/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.jar /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.jar # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 379 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 86 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 24 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 15 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: package ClassAnalysisRec; public class ClassAnalysisRec { A field; public static void main(String[] args) { Random.args = args; ClassAnalysisRec t = new ClassAnalysisRec(); t.field = new A(); t.field = new B(); t.eval(); } public void eval() { int x = Random.random() % 100; this.field.test(x); } } class A { public boolean test(int x) { return this.test(x-1); } } class B extends A { public boolean test(int x) { if (x <= 0) return true; return test(x - 1); } } package ClassAnalysisRec; public class Random { static String[] args; static int index = 0; public static int random() { final String string = args[index]; index++; return string.length(); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: package ClassAnalysisRec; public class ClassAnalysisRec { A field; public static void main(String[] args) { Random.args = args; ClassAnalysisRec t = new ClassAnalysisRec(); t.field = new A(); t.field = new B(); t.eval(); } public void eval() { int x = Random.random() % 100; this.field.test(x); } } class A { public boolean test(int x) { return this.test(x-1); } } class B extends A { public boolean test(int x) { if (x <= 0) return true; return test(x - 1); } } package ClassAnalysisRec; public class Random { static String[] args; static int index = 0; public static int random() { final String string = args[index]; index++; return string.length(); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: ClassAnalysisRec.ClassAnalysisRec.main([Ljava/lang/String;)V: Graph of 44 nodes with 0 SCCs. ClassAnalysisRec.ClassAnalysisRec.eval()V: Graph of 108 nodes with 0 SCCs. ClassAnalysisRec.B.test(I)Z: Graph of 19 nodes with 0 SCCs. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 1 SCCs. ---------------------------------------- (6) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: ClassAnalysisRec.B.test(I)Z SCC calls the following helper methods: ClassAnalysisRec.B.test(I)Z Performed SCC analyses: *Used field analysis yielded the following read fields: *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 11 IRulesP rules: f367_0_test_GT(EOS(STATIC_367), i45, i45, i45) -> f434_0_test_GT(EOS(STATIC_434), i45, i45, i45) :|: TRUE f434_0_test_GT(EOS(STATIC_434), i45, i45, i45) -> f446_0_test_Load(EOS(STATIC_446), i45, i45) :|: i45 > 0 f446_0_test_Load(EOS(STATIC_446), i45, i45) -> f476_0_test_Load(EOS(STATIC_476), i45, i45) :|: TRUE f476_0_test_Load(EOS(STATIC_476), i45, i45) -> f1506_0_test_ConstantStackPush(EOS(STATIC_1506), i45, i45) :|: TRUE f1506_0_test_ConstantStackPush(EOS(STATIC_1506), i45, i45) -> f1533_0_test_IntArithmetic(EOS(STATIC_1533), i45, i45, 1) :|: TRUE f1533_0_test_IntArithmetic(EOS(STATIC_1533), i45, i45, matching1) -> f1542_0_test_InvokeMethod(EOS(STATIC_1542), i45, i45 - 1) :|: i45 > 0 && matching1 = 1 f1542_0_test_InvokeMethod(EOS(STATIC_1542), i45, i121) -> f1631_0_test_Load(EOS(STATIC_1631), i121, i121) :|: i45 >= 1 && i15 >= 1 && i121 < i45 f1542_0_test_InvokeMethod(EOS(STATIC_1542), i45, i121) -> f1631_1_test_Load(EOS(STATIC_1631), i45, i121) :|: i45 >= 1 && i15 >= 1 && i121 < i45 f1631_0_test_Load(EOS(STATIC_1631), i121, i121) -> f1696_0_test_Load(EOS(STATIC_1696), i121, i121) :|: TRUE f1696_0_test_Load(EOS(STATIC_1696), i121, i121) -> f354_0_test_Load(EOS(STATIC_354), i121, i121) :|: TRUE f354_0_test_Load(EOS(STATIC_354), i24, i24) -> f367_0_test_GT(EOS(STATIC_367), i24, i24, i24) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f367_0_test_GT(EOS(STATIC_367), i45:0, i45:0, i45:0) -> f367_0_test_GT(EOS(STATIC_367), i45:0 - 1, i45:0 - 1, i45:0 - 1) :|: i45:0 > 0 && i15:0 > 0 && i45:0 - 1 < i45:0 Removed following non-SCC rules: f367_0_test_GT(EOS(STATIC_367), i45:0, i45:0, i45:0) -> f1631_1_test_Load(EOS(STATIC_1631), i45:0, i45:0 - 1) :|: i45:0 > 0 && i15:0 > 0 && i45:0 - 1 < i45:0 Filtered constant ground arguments: f367_0_test_GT(x1, x2, x3, x4) -> f367_0_test_GT(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f367_0_test_GT(x1, x2, x3) -> f367_0_test_GT(x3) Finished conversion. Obtained 1 rules.P rules: f367_0_test_GT(i45:0) -> f367_0_test_GT(i45:0 - 1) :|: i15:0 > 0 && i45:0 - 1 < i45:0 && i45:0 > 0 ---------------------------------------- (8) Obligation: Rules: f367_0_test_GT(i45:0) -> f367_0_test_GT(i45:0 - 1) :|: i15:0 > 0 && i45:0 - 1 < i45:0 && i45:0 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f367_0_test_GT(i45:0) -> f367_0_test_GT(arith) :|: i15:0 > 0 && i45:0 - 1 < i45:0 && i45:0 > 0 && arith = i45:0 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f367_0_test_GT(i45:0) -> f367_0_test_GT(arith) :|: i15:0 > 0 && i45:0 - 1 < i45:0 && i45:0 > 0 && arith = i45:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f367_0_test_GT(i45:0) -> f367_0_test_GT(arith) :|: i15:0 > 0 && i45:0 - 1 < i45:0 && i45:0 > 0 && arith = i45:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f367_0_test_GT(i45:0:0) -> f367_0_test_GT(i45:0:0 - 1) :|: i15:0:0 > 0 && i45:0:0 - 1 < i45:0:0 && i45:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f367_0_test_GT(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f367_0_test_GT(i45:0:0) -> f367_0_test_GT(c) :|: c = i45:0:0 - 1 && (i15:0:0 > 0 && i45:0:0 - 1 < i45:0:0 && i45:0:0 > 0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f367_0_test_GT(x)] = x The following rules are decreasing: f367_0_test_GT(i45:0:0) -> f367_0_test_GT(c) :|: c = i45:0:0 - 1 && (i15:0:0 > 0 && i45:0:0 - 1 < i45:0:0 && i45:0:0 > 0) The following rules are bounded: f367_0_test_GT(i45:0:0) -> f367_0_test_GT(c) :|: c = i45:0:0 - 1 && (i15:0:0 > 0 && i45:0:0 - 1 < i45:0:0 && i45:0:0 > 0) ---------------------------------------- (18) YES