37") (term "1,0,1,0,0,1,0"))
+ (rule "replace_int_MIN" (formula "37") (term "0,1,1,0,0,1,0"))
+ (rule "replace_int_MIN" (formula "37") (term "0,1,1,0,0"))
+ (rule "replace_int_MAX" (formula "37") (term "1,0,1,0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "37") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "37") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "37") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "37") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "37") (term "0,0,0,1,0,0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "37") (term "1,0,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "37") (term "1,0,0,1,0,0,0,1,0"))
+ (rule "mul_literals" (formula "37") (term "0,1,0,0,1,0,0,0,1,0"))
+ (rule "polySimp_addAssoc" (formula "37") (term "0,0,1,0,0,0,1,0"))
+ (rule "add_literals" (formula "37") (term "0,0,0,1,0,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "37") (term "1,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "37") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "37") (term "0,0,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "37") (term "1,1,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "37") (term "1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "37") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "37") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "37") (term "1,1,0,0,0"))
+ (rule "mul_literals" (formula "37") (term "0,1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "37") (term "1,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "37") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "37") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "37") (term "1,1,0,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "37") (term "1,1,0,0,0,1,0"))
+ (rule "mul_literals" (formula "37") (term "0,1,1,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "37") (term "1,1,1,0,0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "37") (term "1,1,1,0,0,0,1,0"))
+ (rule "nnf_notAnd" (formula "22") (term "0,0,0"))
+ (rule "inEqSimp_notLeq" (formula "22") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "22") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "22") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "22") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "22") (term "0,0,0,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "22") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "22") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "22") (term "1,1,0,0,0"))
+ (rule "mul_literals" (formula "22") (term "0,1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "22") (term "1,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "22") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_notGeq" (formula "22") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,0,0,0,0,0"))
+ (rule "add_literals" (formula "22") (term "0,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "22") (term "0,0,0,0"))
+ (rule "mul_literals" (formula "22") (term "1,0,0,0,0"))
+ (rule "Definition_axiom_for_isSortedSliceTransitive_in_de_wiesler_Functions" (formula "21") (term "0") (inst "j=j") (inst "i=i"))
+ (builtin "One Step Simplification" (formula "21"))
+ (rule "expand_inInt" (formula "21") (term "1,0,0,1,0"))
+ (rule "expand_inInt" (formula "21") (term "1,0,0"))
+ (rule "replace_int_MIN" (formula "21") (term "0,1,1,0,0,1,0"))
+ (rule "replace_int_MAX" (formula "21") (term "1,0,1,0,0,1,0"))
+ (rule "replace_int_MAX" (formula "21") (term "1,0,1,0,0"))
+ (rule "replace_int_MIN" (formula "21") (term "0,1,1,0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "21") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "21") (term "1,0,0,1,0,0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "21") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "21") (term "1,0,0,1,0,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "1,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "0,0,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "1,1,0,0,1,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "1,1,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "21") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "21") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "21") (term "1,1,0,0,0"))
+ (rule "mul_literals" (formula "21") (term "0,1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "21") (term "1,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "21") (term "1,1,1,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "21") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "21") (term "1,1,0,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "21") (term "1,1,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "21") (term "1,1,1,0,0,0,1,0"))
+ (rule "mul_literals" (formula "21") (term "0,1,1,0,0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "21") (term "1,1,1,0,0,0,1,0"))
+ (rule "commute_or_2" (formula "40") (term "0,0"))
+ (rule "nnf_imp2or" (formula "37") (term "0"))
+ (rule "commute_or" (formula "23") (term "1,0,0,1,0"))
+ (rule "onlyCreatedObjectsAreReferencedFinal" (formula "20") (term "0,0") (ifseqformula "1") (ifseqformula "2"))
+ (rule "replace_known_right" (formula "20") (term "1") (ifseqformula "56"))
+ (builtin "One Step Simplification" (formula "20") (ifInst "" (formula "46")))
+ (rule "closeFalse" (formula "20"))
+ )
+)
+(branch "Null reference (t = null)"
+ (builtin "One Step Simplification" (formula "26"))
+ (rule "notRight" (formula "26"))
+ (rule "applyEq" (formula "21") (term "0,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "18") (term "0,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "23") (term "0,0") (ifseqformula "1"))
+ (rule "inEqSimp_subsumption1" (formula "7") (ifseqformula "13"))
+ (rule "leq_literals" (formula "7") (term "0"))
+ (builtin "One Step Simplification" (formula "7"))
+ (rule "true_left" (formula "7"))
+ (rule "inEqSimp_exactShadow3" (formula "13") (ifseqformula "7"))
+ (rule "polySimp_mulComm0" (formula "13") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "13") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "13"))
+ (rule "polySimp_mulLiterals" (formula "13") (term "0"))
+ (rule "polySimp_elimOne" (formula "13") (term "0"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Classifier" (formula "16"))
+ (builtin "One Step Simplification" (formula "16"))
+ (rule "andLeft" (formula "16"))
+ (rule "andLeft" (formula "16"))
+ (rule "andLeft" (formula "16"))
+ (rule "andLeft" (formula "16"))
+ (rule "andLeft" (formula "16"))
+ (rule "andLeft" (formula "16"))
+ (rule "translateJavaSubInt" (formula "21") (term "0,2,1"))
+ (rule "translateJavaSubInt" (formula "21") (term "0,2,0"))
+ (rule "translateJavaMulInt" (formula "18") (term "1,1"))
+ (rule "eqSymm" (formula "21"))
+ (rule "eqSymm" (formula "18"))
+ (rule "polySimp_elimSub" (formula "21") (term "0,2,0"))
+ (rule "mul_literals" (formula "21") (term "1,0,2,0"))
+ (rule "eqSymm" (formula "21"))
+ (rule "polySimp_elimSub" (formula "21") (term "0,2,0"))
+ (rule "mul_literals" (formula "21") (term "1,0,2,0"))
+ (rule "eqSymm" (formula "21"))
+ (rule "polySimp_mulComm0" (formula "18") (term "1,0"))
+ (rule "polySimp_addComm0" (formula "21") (term "0,2,1"))
+ (rule "polySimp_addComm0" (formula "21") (term "0,2,0"))
+ (rule "inEqSimp_commuteLeq" (formula "16"))
+ (rule "applyEq" (formula "18") (term "0,2,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "18") (term "0,0,1,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "21") (term "0,1,0,2,0") (ifseqformula "1"))
+ (rule "eqSymm" (formula "21"))
+ (rule "applyEq" (formula "19") (term "0,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "22") (term "1") (ifseqformula "1"))
+ (rule "applyEq" (formula "20") (term "0,3,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "21") (term "0,1,0,2,0") (ifseqformula "1"))
+ (rule "eqSymm" (formula "21"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Classifier" (formula "11"))
+ (rule "andLeft" (formula "11"))
+ (rule "notLeft" (formula "11"))
+ (rule "close" (formula "23") (ifseqformula "1"))
+)
+)
+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_locally((I,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_locally((I,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..5788b04
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_locally((I,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,9257 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Sep 05 21:23:00 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Sep 05 21:23:00 CEST 2022
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:classify_locally([I,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:classify_locally([I,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "2" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "32088")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,1,1,1,1,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,1,1,1,1,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,1,1,1,1,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "10"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "10"))
+(rule "notLeft" (formula "9"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "notLeft" (formula "12"))
+(rule "notLeft" (formula "11"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "15"))
+(rule "notLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "14"))
+(rule "andLeft" (formula "18"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "22"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "andLeft" (formula "20"))
+(rule "translateJavaAddInt" (formula "14") (term "1"))
+(rule "eqSymm" (formula "35"))
+(rule "replace_known_right" (formula "10") (term "0") (ifseqformula "39"))
+ (builtin "One Step Simplification" (formula "10"))
+(rule "replace_known_right" (formula "4") (term "0") (ifseqformula "40"))
+ (builtin "One Step Simplification" (formula "4"))
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+ (rule "polySimp_addAssoc" (formula "49") (term "5,0"))
+ (rule "polySimp_addAssoc" (formula "49") (term "0,5,0"))
+ (rule "polySimp_addComm0" (formula "49") (term "0,0,5,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "49") (term "0,5,0"))
+ (rule "add_literals" (formula "49") (term "1,1,0,5,0"))
+ (rule "times_zero_1" (formula "49") (term "1,0,5,0"))
+ (rule "add_zero_right" (formula "49") (term "0,5,0"))
+ (rule "jmod_axiom" (formula "2") (term "0"))
+ (rule "polySimp_mulLiterals" (formula "2") (term "1,0"))
+ (rule "inEqSimp_homoInEq1" (formula "2"))
+ (rule "polySimp_mulComm0" (formula "2") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "2") (term "1,0"))
+ (rule "polySimp_mulLiterals" (formula "2") (term "1,1,0"))
+ (rule "polySimp_rightDist" (formula "2") (term "0,1,0"))
+ (rule "polySimp_mulAssoc" (formula "2") (term "0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "2") (term "0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "2") (term "0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "2") (term "0,0,1,0"))
+ (rule "polySimp_addAssoc" (formula "2") (term "0"))
+ (rule "polySimp_addAssoc" (formula "2") (term "0,0"))
+ (rule "jmod_axiom" (formula "3") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "3") (term "1,1"))
+ (rule "jmod_axiom" (formula "41") (term "0,1,2,1,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "41") (term "1,0,1,2,1,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "41") (term "1,2,1,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "41") (term "1,2,1,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "41") (term "1,1,2,1,0,0,1,0"))
+ (rule "polySimp_rightDist" (formula "41") (term "0,1,2,1,0,0,1,0"))
+ (rule "polySimp_mulAssoc" (formula "41") (term "0,0,1,2,1,0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "41") (term "0,0,0,1,2,1,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "41") (term "0,0,1,2,1,0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "41") (term "0,0,1,2,1,0,0,1,0"))
+ (rule "polySimp_addAssoc" (formula "41") (term "2,1,0,0,1,0"))
+ (rule "polySimp_addAssoc" (formula "41") (term "0,2,1,0,0,1,0"))
+ (rule "polySimp_addComm1" (formula "41") (term "0,0,2,1,0,0,1,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "41") (term "0,2,1,0,0,1,0"))
+ (rule "add_literals" (formula "41") (term "1,1,0,2,1,0,0,1,0"))
+ (rule "times_zero_1" (formula "41") (term "1,0,2,1,0,0,1,0"))
+ (rule "add_zero_right" (formula "41") (term "0,2,1,0,0,1,0"))
+ (rule "jmod_axiom" (formula "1") (term "0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,0"))
+ (rule "inEqSimp_homoInEq0" (formula "1"))
+ (rule "polySimp_mulComm0" (formula "1") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "1") (term "1,0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,1,0"))
+ (rule "polySimp_rightDist" (formula "1") (term "0,1,0"))
+ (rule "polySimp_mulAssoc" (formula "1") (term "0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "1") (term "0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "1") (term "0,0,1,0"))
+ (rule "polySimp_addAssoc" (formula "1") (term "0"))
+ (rule "polySimp_addAssoc" (formula "1") (term "0,0"))
+ (rule "jmod_axiom" (formula "89") (term "1,2,1,0,0"))
+ (rule "polySimp_mulLiterals" (formula "89") (term "1,1,2,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "89") (term "2,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "89") (term "0,2,1,0,0"))
+ (rule "jmod_axiom" (formula "47") (term "0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "47") (term "1,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "47") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "47") (term "1,0"))
+ (rule "polySimp_mulLiterals" (formula "47") (term "1,1,0"))
+ (rule "polySimp_rightDist" (formula "47") (term "0,1,0"))
+ (rule "polySimp_mulAssoc" (formula "47") (term "0,0,1,0"))
+ (rule "polySimp_mulComm0" (formula "47") (term "0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "47") (term "0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "47") (term "0,0,1,0"))
+ (rule "polySimp_addComm1" (formula "47") (term "0"))
+ (rule "polySimp_addAssoc" (formula "47") (term "0,0"))
+ (rule "polySimp_addAssoc" (formula "47") (term "0,0,0"))
+ (rule "polySimp_addComm0" (formula "47") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "47") (term "0,0,0"))
+ (rule "add_literals" (formula "47") (term "1,1,0,0,0"))
+ (rule "times_zero_1" (formula "47") (term "1,0,0,0"))
+ (rule "add_zero_right" (formula "47") (term "0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "32") (term "0,0,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "32") (term "1,0,0,0,0,0"))
+ (rule "polySimp_rightDist" (formula "32") (term "1,0,0,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "32") (term "1,1,0,0,0,0,0"))
+ (rule "mul_literals" (formula "32") (term "0,1,0,0,0,0,0"))
+ (rule "polySimp_elimOne" (formula "32") (term "1,1,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "25"))
+ (rule "polySimp_mulComm0" (formula "25") (term "1"))
+ (rule "polySimp_rightDist" (formula "25") (term "1"))
+ (rule "mul_literals" (formula "25") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "25") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "25") (term "1,1"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "57"))
+ (rule "polySimp_mulLiterals" (formula "57") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "2"))
+ (rule "polySimp_mulComm0" (formula "2") (term "1"))
+ (rule "polySimp_rightDist" (formula "2") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "2") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "2") (term "1,1"))
+ (rule "polySimp_rightDist" (formula "2") (term "0,1"))
+ (rule "mul_literals" (formula "2") (term "0,0,1"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "1"))
+ (rule "polySimp_mulComm0" (formula "1") (term "1"))
+ (rule "polySimp_rightDist" (formula "1") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "1") (term "1,1"))
+ (rule "polySimp_rightDist" (formula "1") (term "0,1"))
+ (rule "mul_literals" (formula "1") (term "0,0,1"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "47"))
+ (rule "polySimp_mulLiterals" (formula "47") (term "0"))
+ (rule "polySimp_elimOne" (formula "47") (term "0"))
+ (rule "inEqSimp_subsumption1" (formula "23") (ifseqformula "24"))
+ (rule "leq_literals" (formula "23") (term "0"))
+ (builtin "One Step Simplification" (formula "23"))
+ (rule "true_left" (formula "23"))
+ (rule "inEqSimp_subsumption0" (formula "2") (ifseqformula "56"))
+ (rule "inEqSimp_homoInEq0" (formula "2") (term "0"))
+ (rule "polySimp_mulComm0" (formula "2") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "2") (term "1,0,0"))
+ (rule "polySimp_mulAssoc" (formula "2") (term "0,1,0,0"))
+ (rule "polySimp_mulComm0" (formula "2") (term "0,0,1,0,0"))
+ (rule "polySimp_mulLiterals" (formula "2") (term "0,1,0,0"))
+ (rule "polySimp_elimOne" (formula "2") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "2") (term "0,0"))
+ (rule "polySimp_addComm1" (formula "2") (term "0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "2") (term "0,0"))
+ (rule "add_literals" (formula "2") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "2") (term "1,0,0"))
+ (rule "add_zero_right" (formula "2") (term "0,0"))
+ (rule "polySimp_pullOutFactor2b" (formula "2") (term "0,0"))
+ (rule "add_literals" (formula "2") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "2") (term "1,0,0"))
+ (rule "add_zero_right" (formula "2") (term "0,0"))
+ (rule "qeq_literals" (formula "2") (term "0"))
+ (builtin "One Step Simplification" (formula "2"))
+ (rule "true_left" (formula "2"))
+ (rule "inEqSimp_subsumption1" (formula "28") (ifseqformula "26"))
+ (rule "leq_literals" (formula "28") (term "0"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "true_left" (formula "28"))
+ (rule "inEqSimp_subsumption1" (formula "13") (ifseqformula "24"))
+ (rule "leq_literals" (formula "13") (term "0"))
+ (builtin "One Step Simplification" (formula "13"))
+ (rule "true_left" (formula "13"))
+ (rule "pullOutSelect" (formula "85") (term "0") (inst "selectSK=java_lang_Object_created__0"))
+ (rule "simplifySelectOfMemset" (formula "1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "simplifySelectOfStore" (formula "1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "simplifySelectOfStore" (formula "1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "simplifySelectOfStore" (formula "1"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "simplifySelectOfCreate" (formula "1"))
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "66")))
+ (rule "castDel" (formula "1") (term "0"))
+ (rule "applyEqReverse" (formula "86") (term "0") (ifseqformula "1"))
+ (builtin "One Step Simplification" (formula "86"))
+ (rule "closeTrue" (formula "86"))
+ )
+ )
+ )
+ )
+ )
+ )
+ (branch "Null Reference (newObject = null)"
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "61")))
+ (rule "closeFalse" (formula "1"))
+ )
+ )
+ )
+ )
+ )
+ )
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "65"))
+ (rule "equal_literals" (formula "65") (term "0"))
+ (builtin "One Step Simplification" (formula "65"))
+ (rule "closeTrue" (formula "65"))
+ )
+ )
+ )
+ (branch "Exceptional Post (classify_locally_batched)"
+ (builtin "One Step Simplification" (formula "53"))
+ (builtin "One Step Simplification" (formula "33"))
+ (rule "andLeft" (formula "33"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "34") (term "1,0") (ifseqformula "33"))
+ (rule "andLeft" (formula "34"))
+ (rule "andLeft" (formula "35"))
+ (rule "andLeft" (formula "34"))
+ (rule "andLeft" (formula "36"))
+ (rule "notLeft" (formula "34"))
+ (rule "close" (formula "38") (ifseqformula "37"))
+ )
+ (branch "Pre (classify_locally_batched)"
+ (builtin "One Step Simplification" (formula "51") (ifInst "" (formula "12")) (ifInst "" (formula "50")) (ifInst "" (formula "48")) (ifInst "" (formula "49")) (ifInst "" (formula "1")) (ifInst "" (formula "50")) (ifInst "" (formula "4")) (ifInst "" (formula "48")) (ifInst "" (formula "9")) (ifInst "" (formula "49")) (ifInst "" (formula "10")))
+ (rule "expand_inInt" (formula "51") (term "1"))
+ (rule "expand_inInt" (formula "51") (term "0"))
+ (rule "replace_int_MIN" (formula "51") (term "0,1,1"))
+ (rule "replace_int_MAX" (formula "51") (term "1,0,1"))
+ (rule "replace_int_MAX" (formula "51") (term "1,0,0"))
+ (rule "replace_int_MIN" (formula "51") (term "0,1,0"))
+ (rule "replace_known_left" (formula "51") (term "0,0") (ifseqformula "5"))
+ (builtin "One Step Simplification" (formula "51") (ifInst "" (formula "7")))
+ (rule "inEqSimp_ltToLeq" (formula "24") (term "0,0,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "24") (term "1,0,0,0,0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "51") (term "1"))
+ (rule "replace_known_left" (formula "51") (term "1") (ifseqformula "8"))
+ (builtin "One Step Simplification" (formula "51"))
+ (rule "inEqSimp_leqRight" (formula "51"))
+ (rule "polySimp_mulComm0" (formula "1") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "1") (term "0"))
+ (rule "add_literals" (formula "1") (term "0,0"))
+ (rule "inEqSimp_homoInEq1" (formula "18"))
+ (rule "polySimp_addComm1" (formula "18") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "25") (term "0,0,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "25") (term "1,0,0,0,0,0"))
+ (rule "polySimp_rightDist" (formula "25") (term "1,0,0,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "25") (term "1,1,0,0,0,0,0"))
+ (rule "mul_literals" (formula "25") (term "0,1,0,0,0,0,0"))
+ (rule "polySimp_elimOne" (formula "25") (term "1,1,0,0,0,0,0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "1"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "0"))
+ (rule "polySimp_elimOne" (formula "1") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "18"))
+ (rule "polySimp_mulComm0" (formula "18") (term "1"))
+ (rule "polySimp_rightDist" (formula "18") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "18") (term "1,1"))
+ (rule "mul_literals" (formula "18") (term "0,1"))
+ (rule "polySimp_elimOne" (formula "18") (term "1,1"))
+ (rule "inEqSimp_subsumption0" (formula "6") (ifseqformula "1"))
+ (rule "leq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "inEqSimp_contradInEq0" (formula "6") (ifseqformula "1"))
+ (rule "qeq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "closeFalse" (formula "6"))
+ )
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_locally_batched((I,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_locally_batched((I,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..87454dd
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__classify_locally_batched((I,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,8937 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Apr 17 12:45:31 CEST 2023
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L , finalFields-finalFields\\:immutable
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Apr 17 12:45:31 CEST 2023
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:classify_locally_batched([I,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:classify_locally_batched([I,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "2" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "37667")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,1,1,1,1,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,1,1,1,1,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,1,1,1,1,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "10"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "10"))
+(rule "notLeft" (formula "9"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "notLeft" (formula "12"))
+(rule "notLeft" (formula "11"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "15"))
+(rule "notLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
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+ (rule "polySimp_addAssoc" (formula "32") (term "0,0,1,0,0,0,1,0"))
+ (rule "add_literals" (formula "32") (term "0,0,0,1,0,0,0,1,0"))
+ (rule "add_zero_left" (formula "32") (term "0,0,1,0,0,0,1,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "32") (term "1,0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "32") (term "1,1,0,0,0,1,0"))
+ (rule "polySimp_elimOne" (formula "32") (term "1,1,0,0,0,1,0"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Tree" (formula "53") (term "1") (inst "i_0=i_0") (inst "i=i_1"))
+ (builtin "One Step Simplification" (formula "53") (ifInst "" (formula "60")) (ifInst "" (formula "36")))
+ (rule "expand_inInt" (formula "53") (term "1,0,0,1,1"))
+ (rule "expand_inInt" (formula "53") (term "1,0,0,1,0,1"))
+ (rule "replace_int_MAX" (formula "53") (term "1,0,1,0,0,1,1"))
+ (rule "replace_int_MIN" (formula "53") (term "0,1,1,0,0,1,1"))
+ (rule "replace_int_MAX" (formula "53") (term "1,0,1,0,0,1,0,1"))
+ (rule "replace_int_MIN" (formula "53") (term "0,1,1,0,0,1,0,1"))
+ (rule "translateJavaSubInt" (formula "53") (term "3,0,1,0,0,1"))
+ (rule "translateJavaSubInt" (formula "53") (term "0,2,1,1,0,1,1"))
+ (rule "translateJavaShiftLeftInt" (formula "53") (term "1,1,0,0,0,0,0,1"))
+ (rule "eqSymm" (formula "53") (term "1,0,1,1"))
+ (rule "polySimp_elimSub" (formula "53") (term "3,0,1,0,0,1"))
+ (rule "mul_literals" (formula "53") (term "1,3,0,1,0,0,1"))
+ (rule "polySimp_elimSub" (formula "53") (term "0,2,0,1,0,1,1"))
+ (rule "mul_literals" (formula "53") (term "1,0,2,0,1,0,1,1"))
+ (rule "polySimp_addComm0" (formula "53") (term "3,0,1,0,0,1"))
+ (rule "polySimp_addComm0" (formula "53") (term "0,2,0,1,0,1,1"))
+ (rule "inEqSimp_ltToLeq" (formula "53") (term "1,0,0,0,1,1"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1,0,0,1,0,0,0,1,1"))
+ (rule "inEqSimp_ltToLeq" (formula "53") (term "1,0,0,0,1,0,1"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1,0,0,1,0,0,0,1,0,1"))
+ (rule "inEqSimp_ltToLeq" (formula "53") (term "1,1,0,1,0,1"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1,0,0,1,1,0,1,0,1"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "0,1,0,0,0,0,1"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "0,0,0,0,1,1"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "1,1,0,0,0,0,1"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "1,0,0,0,1"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "1,0,0,0,0,0,0,1"))
+ (rule "replace_known_left" (formula "53") (term "1,0,0,0,0,0,0,1") (ifseqformula "35"))
+ (builtin "One Step Simplification" (formula "53"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "1,1,0,0,1,0,1"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "1,1,0,0,1,1"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "0,1,0,1,0,1"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "0,0,0,0,1,0,1"))
+ (rule "applyEq" (formula "53") (term "1,1,1,0,0,0,0,1") (ifseqformula "29"))
+ (rule "replace_known_left" (formula "53") (term "1,1,0,0,0,0,1") (ifseqformula "43"))
+ (builtin "One Step Simplification" (formula "53"))
+ (rule "applyEq" (formula "53") (term "1,0,1,0,1,1") (ifseqformula "30"))
+ (rule "applyEq" (formula "53") (term "0,0,1,0,0,0,1") (ifseqformula "30"))
+ (rule "inEqSimp_commuteGeq" (formula "53") (term "1,0,0,0,1"))
+ (rule "applyEq" (formula "53") (term "0,0,0,0,0,0,0,0,1") (ifseqformula "30"))
+ (rule "replace_known_right" (formula "53") (term "0,0,0,0,0,0,0,1") (ifseqformula "61"))
+ (builtin "One Step Simplification" (formula "53"))
+ (rule "applyEq" (formula "53") (term "0,1,0,0,0,0,1") (ifseqformula "29"))
+ (rule "replace_known_left" (formula "53") (term "1,0,0,0,0,1") (ifseqformula "28"))
+ (builtin "One Step Simplification" (formula "53"))
+ (rule "applyEq" (formula "53") (term "1,3,0,1,0,0,1") (ifseqformula "29"))
+ (rule "applyEq" (formula "53") (term "1,0,1,0,0,1") (ifseqformula "30"))
+ (rule "applyEq" (formula "53") (term "0,0,0,0,0,1") (ifseqformula "29"))
+ (rule "eqSymm" (formula "53") (term "0,0,0,0,1"))
+ (rule "applyEq" (formula "53") (term "0,1,0,0,0,1") (ifseqformula "29"))
+ (rule "inEqSimp_commuteLeq" (formula "53") (term "1,0,0,0,1"))
+ (rule "replace_known_left" (formula "53") (term "1,0,0,0,1") (ifseqformula "45"))
+ (builtin "One Step Simplification" (formula "53"))
+ (rule "applyEq" (formula "53") (term "0,1,0,0,1,1,0,1,0,1") (ifseqformula "29"))
+ (rule "applyEq" (formula "53") (term "0,1,0,0,1,0,0,0,1,1") (ifseqformula "29"))
+ (rule "applyEq" (formula "53") (term "0,1,0,0,1,0,0,0,1,0,1") (ifseqformula "29"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "53") (term "1,1,0,1,0,1"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1,1,1,0,1,0,1"))
+ (rule "polySimp_rightDist" (formula "53") (term "1,1,1,0,1,0,1"))
+ (rule "polySimp_mulLiterals" (formula "53") (term "1,1,1,1,0,1,0,1"))
+ (rule "mul_literals" (formula "53") (term "0,1,1,1,0,1,0,1"))
+ (rule "polySimp_elimOne" (formula "53") (term "1,1,1,1,0,1,0,1"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "53") (term "1,0,0,0,1,1"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1,1,0,0,0,1,1"))
+ (rule "polySimp_rightDist" (formula "53") (term "1,1,0,0,0,1,1"))
+ (rule "polySimp_mulLiterals" (formula "53") (term "1,1,1,0,0,0,1,1"))
+ (rule "mul_literals" (formula "53") (term "0,1,1,0,0,0,1,1"))
+ (rule "polySimp_elimOne" (formula "53") (term "1,1,1,0,0,0,1,1"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "53") (term "1,0,0,0,1,0,1"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1,1,0,0,0,1,0,1"))
+ (rule "polySimp_rightDist" (formula "53") (term "1,1,0,0,0,1,0,1"))
+ (rule "mul_literals" (formula "53") (term "0,1,1,0,0,0,1,0,1"))
+ (rule "polySimp_mulLiterals" (formula "53") (term "1,1,1,0,0,0,1,0,1"))
+ (rule "polySimp_elimOne" (formula "53") (term "1,1,1,0,0,0,1,0,1"))
+ (rule "javaShiftLeftIntDef" (formula "53") (term "0,0,0,0,1"))
+ (rule "mod_axiom" (formula "53") (term "1,0,0,0,0,0,1"))
+ (rule "polySimp_mulLiterals" (formula "53") (term "1,1,0,0,0,0,0,1"))
+ (rule "applyEq" (formula "53") (term "0,1,1,0,0,0,0,0,1") (ifseqformula "37"))
+ (rule "times_zero_2" (formula "53") (term "1,1,0,0,0,0,0,1"))
+ (rule "add_zero_right" (formula "53") (term "1,0,0,0,0,0,1"))
+ (rule "shiftLeftDef" (formula "53") (term "0,0,0,0,0,1"))
+ (rule "polySimp_elimNeg" (formula "53") (term "1,1,0,0,0,0,0,1"))
+ (rule "shiftLeftPositiveShiftDef" (formula "53") (term "2,0,0,0,0,0,1"))
+ (rule "polySimp_elimOneLeft0" (formula "53") (term "2,0,0,0,0,0,1"))
+ (rule "shiftRightPositiveShiftDef" (formula "53") (term "1,0,0,0,0,0,1"))
+ (rule "inEqSimp_ltToLeq" (formula "53") (term "0,0,0,0,0,0,1"))
+ (rule "times_zero_1" (formula "53") (term "1,0,0,0,0,0,0,0,0,1"))
+ (rule "add_zero_right" (formula "53") (term "0,0,0,0,0,0,0,0,1"))
+ (rule "applyEq" (formula "53") (term "2,0,0,0,0,0,1") (ifseqformula "39"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "53") (term "0,0,0,0,0,0,1"))
+ (rule "mul_literals" (formula "53") (term "1,0,0,0,0,0,0,1"))
+ (rule "inEqSimp_contradInEq1" (formula "53") (term "0,0,0,0,0,0,1") (ifseqformula "35"))
+ (rule "qeq_literals" (formula "53") (term "0,0,0,0,0,0,0,1"))
+ (builtin "One Step Simplification" (formula "53"))
+ (rule "commute_or" (formula "56") (term "1,0,0,0"))
+ (rule "commute_or" (formula "56") (term "1,0,0,1,0"))
+ (rule "commute_or" (formula "57") (term "1,0,0,0"))
+ (rule "commute_or" (formula "32") (term "1,0,0"))
+ (rule "nnf_notAnd" (formula "31") (term "0,0"))
+ (rule "Contract_axiom_for_isSortedSlice_in_Functions" (formula "46") (term "0"))
+ (rule "replace_known_left" (formula "46") (term "0,1") (ifseqformula "47"))
+ (builtin "One Step Simplification" (formula "46") (ifInst "" (formula "62")) (ifInst "" (formula "3")))
+ (rule "replace_known_left" (formula "54") (term "1,0,0,1") (ifseqformula "46"))
+ (builtin "One Step Simplification" (formula "54"))
+ (rule "Definition_axiom_for_isSortedSlice_in_de_wiesler_Functions" (formula "47") (term "0") (inst "i=i_1"))
+ (builtin "One Step Simplification" (formula "47"))
+ (rule "expand_inInt" (formula "47") (term "1,0,0"))
+ (rule "replace_int_MIN" (formula "47") (term "0,1,1,0,0"))
+ (rule "replace_int_MAX" (formula "47") (term "1,0,1,0,0"))
+ (rule "translateJavaSubInt" (formula "47") (term "1,1,0,0,0"))
+ (rule "translateJavaAddInt" (formula "47") (term "0,2,1,1,0"))
+ (rule "polySimp_elimSub" (formula "47") (term "1,1,0,0,0"))
+ (rule "mul_literals" (formula "47") (term "1,1,1,0,0,0"))
+ (rule "polySimp_addComm0" (formula "47") (term "0,2,1,1,0"))
+ (rule "polySimp_addComm1" (formula "47") (term "1,1,0,0,0"))
+ (rule "add_literals" (formula "47") (term "0,1,1,0,0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "47") (term "1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "47") (term "1,0,0,1,0,0,0"))
+ (rule "mul_literals" (formula "47") (term "0,1,0,0,1,0,0,0"))
+ (rule "polySimp_addAssoc" (formula "47") (term "0,0,1,0,0,0"))
+ (rule "add_literals" (formula "47") (term "0,0,0,1,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "47") (term "0,0,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "47") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "47") (term "1,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "47") (term "1,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "47") (term "1,1,0,0,0"))
+ (rule "polySimp_rightDist" (formula "47") (term "1,1,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "47") (term "1,1,1,0,0,0"))
+ (rule "mul_literals" (formula "47") (term "0,1,1,0,0,0"))
+ (rule "polySimp_elimOne" (formula "47") (term "1,1,1,0,0,0"))
+ (rule "commute_or" (formula "48") (term "1,0,0"))
+ (rule "commute_or_2" (formula "50") (term "0,0"))
+ (rule "commute_or_2" (formula "49") (term "0,0"))
+ (rule "arrayLengthNotNegative" (formula "11") (term "0"))
+ (rule "applyEq" (formula "11") (term "0") (ifseqformula "12"))
+ (rule "qeq_literals" (formula "11"))
+ (rule "true_left" (formula "11"))
+ (rule "arrayLengthIsAShort" (formula "11") (term "0"))
+ (rule "expand_inShort" (formula "11"))
+ (rule "replace_short_MIN" (formula "11") (term "0,1"))
+ (rule "replace_short_MAX" (formula "11") (term "1,0"))
+ (rule "andLeft" (formula "11"))
+ (rule "inEqSimp_commuteLeq" (formula "12"))
+ (rule "applyEqRigid" (formula "12") (term "0") (ifseqformula "13"))
+ (rule "qeq_literals" (formula "12"))
+ (rule "true_left" (formula "12"))
+ (rule "applyEqRigid" (formula "11") (term "0") (ifseqformula "12"))
+ (rule "leq_literals" (formula "11"))
+ (rule "closeFalse" (formula "11"))
+ )
+ )
+ (branch "CUT: buffers.buffer = null FALSE"
+ (builtin "One Step Simplification" (formula "77"))
+ (rule "notRight" (formula "77"))
+ (rule "replace_known_right" (formula "51") (term "0,1,0") (ifseqformula "77"))
+ (builtin "One Step Simplification" (formula "51"))
+ (rule "applyEq" (formula "70") (term "1") (ifseqformula "1"))
+ (rule "applyEq" (formula "60") (term "0") (ifseqformula "1"))
+ (rule "eqSymm" (formula "60"))
+ (rule "applyEq" (formula "66") (term "0") (ifseqformula "1"))
+ (rule "eqSymm" (formula "66"))
+ (rule "applyEq" (formula "54") (term "1,2,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "68") (term "1") (ifseqformula "1"))
+ (rule "applyEq" (formula "53") (term "1,0,0,1,1,1,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "12") (term "0,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "63") (term "0") (ifseqformula "1"))
+ (rule "eqSymm" (formula "63"))
+ (rule "applyEq" (formula "14") (term "1,0,0,1,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "14") (term "1,0,1,1,0") (ifseqformula "1"))
+ (rule "applyEq" (formula "25") (term "1,0,1,0") (ifseqformula "1"))
+ (rule "arrayLengthNotNegative" (formula "20") (term "0"))
+ (rule "arrayLengthNotNegative" (formula "11") (term "0"))
+ (rule "applyEq" (formula "11") (term "0") (ifseqformula "12"))
+ (rule "qeq_literals" (formula "11"))
+ (rule "true_left" (formula "11"))
+ (rule "arrayLengthNotNegative" (formula "27") (term "0"))
+ (rule "inEqSimp_subsumption1" (formula "27") (ifseqformula "28"))
+ (rule "leq_literals" (formula "27") (term "0"))
+ (builtin "One Step Simplification" (formula "27"))
+ (rule "true_left" (formula "27"))
+ (rule "arrayLengthIsAShort" (formula "27") (term "0"))
+ (rule "expand_inShort" (formula "27"))
+ (rule "replace_short_MIN" (formula "27") (term "0,1"))
+ (rule "replace_short_MAX" (formula "27") (term "1,0"))
+ (rule "andLeft" (formula "27"))
+ (rule "inEqSimp_commuteLeq" (formula "27"))
+ (rule "inEqSimp_subsumption1" (formula "27") (ifseqformula "28"))
+ (rule "leq_literals" (formula "27") (term "0"))
+ (builtin "One Step Simplification" (formula "27"))
+ (rule "true_left" (formula "27"))
+ (rule "arrayLengthIsAShort" (formula "23") (term "0"))
+ (rule "expand_inShort" (formula "23"))
+ (rule "replace_short_MIN" (formula "23") (term "0,1"))
+ (rule "replace_short_MAX" (formula "23") (term "1,0"))
+ (rule "andLeft" (formula "23"))
+ (rule "inEqSimp_commuteLeq" (formula "23"))
+ (rule "inEqSimp_subsumption1" (formula "23") (ifseqformula "20"))
+ (rule "leq_literals" (formula "23") (term "0"))
+ (builtin "One Step Simplification" (formula "23"))
+ (rule "true_left" (formula "23"))
+ (rule "arrayLengthIsAShort" (formula "11") (term "0"))
+ (rule "expand_inShort" (formula "11"))
+ (rule "replace_short_MAX" (formula "11") (term "1,0"))
+ (rule "replace_short_MIN" (formula "11") (term "0,1"))
+ (rule "andLeft" (formula "11"))
+ (rule "inEqSimp_commuteLeq" (formula "12"))
+ (rule "applyEq" (formula "12") (term "0") (ifseqformula "13"))
+ (rule "qeq_literals" (formula "12"))
+ (rule "true_left" (formula "12"))
+ (rule "applyEq" (formula "11") (term "0") (ifseqformula "12"))
+ (rule "leq_literals" (formula "11"))
+ (rule "closeFalse" (formula "11"))
+ )
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "52") (ifInst "" (formula "12")))
+ (rule "closeTrue" (formula "52"))
+ )
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "52"))
+ (rule "closeTrue" (formula "52"))
+ )
+ )
+ )
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__equal_buckets()).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__equal_buckets()).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..4b29e0d
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__equal_buckets()).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,98 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Thu Jun 02 21:24:55 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Thu Jun 02 21:24:55 CEST 2022
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:equal_buckets()].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:equal_buckets()].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "13")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre_0,o,f"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "2"))
+(rule "assignment" (formula "8"))
+(rule "methodBodyExpand" (formula "8") (term "1") (newnames "heapBefore_equal_buckets,savedHeapBefore_equal_buckets"))
+ (builtin "One Step Simplification" (formula "8"))
+(rule "returnUnfold" (formula "8") (term "1") (inst "#v0=x"))
+(rule "variableDeclarationAssign" (formula "8") (term "1"))
+(rule "variableDeclaration" (formula "8") (term "1") (newnames "x"))
+(rule "assignment_read_attribute_this_final" (formula "8"))
+ (builtin "One Step Simplification" (formula "8"))
+(rule "methodCallReturn" (formula "8") (term "1"))
+(rule "assignment" (formula "8") (term "1"))
+ (builtin "One Step Simplification" (formula "8"))
+(rule "methodCallEmpty" (formula "8") (term "1"))
+(rule "tryEmpty" (formula "8") (term "1"))
+(rule "emptyModality" (formula "8") (term "1"))
+(rule "andRight" (formula "8"))
+(branch "Case 1"
+ (builtin "One Step Simplification" (formula "8") (ifInst "" (formula "5")))
+ (rule "closeTrue" (formula "8"))
+)
+(branch "Case 2"
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "closeTrue" (formula "8"))
+)
+)
+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__finish_batch((I,(I,int,int,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__finish_batch((I,(I,int,int,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..fa37a18
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__finish_batch((I,(I,int,int,int,int,(I,de.wiesler.Buffers)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,9857 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Sun Jun 05 14:06:18 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Sun Jun 05 14:06:18 CEST 2022
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:finish_batch([I,[I,int,int,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:finish_batch([I,[I,int,int,int,int,[I,de.wiesler.Buffers)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "70852")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,0,0,1,0,0,0"))
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+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
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+(rule "translateJavaSubInt" (formula "49") (term "0,0"))
+(rule "replace_known_right" (formula "15") (term "0") (ifseqformula "55"))
+ (builtin "One Step Simplification" (formula "15"))
+(rule "replace_known_right" (formula "14") (term "0") (ifseqformula "56"))
+ (builtin "One Step Simplification" (formula "14"))
+(rule "replace_known_right" (formula "5") (term "0") (ifseqformula "57"))
+ (builtin "One Step Simplification" (formula "5"))
+(rule "replace_known_right" (formula "4") (term "0") (ifseqformula "58"))
+ (builtin "One Step Simplification" (formula "4"))
+(rule "polySimp_elimSub" (formula "48") (term "0,0"))
+(rule "polySimp_elimSub" (formula "49") (term "0,0"))
+(rule "polySimp_addComm0" (formula "19") (term "1"))
+(rule "disjointDefinition" (formula "40"))
+ (builtin "One Step Simplification" (formula "40"))
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+(rule "disjointDefinition" (formula "39"))
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+(rule "inEqSimp_commuteLeq" (formula "9"))
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+(rule "assignment" (formula "59") (term "1"))
+ (builtin "One Step Simplification" (formula "59"))
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+ (builtin "One Step Simplification" (formula "59"))
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+(branch "Invariant Initially Valid"
+ (rule "closeTrue" (formula "65"))
+)
+(branch "Invariant Preserved and Used"
+ (builtin "One Step Simplification" (formula "66"))
+ (rule "expand_inInt" (formula "66") (term "0,0,1,0,0"))
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+ (rule "inEqSimp_sepNegMonomial1" (formula "2"))
+ (rule "polySimp_mulLiterals" (formula "2") (term "0"))
+ (rule "polySimp_elimOne" (formula "2") (term "0"))
+ (rule "inEqSimp_exactShadow3" (formula "46") (ifseqformula "7"))
+ (rule "polySimp_mulComm0" (formula "46") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "46") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "46"))
+ (rule "polySimp_mulLiterals" (formula "46") (term "0"))
+ (rule "polySimp_elimOne" (formula "46") (term "0"))
+ (rule "inEqSimp_exactShadow3" (formula "47") (ifseqformula "48"))
+ (rule "polySimp_mulComm0" (formula "47") (term "0,0"))
+ (rule "polySimp_addAssoc" (formula "47") (term "0"))
+ (rule "polySimp_addComm0" (formula "47") (term "0,0"))
+ (rule "polySimp_pullOutFactor2b" (formula "47") (term "0"))
+ (rule "add_literals" (formula "47") (term "1,1,0"))
+ (rule "times_zero_1" (formula "47") (term "1,0"))
+ (rule "add_zero_right" (formula "47") (term "0"))
+ (rule "elimGcdGeq_antec" (formula "47") (inst "elimGcd=Z(6(1(#)))") (inst "elimGcdLeftDiv=l_0") (inst "elimGcdRightDiv=Z(0(#))"))
+ (rule "add_zero_right" (formula "47") (term "0,0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "47") (term "1,0,1,0"))
+ (rule "leq_literals" (formula "47") (term "0,0"))
+ (builtin "One Step Simplification" (formula "47"))
+ (rule "times_zero_1" (formula "47") (term "1,0,0,0,0"))
+ (rule "add_literals" (formula "47") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "47") (term "0,0"))
+ (rule "add_literals" (formula "47") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "47") (term "1,0,0"))
+ (rule "add_literals" (formula "47") (term "0,0"))
+ (rule "leq_literals" (formula "47") (term "0"))
+ (builtin "One Step Simplification" (formula "47"))
+ (rule "inEqSimp_subsumption1" (formula "27") (ifseqformula "47"))
+ (rule "leq_literals" (formula "27") (term "0"))
+ (builtin "One Step Simplification" (formula "27"))
+ (rule "true_left" (formula "27"))
+ (rule "inEqSimp_exactShadow3" (formula "53") (ifseqformula "49"))
+ (rule "times_zero_1" (formula "53") (term "0,0"))
+ (rule "add_zero_left" (formula "53") (term "0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "53"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1"))
+ (rule "polySimp_rightDist" (formula "53") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "53") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "53") (term "1,1"))
+ (rule "polySimp_mulComm0" (formula "53") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "53") (term "0,1"))
+ (rule "inEqSimp_exactShadow3" (formula "6") (ifseqformula "1"))
+ (rule "mul_literals" (formula "6") (term "0,0"))
+ (rule "add_zero_left" (formula "6") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "6"))
+ (rule "polySimp_mulLiterals" (formula "6") (term "0"))
+ (rule "polySimp_elimOne" (formula "6") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "27") (ifseqformula "6"))
+ (rule "inEqSimp_homoInEq0" (formula "27") (term "0"))
+ (rule "polySimp_mulComm0" (formula "27") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "27") (term "1,0,0"))
+ (rule "polySimp_mulLiterals" (formula "27") (term "1,1,0,0"))
+ (rule "mul_literals" (formula "27") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "27") (term "0,0"))
+ (rule "polySimp_addComm1" (formula "27") (term "0,0,0"))
+ (rule "add_literals" (formula "27") (term "0,0,0,0"))
+ (rule "polySimp_pullOutFactor0b" (formula "27") (term "0,0"))
+ (rule "add_literals" (formula "27") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "27") (term "1,0,0"))
+ (rule "add_literals" (formula "27") (term "0,0"))
+ (rule "qeq_literals" (formula "27") (term "0"))
+ (builtin "One Step Simplification" (formula "27"))
+ (rule "true_left" (formula "27"))
+ (rule "inEqSimp_exactShadow3" (formula "3") (ifseqformula "55"))
+ (rule "polySimp_rightDist" (formula "3") (term "0,0"))
+ (rule "mul_literals" (formula "3") (term "0,0,0"))
+ (rule "polySimp_addComm1" (formula "3") (term "0"))
+ (rule "add_literals" (formula "3") (term "0,0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "3"))
+ (rule "polySimp_mulLiterals" (formula "3") (term "0"))
+ (rule "polySimp_elimOne" (formula "3") (term "0"))
+ (rule "inEqSimp_exactShadow3" (formula "27") (ifseqformula "49"))
+ (rule "mul_literals" (formula "27") (term "0,0"))
+ (rule "polySimp_addAssoc" (formula "27") (term "0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "27"))
+ (rule "polySimp_mulComm0" (formula "27") (term "1"))
+ (rule "polySimp_rightDist" (formula "27") (term "1"))
+ (rule "polySimp_mulLiterals" (formula "27") (term "1,1"))
+ (rule "mul_literals" (formula "27") (term "0,1"))
+ (rule "inEqSimp_exactShadow3" (formula "41") (ifseqformula "44"))
+ (rule "polySimp_mulComm0" (formula "41") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "41") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "41"))
+ (rule "polySimp_mulLiterals" (formula "41") (term "0"))
+ (rule "polySimp_elimOne" (formula "41") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "24") (ifseqformula "41"))
+ (rule "leq_literals" (formula "24") (term "0"))
+ (builtin "One Step Simplification" (formula "24"))
+ (rule "true_left" (formula "24"))
+ (rule "inEqSimp_exactShadow3" (formula "39") (ifseqformula "7"))
+ (rule "times_zero_1" (formula "39") (term "0,0"))
+ (rule "add_zero_left" (formula "39") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "39"))
+ (rule "polySimp_mulLiterals" (formula "39") (term "0"))
+ (rule "inEqSimp_contradInEq5" (formula "39") (ifseqformula "48"))
+ (rule "greater_literals" (formula "39") (term "0,0"))
+ (builtin "One Step Simplification" (formula "39"))
+ (rule "times_zero_1" (formula "39") (term "1,0"))
+ (rule "qeq_literals" (formula "39") (term "0"))
+ (builtin "One Step Simplification" (formula "39"))
+ (rule "closeFalse" (formula "39"))
+ )
+ )
+ )
+ )
+ (branch "Null Reference (_indices = null)"
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "81")))
+ (rule "closeFalse" (formula "1"))
+ )
+ (branch "Index Out of Bounds (_indices != null, but j Out of Bounds!)"
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "81")))
+ (rule "false_right" (formula "82"))
+ (rule "inEqSimp_ltToLeq" (formula "2"))
+ (rule "polySimp_mulComm0" (formula "2") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "2") (term "0"))
+ (rule "inEqSimp_ltToLeq" (formula "53") (term "0,0,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1,0,0,0,0,0,0,0"))
+ (rule "inEqSimp_ltToLeq" (formula "1") (term "1"))
+ (rule "times_zero_1" (formula "1") (term "1,0,0,1"))
+ (rule "add_literals" (formula "1") (term "0,0,1"))
+ (rule "inEqSimp_homoInEq0" (formula "46"))
+ (rule "polySimp_mulComm0" (formula "46") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "46") (term "1,0"))
+ (rule "polySimp_mulComm0" (formula "46") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "46") (term "0"))
+ (rule "inEqSimp_homoInEq1" (formula "36"))
+ (rule "polySimp_addComm1" (formula "36") (term "0"))
+ (rule "jmod_axiom" (formula "48") (term "0"))
+ (rule "polySimp_mulLiterals" (formula "48") (term "1,0"))
+ (rule "polySimp_sepNegMonomial" (formula "48"))
+ (rule "polySimp_mulLiterals" (formula "48") (term "0"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "2"))
+ (rule "polySimp_mulLiterals" (formula "2") (term "0"))
+ (rule "polySimp_elimOne" (formula "2") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "53") (term "0,0,0,0,0"))
+ (rule "polySimp_mulComm0" (formula "53") (term "1,0,0,0,0,0"))
+ (rule "polySimp_rightDist" (formula "53") (term "1,0,0,0,0,0"))
+ (rule "polySimp_mulLiterals" (formula "53") (term "1,1,0,0,0,0,0"))
+ (rule "mul_literals" (formula "53") (term "0,1,0,0,0,0,0"))
+ (rule "polySimp_elimOne" (formula "53") (term "1,1,0,0,0,0,0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "1") (term "1"))
+ (rule "mul_literals" (formula "1") (term "1,1"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "46"))
+ (rule "polySimp_mulLiterals" (formula "46") (term "0"))
+ (rule "polySimp_elimOne" (formula "46") (term "0"))
+ (rule "inEqSimp_sepPosMonomial0" (formula "36"))
+ (rule "polySimp_mulComm0" (formula "36") (term "1"))
+ (rule "polySimp_rightDist" (formula "36") (term "1"))
+ (rule "mul_literals" (formula "36") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "36") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "36") (term "1,1"))
+ (rule "inEqSimp_subsumption1" (formula "51") (ifseqformula "49"))
+ (rule "leq_literals" (formula "51") (term "0"))
+ (builtin "One Step Simplification" (formula "51"))
+ (rule "true_left" (formula "51"))
+ (rule "inEqSimp_subsumption1" (formula "35") (ifseqformula "33"))
+ (rule "leq_literals" (formula "35") (term "0"))
+ (builtin "One Step Simplification" (formula "35"))
+ (rule "true_left" (formula "35"))
+ (rule "inEqSimp_subsumption0" (formula "49") (ifseqformula "50"))
+ (rule "leq_literals" (formula "49") (term "0"))
+ (builtin "One Step Simplification" (formula "49"))
+ (rule "true_left" (formula "49"))
+ (rule "inEqSimp_subsumption1" (formula "41") (ifseqformula "39"))
+ (rule "leq_literals" (formula "41") (term "0"))
+ (builtin "One Step Simplification" (formula "41"))
+ (rule "true_left" (formula "41"))
+ (rule "inEqSimp_contradInEq1" (formula "1") (term "0") (ifseqformula "2"))
+ (rule "inEqSimp_homoInEq1" (formula "1") (term "0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "1") (term "0,0,0"))
+ (rule "add_literals" (formula "1") (term "1,1,0,0,0"))
+ (rule "times_zero_1" (formula "1") (term "1,0,0,0"))
+ (rule "add_literals" (formula "1") (term "0,0,0"))
+ (rule "leq_literals" (formula "1") (term "0,0"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "inEqSimp_subsumption1" (formula "6") (ifseqformula "2"))
+ (rule "inEqSimp_homoInEq0" (formula "6") (term "0"))
+ (rule "polySimp_pullOutFactor1b" (formula "6") (term "0,0"))
+ (rule "add_literals" (formula "6") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "6") (term "1,0,0"))
+ (rule "add_zero_right" (formula "6") (term "0,0"))
+ (rule "qeq_literals" (formula "6") (term "0"))
+ (builtin "One Step Simplification" (formula "6"))
+ (rule "true_left" (formula "6"))
+ (rule "inEqSimp_subsumption1" (formula "20") (ifseqformula "36"))
+ (rule "leq_literals" (formula "20") (term "0"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "true_left" (formula "20"))
+ (rule "inEqSimp_contradInEq0" (formula "5") (ifseqformula "1"))
+ (rule "qeq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "closeFalse" (formula "5"))
+ )
+ )
+ (branch "if x_2 false"
+ (builtin "One Step Simplification" (formula "81"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "notLeft" (formula "1"))
+ (rule "elim_double_block_2" (formula "81") (term "1"))
+ (rule "blockBreak" (formula "81") (term "1"))
+ (rule "lsBreak" (formula "81") (term "1"))
+ (rule "assignment" (formula "81") (term "1"))
+ (builtin "One Step Simplification" (formula "81"))
+ (rule "methodCallReturn" (formula "81") (term "1"))
+ (rule "assignment" (formula "81") (term "1"))
+ (builtin "One Step Simplification" (formula "81"))
+ (rule "methodCallEmpty" (formula "81") (term "1"))
+ (rule "tryEmpty" (formula "81") (term "1"))
+ (rule "emptyModality" (formula "81") (term "1"))
+ (rule "andRight" (formula "81"))
+ (branch "Case 1"
+ (rule "impRight" (formula "81"))
+ (rule "andRight" (formula "82"))
+ (branch "Case 1"
+ (rule "andRight" (formula "82"))
+ (branch "Case 1"
+ (builtin "One Step Simplification" (formula "82") (ifInst "" (formula "11")))
+ (rule "closeTrue" (formula "82"))
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "82") (ifInst "" (formula "12")))
+ (rule "closeTrue" (formula "82"))
+ )
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "1"))
+ (builtin "One Step Simplification" (formula "82"))
+ (rule "closeTrue" (formula "82"))
+ )
+ )
+ (branch "Case 2"
+ (rule "impRight" (formula "81"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "closeFalse" (formula "1"))
+ )
+ )
+ )
+ (branch "Null Reference (_indices = null)"
+ (builtin "One Step Simplification" (formula "1") (ifInst "" (formula "80")))
+ (rule "closeFalse" (formula "1"))
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__from_sorted_samples((I,(I,int,int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__from_sorted_samples((I,(I,int,int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..520f58e
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__from_sorted_samples((I,(I,int,int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,5134 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Sep 05 21:28:36 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Sep 05 21:28:36 CEST 2022
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:from_sorted_samples([I,[I,int,int)].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:from_sorted_samples([I,[I,int,int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "2" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "51524")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,1,1,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,1,1,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,1,1,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "4"))
+(rule "notLeft" (formula "4"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "8"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "11"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "15"))
+(rule "andLeft" (formula "16"))
+(rule "andLeft" (formula "15"))
+(rule "translateJavaSubInt" (formula "11") (term "1,1,0,0,0"))
+(rule "translateJavaAddInt" (formula "11") (term "0,2,1,1,0"))
+(rule "translateJavaSubInt" (formula "14") (term "1"))
+(rule "replace_known_right" (formula "3") (term "0") (ifseqformula "19"))
+ (builtin "One Step Simplification" (formula "3"))
+(rule "replace_known_right" (formula "2") (term "0") (ifseqformula "20"))
+ (builtin "One Step Simplification" (formula "2"))
+(rule "polySimp_elimSub" (formula "11") (term "1,1,0,0,0"))
+(rule "mul_literals" (formula "11") (term "1,1,1,0,0,0"))
+(rule "polySimp_elimSub" (formula "14") (term "1"))
+(rule "mul_literals" (formula "14") (term "1,1"))
+(rule "polySimp_addComm0" (formula "11") (term "0,2,1,1,0"))
+(rule "polySimp_addComm0" (formula "11") (term "1,1,0,0,0"))
+(rule "polySimp_addComm0" (formula "14") (term "1"))
+(rule "disjointDefinition" (formula "12"))
+ (builtin "One Step Simplification" (formula "12"))
+(rule "notLeft" (formula "12"))
+(rule "eqSymm" (formula "18"))
+(rule "inEqSimp_commuteLeq" (formula "11") (term "0,0,0,0"))
+(rule "inEqSimp_commuteLeq" (formula "11") (term "1,1,0,0"))
+(rule "inEqSimp_commuteLeq" (formula "10"))
+(rule "inEqSimp_commuteLeq" (formula "9"))
+(rule "inEqSimp_commuteLeq" (formula "7"))
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+ (rule "qeq_literals" (formula "1") (term "0"))
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+ (rule "closeFalse" (formula "1"))
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+}
diff --git a/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__num_buckets()).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__num_buckets()).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..f9f5949
--- /dev/null
+++ b/src/main/key-overflow/Classifier/de.wiesler.Classifier(de.wiesler.Classifier__num_buckets()).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,98 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Thu Jun 02 21:25:12 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Thu Jun 02 21:25:12 CEST 2022
+contract=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:num_buckets()].JML normal_behavior operation contract.0
+name=de.wiesler.Classifier[de.wiesler.Classifier\\:\\:num_buckets()].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "13")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre_0,o,f"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
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+(rule "andLeft" (formula "1"))
+(rule "notLeft" (formula "2"))
+(rule "assignment" (formula "8"))
+(rule "methodBodyExpand" (formula "8") (term "1") (newnames "heapBefore_num_buckets,savedHeapBefore_num_buckets"))
+ (builtin "One Step Simplification" (formula "8"))
+(rule "returnUnfold" (formula "8") (term "1") (inst "#v0=x"))
+(rule "variableDeclarationAssign" (formula "8") (term "1"))
+(rule "variableDeclaration" (formula "8") (term "1") (newnames "x"))
+(rule "assignment_read_attribute_this_final" (formula "8"))
+ (builtin "One Step Simplification" (formula "8"))
+(rule "methodCallReturn" (formula "8") (term "1"))
+(rule "assignment" (formula "8") (term "1"))
+ (builtin "One Step Simplification" (formula "8"))
+(rule "methodCallEmpty" (formula "8") (term "1"))
+(rule "tryEmpty" (formula "8") (term "1"))
+(rule "emptyModality" (formula "8") (term "1"))
+(rule "andRight" (formula "8"))
+(branch "Case 1"
+ (builtin "One Step Simplification" (formula "8") (ifInst "" (formula "5")))
+ (rule "closeTrue" (formula "8"))
+)
+(branch "Case 2"
+ (builtin "One Step Simplification" (formula "8"))
+ (rule "closeTrue" (formula "8"))
+)
+)
+}
diff --git a/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__partition((I,int,int,(I,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__partition((I,int,int,(I,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..f353930
--- /dev/null
+++ b/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__partition((I,int,int,(I,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,9307 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Apr 17 12:52:46 CEST 2023
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L , finalFields-finalFields\\:immutable
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Apr 17 12:52:46 CEST 2023
+contract=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:partition([I,int,int,[I,de.wiesler.Storage)].JML normal_behavior operation contract.0
+name=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:partition([I,int,int,[I,de.wiesler.Storage)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "62593")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,1,1,1,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,1,1,1,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,1,1,1,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
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+(rule "translateJavaSubInt" (formula "17") (term "0"))
+(rule "replace_known_right" (formula "8") (term "0") (ifseqformula "22"))
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+(rule "replace_known_right" (formula "2") (term "0") (ifseqformula "24"))
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+(rule "inEqSimp_commuteLeq" (formula "6"))
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+(rule "assignment" (formula "25") (term "1"))
+ (builtin "One Step Simplification" (formula "25"))
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+(rule "commute_and_2" (formula "15") (term "0,0,0"))
+(rule "methodBodyExpand" (formula "25") (term "1") (newnames "heapBefore_partition,savedHeapBefore_partition"))
+ (builtin "One Step Simplification" (formula "25"))
+ (builtin "Block Contract (Internal)" (formula "25") (newnames "anonOut_heap,result_219,exc_259,heap_Before_BLOCK,savedHeap_Before_BLOCK,o,f"))
+(branch "Validity"
+ (builtin "One Step Simplification" (formula "21") (ifInst "" (formula "1")))
+ (builtin "One Step Simplification" (formula "26"))
+ (rule "translateJavaSubInt" (formula "21") (term "0,0"))
+ (rule "polySimp_elimSub" (formula "21") (term "0,0"))
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+ (rule "variableDeclaration" (formula "25") (term "1") (newnames "exc_259_1"))
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+ (builtin "One Step Simplification" (formula "25"))
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+ (rule "emptyModality" (formula "25") (term "1"))
+ (builtin "One Step Simplification" (formula "25"))
+ (rule "closeTrue" (formula "25"))
+)
+(branch "Precondition"
+ (rule "andRight" (formula "25"))
+ (branch
+ (builtin "One Step Simplification" (formula "25"))
+ (rule "translateJavaSubInt" (formula "25") (term "0,0"))
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+ (rule "polySimp_addComm0" (formula "25") (term "0,0"))
+ (rule "close" (formula "25") (ifseqformula "9"))
+ )
+ (branch
+ (builtin "One Step Simplification" (formula "25") (ifInst "" (formula "1")))
+ (rule "closeTrue" (formula "25"))
+ )
+)
+(branch "Usage"
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+ (rule "polySimp_elimOne" (formula "19") (term "1,1"))
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+ (rule "polySimp_elimOne" (formula "20") (term "0"))
+ (rule "inEqSimp_subsumption1" (formula "12") (ifseqformula "19"))
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+ (rule "add_literals" (formula "16") (term "0,0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "16"))
+ (rule "polySimp_mulLiterals" (formula "16") (term "0"))
+ (rule "polySimp_elimOne" (formula "16") (term "0"))
+ (rule "inEqSimp_subsumption0" (formula "15") (ifseqformula "16"))
+ (rule "leq_literals" (formula "15") (term "0"))
+ (builtin "One Step Simplification" (formula "15"))
+ (rule "true_left" (formula "15"))
+ (rule "inEqSimp_and_subsumption3" (formula "14") (term "0,0,0"))
+ (rule "leq_literals" (formula "14") (term "0,1,0,0,0,0"))
+ (builtin "One Step Simplification" (formula "14"))
+ (rule "nnf_imp2or" (formula "14") (term "0"))
+ (rule "nnf_notAnd" (formula "14") (term "0,0"))
+ (rule "inEqSimp_notLeq" (formula "14") (term "1,0,0"))
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+ (rule "mul_literals" (formula "14") (term "1,1,0,0"))
+ (rule "nnf_notAnd" (formula "14") (term "0,0,0"))
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+ (rule "add_zero_right" (formula "14") (term "0,0,1,0,0,0"))
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+ (rule "mul_literals" (formula "14") (term "1,1,0,0,0"))
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+ (rule "mul_literals" (formula "14") (term "1,0,0,0,0"))
+ (rule "Free_class_invariant_axiom_for_de_wiesler_Storage" (formula "18"))
+ (builtin "One Step Simplification" (formula "18"))
+ (rule "andLeft" (formula "18"))
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+ (rule "andLeft" (formula "27"))
+ (rule "andLeft" (formula "27"))
+ (rule "andLeft" (formula "27"))
+ (rule "andLeft" (formula "27"))
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+ (rule "mul_literals" (formula "21") (term "1"))
+ (rule "translateJavaMulInt" (formula "20") (term "1"))
+ (rule "mul_literals" (formula "20") (term "1"))
+ (rule "disjointDefinition" (formula "54"))
+ (builtin "One Step Simplification" (formula "54") (ifInst "" (formula "103")))
+ (rule "true_left" (formula "54"))
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+ (rule "true_left" (formula "53"))
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+ (builtin "One Step Simplification" (formula "52"))
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+ (rule "disjointDefinition" (formula "39"))
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+ (builtin "One Step Simplification" (formula "38"))
+ (rule "notLeft" (formula "38"))
+ (rule "eqSymm" (formula "43"))
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+ (rule "eqSymm" (formula "42"))
+ (rule "disjointDefinition" (formula "36"))
+ (builtin "One Step Simplification" (formula "36") (ifInst "" (formula "67")))
+ (rule "true_left" (formula "36"))
+ (rule "disjointDefinition" (formula "35"))
+ (builtin "One Step Simplification" (formula "35") (ifInst "" (formula "65")))
+ (rule "true_left" (formula "35"))
+ (rule "disjointDefinition" (formula "34"))
+ (builtin "One Step Simplification" (formula "34") (ifInst "" (formula "63")))
+ (rule "true_left" (formula "34"))
+ (rule "disjointDefinition" (formula "33"))
+ (builtin "One Step Simplification" (formula "33") (ifInst "" (formula "61")))
+ (rule "true_left" (formula "33"))
+ (rule "disjointDefinition" (formula "32"))
+ (builtin "One Step Simplification" (formula "32") (ifInst "" (formula "59")))
+ (rule "true_left" (formula "32"))
+ (rule "disjointDefinition" (formula "31"))
+ (builtin "One Step Simplification" (formula "31") (ifInst "" (formula "57")))
+ (rule "true_left" (formula "31"))
+ (rule "disjointDefinition" (formula "30"))
+ (builtin "One Step Simplification" (formula "30") (ifInst "" (formula "55")))
+ (rule "true_left" (formula "30"))
+ (rule "disjointDefinition" (formula "29"))
+ (builtin "One Step Simplification" (formula "29") (ifInst "" (formula "53")))
+ (rule "true_left" (formula "29"))
+ (rule "disjointDefinition" (formula "27"))
+ (builtin "One Step Simplification" (formula "27") (ifInst "" (formula "50")))
+ (rule "true_left" (formula "27"))
+ (rule "disjointDefinition" (formula "27"))
+ (builtin "One Step Simplification" (formula "27") (ifInst "" (formula "50")))
+ (rule "true_left" (formula "27"))
+ (rule "applyEq" (formula "27") (term "1,0") (ifseqformula "26"))
+ (rule "applyEq" (formula "28") (term "1,0") (ifseqformula "26"))
+ (rule "distributeIntersection" (formula "27") (term "0"))
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+ (rule "distributeIntersection" (formula "27") (term "0,0"))
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+ (rule "unionEqualsEmpty" (formula "28"))
+ (rule "andLeft" (formula "28"))
+ (rule "distributeIntersection" (formula "27") (term "0,0,0"))
+ (rule "distributeIntersection" (formula "27") (term "1,0,0"))
+ (rule "distributeIntersection" (formula "27") (term "0,1,0"))
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+ (rule "distributeIntersection" (formula "28") (term "0"))
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+ (rule "unionEqualsEmpty" (formula "27"))
+ (rule "andLeft" (formula "27"))
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+ (rule "distributeIntersection" (formula "30") (term "0,0"))
+ (rule "distributeIntersection" (formula "30") (term "1,0"))
+ (rule "unionEqualsEmpty" (formula "28"))
+ (rule "andLeft" (formula "28"))
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+ (rule "eqSymm" (formula "38"))
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+ (rule "andLeft" (formula "29"))
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+ (builtin "One Step Simplification" (formula "27"))
+ (rule "andLeft" (formula "27"))
+ (rule "notLeft" (formula "27"))
+ (rule "notLeft" (formula "27"))
+ (rule "eqSymm" (formula "31"))
+ (rule "eqSymm" (formula "30"))
+ (rule "commuteUnion" (formula "26") (term "0,0,1"))
+ (rule "commuteUnion" (formula "26") (term "1,1,1"))
+ (rule "commuteUnion_2" (formula "26") (term "0,1"))
+ (rule "commuteUnion" (formula "26") (term "0,0,1"))
+ (rule "commuteUnion_2" (formula "26") (term "1"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Storage" (formula "7"))
+ (rule "andLeft" (formula "7"))
+ (rule "andLeft" (formula "7"))
+ (rule "notLeft" (formula "9"))
+ (rule "andLeft" (formula "7"))
+ (rule "notLeft" (formula "9"))
+ (rule "andLeft" (formula "7"))
+ (rule "notLeft" (formula "9"))
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+ (rule "andLeft" (formula "7"))
+ (rule "notLeft" (formula "8"))
+ (rule "andLeft" (formula "7"))
+ (rule "notLeft" (formula "8"))
+ (rule "andLeft" (formula "7"))
+ (rule "notLeft" (formula "7"))
+ (rule "notLeft" (formula "7"))
+ (rule "Class_invariant_axiom_for_de_wiesler_Storage" (formula "85"))
+ (rule "replace_known_right" (formula "85") (term "0,1,0,0") (ifseqformula "34"))
+ (builtin "One Step Simplification" (formula "85") (ifInst "" (formula "30")) (ifInst "" (formula "29")) (ifInst "" (formula "31")) (ifInst "" (formula "32")) (ifInst "" (formula "33")) (ifInst "" (formula "35")) (ifInst "" (formula "36")))
+ (rule "closeTrue" (formula "85"))
+ )
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample((I,int,int,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample((I,int,int,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..1d42530
--- /dev/null
+++ b/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample((I,int,int,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,3713 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Thu Jun 02 21:45:21 CEST 2022
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , finalFields-finalFields\\:immutable , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Thu Jun 02 21:45:21 CEST 2022
+contract=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:sample([I,int,int,de.wiesler.Storage)].JML normal_behavior operation contract.0
+name=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:sample([I,int,int,de.wiesler.Storage)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "5899")
+
+(branch "dummy ID"
+(rule "eqSymm" (formula "1") (term "1,0,0,1,0,1,1") (newnames "heapAtPre_0,o,f"))
+ (builtin "One Step Simplification" (formula "1"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "7"))
+(rule "andLeft" (formula "9"))
+(rule "andLeft" (formula "2"))
+(rule "notLeft" (formula "6"))
+(rule "notLeft" (formula "6"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "9"))
+(rule "andLeft" (formula "11"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "3"))
+(rule "translateJavaSubInt" (formula "8") (term "0,0"))
+(rule "translateJavaSubInt" (formula "13") (term "1"))
+(rule "translateJavaSubInt" (formula "14") (term "0"))
+(rule "replace_known_right" (formula "7") (term "0") (ifseqformula "17"))
+ (builtin "One Step Simplification" (formula "7"))
+(rule "replace_known_right" (formula "2") (term "0") (ifseqformula "18"))
+ (builtin "One Step Simplification" (formula "2"))
+(rule "polySimp_elimSub" (formula "8") (term "0,0"))
+(rule "polySimp_elimSub" (formula "13") (term "1"))
+(rule "polySimp_elimSub" (formula "14") (term "0"))
+(rule "polySimp_addComm0" (formula "8") (term "0,0"))
+(rule "polySimp_addComm0" (formula "13") (term "1"))
+(rule "polySimp_addComm0" (formula "14") (term "0"))
+(rule "disjointDefinition" (formula "16"))
+(rule "inEqSimp_commuteLeq" (formula "12"))
+(rule "inEqSimp_commuteLeq" (formula "10"))
+(rule "inEqSimp_commuteLeq" (formula "11"))
+(rule "inEqSimp_commuteLeq" (formula "6"))
+(rule "inEqSimp_commuteLeq" (formula "4"))
+(rule "assignment" (formula "19") (term "1"))
+ (builtin "One Step Simplification" (formula "19"))
+(rule "commuteIntersection" (formula "16") (term "0"))
+(rule "methodBodyExpand" (formula "19") (term "1") (newnames "heapBefore_sample,savedHeapBefore_sample,savedHeapBefore_sample_0"))
+ (builtin "One Step Simplification" (formula "19"))
+(rule "variableDeclarationAssign" (formula "19") (term "1"))
+(rule "variableDeclaration" (formula "19") (term "1") (newnames "parameters"))
+(rule "instanceCreationAssignmentUnfoldArguments" (formula "19") (term "1"))
+(rule "variableDeclarationAssign" (formula "19") (term "1"))
+(rule "variableDeclaration" (formula "19") (term "1") (newnames "var"))
+(rule "assignmentSubtractionInt" (formula "19") (term "1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "19"))
+ (rule "expand_inInt" (formula "19"))
+ (rule "replace_int_MIN" (formula "19") (term "0,1"))
+ (rule "replace_int_MAX" (formula "19") (term "1,0"))
+ (rule "polySimp_elimSub" (formula "19") (term "0,0"))
+ (rule "polySimp_elimSub" (formula "19") (term "1,1"))
+ (rule "polySimp_addComm0" (formula "19") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "19") (term "1,1"))
+ (rule "inEqSimp_ltToLeq" (formula "13"))
+ (rule "polySimp_rightDist" (formula "13") (term "1,0,0"))
+ (rule "polySimp_mulAssoc" (formula "13") (term "0,1,0,0"))
+ (rule "polySimp_mulComm0" (formula "13") (term "0,0,1,0,0"))
+ (rule "polySimp_mulLiterals" (formula "13") (term "0,1,0,0"))
+ (rule "polySimp_elimOne" (formula "13") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "13") (term "0,0"))
+ (rule "polySimp_addComm1" (formula "13") (term "0"))
+ (rule "polySimp_addComm1" (formula "13") (term "0,0"))
+ (rule "add_literals" (formula "13") (term "0,0,0"))
+ (rule "inEqSimp_homoInEq0" (formula "14"))
+ (rule "polySimp_mulComm0" (formula "14") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "14") (term "1,0"))
+ (rule "polySimp_mulAssoc" (formula "14") (term "0,1,0"))
+ (rule "polySimp_mulComm0" (formula "14") (term "0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "0,1,0"))
+ (rule "polySimp_elimOne" (formula "14") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "14") (term "0"))
+ (rule "inEqSimp_homoInEq0" (formula "19") (term "0"))
+ (rule "polySimp_mulComm0" (formula "19") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "19") (term "1,0,0"))
+ (rule "polySimp_mulAssoc" (formula "19") (term "0,1,0,0"))
+ (rule "polySimp_mulComm0" (formula "19") (term "0,0,1,0,0"))
+ (rule "polySimp_mulLiterals" (formula "19") (term "0,1,0,0"))
+ (rule "polySimp_elimOne" (formula "19") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "19") (term "0,0"))
+ (rule "inEqSimp_homoInEq0" (formula "19") (term "1"))
+ (rule "mul_literals" (formula "19") (term "1,0,1"))
+ (rule "polySimp_addComm1" (formula "19") (term "0,1"))
+ (rule "polySimp_addComm0" (formula "19") (term "0,0,1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "13"))
+ (rule "polySimp_mulLiterals" (formula "13") (term "0"))
+ (rule "polySimp_elimOne" (formula "13") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "14"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "0"))
+ (rule "polySimp_elimOne" (formula "14") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "19") (term "0"))
+ (rule "polySimp_mulLiterals" (formula "19") (term "0,0"))
+ (rule "polySimp_elimOne" (formula "19") (term "0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "19") (term "1"))
+ (rule "polySimp_mulComm0" (formula "19") (term "1,1"))
+ (rule "polySimp_rightDist" (formula "19") (term "1,1"))
+ (rule "mul_literals" (formula "19") (term "0,1,1"))
+ (rule "polySimp_mulLiterals" (formula "19") (term "1,1,1"))
+ (rule "polySimp_elimOne" (formula "19") (term "1,1,1"))
+ (rule "inEqSimp_subsumption1" (formula "11") (ifseqformula "13"))
+ (rule "inEqSimp_homoInEq0" (formula "11") (term "0"))
+ (rule "polySimp_pullOutFactor1b" (formula "11") (term "0,0"))
+ (rule "add_literals" (formula "11") (term "1,1,0,0"))
+ (rule "times_zero_1" (formula "11") (term "1,0,0"))
+ (rule "add_zero_right" (formula "11") (term "0,0"))
+ (rule "qeq_literals" (formula "11") (term "0"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "true_left" (formula "11"))
+ (rule "inEqSimp_subsumption1" (formula "4") (ifseqformula "10"))
+ (rule "leq_literals" (formula "4") (term "0"))
+ (builtin "One Step Simplification" (formula "4"))
+ (rule "true_left" (formula "4"))
+ (rule "inEqSimp_subsumption1" (formula "17") (term "1") (ifseqformula "11"))
+ (rule "inEqSimp_homoInEq0" (formula "17") (term "0,1"))
+ (rule "polySimp_mulComm0" (formula "17") (term "1,0,0,1"))
+ (rule "polySimp_rightDist" (formula "17") (term "1,0,0,1"))
+ (rule "mul_literals" (formula "17") (term "0,1,0,0,1"))
+ (rule "polySimp_addAssoc" (formula "17") (term "0,0,1"))
+ (rule "polySimp_addComm1" (formula "17") (term "0,0,0,1"))
+ (rule "add_literals" (formula "17") (term "0,0,0,0,1"))
+ (rule "polySimp_pullOutFactor1b" (formula "17") (term "0,0,1"))
+ (rule "add_literals" (formula "17") (term "1,1,0,0,1"))
+ (rule "times_zero_1" (formula "17") (term "1,0,0,1"))
+ (rule "add_zero_right" (formula "17") (term "0,0,1"))
+ (rule "qeq_literals" (formula "17") (term "0,1"))
+ (builtin "One Step Simplification" (formula "17"))
+ (rule "inEqSimp_leqRight" (formula "17"))
+ (rule "polySimp_rightDist" (formula "1") (term "1,0,0"))
+ (rule "mul_literals" (formula "1") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "1") (term "0,0"))
+ (rule "add_literals" (formula "1") (term "0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "1"))
+ (rule "polySimp_mulComm0" (formula "1") (term "1"))
+ (rule "polySimp_rightDist" (formula "1") (term "1"))
+ (rule "mul_literals" (formula "1") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "1") (term "1,1"))
+ (rule "inEqSimp_contradInEq1" (formula "13") (ifseqformula "1"))
+ (rule "andLeft" (formula "13"))
+ (rule "inEqSimp_homoInEq1" (formula "13"))
+ (rule "polySimp_mulComm0" (formula "13") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "13") (term "1,0"))
+ (rule "mul_literals" (formula "13") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "13") (term "0"))
+ (rule "polySimp_addComm1" (formula "13") (term "0,0"))
+ (rule "add_literals" (formula "13") (term "0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "13") (term "0"))
+ (rule "add_literals" (formula "13") (term "1,1,0"))
+ (rule "times_zero_1" (formula "13") (term "1,0"))
+ (rule "add_zero_right" (formula "13") (term "0"))
+ (rule "leq_literals" (formula "13"))
+ (rule "closeFalse" (formula "13"))
+)
+(branch "Usage"
+ (builtin "One Step Simplification" (formula "19"))
+ (rule "translateJavaSubInt" (formula "19") (term "0,1,0"))
+ (rule "polySimp_elimSub" (formula "19") (term "0,1,0"))
+ (rule "polySimp_addComm0" (formula "19") (term "0,1,0"))
+ (builtin "Use Operation Contract" (formula "19") (newnames "heapBefore_SampleParameters,self_77,exc_77,heapAfter_SampleParameters,anon_heap_SampleParameters") (contract "de.wiesler.SampleParameters[de.wiesler.SampleParameters::SampleParameters(int)].JML normal_behavior operation contract.0"))
+ (branch "Post (SampleParameters)"
+ (builtin "One Step Simplification" (formula "18"))
+ (builtin "One Step Simplification" (formula "21"))
+ (rule "andLeft" (formula "18"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "19") (term "1,1,0,0,1,0") (ifseqformula "18"))
+ (rule "andLeft" (formula "19"))
+ (rule "andLeft" (formula "19"))
+ (rule "andLeft" (formula "21"))
+ (rule "andLeft" (formula "20"))
+ (rule "andLeft" (formula "21"))
+ (rule "andLeft" (formula "20"))
+ (rule "andLeft" (formula "22"))
+ (rule "andLeft" (formula "20"))
+ (rule "notLeft" (formula "20"))
+ (rule "andLeft" (formula "20"))
+ (rule "notLeft" (formula "20"))
+ (rule "replace_known_right" (formula "20") (term "0") (ifseqformula "26"))
+ (builtin "One Step Simplification" (formula "20"))
+ (rule "assignment" (formula "30") (term "1"))
+ (builtin "One Step Simplification" (formula "30"))
+ (rule "blockEmpty" (formula "30") (term "1"))
+ (builtin "Block Contract (Internal)" (formula "30") (newnames "anonOut_heap,result_65,exc_78,heap_Before_BLOCK,savedHeap_Before_BLOCK,o,f"))
+ (branch "Validity"
+ (builtin "One Step Simplification" (formula "26"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "andLeft" (formula "26"))
+ (rule "translateJavaSubInt" (formula "26") (term "0,0"))
+ (rule "polySimp_elimSub" (formula "26") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "26") (term "0,0"))
+ (rule "variableDeclarationAssign" (formula "31") (term "1"))
+ (rule "variableDeclaration" (formula "31") (term "1") (newnames "exc_78_1"))
+ (rule "assignment" (formula "31") (term "1"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "emptyStatement" (formula "31") (term "1"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "emptyStatement" (formula "31") (term "1"))
+ (rule "tryEmpty" (formula "31") (term "1"))
+ (rule "blockEmptyLabel" (formula "31") (term "1"))
+ (rule "blockEmpty" (formula "31") (term "1"))
+ (rule "methodCallEmpty" (formula "31") (term "1"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "emptyModality" (formula "31") (term "1"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "closeTrue" (formula "31"))
+ )
+ (branch "Precondition"
+ (rule "andRight" (formula "30"))
+ (branch "Case 1"
+ (builtin "One Step Simplification" (formula "30"))
+ (rule "translateJavaSubInt" (formula "30") (term "0,0"))
+ (rule "polySimp_elimSub" (formula "30") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "30") (term "0,0"))
+ (rule "close" (formula "30") (ifseqformula "8"))
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "30"))
+ (rule "wellFormedAnonEQ" (formula "30") (ifseqformula "18"))
+ (rule "replace_known_left" (formula "30") (term "0") (ifseqformula "1"))
+ (builtin "One Step Simplification" (formula "30") (ifInst "" (formula "17")))
+ (rule "closeTrue" (formula "30"))
+ )
+ )
+ (branch "Usage"
+ (builtin "One Step Simplification" (formula "26"))
+ (builtin "One Step Simplification" (formula "31"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "26") (term "0,1,1,1,0") (ifseqformula "18"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "26") (term "0,1,0,1,0") (ifseqformula "18"))
+ (rule "andLeft" (formula "26"))
+ (rule "andLeft" (formula "26"))
+ (rule "andLeft" (formula "27"))
+ (rule "andLeft" (formula "26"))
+ (rule "replace_known_left" (formula "29") (term "0") (ifseqformula "26"))
+ (builtin "One Step Simplification" (formula "29"))
+ (rule "true_left" (formula "29"))
+ (rule "narrowSelectArrayType" (formula "29") (term "2,1") (ifseqformula "1") (ifseqformula "33"))
+ (rule "shift_paren_or" (formula "28"))
+ (rule "shift_paren_or" (formula "28") (term "0"))
+ (rule "commute_or_2" (formula "28"))
+ (rule "ifUnfold" (formula "34") (term "1") (inst "#boolv=x"))
+ (rule "variableDeclaration" (formula "34") (term "1") (newnames "x"))
+ (rule "inequality_comparison_simple" (formula "34") (term "1"))
+ (builtin "One Step Simplification" (formula "34"))
+ (rule "replace_known_left" (formula "34") (term "0,0,1,0") (ifseqformula "26"))
+ (builtin "One Step Simplification" (formula "34"))
+ (rule "arrayLengthNotNegative" (formula "12") (term "0"))
+ (rule "arrayLengthIsAShort" (formula "13") (term "0"))
+ (rule "expand_inShort" (formula "13"))
+ (rule "replace_short_MIN" (formula "13") (term "0,1"))
+ (rule "replace_short_MAX" (formula "13") (term "1,0"))
+ (rule "andLeft" (formula "13"))
+ (rule "inEqSimp_commuteLeq" (formula "14"))
+ (rule "ifSplit" (formula "37"))
+ (branch "if x true"
+ (builtin "One Step Simplification" (formula "38"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "closeFalse" (formula "1"))
+ )
+ (branch "if x false"
+ (builtin "One Step Simplification" (formula "38"))
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "true_left" (formula "1"))
+ (rule "blockEmpty" (formula "37") (term "1"))
+ (rule "methodCallUnfoldArguments" (formula "37") (term "1"))
+ (rule "variableDeclarationAssign" (formula "37") (term "1"))
+ (rule "variableDeclaration" (formula "37") (term "1") (newnames "var_1"))
+ (rule "assignment" (formula "37") (term "1"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "variableDeclarationAssign" (formula "37") (term "1"))
+ (rule "variableDeclaration" (formula "37") (term "1") (newnames "var_2"))
+ (rule "assignment" (formula "37") (term "1"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "variableDeclarationAssign" (formula "37") (term "1"))
+ (rule "variableDeclaration" (formula "37") (term "1") (newnames "var_3"))
+ (rule "assignment" (formula "37") (term "1"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "variableDeclarationAssign" (formula "37") (term "1"))
+ (rule "variableDeclaration" (formula "37") (term "1") (newnames "var_4"))
+ (rule "assignment_read_attribute_final" (formula "37"))
+ (branch "Normal Execution (parameters != null)"
+ (builtin "One Step Simplification" (formula "37"))
+ (builtin "Use Operation Contract" (formula "37") (newnames "heapBefore_select_n,exc_79,heapAfter_select_n,anon_heap_select_n") (contract "de.wiesler.Functions[de.wiesler.Functions::select_n([I,int,int,int)].JML normal_behavior operation contract.0"))
+ (branch "Post (select_n)"
+ (builtin "One Step Simplification" (formula "39"))
+ (builtin "One Step Simplification" (formula "34"))
+ (rule "andLeft" (formula "34"))
+ (rule "andLeft" (formula "35"))
+ (rule "andLeft" (formula "35"))
+ (rule "translateJavaSubInt" (formula "34") (term "2,1,0"))
+ (rule "polySimp_elimSub" (formula "34") (term "2,1,0"))
+ (rule "mul_literals" (formula "34") (term "1,2,1,0"))
+ (rule "polySimp_addComm0" (formula "34") (term "2,1,0"))
+ (rule "blockEmpty" (formula "41") (term "1"))
+ (builtin "Block Contract (Internal)" (formula "41") (newnames "anonOut_heap_0,result_66,exc_80,heap_Before_BLOCK_0,savedHeap_Before_BLOCK_0,o,f"))
+ (branch "Validity"
+ (builtin "One Step Simplification" (formula "37"))
+ (builtin "One Step Simplification" (formula "42"))
+ (rule "andLeft" (formula "37"))
+ (rule "translateJavaSubInt" (formula "37") (term "0,0"))
+ (rule "polySimp_elimSub" (formula "37") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "37") (term "0,0"))
+ (rule "narrowSelectArrayType" (formula "35") (term "2,0") (ifseqformula "37") (ifseqformula "41"))
+ (rule "variableDeclarationAssign" (formula "42") (term "1"))
+ (rule "variableDeclaration" (formula "42") (term "1") (newnames "exc_80_1"))
+ (rule "assignment" (formula "42") (term "1"))
+ (builtin "One Step Simplification" (formula "42"))
+ (rule "emptyStatement" (formula "42") (term "1"))
+ (builtin "One Step Simplification" (formula "42"))
+ (rule "emptyStatement" (formula "42") (term "1"))
+ (rule "tryEmpty" (formula "42") (term "1"))
+ (rule "blockEmptyLabel" (formula "42") (term "1"))
+ (rule "blockEmpty" (formula "42") (term "1"))
+ (rule "methodCallEmpty" (formula "42") (term "1"))
+ (builtin "One Step Simplification" (formula "42"))
+ (rule "emptyModality" (formula "42") (term "1"))
+ (builtin "One Step Simplification" (formula "42"))
+ (rule "closeTrue" (formula "42"))
+ )
+ (branch "Precondition"
+ (rule "andRight" (formula "41"))
+ (branch "Case 1"
+ (builtin "One Step Simplification" (formula "41"))
+ (rule "translateJavaSubInt" (formula "41") (term "0,0"))
+ (rule "polySimp_elimSub" (formula "41") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "41") (term "0,0"))
+ (rule "close" (formula "41") (ifseqformula "8"))
+ )
+ (branch "Case 2"
+ (builtin "One Step Simplification" (formula "41"))
+ (rule "wellFormedAnonEQ" (formula "41") (ifseqformula "34"))
+ (rule "wellFormedAnon" (formula "41") (term "0"))
+ (rule "replace_known_left" (formula "41") (term "1,0") (ifseqformula "30"))
+ (builtin "One Step Simplification" (formula "41") (ifInst "" (formula "33")))
+ (rule "wellFormedAnonEQ" (formula "41") (ifseqformula "21"))
+ (rule "replace_known_left" (formula "41") (term "0") (ifseqformula "1"))
+ (builtin "One Step Simplification" (formula "41") (ifInst "" (formula "20")))
+ (rule "closeTrue" (formula "41"))
+ )
+ )
+ (branch "Usage"
+ (builtin "One Step Simplification" (formula "37"))
+ (builtin "One Step Simplification" (formula "42"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "37") (term "0,1,1,1,0") (ifseqformula "34"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "37") (term "0,1,0,1,0") (ifseqformula "34"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "37") (term "0,0,0,1,1,1,0") (ifseqformula "21"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "37") (term "0,0,0,1,0,1,0") (ifseqformula "21"))
+ (rule "andLeft" (formula "37"))
+ (rule "andLeft" (formula "37"))
+ (rule "andLeft" (formula "37"))
+ (rule "andLeft" (formula "39"))
+ (rule "replace_known_left" (formula "40") (term "0") (ifseqformula "37"))
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+ (rule "polySimp_mulComm0" (formula "14") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "14") (term "1,0"))
+ (rule "polySimp_mulAssoc" (formula "14") (term "0,1,0"))
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+ (rule "polySimp_mulLiterals" (formula "14") (term "0,1,0"))
+ (rule "polySimp_elimOne" (formula "14") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "14") (term "0"))
+ (rule "inEqSimp_homoInEq0" (formula "19") (term "0"))
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+ (rule "polySimp_mulAssoc" (formula "19") (term "0,1,0,0"))
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+ (rule "polySimp_mulLiterals" (formula "19") (term "0,1,0,0"))
+ (rule "polySimp_elimOne" (formula "19") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "19") (term "0,0"))
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+ (rule "mul_literals" (formula "19") (term "1,0,1"))
+ (rule "polySimp_addComm1" (formula "19") (term "0,1"))
+ (rule "polySimp_addComm0" (formula "19") (term "0,0,1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "13"))
+ (rule "polySimp_mulLiterals" (formula "13") (term "0"))
+ (rule "polySimp_elimOne" (formula "13") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "14"))
+ (rule "polySimp_mulLiterals" (formula "14") (term "0"))
+ (rule "polySimp_elimOne" (formula "14") (term "0"))
+ (rule "inEqSimp_sepNegMonomial1" (formula "19") (term "0"))
+ (rule "polySimp_mulLiterals" (formula "19") (term "0,0"))
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+ (rule "polySimp_mulComm0" (formula "19") (term "1,1"))
+ (rule "polySimp_rightDist" (formula "19") (term "1,1"))
+ (rule "polySimp_mulLiterals" (formula "19") (term "1,1,1"))
+ (rule "mul_literals" (formula "19") (term "0,1,1"))
+ (rule "polySimp_elimOne" (formula "19") (term "1,1,1"))
+ (rule "inEqSimp_subsumption1" (formula "19") (term "1") (ifseqformula "13"))
+ (rule "inEqSimp_homoInEq0" (formula "19") (term "0,1"))
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+ (rule "mul_literals" (formula "19") (term "0,1,0,0,1"))
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+ (rule "polySimp_addComm1" (formula "19") (term "0,0,0,1"))
+ (rule "add_literals" (formula "19") (term "0,0,0,0,1"))
+ (rule "polySimp_pullOutFactor1b" (formula "19") (term "0,0,1"))
+ (rule "add_literals" (formula "19") (term "1,1,0,0,1"))
+ (rule "times_zero_1" (formula "19") (term "1,0,0,1"))
+ (rule "add_zero_right" (formula "19") (term "0,0,1"))
+ (rule "qeq_literals" (formula "19") (term "0,1"))
+ (builtin "One Step Simplification" (formula "19"))
+ (rule "inEqSimp_leqRight" (formula "19"))
+ (rule "polySimp_rightDist" (formula "1") (term "1,0,0"))
+ (rule "mul_literals" (formula "1") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "1") (term "0,0"))
+ (rule "add_literals" (formula "1") (term "0,0,0"))
+ (rule "inEqSimp_sepPosMonomial1" (formula "1"))
+ (rule "polySimp_mulComm0" (formula "1") (term "1"))
+ (rule "polySimp_rightDist" (formula "1") (term "1"))
+ (rule "mul_literals" (formula "1") (term "0,1"))
+ (rule "polySimp_mulLiterals" (formula "1") (term "1,1"))
+ (rule "polySimp_elimOne" (formula "1") (term "1,1"))
+ (rule "inEqSimp_subsumption1" (formula "5") (ifseqformula "11"))
+ (rule "leq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "true_left" (formula "5"))
+ (rule "inEqSimp_subsumption1" (formula "11") (ifseqformula "13"))
+ (rule "inEqSimp_homoInEq0" (formula "11") (term "0"))
+ (rule "polySimp_pullOutFactor1b" (formula "11") (term "0,0"))
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+ (rule "times_zero_1" (formula "11") (term "1,0,0"))
+ (rule "add_zero_right" (formula "11") (term "0,0"))
+ (rule "qeq_literals" (formula "11") (term "0"))
+ (builtin "One Step Simplification" (formula "11"))
+ (rule "true_left" (formula "11"))
+ (rule "inEqSimp_subsumption1" (formula "12") (ifseqformula "1"))
+ (rule "inEqSimp_homoInEq0" (formula "12") (term "0"))
+ (rule "polySimp_mulComm0" (formula "12") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "12") (term "1,0,0"))
+ (rule "mul_literals" (formula "12") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "12") (term "0,0"))
+ (rule "polySimp_addComm1" (formula "12") (term "0,0,0"))
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+ (rule "add_literals" (formula "12") (term "1,1,0,0"))
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+ (rule "add_zero_right" (formula "12") (term "0,0"))
+ (rule "qeq_literals" (formula "12") (term "0"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "true_left" (formula "12"))
+ (rule "inEqSimp_contradInEq1" (formula "12") (ifseqformula "1"))
+ (rule "andLeft" (formula "12"))
+ (rule "inEqSimp_homoInEq1" (formula "12"))
+ (rule "polySimp_mulComm0" (formula "12") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "12") (term "1,0"))
+ (rule "mul_literals" (formula "12") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "12") (term "0"))
+ (rule "polySimp_addComm1" (formula "12") (term "0,0"))
+ (rule "add_literals" (formula "12") (term "0,0,0"))
+ (rule "polySimp_pullOutFactor1b" (formula "12") (term "0"))
+ (rule "add_literals" (formula "12") (term "1,1,0"))
+ (rule "times_zero_1" (formula "12") (term "1,0"))
+ (rule "add_zero_right" (formula "12") (term "0"))
+ (rule "leq_literals" (formula "12"))
+ (rule "closeFalse" (formula "12"))
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample_sort((I,int,int,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample_sort((I,int,int,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..630c320
--- /dev/null
+++ b/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample_sort((I,int,int,de.wiesler.Storage)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,10928 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Apr 17 12:54:41 CEST 2023
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L , finalFields-finalFields\\:immutable
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Apr 17 12:54:41 CEST 2023
+contract=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:sample_sort([I,int,int,de.wiesler.Storage)].JML normal_behavior operation contract.0
+name=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:sample_sort([I,int,int,de.wiesler.Storage)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "99441")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "8"))
+(rule "andLeft" (formula "5"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "8"))
+(rule "andLeft" (formula "12"))
+(rule "notLeft" (formula "6"))
+(rule "notLeft" (formula "6"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "12"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "3"))
+(rule "translateJavaSubInt" (formula "8") (term "0,0"))
+(rule "translateJavaSubInt" (formula "13") (term "0"))
+(rule "translateJavaSubInt" (formula "14") (term "0"))
+(rule "replace_known_right" (formula "7") (term "0") (ifseqformula "17"))
+ (builtin "One Step Simplification" (formula "7"))
+(rule "replace_known_right" (formula "2") (term "0") (ifseqformula "18"))
+ (builtin "One Step Simplification" (formula "2"))
+(rule "polySimp_elimSub" (formula "8") (term "0,0"))
+(rule "polySimp_elimSub" (formula "13") (term "0"))
+(rule "polySimp_elimSub" (formula "14") (term "0"))
+(rule "polySimp_addComm0" (formula "8") (term "0,0"))
+(rule "polySimp_addComm0" (formula "13") (term "0"))
+(rule "polySimp_addComm0" (formula "14") (term "0"))
+(rule "disjointDefinition" (formula "16"))
+(rule "inEqSimp_commuteLeq" (formula "12"))
+(rule "inEqSimp_commuteLeq" (formula "11"))
+(rule "inEqSimp_commuteLeq" (formula "10"))
+(rule "inEqSimp_commuteLeq" (formula "6"))
+(rule "inEqSimp_commuteLeq" (formula "4"))
+(rule "assignment" (formula "19") (term "1"))
+ (builtin "One Step Simplification" (formula "19"))
+(rule "commuteIntersection" (formula "16") (term "0"))
+(rule "methodBodyExpand" (formula "19") (term "1") (newnames "heapBefore_sample_sort,savedHeapBefore_sample_sort,_beginBefore_sample_sort,_endBefore_sample_sort,_storageBefore_sample_sort,_valuesBefore_sample_sort,bucket_startsBefore_sample_sort,equal_bucketsBefore_sample_sort,num_bucketsBefore_sample_sort,num_bucketsBefore_sample_sort_0"))
+ (builtin "One Step Simplification" (formula "19"))
+(rule "variableDeclarationAssign" (formula "19") (term "1"))
+(rule "variableDeclaration" (formula "19") (term "1") (newnames "bucket_starts"))
+(rule "methodCallWithAssignmentUnfoldArguments" (formula "19") (term "1"))
+(rule "variableDeclarationAssign" (formula "19") (term "1"))
+(rule "variableDeclaration" (formula "19") (term "1") (newnames "var"))
+(rule "assignmentAdditionInt" (formula "19") (term "1"))
+(branch "Overflow check"
+ (builtin "One Step Simplification" (formula "19"))
+ (rule "add_literals" (formula "19") (term "0"))
+ (rule "expand_inInt" (formula "19"))
+ (rule "replace_int_MIN" (formula "19") (term "0,1"))
+ (rule "replace_int_MAX" (formula "19") (term "1,0"))
+ (rule "leq_literals" (formula "19") (term "1"))
+ (builtin "One Step Simplification" (formula "19"))
+ (rule "leq_literals" (formula "19"))
+ (rule "closeTrue" (formula "19"))
+)
+(branch "Usage"
+ (builtin "One Step Simplification" (formula "19"))
+ (rule "translateJavaAddInt" (formula "19") (term "0,1,0"))
+ (rule "add_literals" (formula "19") (term "0,1,0"))
+ (builtin "Use Operation Contract" (formula "19") (newnames "heapBefore_createArray,result_241,exc_285,heapAfter_createArray,anon_heap_createArray") (contract "de.wiesler.Storage[de.wiesler.Storage::createArray(int)].JML normal_behavior operation contract.0"))
+ (branch "Post (createArray)"
+ (builtin "One Step Simplification" (formula "21"))
+ (builtin "One Step Simplification" (formula "18"))
+ (rule "expand_inInt" (formula "18") (term "1,0,0,1,1,1,1,0,1"))
+ (rule "replace_int_MAX" (formula "18") (term "1,0,1,0,0,1,1,1,1,0,1"))
+ (rule "replace_int_MIN" (formula "18") (term "0,1,1,0,0,1,1,1,1,0,1"))
+ (rule "andLeft" (formula "18"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "19") (term "1,0,1,0") (ifseqformula "18"))
+ (rule "andLeft" (formula "19"))
+ (rule "andLeft" (formula "20"))
+ (rule "andLeft" (formula "19"))
+ (rule "notLeft" (formula "20"))
+ (rule "andLeft" (formula "19"))
+ (rule "andLeft" (formula "20"))
+ (rule "andLeft" (formula "21"))
+ (rule "andLeft" (formula "21"))
+ (rule "notLeft" (formula "21"))
+ (rule "notLeft" (formula "21"))
+ (rule "replace_known_right" (formula "19") (term "0,1") (ifseqformula "23"))
+ (builtin "One Step Simplification" (formula "19") (ifInst "" (formula "24")))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "1,1,0,0"))
+ (rule "inEqSimp_commuteLeq" (formula "21") (term "0,0,0,0"))
+ (rule "assignment" (formula "27") (term "1"))
+ (builtin "One Step Simplification" (formula "27"))
+ (rule "blockEmpty" (formula "27") (term "1"))
+ (builtin "Block Contract (Internal)" (formula "27") (newnames "anonOut_heap,exc_286,heap_Before_BLOCK,savedHeap_Before_BLOCK,o,f"))
+ (branch "Validity"
+ (builtin "One Step Simplification" (formula "28"))
+ (builtin "One Step Simplification" (formula "23"))
+ (rule "andLeft" (formula "23"))
+ (rule "translateJavaSubInt" (formula "23") (term "0,0"))
+ (rule "polySimp_elimSub" (formula "23") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "23") (term "0,0"))
+ (rule "variableDeclarationAssign" (formula "28") (term "1"))
+ (rule "variableDeclaration" (formula "28") (term "1") (newnames "exc_286_1"))
+ (rule "assignment" (formula "28") (term "1"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "emptyStatement" (formula "28") (term "1"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "emptyStatement" (formula "28") (term "1"))
+ (rule "commute_and" (formula "21") (term "1,0,0"))
+ (rule "commute_and" (formula "21") (term "0,0,0"))
+ (rule "shift_paren_and" (formula "21") (term "0,0"))
+ (rule "commute_and_2" (formula "21") (term "0,0,0"))
+ (rule "tryEmpty" (formula "28") (term "1"))
+ (rule "blockEmptyLabel" (formula "28") (term "1"))
+ (rule "blockEmpty" (formula "28") (term "1"))
+ (rule "methodCallEmpty" (formula "28") (term "1"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "emptyModality" (formula "28") (term "1"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "closeTrue" (formula "28"))
+ )
+ (branch "Precondition"
+ (rule "andRight" (formula "27"))
+ (branch
+ (builtin "One Step Simplification" (formula "27"))
+ (rule "translateJavaSubInt" (formula "27") (term "0,0"))
+ (rule "polySimp_elimSub" (formula "27") (term "0,0"))
+ (rule "polySimp_addComm0" (formula "27") (term "0,0"))
+ (rule "close" (formula "27") (ifseqformula "8"))
+ )
+ (branch
+ (builtin "One Step Simplification" (formula "27"))
+ (rule "wellFormedAnonEQ" (formula "27") (ifseqformula "18"))
+ (rule "replace_known_left" (formula "27") (term "0") (ifseqformula "1"))
+ (builtin "One Step Simplification" (formula "27") (ifInst "" (formula "17")))
+ (rule "closeTrue" (formula "27"))
+ )
+ )
+ (branch "Usage"
+ (builtin "One Step Simplification" (formula "23"))
+ (builtin "One Step Simplification" (formula "28"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "23") (term "0,1,1,0") (ifseqformula "18"))
+ (rule "andLeft" (formula "23"))
+ (rule "andLeft" (formula "23"))
+ (rule "andLeft" (formula "25"))
+ (rule "andLeft" (formula "23"))
+ (rule "andLeft" (formula "27"))
+ (rule "andLeft" (formula "27"))
+ (rule "andLeft" (formula "27"))
+ (rule "replace_known_left" (formula "25") (term "0") (ifseqformula "23"))
+ (builtin "One Step Simplification" (formula "25"))
+ (rule "true_left" (formula "25"))
+ (rule "disjointDefinition" (formula "29"))
+ (rule "disjointDefinition" (formula "28"))
+ (rule "disjointDefinition" (formula "27"))
+ (rule "disjointDefinition" (formula "26"))
+ (builtin "One Step Simplification" (formula "26"))
+ (rule "notLeft" (formula "26"))
+ (rule "narrowSelectArrayType" (formula "25") (term "2,1") (ifseqformula "1") (ifseqformula "32"))
+ (rule "commute_and" (formula "21") (term "1,0,0"))
+ (rule "commute_and" (formula "21") (term "0,0,0"))
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+ (rule "ifUnfold" (formula "33") (term "1") (inst "#boolv=x"))
+ (rule "variableDeclaration" (formula "33") (term "1") (newnames "x"))
+ (rule "inequality_comparison_simple" (formula "33") (term "1"))
+ (builtin "One Step Simplification" (formula "33"))
+ (rule "replace_known_left" (formula "33") (term "0,0,1,0") (ifseqformula "23"))
+ (builtin "One Step Simplification" (formula "33"))
+ (rule "arrayLengthNotNegative" (formula "12") (term "0"))
+ (rule "arrayLengthIsAShort" (formula "13") (term "0"))
+ (rule "expand_inShort" (formula "13"))
+ (rule "replace_short_MAX" (formula "13") (term "1,0"))
+ (rule "replace_short_MIN" (formula "13") (term "0,1"))
+ (rule "andLeft" (formula "13"))
+ (rule "inEqSimp_commuteLeq" (formula "14"))
+ (rule "ifSplit" (formula "36"))
+ (branch "if x true"
+ (builtin "One Step Simplification" (formula "1"))
+ (rule "closeFalse" (formula "1"))
+ )
+ (branch "if x false"
+ (builtin "One Step Simplification" (formula "1"))
+ (builtin "One Step Simplification" (formula "37"))
+ (rule "true_left" (formula "1"))
+ (rule "blockEmpty" (formula "36") (term "1"))
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+ (branch "Exceptional Post (createArray)"
+ (builtin "One Step Simplification" (formula "21"))
+ (builtin "One Step Simplification" (formula "18"))
+ (rule "andLeft" (formula "18"))
+ (rule "selectCreatedOfAnonAsFormulaEQ" (formula "19") (term "1,0") (ifseqformula "18"))
+ (rule "andLeft" (formula "19"))
+ (rule "andLeft" (formula "20"))
+ (rule "andLeft" (formula "19"))
+ (rule "notLeft" (formula "21"))
+ (rule "notLeft" (formula "19"))
+ (rule "close" (formula "21") (ifseqformula "20"))
+ )
+ (branch "Pre (createArray)"
+ (builtin "One Step Simplification" (formula "19") (ifInst "" (formula "1")))
+ (rule "expand_inInt" (formula "19"))
+ (rule "replace_int_MAX" (formula "19") (term "1,0"))
+ (rule "replace_int_MIN" (formula "19") (term "0,1"))
+ (rule "leq_literals" (formula "19") (term "0"))
+ (builtin "One Step Simplification" (formula "19"))
+ (rule "leq_literals" (formula "19"))
+ (rule "closeTrue" (formula "19"))
+ )
+)
+)
+}
diff --git a/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample_sort_recurse_on((I,int,int,de.wiesler.Storage,(I,int,boolean,int)).JML normal_behavior operation contract.0.proof b/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample_sort_recurse_on((I,int,int,de.wiesler.Storage,(I,int,boolean,int)).JML normal_behavior operation contract.0.proof
new file mode 100644
index 0000000..52782b7
--- /dev/null
+++ b/src/main/key-overflow/Sorter/de.wiesler.Sorter(de.wiesler.Sorter__sample_sort_recurse_on((I,int,int,de.wiesler.Storage,(I,int,boolean,int)).JML normal_behavior operation contract.0.proof
@@ -0,0 +1,7251 @@
+\profile "Java Profile";
+
+\settings {
+"#Proof-Settings-Config-File
+#Mon Apr 17 12:55:45 CEST 2023
+[NewSMT]NoTypeHierarchy=false
+[Labels]UseOriginLabels=true
+[StrategyProperty]QUERYAXIOM_OPTIONS_KEY=QUERYAXIOM_ON
+[NewSMT]Presburger=false
+[SMTSettings]invariantForall=false
+[Strategy]ActiveStrategy=JavaCardDLStrategy
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY1=USER_TACLETS_OFF
+[StrategyProperty]QUANTIFIERS_OPTIONS_KEY=QUANTIFIERS_NON_SPLITTING_WITH_PROGS
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY2=USER_TACLETS_OFF
+[Choice]DefaultChoices=JavaCard-JavaCard\\:on , Strings-Strings\\:on , assertions-assertions\\:safe , bigint-bigint\\:on , floatRules-floatRules\\:strictfpOnly , initialisation-initialisation\\:disableStaticInitialisation , intRules-intRules\\:arithmeticSemanticsCheckingOF , integerSimplificationRules-integerSimplificationRules\\:full , javaLoopTreatment-javaLoopTreatment\\:efficient , mergeGenerateIsWeakeningGoal-mergeGenerateIsWeakeningGoal\\:off , methodExpansion-methodExpansion\\:modularOnly , modelFields-modelFields\\:treatAsAxiom , moreSeqRules-moreSeqRules\\:on , permissions-permissions\\:off , programRules-programRules\\:Java , reach-reach\\:on , runtimeExceptions-runtimeExceptions\\:ban , sequences-sequences\\:on , wdChecks-wdChecks\\:off , wdOperator-wdOperator\\:L , finalFields-finalFields\\:immutable
+[StrategyProperty]LOOP_OPTIONS_KEY=LOOP_SCOPE_INV_TACLET
+[StrategyProperty]INF_FLOW_CHECK_PROPERTY=INF_FLOW_CHECK_FALSE
+[SMTSettings]UseBuiltUniqueness=false
+[SMTSettings]explicitTypeHierarchy=false
+[SMTSettings]instantiateHierarchyAssumptions=true
+[StrategyProperty]NON_LIN_ARITH_OPTIONS_KEY=NON_LIN_ARITH_DEF_OPS
+[SMTSettings]SelectedTaclets=
+[StrategyProperty]DEP_OPTIONS_KEY=DEP_ON
+[StrategyProperty]AUTO_INDUCTION_OPTIONS_KEY=AUTO_INDUCTION_OFF
+[Strategy]MaximumNumberOfAutomaticApplications=10000
+[StrategyProperty]STOPMODE_OPTIONS_KEY=STOPMODE_DEFAULT
+[StrategyProperty]CLASS_AXIOM_OPTIONS_KEY=CLASS_AXIOM_DELAYED
+[SMTSettings]useConstantsForBigOrSmallIntegers=true
+[StrategyProperty]MPS_OPTIONS_KEY=MPS_MERGE
+[StrategyProperty]SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OPTIONS_KEY=SYMBOLIC_EXECUTION_NON_EXECUTION_BRANCH_HIDING_OFF
+[Strategy]Timeout=-1
+[StrategyProperty]SYMBOLIC_EXECUTION_ALIAS_CHECK_OPTIONS_KEY=SYMBOLIC_EXECUTION_ALIAS_CHECK_NEVER
+[StrategyProperty]QUERY_NEW_OPTIONS_KEY=QUERY_OFF
+[SMTSettings]useUninterpretedMultiplication=true
+[NewSMT]sqrtSMTTranslation=SMT
+[StrategyProperty]BLOCK_OPTIONS_KEY=BLOCK_CONTRACT_INTERNAL
+[StrategyProperty]METHOD_OPTIONS_KEY=METHOD_CONTRACT
+[StrategyProperty]USER_TACLETS_OPTIONS_KEY3=USER_TACLETS_OFF
+[NewSMT]identifier=OPEN
+[SMTSettings]maxGenericSorts=2
+[StrategyProperty]OSS_OPTIONS_KEY=OSS_ON
+[NewSMT]Axiomatisations=false
+[StrategyProperty]SPLITTING_OPTIONS_KEY=SPLITTING_DELAYED
+[SMTSettings]integersMinimum=-2147483645
+[StrategyProperty]VBT_PHASE=VBT_SYM_EX
+[SMTSettings]integersMaximum=2147483645
+"
+}
+
+\javaSource "../../java-overflow";
+
+\proofObligation "#Proof Obligation Settings
+#Mon Apr 17 12:55:45 CEST 2023
+contract=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:sample_sort_recurse_on([I,int,int,de.wiesler.Storage,[I,int,boolean,int)].JML normal_behavior operation contract.0
+name=de.wiesler.Sorter[de.wiesler.Sorter\\:\\:sample_sort_recurse_on([I,int,int,de.wiesler.Storage,[I,int,boolean,int)].JML normal_behavior operation contract.0
+class=de.uka.ilkd.key.proof.init.FunctionalOperationContractPO
+";
+
+\proof {
+(keyLog "0" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+(keyLog "1" (keyUser "Julian" ) (keyVersion "e1a85b31e7"))
+
+(autoModeTime "60802")
+
+(branch "dummy ID"
+ (builtin "One Step Simplification" (formula "1") (newnames "heapAtPre,o,f"))
+(rule "expand_inInt" (formula "1") (term "1,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,0,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,1,0,0,0"))
+(rule "expand_inInt" (formula "1") (term "1,0,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,1,0,0,0"))
+(rule "replace_int_MIN" (formula "1") (term "0,1,1,0,0,0,0,0,1,0,0,0"))
+(rule "replace_int_MAX" (formula "1") (term "1,0,1,0,0,0,0,0,1,0,0,0"))
+(rule "impRight" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "1"))
+(rule "andLeft" (formula "4"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "6"))
+(rule "andLeft" (formula "9"))
+(rule "andLeft" (formula "8"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "notLeft" (formula "8"))
+(rule "andLeft" (formula "8"))
+(rule "andLeft" (formula "13"))
+(rule "andLeft" (formula "10"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "4"))
+(rule "notLeft" (formula "11"))
+(rule "notLeft" (formula "10"))
+(rule "andLeft" (formula "14"))
+(rule "andLeft" (formula "16"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "18"))
+(rule "andLeft" (formula "17"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "21"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "2"))
+(rule "andLeft" (formula "24"))
+(rule "andLeft" (formula "3"))
+(rule "andLeft" (formula "26"))
+(rule "andLeft" (formula "27"))
+(rule "andLeft" (formula "28"))
+(rule "andLeft" (formula "28"))
+(rule "andLeft" (formula "28"))
+(rule "translateJavaSubInt" (formula "13") (term "0,0"))
+(rule "translateJavaSubInt" (formula "18") (term "0"))
+(rule "translateJavaSubInt" (formula "22") (term "1"))
+(rule "translateJavaAddInt" (formula "26") (term "6,0,1,1"))
+(rule "translateJavaSubInt" (formula "26") (term "7,0,1,1"))
+(rule "translateJavaMod" (formula "26") (term "0,0,0,1"))
+(rule "eqSymm" (formula "26") (term "1,0,1"))
+(rule "translateJavaSubInt" (formula "27") (term "3,0"))
+(rule "translateJavaSubInt" (formula "26") (term "0,1,0,1"))
+(rule "replace_known_right" (formula "7") (term "0") (ifseqformula "32"))
+ (builtin "One Step Simplification" (formula "7"))
+(rule "replace_known_right" (formula "8") (term "0") (ifseqformula "33"))
+ (builtin "One Step Simplification" (formula "8"))
+(rule "replace_known_right" (formula "2") (term "0") (ifseqformula "34"))
+ (builtin "One Step Simplification" (formula "2"))
+(rule "polySimp_elimSub" (formula "13") (term "0,0"))
+(rule "polySimp_elimSub" (formula "18") (term "0"))
+(rule "polySimp_elimSub" (formula "22") (term "1"))
+(rule "polySimp_elimSub" (formula "26") (term "7,0,1,1"))
+(rule "mul_literals" (formula "26") (term "1,7,0,1,1"))
+(rule "polySimp_elimSub" (formula "27") (term "3,0"))
+(rule "polySimp_elimSub" (formula "26") (term "0,1,0,1"))
+(rule "mul_literals" (formula "26") (term "1,0,1,0,1"))
+(rule "polySimp_addComm0" (formula "26") (term "6,0,1,1"))
+(rule "polySimp_addComm0" (formula "13") (term "0,0"))
+(rule "polySimp_addComm0" (formula "18") (term "0"))
+(rule "polySimp_addComm0" (formula "22") (term "1"))
+(rule "polySimp_addComm0" (formula "26") (term "7,0,1,1"))
+(rule "polySimp_addComm0" (formula "27") (term "3,0"))
+(rule "polySimp_addComm0" (formula "26") (term "0,1,0,1"))
+(rule "disjointDefinition" (formula "30"))
+ (builtin "One Step Simplification" (formula "30"))
+(rule "notLeft" (formula "30"))
+(rule "disjointDefinition" (formula "28"))
+(rule "disjointDefinition" (formula "29"))
+(rule "inEqSimp_commuteLeq" (formula "17"))
+(rule "inEqSimp_commuteLeq" (formula "12"))
+(rule "inEqSimp_commuteLeq" (formula "15"))
+(rule "inEqSimp_commuteLeq" (formula "16"))
+(rule "inEqSimp_commuteLeq" (formula "10"))
+(rule "inEqSimp_commuteLeq" (formula "19"))
+(rule "inEqSimp_commuteLeq" (formula "6"))
+(rule "inEqSimp_commuteLeq" (formula "4"))
+(rule "assignment" (formula "35") (term "1"))
+ (builtin "One Step Simplification" (formula "35"))
+(rule "commuteIntersection" (formula "28") (term "0"))
+(rule "commuteIntersection" (formula "29") (term "0"))
+(rule "commute_or" (formula "26") (term "0,1"))
+(rule "commute_and" (formula "26") (term "1"))
+(rule "methodBodyExpand" (formula "35") (term "1") (newnames "heapBefore_sample_sort_recurse_on,savedHeapBefore_sample_sort_recurse_on,_storageBefore_sample_sort_recurse_on,_valuesBefore_sample_sort_recurse_on,inner_beginBefore_sample_sort_recurse_on,inner_endBefore_sample_sort_recurse_on"))
+ (builtin "One Step Simplification" (formula "35"))
+(rule "variableDeclarationAssign" (formula "35") (term "1"))
+(rule "variableDeclaration" (formula "35") (term "1") (newnames "inner_begin"))
+(rule "compound_addition_2" (formula "35") (term "1") (inst "#v0=x") (inst "#v1=x_1"))
+(rule "variableDeclarationAssign" (formula "35") (term "1"))
+(rule "variableDeclaration" (formula "35") (term "1") (newnames "x"))
+(rule "assignment" (formula "35") (term "1"))
+ (builtin "One Step Simplification" (formula "35"))
+(rule "variableDeclarationAssign" (formula "35") (term "1"))
+(rule "variableDeclaration" (formula "35") (term "1") (newnames "x_1"))
+(rule "assignment_array2" (formula "35"))
+(branch "Normal Execution (_bucket_starts != null)"
+ (builtin "One Step Simplification" (formula "35"))
+ (rule "assignmentAdditionInt" (formula "35") (term "1"))
+ (branch "Overflow check"
+ (builtin "One Step Simplification" (formula "35"))
+ (rule "expand_inInt" (formula "35"))
+ (rule "replace_int_MIN" (formula "35") (term "0,1"))
+ (rule "replace_int_MAX" (formula "35") (term "1,0"))
+ (rule "polySimp_homoEq" (formula "26") (term "0,1,1"))
+ (rule "polySimp_mulComm0" (formula "26") (term "1,0,0,1,1"))
+ (rule "polySimp_rightDist" (formula "26") (term "1,0,0,1,1"))
+ (rule "mul_literals" (formula "26") (term "0,1,0,0,1,1"))
+ (rule "polySimp_addAssoc" (formula "26") (term "0,0,1,1"))
+ (rule "polySimp_addComm0" (formula "26") (term "0,0,0,1,1"))
+ (rule "inEqSimp_ltToLeq" (formula "20"))
+ (rule "polySimp_mulComm0" (formula "20") (term "1,0,0"))
+ (rule "polySimp_addComm1" (formula "20") (term "0"))
+ (rule "inEqSimp_homoInEq0" (formula "18"))
+ (rule "polySimp_mulComm0" (formula "18") (term "1,0"))
+ (rule "polySimp_rightDist" (formula "18") (term "1,0"))
+ (rule "polySimp_mulAssoc" (formula "18") (term "0,1,0"))
+ (rule "polySimp_mulComm0" (formula "18") (term "0,0,1,0"))
+ (rule "polySimp_mulLiterals" (formula "18") (term "0,1,0"))
+ (rule "polySimp_elimOne" (formula "18") (term "0,1,0"))
+ (rule "polySimp_addAssoc" (formula "18") (term "0"))
+ (rule "inEqSimp_homoInEq0" (formula "35") (term "1"))
+ (rule "mul_literals" (formula "35") (term "1,0,1"))
+ (rule "polySimp_addComm1" (formula "35") (term "0,1"))
+ (rule "polySimp_addComm0" (formula "35") (term "0,0,1"))
+ (rule "inEqSimp_homoInEq0" (formula "35") (term "0"))
+ (rule "polySimp_mulComm0" (formula "35") (term "1,0,0"))
+ (rule "polySimp_rightDist" (formula "35") (term "1,0,0"))
+ (rule "polySimp_mulComm0" (formula "35") (term "0,1,0,0"))
+ (rule "polySimp_addAssoc" (formula "35") (term "0,0"))
+ (rule "jmod_axiom" (formula "26") (term "0,1,1,1"))
+ (rule "polySimp_mulLiterals" (formula "26") (term "1,0,1,1,1"))
+ (rule "polySimp_sepNegMonomial" (formula "26") (term "0,1,1"))
+ (rule "polySimp_mulLiterals" (formula "26") (term "0,0,1,1"))
+ (rule "polySimp_elimOne" (formula "26") (term "0,0,1,1"))
+ (rule "polySimp_sepNegMonomial" (formula "26") (term "1,1,1"))
+ (rule "polySimp_mulLiterals" (formula "26") (term "0,1,1,1"))
+ (rule "inEqSimp_sepNegMonomial0" (formula "20"))
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+ (rule "inEqSimp_subsumption1" (formula "12") (ifseqformula "19"))
+ (rule "leq_literals" (formula "12") (term "0"))
+ (builtin "One Step Simplification" (formula "12"))
+ (rule "true_left" (formula "12"))
+ (rule "inEqSimp_subsumption1" (formula "4") (ifseqformula "14"))
+ (rule "leq_literals" (formula "4") (term "0"))
+ (builtin "One Step Simplification" (formula "4"))
+ (rule "true_left" (formula "4"))
+ (rule "inEqSimp_exactShadow3" (formula "14") (ifseqformula "4"))
+ (rule "polySimp_mulComm0" (formula "14") (term "0,0"))
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+ (rule "leq_literals" (formula "5") (term "0"))
+ (builtin "One Step Simplification" (formula "5"))
+ (rule "true_left" (formula "5"))
+ (rule "inEqSimp_exactShadow3" (formula "18") (ifseqformula "8"))
+ (rule "polySimp_rightDist" (formula "18") (term "0,0"))
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+ (rule "leq_literals" (formula "10") (term "0"))
+ (builtin "One Step Simplification" (formula "10"))
+ (rule "true_left" (formula "10"))
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+ (rule "Free_class_invariant_axiom_for_de_wiesler_Storage" (formula "27"))
+ (builtin "One Step Simplification" (formula "27"))
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+ (builtin "One Step Simplification" (formula "62"))
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+ (builtin "One Step Simplification" (formula "53"))
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+ (builtin "One Step Simplification" (formula "94"))
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+ (branch "CUT: bucket_starts[1 + bucket] <