/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 365 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 192 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 72 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 51 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) IntTRS (19) RankingReductionPairProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: /** * Example taken from "A Term Rewriting Approach to the Automated Termination * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) * and converted to Java. */ public class PastaC9 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0 && y > 0) { if (Random.random() < 42) { x--; y = Random.random(); } else { y--; } } } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: /** * Example taken from "A Term Rewriting Approach to the Automated Termination * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) * and converted to Java. */ public class PastaC9 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x > 0 && y > 0) { if (Random.random() < 42) { x--; y = Random.random(); } else { y--; } } } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: PastaC9.main([Ljava/lang/String;)V: Graph of 318 nodes with 1 SCC. ---------------------------------------- (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: PastaC9.main([Ljava/lang/String;)V SCC calls the following helper methods: Performed SCC analyses: *Used field analysis yielded the following read fields: *java.lang.String: [count] *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 56 IRulesP rules: f344_0_main_LE(EOS(STATIC_344(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i44, i52) -> f350_0_main_LE(EOS(STATIC_350(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i44, i52) :|: TRUE f350_0_main_LE(EOS(STATIC_350(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i44, i52) -> f362_0_main_Load(EOS(STATIC_362(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i44) :|: i52 > 0 f362_0_main_Load(EOS(STATIC_362(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i44) -> f367_0_main_LE(EOS(STATIC_367(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i44, i44) :|: TRUE f367_0_main_LE(EOS(STATIC_367(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i53) -> f371_0_main_LE(EOS(STATIC_371(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i53) :|: TRUE f371_0_main_LE(EOS(STATIC_371(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i53) -> f375_0_main_InvokeMethod(EOS(STATIC_375(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53) :|: i53 > 0 f375_0_main_InvokeMethod(EOS(STATIC_375(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53) -> f378_0_random_FieldAccess(EOS(STATIC_378(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53) :|: TRUE f378_0_random_FieldAccess(EOS(STATIC_378(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53) -> f383_0_random_FieldAccess(EOS(STATIC_383(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(ARRAY(i4))) :|: TRUE f383_0_random_FieldAccess(EOS(STATIC_383(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(ARRAY(i4))) -> f386_0_random_ArrayAccess(EOS(STATIC_386(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(ARRAY(i4))) :|: TRUE f386_0_random_ArrayAccess(EOS(STATIC_386(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(ARRAY(i4))) -> f389_0_random_ArrayAccess(EOS(STATIC_389(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(ARRAY(i4))) :|: TRUE f389_0_random_ArrayAccess(EOS(STATIC_389(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(ARRAY(i4))) -> f393_0_random_Store(EOS(STATIC_393(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) :|: TRUE f393_0_random_Store(EOS(STATIC_393(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) -> f397_0_random_FieldAccess(EOS(STATIC_397(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) :|: TRUE f397_0_random_FieldAccess(EOS(STATIC_397(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) -> f399_0_random_ConstantStackPush(EOS(STATIC_399(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) :|: TRUE f399_0_random_ConstantStackPush(EOS(STATIC_399(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) -> f402_0_random_IntArithmetic(EOS(STATIC_402(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) :|: TRUE f402_0_random_IntArithmetic(EOS(STATIC_402(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) -> f405_0_random_FieldAccess(EOS(STATIC_405(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) :|: TRUE f405_0_random_FieldAccess(EOS(STATIC_405(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) -> f407_0_random_Load(EOS(STATIC_407(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) :|: TRUE f407_0_random_Load(EOS(STATIC_407(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) -> f409_0_random_InvokeMethod(EOS(STATIC_409(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, o53) :|: TRUE f409_0_random_InvokeMethod(EOS(STATIC_409(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(o60sub)) -> f411_0_random_InvokeMethod(EOS(STATIC_411(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(o60sub)) :|: TRUE f411_0_random_InvokeMethod(EOS(STATIC_411(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(o61sub)) -> f413_0_random_InvokeMethod(EOS(STATIC_413(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(o61sub)) :|: TRUE f413_0_random_InvokeMethod(EOS(STATIC_413(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(o61sub)) -> f416_0_length_Load(EOS(STATIC_416(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(o61sub)) :|: TRUE f416_0_length_Load(EOS(STATIC_416(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(o61sub)) -> f419_0_length_FieldAccess(EOS(STATIC_419(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(o61sub)) :|: TRUE f419_0_length_FieldAccess(EOS(STATIC_419(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(java.lang.String(EOC, i75))) -> f422_0_length_FieldAccess(EOS(STATIC_422(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(java.lang.String(EOC, i75))) :|: i75 >= 0 f422_0_length_FieldAccess(EOS(STATIC_422(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, java.lang.Object(java.lang.String(EOC, i75))) -> f424_0_length_Return(EOS(STATIC_424(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i75) :|: TRUE f424_0_length_Return(EOS(STATIC_424(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i75) -> f426_0_random_Return(EOS(STATIC_426(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i75) :|: TRUE f426_0_random_Return(EOS(STATIC_426(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i75) -> f429_0_main_ConstantStackPush(EOS(STATIC_429(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i75) :|: TRUE f429_0_main_ConstantStackPush(EOS(STATIC_429(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i75) -> f431_0_main_GE(EOS(STATIC_431(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i75, 42) :|: TRUE f431_0_main_GE(EOS(STATIC_431(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i77, matching1) -> f435_0_main_GE(EOS(STATIC_435(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i77, 42) :|: TRUE && matching1 = 42 f431_0_main_GE(EOS(STATIC_431(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i80, matching1) -> f437_0_main_GE(EOS(STATIC_437(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i80, 42) :|: TRUE && matching1 = 42 f435_0_main_GE(EOS(STATIC_435(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i77, matching1) -> f444_0_main_Inc(EOS(STATIC_444(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52) :|: i77 < 42 && matching1 = 42 f444_0_main_Inc(EOS(STATIC_444(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52) -> f465_0_main_InvokeMethod(EOS(STATIC_465(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52 + -1) :|: TRUE f465_0_main_InvokeMethod(EOS(STATIC_465(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83) -> f481_0_random_FieldAccess(EOS(STATIC_481(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83) :|: TRUE f481_0_random_FieldAccess(EOS(STATIC_481(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83) -> f1032_0_random_FieldAccess(EOS(STATIC_1032(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(ARRAY(i4))) :|: TRUE f1032_0_random_FieldAccess(EOS(STATIC_1032(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(ARRAY(i4))) -> f1044_0_random_ArrayAccess(EOS(STATIC_1044(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(ARRAY(i4))) :|: TRUE f1044_0_random_ArrayAccess(EOS(STATIC_1044(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(ARRAY(i4))) -> f1059_0_random_ArrayAccess(EOS(STATIC_1059(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(ARRAY(i4))) :|: TRUE f1059_0_random_ArrayAccess(EOS(STATIC_1059(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(ARRAY(i4))) -> f1074_0_random_Store(EOS(STATIC_1074(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) :|: TRUE f1074_0_random_Store(EOS(STATIC_1074(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) -> f1086_0_random_FieldAccess(EOS(STATIC_1086(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) :|: TRUE f1086_0_random_FieldAccess(EOS(STATIC_1086(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) -> f1098_0_random_ConstantStackPush(EOS(STATIC_1098(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) :|: TRUE f1098_0_random_ConstantStackPush(EOS(STATIC_1098(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) -> f1116_0_random_IntArithmetic(EOS(STATIC_1116(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) :|: TRUE f1116_0_random_IntArithmetic(EOS(STATIC_1116(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) -> f1125_0_random_FieldAccess(EOS(STATIC_1125(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) :|: TRUE f1125_0_random_FieldAccess(EOS(STATIC_1125(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) -> f1128_0_random_Load(EOS(STATIC_1128(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) :|: TRUE f1128_0_random_Load(EOS(STATIC_1128(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) -> f1135_0_random_InvokeMethod(EOS(STATIC_1135(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, o136) :|: TRUE f1135_0_random_InvokeMethod(EOS(STATIC_1135(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(o150sub)) -> f1138_0_random_InvokeMethod(EOS(STATIC_1138(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(o150sub)) :|: TRUE f1138_0_random_InvokeMethod(EOS(STATIC_1138(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(o151sub)) -> f1141_0_random_InvokeMethod(EOS(STATIC_1141(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(o151sub)) :|: TRUE f1141_0_random_InvokeMethod(EOS(STATIC_1141(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(o151sub)) -> f1144_0_length_Load(EOS(STATIC_1144(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(o151sub)) :|: TRUE f1144_0_length_Load(EOS(STATIC_1144(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(o151sub)) -> f1147_0_length_FieldAccess(EOS(STATIC_1147(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(o151sub)) :|: TRUE f1147_0_length_FieldAccess(EOS(STATIC_1147(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(java.lang.String(EOC, i196))) -> f1155_0_length_FieldAccess(EOS(STATIC_1155(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(java.lang.String(EOC, i196))) :|: i196 >= 0 f1155_0_length_FieldAccess(EOS(STATIC_1155(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, java.lang.Object(java.lang.String(EOC, i196))) -> f1160_0_length_Return(EOS(STATIC_1160(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) :|: TRUE f1160_0_length_Return(EOS(STATIC_1160(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) -> f1166_0_random_Return(EOS(STATIC_1166(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) :|: TRUE f1166_0_random_Return(EOS(STATIC_1166(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) -> f1170_0_main_Store(EOS(STATIC_1170(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) :|: TRUE f1170_0_main_Store(EOS(STATIC_1170(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) -> f1172_0_main_JMP(EOS(STATIC_1172(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) :|: TRUE f1172_0_main_JMP(EOS(STATIC_1172(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) -> f1236_0_main_Load(EOS(STATIC_1236(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) :|: TRUE f1236_0_main_Load(EOS(STATIC_1236(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) -> f335_0_main_Load(EOS(STATIC_335(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i83, i196) :|: TRUE f335_0_main_Load(EOS(STATIC_335(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i14, i44) -> f344_0_main_LE(EOS(STATIC_344(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i14, i44, i14) :|: TRUE f437_0_main_GE(EOS(STATIC_437(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53, i80, matching1) -> f448_0_main_Inc(EOS(STATIC_448(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53) :|: i80 >= 42 && matching1 = 42 f448_0_main_Inc(EOS(STATIC_448(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53) -> f468_0_main_JMP(EOS(STATIC_468(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i53 + -1) :|: TRUE f468_0_main_JMP(EOS(STATIC_468(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i84) -> f534_0_main_Load(EOS(STATIC_534(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i84) :|: TRUE f534_0_main_Load(EOS(STATIC_534(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i84) -> f335_0_main_Load(EOS(STATIC_335(java.lang.Object(ARRAY(i4)))), java.lang.Object(ARRAY(i4)), i52, i84) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f344_0_main_LE(EOS(STATIC_344(java.lang.Object(ARRAY(i4:0)))), java.lang.Object(ARRAY(i4:0)), i52:0, i44:0, i52:0) -> f344_0_main_LE(EOS(STATIC_344(java.lang.Object(ARRAY(i4:0)))), java.lang.Object(ARRAY(i4:0)), i52:0 - 1, i196:0, i52:0 - 1) :|: i52:0 > 0 && i44:0 > 0 && i75:0 > -1 && i196:0 > -1 && i75:0 < 42 f344_0_main_LE(EOS(STATIC_344(java.lang.Object(ARRAY(i4:0)))), java.lang.Object(ARRAY(i4:0)), i52:0, i44:0, i52:0) -> f344_0_main_LE(EOS(STATIC_344(java.lang.Object(ARRAY(i4:0)))), java.lang.Object(ARRAY(i4:0)), i52:0, i44:0 - 1, i52:0) :|: i75:0 > 41 && i44:0 > 0 && i52:0 > 0 Filtered duplicate arguments: f344_0_main_LE(x1, x2, x3, x4, x5) -> f344_0_main_LE(x1, x2, x4, x5) Filtered unneeded arguments: f344_0_main_LE(x1, x2, x3, x4) -> f344_0_main_LE(x3, x4) Finished conversion. Obtained 2 rules.P rules: f344_0_main_LE(i44:0, i52:0) -> f344_0_main_LE(i196:0, i52:0 - 1) :|: i44:0 > 0 && i52:0 > 0 && i75:0 > -1 && i75:0 < 42 && i196:0 > -1 f344_0_main_LE(i44:0, i52:0) -> f344_0_main_LE(i44:0 - 1, i52:0) :|: i44:0 > 0 && i52:0 > 0 && i75:0 > 41 ---------------------------------------- (8) Obligation: Rules: f344_0_main_LE(i44:0, i52:0) -> f344_0_main_LE(i196:0, i52:0 - 1) :|: i44:0 > 0 && i52:0 > 0 && i75:0 > -1 && i75:0 < 42 && i196:0 > -1 f344_0_main_LE(x, x1) -> f344_0_main_LE(x - 1, x1) :|: x > 0 && x1 > 0 && x2 > 41 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f344_0_main_LE(i44:0, i52:0) -> f344_0_main_LE(i196:0, arith) :|: i44:0 > 0 && i52:0 > 0 && i75:0 > -1 && i75:0 < 42 && i196:0 > -1 && arith = i52:0 - 1 f344_0_main_LE(x3, x4) -> f344_0_main_LE(x5, x4) :|: x3 > 0 && x4 > 0 && x6 > 41 && x5 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f344_0_main_LE(i44:0, i52:0) -> f344_0_main_LE(i196:0, arith) :|: i44:0 > 0 && i52:0 > 0 && i75:0 > -1 && i75:0 < 42 && i196:0 > -1 && arith = i52:0 - 1 (2) f344_0_main_LE(x3, x4) -> f344_0_main_LE(x5, x4) :|: x3 > 0 && x4 > 0 && x6 > 41 && x5 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f344_0_main_LE(i44:0, i52:0) -> f344_0_main_LE(i196:0, arith) :|: i44:0 > 0 && i52:0 > 0 && i75:0 > -1 && i75:0 < 42 && i196:0 > -1 && arith = i52:0 - 1 (2) f344_0_main_LE(x3, x4) -> f344_0_main_LE(x5, x4) :|: x3 > 0 && x4 > 0 && x6 > 41 && x5 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f344_0_main_LE(x3:0, x4:0) -> f344_0_main_LE(x3:0 - 1, x4:0) :|: x3:0 > 0 && x4:0 > 0 && x6:0 > 41 f344_0_main_LE(i44:0:0, i52:0:0) -> f344_0_main_LE(i196:0:0, i52:0:0 - 1) :|: i75:0:0 < 42 && i196:0:0 > -1 && i75:0:0 > -1 && i52:0:0 > 0 && i44:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f344_0_main_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f344_0_main_LE(x3:0, x4:0) -> f344_0_main_LE(c, x4:0) :|: c = x3:0 - 1 && (x3:0 > 0 && x4:0 > 0 && x6:0 > 41) f344_0_main_LE(i44:0:0, i52:0:0) -> f344_0_main_LE(i196:0:0, c1) :|: c1 = i52:0:0 - 1 && (i75:0:0 < 42 && i196:0:0 > -1 && i75:0:0 > -1 && i52:0:0 > 0 && i44:0:0 > 0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f344_0_main_LE(x, x1)] = x1 The following rules are decreasing: f344_0_main_LE(i44:0:0, i52:0:0) -> f344_0_main_LE(i196:0:0, c1) :|: c1 = i52:0:0 - 1 && (i75:0:0 < 42 && i196:0:0 > -1 && i75:0:0 > -1 && i52:0:0 > 0 && i44:0:0 > 0) The following rules are bounded: f344_0_main_LE(x3:0, x4:0) -> f344_0_main_LE(c, x4:0) :|: c = x3:0 - 1 && (x3:0 > 0 && x4:0 > 0 && x6:0 > 41) f344_0_main_LE(i44:0:0, i52:0:0) -> f344_0_main_LE(i196:0:0, c1) :|: c1 = i52:0:0 - 1 && (i75:0:0 < 42 && i196:0:0 > -1 && i75:0:0 > -1 && i52:0:0 > 0 && i44:0:0 > 0) ---------------------------------------- (18) Obligation: Rules: f344_0_main_LE(x3:0, x4:0) -> f344_0_main_LE(c, x4:0) :|: c = x3:0 - 1 && (x3:0 > 0 && x4:0 > 0 && x6:0 > 41) ---------------------------------------- (19) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f344_0_main_LE ] = f344_0_main_LE_1 The following rules are decreasing: f344_0_main_LE(x3:0, x4:0) -> f344_0_main_LE(c, x4:0) :|: c = x3:0 - 1 && (x3:0 > 0 && x4:0 > 0 && x6:0 > 41) The following rules are bounded: f344_0_main_LE(x3:0, x4:0) -> f344_0_main_LE(c, x4:0) :|: c = x3:0 - 1 && (x3:0 > 0 && x4:0 > 0 && x6:0 > 41) ---------------------------------------- (20) YES