7.65/2.97 YES 7.65/2.99 proof of /export/starexec/sandbox/benchmark/theBenchmark.jar 7.65/2.99 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.65/2.99 7.65/2.99 7.65/2.99 termination of the given Bare JBC problem could be proven: 7.65/2.99 7.65/2.99 (0) Bare JBC problem 7.65/2.99 (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] 7.65/2.99 (2) JBC problem 7.65/2.99 (3) JBCToGraph [EQUIVALENT, 332 ms] 7.65/2.99 (4) JBCTerminationGraph 7.65/2.99 (5) TerminationGraphToSCCProof [SOUND, 0 ms] 7.65/2.99 (6) JBCTerminationSCC 7.65/2.99 (7) SCCToIRSProof [SOUND, 140 ms] 7.65/2.99 (8) IRSwT 7.65/2.99 (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] 7.65/2.99 (10) IRSwT 7.65/2.99 (11) IRSwTTerminationDigraphProof [EQUIVALENT, 73 ms] 7.65/2.99 (12) IRSwT 7.65/2.99 (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] 7.65/2.99 (14) IRSwT 7.65/2.99 (15) TempFilterProof [SOUND, 48 ms] 7.65/2.99 (16) IntTRS 7.65/2.99 (17) PolynomialOrderProcessor [EQUIVALENT, 13 ms] 7.65/2.99 (18) IntTRS 7.65/2.99 (19) PolynomialOrderProcessor [EQUIVALENT, 0 ms] 7.65/2.99 (20) YES 7.65/2.99 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (0) 7.65/2.99 Obligation: 7.65/2.99 need to prove termination of the following program: 7.65/2.99 /** 7.65/2.99 * Example taken from "A Term Rewriting Approach to the Automated Termination 7.65/2.99 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) 7.65/2.99 * and converted to Java. 7.65/2.99 */ 7.65/2.99 7.65/2.99 public class PastaC9 { 7.65/2.99 public static void main(String[] args) { 7.65/2.99 Random.args = args; 7.65/2.99 int x = Random.random(); 7.65/2.99 int y = Random.random(); 7.65/2.99 7.65/2.99 while (x > 0 && y > 0) { 7.65/2.99 if (Random.random() < 42) { 7.65/2.99 x--; 7.65/2.99 y = Random.random(); 7.65/2.99 } else { 7.65/2.99 y--; 7.65/2.99 } 7.65/2.99 } 7.65/2.99 } 7.65/2.99 } 7.65/2.99 7.65/2.99 7.65/2.99 public class Random { 7.65/2.99 static String[] args; 7.65/2.99 static int index = 0; 7.65/2.99 7.65/2.99 public static int random() { 7.65/2.99 String string = args[index]; 7.65/2.99 index++; 7.65/2.99 return string.length(); 7.65/2.99 } 7.65/2.99 } 7.65/2.99 7.65/2.99 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (1) BareJBCToJBCProof (EQUIVALENT) 7.65/2.99 initialized classpath 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (2) 7.65/2.99 Obligation: 7.65/2.99 need to prove termination of the following program: 7.65/2.99 /** 7.65/2.99 * Example taken from "A Term Rewriting Approach to the Automated Termination 7.65/2.99 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf) 7.65/2.99 * and converted to Java. 7.65/2.99 */ 7.65/2.99 7.65/2.99 public class PastaC9 { 7.65/2.99 public static void main(String[] args) { 7.65/2.99 Random.args = args; 7.65/2.99 int x = Random.random(); 7.65/2.99 int y = Random.random(); 7.65/2.99 7.65/2.99 while (x > 0 && y > 0) { 7.65/2.99 if (Random.random() < 42) { 7.65/2.99 x--; 7.65/2.99 y = Random.random(); 7.65/2.99 } else { 7.65/2.99 y--; 7.65/2.99 } 7.65/2.99 } 7.65/2.99 } 7.65/2.99 } 7.65/2.99 7.65/2.99 7.65/2.99 public class Random { 7.65/2.99 static String[] args; 7.65/2.99 static int index = 0; 7.65/2.99 7.65/2.99 public static int random() { 7.65/2.99 String string = args[index]; 7.65/2.99 index++; 7.65/2.99 return string.length(); 7.65/2.99 } 7.65/2.99 } 7.65/2.99 7.65/2.99 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (3) JBCToGraph (EQUIVALENT) 7.65/2.99 Constructed TerminationGraph. 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (4) 7.65/2.99 Obligation: 7.65/2.99 Termination Graph based on JBC Program: 7.65/2.99 PastaC9.main([Ljava/lang/String;)V: Graph of 318 nodes with 1 SCC. 7.65/2.99 7.65/2.99 7.65/2.99 7.65/2.99 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (5) TerminationGraphToSCCProof (SOUND) 7.65/2.99 Splitted TerminationGraph to 1 SCCs. 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (6) 7.65/2.99 Obligation: 7.65/2.99 SCC of termination graph based on JBC Program. 7.65/2.99 SCC contains nodes from the following methods: PastaC9.main([Ljava/lang/String;)V 7.65/2.99 SCC calls the following helper methods: 7.65/2.99 Performed SCC analyses: 7.65/2.99 *Used field analysis yielded the following read fields: 7.65/2.99 *java.lang.String: [count] 7.65/2.99 *Marker field analysis yielded the following relations that could be markers: 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (7) SCCToIRSProof (SOUND) 7.65/2.99 Transformed FIGraph SCCs to intTRSs. Log: 7.65/2.99 Generated rules. Obtained 56 IRulesP rules: 7.65/2.99 f356_0_main_LE(EOS(STATIC_356(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i50, i52) -> f360_0_main_LE(EOS(STATIC_360(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i50, i52) :|: TRUE 7.65/2.99 f360_0_main_LE(EOS(STATIC_360(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i50, i52) -> f363_0_main_Load(EOS(STATIC_363(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i50) :|: i52 > 0 7.65/2.99 f363_0_main_Load(EOS(STATIC_363(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i50) -> f367_0_main_LE(EOS(STATIC_367(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i50, i50) :|: TRUE 7.65/2.99 f367_0_main_LE(EOS(STATIC_367(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i53) -> f371_0_main_LE(EOS(STATIC_371(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i53) :|: TRUE 7.65/2.99 f371_0_main_LE(EOS(STATIC_371(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i53) -> f375_0_main_InvokeMethod(EOS(STATIC_375(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53) :|: i53 > 0 7.65/2.99 f375_0_main_InvokeMethod(EOS(STATIC_375(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53) -> f378_0_random_FieldAccess(EOS(STATIC_378(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53) :|: TRUE 7.65/2.99 f378_0_random_FieldAccess(EOS(STATIC_378(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53) -> f383_0_random_FieldAccess(EOS(STATIC_383(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(ARRAY(i6))) :|: TRUE 7.65/2.99 f383_0_random_FieldAccess(EOS(STATIC_383(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(ARRAY(i6))) -> f386_0_random_ArrayAccess(EOS(STATIC_386(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(ARRAY(i6))) :|: TRUE 7.65/2.99 f386_0_random_ArrayAccess(EOS(STATIC_386(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(ARRAY(i6))) -> f389_0_random_ArrayAccess(EOS(STATIC_389(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(ARRAY(i6))) :|: TRUE 7.65/2.99 f389_0_random_ArrayAccess(EOS(STATIC_389(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(ARRAY(i6))) -> f393_0_random_Store(EOS(STATIC_393(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) :|: TRUE 7.65/2.99 f393_0_random_Store(EOS(STATIC_393(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) -> f397_0_random_FieldAccess(EOS(STATIC_397(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) :|: TRUE 7.65/2.99 f397_0_random_FieldAccess(EOS(STATIC_397(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) -> f399_0_random_ConstantStackPush(EOS(STATIC_399(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) :|: TRUE 7.65/2.99 f399_0_random_ConstantStackPush(EOS(STATIC_399(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) -> f402_0_random_IntArithmetic(EOS(STATIC_402(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) :|: TRUE 7.65/2.99 f402_0_random_IntArithmetic(EOS(STATIC_402(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) -> f405_0_random_FieldAccess(EOS(STATIC_405(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) :|: TRUE 7.65/2.99 f405_0_random_FieldAccess(EOS(STATIC_405(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) -> f407_0_random_Load(EOS(STATIC_407(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) :|: TRUE 7.65/2.99 f407_0_random_Load(EOS(STATIC_407(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) -> f409_0_random_InvokeMethod(EOS(STATIC_409(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, o53) :|: TRUE 7.65/2.99 f409_0_random_InvokeMethod(EOS(STATIC_409(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(o60sub)) -> f411_0_random_InvokeMethod(EOS(STATIC_411(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(o60sub)) :|: TRUE 7.65/2.99 f411_0_random_InvokeMethod(EOS(STATIC_411(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(o61sub)) -> f413_0_random_InvokeMethod(EOS(STATIC_413(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(o61sub)) :|: TRUE 7.65/2.99 f413_0_random_InvokeMethod(EOS(STATIC_413(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(o61sub)) -> f416_0_length_Load(EOS(STATIC_416(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(o61sub)) :|: TRUE 7.65/2.99 f416_0_length_Load(EOS(STATIC_416(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(o61sub)) -> f419_0_length_FieldAccess(EOS(STATIC_419(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(o61sub)) :|: TRUE 7.65/2.99 f419_0_length_FieldAccess(EOS(STATIC_419(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(java.lang.String(EOC, i75))) -> f422_0_length_FieldAccess(EOS(STATIC_422(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(java.lang.String(EOC, i75))) :|: i75 >= 0 7.65/2.99 f422_0_length_FieldAccess(EOS(STATIC_422(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, java.lang.Object(java.lang.String(EOC, i75))) -> f424_0_length_Return(EOS(STATIC_424(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i75) :|: TRUE 7.65/2.99 f424_0_length_Return(EOS(STATIC_424(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i75) -> f426_0_random_Return(EOS(STATIC_426(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i75) :|: TRUE 7.65/2.99 f426_0_random_Return(EOS(STATIC_426(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i75) -> f429_0_main_ConstantStackPush(EOS(STATIC_429(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i75) :|: TRUE 7.65/2.99 f429_0_main_ConstantStackPush(EOS(STATIC_429(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i75) -> f431_0_main_GE(EOS(STATIC_431(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i75, 42) :|: TRUE 7.65/2.99 f431_0_main_GE(EOS(STATIC_431(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i78, matching1) -> f434_0_main_GE(EOS(STATIC_434(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i78, 42) :|: TRUE && matching1 = 42 7.65/2.99 f431_0_main_GE(EOS(STATIC_431(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i80, matching1) -> f437_0_main_GE(EOS(STATIC_437(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i80, 42) :|: TRUE && matching1 = 42 7.65/2.99 f434_0_main_GE(EOS(STATIC_434(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i78, matching1) -> f444_0_main_Inc(EOS(STATIC_444(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52) :|: i78 < 42 && matching1 = 42 7.65/2.99 f444_0_main_Inc(EOS(STATIC_444(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52) -> f460_0_main_InvokeMethod(EOS(STATIC_460(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52 + -1) :|: TRUE 7.65/2.99 f460_0_main_InvokeMethod(EOS(STATIC_460(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83) -> f471_0_random_FieldAccess(EOS(STATIC_471(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83) :|: TRUE 7.65/2.99 f471_0_random_FieldAccess(EOS(STATIC_471(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83) -> f990_0_random_FieldAccess(EOS(STATIC_990(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(ARRAY(i6))) :|: TRUE 7.65/2.99 f990_0_random_FieldAccess(EOS(STATIC_990(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(ARRAY(i6))) -> f1010_0_random_ArrayAccess(EOS(STATIC_1010(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(ARRAY(i6))) :|: TRUE 7.65/2.99 f1010_0_random_ArrayAccess(EOS(STATIC_1010(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(ARRAY(i6))) -> f1028_0_random_ArrayAccess(EOS(STATIC_1028(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(ARRAY(i6))) :|: TRUE 7.65/2.99 f1028_0_random_ArrayAccess(EOS(STATIC_1028(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(ARRAY(i6))) -> f1041_0_random_Store(EOS(STATIC_1041(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) :|: TRUE 7.65/2.99 f1041_0_random_Store(EOS(STATIC_1041(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) -> f1051_0_random_FieldAccess(EOS(STATIC_1051(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) :|: TRUE 7.65/2.99 f1051_0_random_FieldAccess(EOS(STATIC_1051(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) -> f1061_0_random_ConstantStackPush(EOS(STATIC_1061(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) :|: TRUE 7.65/2.99 f1061_0_random_ConstantStackPush(EOS(STATIC_1061(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) -> f1077_0_random_IntArithmetic(EOS(STATIC_1077(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) :|: TRUE 7.65/2.99 f1077_0_random_IntArithmetic(EOS(STATIC_1077(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) -> f1090_0_random_FieldAccess(EOS(STATIC_1090(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) :|: TRUE 7.65/2.99 f1090_0_random_FieldAccess(EOS(STATIC_1090(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) -> f1095_0_random_Load(EOS(STATIC_1095(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) :|: TRUE 7.65/2.99 f1095_0_random_Load(EOS(STATIC_1095(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) -> f1116_0_random_InvokeMethod(EOS(STATIC_1116(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, o132) :|: TRUE 7.65/2.99 f1116_0_random_InvokeMethod(EOS(STATIC_1116(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(o148sub)) -> f1124_0_random_InvokeMethod(EOS(STATIC_1124(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(o148sub)) :|: TRUE 7.65/2.99 f1124_0_random_InvokeMethod(EOS(STATIC_1124(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(o149sub)) -> f1129_0_random_InvokeMethod(EOS(STATIC_1129(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(o149sub)) :|: TRUE 7.65/2.99 f1129_0_random_InvokeMethod(EOS(STATIC_1129(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(o149sub)) -> f1138_0_length_Load(EOS(STATIC_1138(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(o149sub)) :|: TRUE 7.65/2.99 f1138_0_length_Load(EOS(STATIC_1138(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(o149sub)) -> f1146_0_length_FieldAccess(EOS(STATIC_1146(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(o149sub)) :|: TRUE 7.65/2.99 f1146_0_length_FieldAccess(EOS(STATIC_1146(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(java.lang.String(EOC, i195))) -> f1150_0_length_FieldAccess(EOS(STATIC_1150(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(java.lang.String(EOC, i195))) :|: i195 >= 0 7.65/2.99 f1150_0_length_FieldAccess(EOS(STATIC_1150(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, java.lang.Object(java.lang.String(EOC, i195))) -> f1157_0_length_Return(EOS(STATIC_1157(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) :|: TRUE 7.65/2.99 f1157_0_length_Return(EOS(STATIC_1157(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) -> f1166_0_random_Return(EOS(STATIC_1166(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) :|: TRUE 7.65/2.99 f1166_0_random_Return(EOS(STATIC_1166(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) -> f1170_0_main_Store(EOS(STATIC_1170(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) :|: TRUE 7.65/2.99 f1170_0_main_Store(EOS(STATIC_1170(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) -> f1172_0_main_JMP(EOS(STATIC_1172(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) :|: TRUE 7.65/2.99 f1172_0_main_JMP(EOS(STATIC_1172(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) -> f1178_0_main_Load(EOS(STATIC_1178(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) :|: TRUE 7.65/2.99 f1178_0_main_Load(EOS(STATIC_1178(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) -> f353_0_main_Load(EOS(STATIC_353(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i83, i195) :|: TRUE 7.65/2.99 f353_0_main_Load(EOS(STATIC_353(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i19, i50) -> f356_0_main_LE(EOS(STATIC_356(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i19, i50, i19) :|: TRUE 7.65/2.99 f437_0_main_GE(EOS(STATIC_437(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53, i80, matching1) -> f446_0_main_Inc(EOS(STATIC_446(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53) :|: i80 >= 42 && matching1 = 42 7.65/2.99 f446_0_main_Inc(EOS(STATIC_446(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53) -> f463_0_main_JMP(EOS(STATIC_463(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i53 + -1) :|: TRUE 7.65/2.99 f463_0_main_JMP(EOS(STATIC_463(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i84) -> f511_0_main_Load(EOS(STATIC_511(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i84) :|: TRUE 7.65/2.99 f511_0_main_Load(EOS(STATIC_511(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i84) -> f353_0_main_Load(EOS(STATIC_353(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i52, i84) :|: TRUE 7.65/2.99 Combined rules. Obtained 2 IRulesP rules: 7.65/2.99 f356_0_main_LE(EOS(STATIC_356(java.lang.Object(ARRAY(i6:0)))), java.lang.Object(ARRAY(i6:0)), i52:0, i50:0, i52:0) -> f356_0_main_LE(EOS(STATIC_356(java.lang.Object(ARRAY(i6:0)))), java.lang.Object(ARRAY(i6:0)), i52:0, i50:0 - 1, i52:0) :|: i75:0 > 41 && i50:0 > 0 && i52:0 > 0 7.65/2.99 f356_0_main_LE(EOS(STATIC_356(java.lang.Object(ARRAY(i6:0)))), java.lang.Object(ARRAY(i6:0)), i52:0, i50:0, i52:0) -> f356_0_main_LE(EOS(STATIC_356(java.lang.Object(ARRAY(i6:0)))), java.lang.Object(ARRAY(i6:0)), i52:0 - 1, i195:0, i52:0 - 1) :|: i52:0 > 0 && i50:0 > 0 && i75:0 > -1 && i195:0 > -1 && i75:0 < 42 7.65/2.99 Filtered duplicate arguments: 7.65/2.99 f356_0_main_LE(x1, x2, x3, x4, x5) -> f356_0_main_LE(x1, x2, x4, x5) 7.65/2.99 Filtered unneeded arguments: 7.65/2.99 f356_0_main_LE(x1, x2, x3, x4) -> f356_0_main_LE(x3, x4) 7.65/2.99 Finished conversion. Obtained 2 rules.P rules: 7.65/2.99 f356_0_main_LE(i50:0, i52:0) -> f356_0_main_LE(i50:0 - 1, i52:0) :|: i50:0 > 0 && i52:0 > 0 && i75:0 > 41 7.65/2.99 f356_0_main_LE(i50:0, i52:0) -> f356_0_main_LE(i195:0, i52:0 - 1) :|: i50:0 > 0 && i52:0 > 0 && i75:0 > -1 && i75:0 < 42 && i195:0 > -1 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (8) 7.65/2.99 Obligation: 7.65/2.99 Rules: 7.65/2.99 f356_0_main_LE(i50:0, i52:0) -> f356_0_main_LE(i50:0 - 1, i52:0) :|: i50:0 > 0 && i52:0 > 0 && i75:0 > 41 7.65/2.99 f356_0_main_LE(x, x1) -> f356_0_main_LE(x2, x1 - 1) :|: x > 0 && x1 > 0 && x3 > -1 && x3 < 42 && x2 > -1 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (9) IRSFormatTransformerProof (EQUIVALENT) 7.65/2.99 Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (10) 7.65/2.99 Obligation: 7.65/2.99 Rules: 7.65/2.99 f356_0_main_LE(i50:0, i52:0) -> f356_0_main_LE(arith, i52:0) :|: i50:0 > 0 && i52:0 > 0 && i75:0 > 41 && arith = i50:0 - 1 7.65/2.99 f356_0_main_LE(x4, x5) -> f356_0_main_LE(x6, x7) :|: x4 > 0 && x5 > 0 && x8 > -1 && x8 < 42 && x6 > -1 && x7 = x5 - 1 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (11) IRSwTTerminationDigraphProof (EQUIVALENT) 7.65/2.99 Constructed termination digraph! 7.65/2.99 Nodes: 7.65/2.99 (1) f356_0_main_LE(i50:0, i52:0) -> f356_0_main_LE(arith, i52:0) :|: i50:0 > 0 && i52:0 > 0 && i75:0 > 41 && arith = i50:0 - 1 7.65/2.99 (2) f356_0_main_LE(x4, x5) -> f356_0_main_LE(x6, x7) :|: x4 > 0 && x5 > 0 && x8 > -1 && x8 < 42 && x6 > -1 && x7 = x5 - 1 7.65/2.99 7.65/2.99 Arcs: 7.65/2.99 (1) -> (1), (2) 7.65/2.99 (2) -> (1), (2) 7.65/2.99 7.65/2.99 This digraph is fully evaluated! 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (12) 7.65/2.99 Obligation: 7.65/2.99 7.65/2.99 Termination digraph: 7.65/2.99 Nodes: 7.65/2.99 (1) f356_0_main_LE(i50:0, i52:0) -> f356_0_main_LE(arith, i52:0) :|: i50:0 > 0 && i52:0 > 0 && i75:0 > 41 && arith = i50:0 - 1 7.65/2.99 (2) f356_0_main_LE(x4, x5) -> f356_0_main_LE(x6, x7) :|: x4 > 0 && x5 > 0 && x8 > -1 && x8 < 42 && x6 > -1 && x7 = x5 - 1 7.65/2.99 7.65/2.99 Arcs: 7.65/2.99 (1) -> (1), (2) 7.65/2.99 (2) -> (1), (2) 7.65/2.99 7.65/2.99 This digraph is fully evaluated! 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (13) IntTRSCompressionProof (EQUIVALENT) 7.65/2.99 Compressed rules. 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (14) 7.65/2.99 Obligation: 7.65/2.99 Rules: 7.65/2.99 f356_0_main_LE(i50:0:0, i52:0:0) -> f356_0_main_LE(i50:0:0 - 1, i52:0:0) :|: i50:0:0 > 0 && i52:0:0 > 0 && i75:0:0 > 41 7.65/2.99 f356_0_main_LE(x4:0, x5:0) -> f356_0_main_LE(x6:0, x5:0 - 1) :|: x8:0 < 42 && x6:0 > -1 && x8:0 > -1 && x5:0 > 0 && x4:0 > 0 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (15) TempFilterProof (SOUND) 7.65/2.99 Used the following sort dictionary for filtering: 7.65/2.99 f356_0_main_LE(INTEGER, INTEGER) 7.65/2.99 Replaced non-predefined constructor symbols by 0. 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (16) 7.65/2.99 Obligation: 7.65/2.99 Rules: 7.65/2.99 f356_0_main_LE(i50:0:0, i52:0:0) -> f356_0_main_LE(c, i52:0:0) :|: c = i50:0:0 - 1 && (i50:0:0 > 0 && i52:0:0 > 0 && i75:0:0 > 41) 7.65/2.99 f356_0_main_LE(x4:0, x5:0) -> f356_0_main_LE(x6:0, c1) :|: c1 = x5:0 - 1 && (x8:0 < 42 && x6:0 > -1 && x8:0 > -1 && x5:0 > 0 && x4:0 > 0) 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (17) PolynomialOrderProcessor (EQUIVALENT) 7.65/2.99 Found the following polynomial interpretation: 7.65/2.99 [f356_0_main_LE(x, x1)] = x1 7.65/2.99 7.65/2.99 The following rules are decreasing: 7.65/2.99 f356_0_main_LE(x4:0, x5:0) -> f356_0_main_LE(x6:0, c1) :|: c1 = x5:0 - 1 && (x8:0 < 42 && x6:0 > -1 && x8:0 > -1 && x5:0 > 0 && x4:0 > 0) 7.65/2.99 The following rules are bounded: 7.65/2.99 f356_0_main_LE(i50:0:0, i52:0:0) -> f356_0_main_LE(c, i52:0:0) :|: c = i50:0:0 - 1 && (i50:0:0 > 0 && i52:0:0 > 0 && i75:0:0 > 41) 7.65/2.99 f356_0_main_LE(x4:0, x5:0) -> f356_0_main_LE(x6:0, c1) :|: c1 = x5:0 - 1 && (x8:0 < 42 && x6:0 > -1 && x8:0 > -1 && x5:0 > 0 && x4:0 > 0) 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (18) 7.65/2.99 Obligation: 7.65/2.99 Rules: 7.65/2.99 f356_0_main_LE(i50:0:0, i52:0:0) -> f356_0_main_LE(c, i52:0:0) :|: c = i50:0:0 - 1 && (i50:0:0 > 0 && i52:0:0 > 0 && i75:0:0 > 41) 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (19) PolynomialOrderProcessor (EQUIVALENT) 7.65/2.99 Found the following polynomial interpretation: 7.65/2.99 [f356_0_main_LE(x, x1)] = x 7.65/2.99 7.65/2.99 The following rules are decreasing: 7.65/2.99 f356_0_main_LE(i50:0:0, i52:0:0) -> f356_0_main_LE(c, i52:0:0) :|: c = i50:0:0 - 1 && (i50:0:0 > 0 && i52:0:0 > 0 && i75:0:0 > 41) 7.65/2.99 The following rules are bounded: 7.65/2.99 f356_0_main_LE(i50:0:0, i52:0:0) -> f356_0_main_LE(c, i52:0:0) :|: c = i50:0:0 - 1 && (i50:0:0 > 0 && i52:0:0 > 0 && i75:0:0 > 41) 7.65/2.99 7.65/2.99 ---------------------------------------- 7.65/2.99 7.65/2.99 (20) 7.65/2.99 YES 7.65/3.01 EOF