/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 95 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 470 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) AND (7) JBCTerminationSCC (8) SCCToIRSProof [SOUND, 103 ms] (9) IRSwT (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (11) IRSwT (12) IRSwTTerminationDigraphProof [EQUIVALENT, 20 ms] (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) TempFilterProof [SOUND, 4 ms] (17) IntTRS (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (19) YES (20) JBCTerminationSCC (21) SCCToIRSProof [SOUND, 54 ms] (22) IRSwT (23) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (24) IRSwT (25) IRSwTTerminationDigraphProof [EQUIVALENT, 14 ms] (26) IRSwT (27) IntTRSCompressionProof [EQUIVALENT, 0 ms] (28) IRSwT (29) TempFilterProof [SOUND, 14 ms] (30) IntTRS (31) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (32) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class CAppE { CAppE next; public static void main(String[] args) { Random.args = args; CAppE list = createList(); cappE(Random.random()); } public static void cappE(int j) { CAppE a = new CAppE(); if (j > 0) { a.appE(j); while (a.next == null) {} } } public void appE(int i) { if (next == null) { if (i <= 0) { return; } else { next = new CAppE(); } i--; } next.appE(i); } public static CAppE createList() { CAppE result = null; int length = Random.random(); while (length > 0) { result = new CAppE(result); length--; } return result; } public CAppE() { this.next = null; } public CAppE(CAppE n) { this.next = n; } } 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: public class CAppE { CAppE next; public static void main(String[] args) { Random.args = args; CAppE list = createList(); cappE(Random.random()); } public static void cappE(int j) { CAppE a = new CAppE(); if (j > 0) { a.appE(j); while (a.next == null) {} } } public void appE(int i) { if (next == null) { if (i <= 0) { return; } else { next = new CAppE(); } i--; } next.appE(i); } public static CAppE createList() { CAppE result = null; int length = Random.random(); while (length > 0) { result = new CAppE(result); length--; } return result; } public CAppE() { this.next = null; } public CAppE(CAppE n) { this.next = n; } } 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: CAppE.main([Ljava/lang/String;)V: Graph of 116 nodes with 0 SCCs. CAppE.createList()LCAppE;: Graph of 118 nodes with 1 SCC. CAppE.appE(I)V: Graph of 36 nodes with 0 SCCs. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 2 SCCss. ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: CAppE.appE(I)V SCC calls the following helper methods: CAppE.appE(I)V Performed SCC analyses: *Used field analysis yielded the following read fields: *CAppE: [next] *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (8) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 25 IRulesP rules: f1680_0_appE_FieldAccess(EOS(STATIC_1680), i183, i183) -> f1682_0_appE_NONNULL(EOS(STATIC_1682), i183, i183) :|: TRUE f1682_0_appE_NONNULL(EOS(STATIC_1682), i183, i183) -> f1683_0_appE_Load(EOS(STATIC_1683), i183, i183) :|: TRUE f1683_0_appE_Load(EOS(STATIC_1683), i183, i183) -> f1686_0_appE_GT(EOS(STATIC_1686), i183, i183, i183) :|: TRUE f1686_0_appE_GT(EOS(STATIC_1686), i185, i185, i185) -> f1690_0_appE_GT(EOS(STATIC_1690), i185, i185, i185) :|: TRUE f1690_0_appE_GT(EOS(STATIC_1690), i185, i185, i185) -> f1695_0_appE_Load(EOS(STATIC_1695), i185, i185) :|: i185 > 0 f1695_0_appE_Load(EOS(STATIC_1695), i185, i185) -> f1699_0_appE_New(EOS(STATIC_1699), i185, i185) :|: TRUE f1699_0_appE_New(EOS(STATIC_1699), i185, i185) -> f1820_0_appE_Duplicate(EOS(STATIC_1820), i185, i185) :|: TRUE f1820_0_appE_Duplicate(EOS(STATIC_1820), i185, i185) -> f1822_0_appE_InvokeMethod(EOS(STATIC_1822), i185, i185) :|: TRUE f1822_0_appE_InvokeMethod(EOS(STATIC_1822), i185, i185) -> f1824_0__init__Load(EOS(STATIC_1824), i185, i185) :|: TRUE f1824_0__init__Load(EOS(STATIC_1824), i185, i185) -> f1826_0__init__InvokeMethod(EOS(STATIC_1826), i185, i185) :|: TRUE f1826_0__init__InvokeMethod(EOS(STATIC_1826), i185, i185) -> f1827_0__init__Load(EOS(STATIC_1827), i185, i185) :|: TRUE f1827_0__init__Load(EOS(STATIC_1827), i185, i185) -> f1831_0__init__ConstantStackPush(EOS(STATIC_1831), i185, i185) :|: TRUE f1831_0__init__ConstantStackPush(EOS(STATIC_1831), i185, i185) -> f1833_0__init__FieldAccess(EOS(STATIC_1833), i185, i185) :|: TRUE f1833_0__init__FieldAccess(EOS(STATIC_1833), i185, i185) -> f1836_0__init__Return(EOS(STATIC_1836), i185, i185) :|: TRUE f1836_0__init__Return(EOS(STATIC_1836), i185, i185) -> f1838_0_appE_FieldAccess(EOS(STATIC_1838), i185, i185) :|: TRUE f1838_0_appE_FieldAccess(EOS(STATIC_1838), i185, i185) -> f1840_0_appE_Inc(EOS(STATIC_1840), i185, i185) :|: TRUE f1840_0_appE_Inc(EOS(STATIC_1840), i185, i185) -> f1843_0_appE_Load(EOS(STATIC_1843), i185, i185 + -1) :|: TRUE f1843_0_appE_Load(EOS(STATIC_1843), i185, i196) -> f1845_0_appE_FieldAccess(EOS(STATIC_1845), i185, i196) :|: TRUE f1845_0_appE_FieldAccess(EOS(STATIC_1845), i185, i196) -> f1847_0_appE_Load(EOS(STATIC_1847), i185, i196) :|: TRUE f1847_0_appE_Load(EOS(STATIC_1847), i185, i196) -> f1849_0_appE_InvokeMethod(EOS(STATIC_1849), i185, i196) :|: TRUE f1849_0_appE_InvokeMethod(EOS(STATIC_1849), i185, i196) -> f1851_0_appE_Load(EOS(STATIC_1851), i196, i196) :|: i185 >= 1 && i159 > 1 && i196 < i185 f1849_0_appE_InvokeMethod(EOS(STATIC_1849), i185, i196) -> f1851_1_appE_Load(EOS(STATIC_1851), i185, i196) :|: i185 >= 1 && i159 > 1 && i196 < i185 f1851_0_appE_Load(EOS(STATIC_1851), i196, i196) -> f1858_0_appE_Load(EOS(STATIC_1858), i196, i196) :|: TRUE f1858_0_appE_Load(EOS(STATIC_1858), i196, i196) -> f1670_0_appE_Load(EOS(STATIC_1670), i196, i196) :|: TRUE f1670_0_appE_Load(EOS(STATIC_1670), i183, i183) -> f1680_0_appE_FieldAccess(EOS(STATIC_1680), i183, i183) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f1680_0_appE_FieldAccess(EOS(STATIC_1680), i183:0, i183:0) -> f1680_0_appE_FieldAccess(EOS(STATIC_1680), i183:0 - 1, i183:0 - 1) :|: i183:0 > 0 && i159:0 > 1 && i183:0 - 1 < i183:0 Removed following non-SCC rules: f1680_0_appE_FieldAccess(EOS(STATIC_1680), i183:0, i183:0) -> f1851_1_appE_Load(EOS(STATIC_1851), i183:0, i183:0 - 1) :|: i183:0 > 0 && i159:0 > 1 && i183:0 - 1 < i183:0 Filtered constant ground arguments: f1680_0_appE_FieldAccess(x1, x2, x3) -> f1680_0_appE_FieldAccess(x2, x3) EOS(x1) -> EOS Filtered duplicate arguments: f1680_0_appE_FieldAccess(x1, x2) -> f1680_0_appE_FieldAccess(x2) Finished conversion. Obtained 1 rules.P rules: f1680_0_appE_FieldAccess(i183:0) -> f1680_0_appE_FieldAccess(i183:0 - 1) :|: i159:0 > 1 && i183:0 - 1 < i183:0 && i183:0 > 0 ---------------------------------------- (9) Obligation: Rules: f1680_0_appE_FieldAccess(i183:0) -> f1680_0_appE_FieldAccess(i183:0 - 1) :|: i159:0 > 1 && i183:0 - 1 < i183:0 && i183:0 > 0 ---------------------------------------- (10) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (11) Obligation: Rules: f1680_0_appE_FieldAccess(i183:0) -> f1680_0_appE_FieldAccess(arith) :|: i159:0 > 1 && i183:0 - 1 < i183:0 && i183:0 > 0 && arith = i183:0 - 1 ---------------------------------------- (12) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1680_0_appE_FieldAccess(i183:0) -> f1680_0_appE_FieldAccess(arith) :|: i159:0 > 1 && i183:0 - 1 < i183:0 && i183:0 > 0 && arith = i183:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f1680_0_appE_FieldAccess(i183:0) -> f1680_0_appE_FieldAccess(arith) :|: i159:0 > 1 && i183:0 - 1 < i183:0 && i183:0 > 0 && arith = i183:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f1680_0_appE_FieldAccess(i183:0:0) -> f1680_0_appE_FieldAccess(i183:0:0 - 1) :|: i159:0:0 > 1 && i183:0:0 - 1 < i183:0:0 && i183:0:0 > 0 ---------------------------------------- (16) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1680_0_appE_FieldAccess(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (17) Obligation: Rules: f1680_0_appE_FieldAccess(i183:0:0) -> f1680_0_appE_FieldAccess(c) :|: c = i183:0:0 - 1 && (i159:0:0 > 1 && i183:0:0 - 1 < i183:0:0 && i183:0:0 > 0) ---------------------------------------- (18) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1680_0_appE_FieldAccess(x)] = x The following rules are decreasing: f1680_0_appE_FieldAccess(i183:0:0) -> f1680_0_appE_FieldAccess(c) :|: c = i183:0:0 - 1 && (i159:0:0 > 1 && i183:0:0 - 1 < i183:0:0 && i183:0:0 > 0) The following rules are bounded: f1680_0_appE_FieldAccess(i183:0:0) -> f1680_0_appE_FieldAccess(c) :|: c = i183:0:0 - 1 && (i159:0:0 > 1 && i183:0:0 - 1 < i183:0:0 && i183:0:0 > 0) ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: CAppE.createList()LCAppE; SCC calls the following helper methods: Performed SCC analyses: *Used field analysis yielded the following read fields: *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (21) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 17 IRulesP rules: f1156_0_createList_LE(EOS(STATIC_1156), i138, i138) -> f1218_0_createList_LE(EOS(STATIC_1218), i138, i138) :|: TRUE f1218_0_createList_LE(EOS(STATIC_1218), i138, i138) -> f1229_0_createList_New(EOS(STATIC_1229), i138) :|: i138 > 0 f1229_0_createList_New(EOS(STATIC_1229), i138) -> f1238_0_createList_Duplicate(EOS(STATIC_1238), i138) :|: TRUE f1238_0_createList_Duplicate(EOS(STATIC_1238), i138) -> f1247_0_createList_Load(EOS(STATIC_1247), i138) :|: TRUE f1247_0_createList_Load(EOS(STATIC_1247), i138) -> f1313_0_createList_InvokeMethod(EOS(STATIC_1313), i138) :|: TRUE f1313_0_createList_InvokeMethod(EOS(STATIC_1313), i138) -> f1318_0__init__Load(EOS(STATIC_1318), i138) :|: TRUE f1318_0__init__Load(EOS(STATIC_1318), i138) -> f1321_0__init__InvokeMethod(EOS(STATIC_1321), i138) :|: TRUE f1321_0__init__InvokeMethod(EOS(STATIC_1321), i138) -> f1323_0__init__Load(EOS(STATIC_1323), i138) :|: TRUE f1323_0__init__Load(EOS(STATIC_1323), i138) -> f1324_0__init__Load(EOS(STATIC_1324), i138) :|: TRUE f1324_0__init__Load(EOS(STATIC_1324), i138) -> f1326_0__init__FieldAccess(EOS(STATIC_1326), i138) :|: TRUE f1326_0__init__FieldAccess(EOS(STATIC_1326), i138) -> f1328_0__init__Return(EOS(STATIC_1328), i138) :|: TRUE f1328_0__init__Return(EOS(STATIC_1328), i138) -> f1331_0_createList_Store(EOS(STATIC_1331), i138) :|: TRUE f1331_0_createList_Store(EOS(STATIC_1331), i138) -> f1334_0_createList_Inc(EOS(STATIC_1334), i138) :|: TRUE f1334_0_createList_Inc(EOS(STATIC_1334), i138) -> f1336_0_createList_JMP(EOS(STATIC_1336), i138 + -1) :|: TRUE f1336_0_createList_JMP(EOS(STATIC_1336), i156) -> f1339_0_createList_Load(EOS(STATIC_1339), i156) :|: TRUE f1339_0_createList_Load(EOS(STATIC_1339), i156) -> f1145_0_createList_Load(EOS(STATIC_1145), i156) :|: TRUE f1145_0_createList_Load(EOS(STATIC_1145), i126) -> f1156_0_createList_LE(EOS(STATIC_1156), i126, i126) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f1156_0_createList_LE(EOS(STATIC_1156), i138:0, i138:0) -> f1156_0_createList_LE(EOS(STATIC_1156), i138:0 - 1, i138:0 - 1) :|: i138:0 > 0 Filtered constant ground arguments: f1156_0_createList_LE(x1, x2, x3) -> f1156_0_createList_LE(x2, x3) EOS(x1) -> EOS Filtered duplicate arguments: f1156_0_createList_LE(x1, x2) -> f1156_0_createList_LE(x2) Finished conversion. Obtained 1 rules.P rules: f1156_0_createList_LE(i138:0) -> f1156_0_createList_LE(i138:0 - 1) :|: i138:0 > 0 ---------------------------------------- (22) Obligation: Rules: f1156_0_createList_LE(i138:0) -> f1156_0_createList_LE(i138:0 - 1) :|: i138:0 > 0 ---------------------------------------- (23) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (24) Obligation: Rules: f1156_0_createList_LE(i138:0) -> f1156_0_createList_LE(arith) :|: i138:0 > 0 && arith = i138:0 - 1 ---------------------------------------- (25) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1156_0_createList_LE(i138:0) -> f1156_0_createList_LE(arith) :|: i138:0 > 0 && arith = i138:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (26) Obligation: Termination digraph: Nodes: (1) f1156_0_createList_LE(i138:0) -> f1156_0_createList_LE(arith) :|: i138:0 > 0 && arith = i138:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (27) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (28) Obligation: Rules: f1156_0_createList_LE(i138:0:0) -> f1156_0_createList_LE(i138:0:0 - 1) :|: i138:0:0 > 0 ---------------------------------------- (29) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1156_0_createList_LE(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (30) Obligation: Rules: f1156_0_createList_LE(i138:0:0) -> f1156_0_createList_LE(c) :|: c = i138:0:0 - 1 && i138:0:0 > 0 ---------------------------------------- (31) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1156_0_createList_LE(x)] = x The following rules are decreasing: f1156_0_createList_LE(i138:0:0) -> f1156_0_createList_LE(c) :|: c = i138:0:0 - 1 && i138:0:0 > 0 The following rules are bounded: f1156_0_createList_LE(i138:0:0) -> f1156_0_createList_LE(c) :|: c = i138:0:0 - 1 && i138:0:0 > 0 ---------------------------------------- (32) YES