/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 363 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 6 ms] (6) AND (7) JBCTerminationSCC (8) SCCToQDPProof [SOUND, 108 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) JBCTerminationSCC (13) SCCToIRSProof [SOUND, 84 ms] (14) IRSwT (15) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (16) IRSwT (17) IRSwTTerminationDigraphProof [EQUIVALENT, 48 ms] (18) IRSwT (19) IntTRSCompressionProof [EQUIVALENT, 0 ms] (20) IRSwT (21) TempFilterProof [SOUND, 52 ms] (22) IntTRS (23) PolynomialOrderProcessor [EQUIVALENT, 17 ms] (24) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class List1 { List1 pred, next; List1(List1 pred) { if (pred != null) { pred.next = this; } this.pred = pred; } static int length(List1 l) { int r = 1; while (null != (l = l.next)) r++; return r; } public static void main(String[] args) { //Create doubly-linked list: int length = args.length; List1 cur = new List1(null); List1 first = cur; while (length-- > 0) { cur = new List1(cur); } length(first); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class List1 { List1 pred, next; List1(List1 pred) { if (pred != null) { pred.next = this; } this.pred = pred; } static int length(List1 l) { int r = 1; while (null != (l = l.next)) r++; return r; } public static void main(String[] args) { //Create doubly-linked list: int length = args.length; List1 cur = new List1(null); List1 first = cur; while (length-- > 0) { cur = new List1(cur); } length(first); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: List1.main([Ljava/lang/String;)V: Graph of 79 nodes with 2 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: List1.main([Ljava/lang/String;)V SCC calls the following helper methods: Performed SCC analyses: *Used field analysis yielded the following read fields: *List1: [next] *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (8) SCCToQDPProof (SOUND) Transformed TerminationGraph SCC to QDP. Log: Generated 11 rules for P and 0 rules for R.P rules: f1272_0_length_Load(EOS(STATIC_1272), java.lang.Object(o184sub)) -> f1273_0_length_FieldAccess(EOS(STATIC_1273), java.lang.Object(o184sub)) :|: TRUE f1273_0_length_FieldAccess(EOS(STATIC_1273), java.lang.Object(List1(EOC, o189))) -> f1274_0_length_FieldAccess(EOS(STATIC_1274), java.lang.Object(List1(EOC, o189))) :|: TRUE f1274_0_length_FieldAccess(EOS(STATIC_1274), java.lang.Object(List1(EOC, o189))) -> f1275_0_length_Duplicate(EOS(STATIC_1275), o189) :|: TRUE f1275_0_length_Duplicate(EOS(STATIC_1275), o189) -> f1276_0_length_Store(EOS(STATIC_1276), o189, o189) :|: TRUE f1276_0_length_Store(EOS(STATIC_1276), o189, o189) -> f1277_0_length_EQ(EOS(STATIC_1277), o189, o189) :|: TRUE f1277_0_length_EQ(EOS(STATIC_1277), java.lang.Object(o190sub), java.lang.Object(o190sub)) -> f1278_0_length_EQ(EOS(STATIC_1278), java.lang.Object(o190sub), java.lang.Object(o190sub)) :|: TRUE f1278_0_length_EQ(EOS(STATIC_1278), java.lang.Object(o190sub), java.lang.Object(o190sub)) -> f1280_0_length_Inc(EOS(STATIC_1280), java.lang.Object(o190sub)) :|: TRUE f1280_0_length_Inc(EOS(STATIC_1280), java.lang.Object(o190sub)) -> f1282_0_length_JMP(EOS(STATIC_1282), java.lang.Object(o190sub)) :|: TRUE f1282_0_length_JMP(EOS(STATIC_1282), java.lang.Object(o190sub)) -> f1288_0_length_ConstantStackPush(EOS(STATIC_1288), java.lang.Object(o190sub)) :|: TRUE f1288_0_length_ConstantStackPush(EOS(STATIC_1288), java.lang.Object(o190sub)) -> f1271_0_length_ConstantStackPush(EOS(STATIC_1271), java.lang.Object(o190sub)) :|: TRUE f1271_0_length_ConstantStackPush(EOS(STATIC_1271), java.lang.Object(o184sub)) -> f1272_0_length_Load(EOS(STATIC_1272), java.lang.Object(o184sub)) :|: TRUE R rules: Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules: f1272_0_length_Load(EOS(STATIC_1272), java.lang.Object(List1(EOC, java.lang.Object(o190sub:0)))) -> f1272_0_length_Load(EOS(STATIC_1272), java.lang.Object(o190sub:0)) :|: TRUE R rules: Filtered ground terms: f1272_0_length_Load(x1, x2) -> f1272_0_length_Load(x2) EOS(x1) -> EOS List1(x1, x2) -> List1(x2) Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules: F1272_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o190sub:0:0)))) -> F1272_0_LENGTH_LOAD(java.lang.Object(o190sub:0:0)) :|: TRUE R rules: ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: F1272_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o190sub:0:0)))) -> F1272_0_LENGTH_LOAD(java.lang.Object(o190sub:0:0)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (10) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F1272_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o190sub:0:0)))) -> F1272_0_LENGTH_LOAD(java.lang.Object(o190sub:0:0)) The graph contains the following edges 1 > 1 ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: List1.main([Ljava/lang/String;)V 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: ---------------------------------------- (13) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 33 IRulesP rules: f965_0_main_Inc(EOS(STATIC_965), i77, i77, o119[List1.next]o117) -> f968_0_main_LE(EOS(STATIC_968), i77 + -1, i77, o119[List1.next]o117) :|: TRUE f968_0_main_LE(EOS(STATIC_968), i84, i87, o119[List1.next]o117) -> f971_0_main_LE(EOS(STATIC_971), i84, i87, o119[List1.next]o117) :|: TRUE f971_0_main_LE(EOS(STATIC_971), i84, i87, o119[List1.next]o117) -> f973_0_main_New(EOS(STATIC_973), i84, o119[List1.next]o117) :|: i87 > 0 f973_0_main_New(EOS(STATIC_973), i84, o119[List1.next]o117) -> f975_0_main_Duplicate(EOS(STATIC_975), i84, o119[List1.next]o117) :|: TRUE f975_0_main_Duplicate(EOS(STATIC_975), i84, o119[List1.next]o117) -> f977_0_main_Load(EOS(STATIC_977), i84, o119[List1.next]o117) :|: TRUE f977_0_main_Load(EOS(STATIC_977), i84, o119[List1.next]o117) -> f980_0_main_InvokeMethod(EOS(STATIC_980), i84, o119[List1.next]o117) :|: TRUE f980_0_main_InvokeMethod(EOS(STATIC_980), i84, o119[List1.next]o117) -> f985_0__init__Load(EOS(STATIC_985), i84, o119[List1.next]o117) :|: TRUE f985_0__init__Load(EOS(STATIC_985), i84, o119[List1.next]o117) -> f994_0__init__InvokeMethod(EOS(STATIC_994), i84, o119[List1.next]o117) :|: TRUE f994_0__init__InvokeMethod(EOS(STATIC_994), i84, o119[List1.next]o117) -> f998_0__init__Load(EOS(STATIC_998), i84, o119[List1.next]o117) :|: TRUE f998_0__init__Load(EOS(STATIC_998), i84, o119[List1.next]o117) -> f1000_0__init__NULL(EOS(STATIC_1000), i84, o119[List1.next]o117) :|: TRUE f1000_0__init__NULL(EOS(STATIC_1000), i84, o119[List1.next]o117) -> f1002_0__init__Load(EOS(STATIC_1002), i84, o119[List1.next]o117) :|: TRUE f1002_0__init__Load(EOS(STATIC_1002), i84, o119[List1.next]o117) -> f1004_0__init__Load(EOS(STATIC_1004), i84, o119[List1.next]o117) :|: TRUE f1004_0__init__Load(EOS(STATIC_1004), i84, o119[List1.next]o117) -> f1006_0__init__FieldAccess(EOS(STATIC_1006), i84, o119[List1.next]o117) :|: TRUE f1006_0__init__FieldAccess(EOS(STATIC_1006), i84, o119[List1.next]o117) -> f1022_0__init__FieldAccess(EOS(STATIC_1022), i84, o119[List1.next]o117) :|: o119[List1.next]o117 > 0 f1006_0__init__FieldAccess(EOS(STATIC_1006), i84, o136[List1.next]o136) -> f1023_0__init__FieldAccess(EOS(STATIC_1023), i84) :|: TRUE f1022_0__init__FieldAccess(EOS(STATIC_1022), i84, o119[List1.next]o117) -> f1035_0__init__Load(EOS(STATIC_1035), i84, o119[List1.next]o117) :|: TRUE f1035_0__init__Load(EOS(STATIC_1035), i84, o119[List1.next]o117) -> f1044_0__init__Load(EOS(STATIC_1044), i84, o119[List1.next]o117) :|: TRUE f1044_0__init__Load(EOS(STATIC_1044), i84, o119[List1.next]o117) -> f1072_0__init__FieldAccess(EOS(STATIC_1072), i84, o119[List1.next]o117) :|: TRUE f1072_0__init__FieldAccess(EOS(STATIC_1072), i84, o119[List1.next]o117) -> f1094_0__init__Return(EOS(STATIC_1094), i84, o119[List1.next]o117) :|: TRUE f1094_0__init__Return(EOS(STATIC_1094), i84, o119[List1.next]o117) -> f1104_0_main_Store(EOS(STATIC_1104), i84, o119[List1.next]o117) :|: TRUE f1104_0_main_Store(EOS(STATIC_1104), i84, o119[List1.next]o117) -> f1118_0_main_JMP(EOS(STATIC_1118), i84, o119[List1.next]o117) :|: TRUE f1118_0_main_JMP(EOS(STATIC_1118), i84, o119[List1.next]o117) -> f1136_0_main_Load(EOS(STATIC_1136), i84, o119[List1.next]o117) :|: TRUE f1136_0_main_Load(EOS(STATIC_1136), i84, o119[List1.next]o117) -> f960_0_main_Load(EOS(STATIC_960), i84, o119[List1.next]o124) :|: TRUE f960_0_main_Load(EOS(STATIC_960), i77, o119[List1.next]o117) -> f965_0_main_Inc(EOS(STATIC_965), i77, i77, o119[List1.next]o117) :|: TRUE f1023_0__init__FieldAccess(EOS(STATIC_1023), i84) -> f1038_0__init__FieldAccess(EOS(STATIC_1038), i84) :|: TRUE f1038_0__init__FieldAccess(EOS(STATIC_1038), i84) -> f1052_0__init__Load(EOS(STATIC_1052), i84) :|: TRUE f1052_0__init__Load(EOS(STATIC_1052), i84) -> f1076_0__init__Load(EOS(STATIC_1076), i84) :|: TRUE f1076_0__init__Load(EOS(STATIC_1076), i84) -> f1099_0__init__FieldAccess(EOS(STATIC_1099), i84) :|: TRUE f1099_0__init__FieldAccess(EOS(STATIC_1099), i84) -> f1111_0__init__Return(EOS(STATIC_1111), i84) :|: TRUE f1111_0__init__Return(EOS(STATIC_1111), i84) -> f1119_0_main_Store(EOS(STATIC_1119), i84) :|: TRUE f1119_0_main_Store(EOS(STATIC_1119), i84) -> f1137_0_main_JMP(EOS(STATIC_1137), i84) :|: TRUE f1137_0_main_JMP(EOS(STATIC_1137), i84) -> f1209_0_main_Load(EOS(STATIC_1209), i84) :|: TRUE f1209_0_main_Load(EOS(STATIC_1209), i84) -> f960_0_main_Load(EOS(STATIC_960), i84, o139[List1.next]o124) :|: o139[List1.next]o124 = 1 Combined rules. Obtained 2 IRulesP rules: f965_0_main_Inc(EOS(STATIC_965), i77:0, i77:0, o119[List1.next]o117:0) -> f965_0_main_Inc(EOS(STATIC_965), i77:0 - 1, i77:0 - 1, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i77:0 > 0 f965_0_main_Inc(EOS(STATIC_965), i77:0, i77:0, o119[List1.next]o117:0) -> f965_0_main_Inc(EOS(STATIC_965), i77:0 - 1, i77:0 - 1, 1) :|: i77:0 > 0 Filtered constant ground arguments: f965_0_main_Inc(x1, x2, x3, x4) -> f965_0_main_Inc(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f965_0_main_Inc(x1, x2, x3) -> f965_0_main_Inc(x2, x3) Finished conversion. Obtained 2 rules.P rules: f965_0_main_Inc(i77:0, o119[List1.next]o117:0) -> f965_0_main_Inc(i77:0 - 1, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i77:0 > 0 f965_0_main_Inc(i77:0, o119[List1.next]o117:0) -> f965_0_main_Inc(i77:0 - 1, 1) :|: i77:0 > 0 ---------------------------------------- (14) Obligation: Rules: f965_0_main_Inc(i77:0, o119[List1.next]o117:0) -> f965_0_main_Inc(i77:0 - 1, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i77:0 > 0 f965_0_main_Inc(x, x1) -> f965_0_main_Inc(x - 1, 1) :|: x > 0 ---------------------------------------- (15) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (16) Obligation: Rules: f965_0_main_Inc(i77:0, o119[List1.next]o117:0) -> f965_0_main_Inc(arith, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i77:0 > 0 && arith = i77:0 - 1 f965_0_main_Inc(x2, x3) -> f965_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1 ---------------------------------------- (17) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f965_0_main_Inc(i77:0, o119[List1.next]o117:0) -> f965_0_main_Inc(arith, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i77:0 > 0 && arith = i77:0 - 1 (2) f965_0_main_Inc(x2, x3) -> f965_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (18) Obligation: Termination digraph: Nodes: (1) f965_0_main_Inc(i77:0, o119[List1.next]o117:0) -> f965_0_main_Inc(arith, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i77:0 > 0 && arith = i77:0 - 1 (2) f965_0_main_Inc(x2, x3) -> f965_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (19) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (20) Obligation: Rules: f965_0_main_Inc(x2:0, x3:0) -> f965_0_main_Inc(x2:0 - 1, 1) :|: x2:0 > 0 f965_0_main_Inc(i77:0:0, o119[List1.next]o117:0:0) -> f965_0_main_Inc(i77:0:0 - 1, o119[List1.next]o124:0:0) :|: o119[List1.next]o117:0:0 > 0 && i77:0:0 > 0 ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f965_0_main_Inc(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (22) Obligation: Rules: f965_0_main_Inc(x2:0, x3:0) -> f965_0_main_Inc(c, c1) :|: c1 = 1 && c = x2:0 - 1 && x2:0 > 0 f965_0_main_Inc(i77:0:0, o119[List1.next]o117:0:0) -> f965_0_main_Inc(c2, o119[List1.next]o124:0:0) :|: c2 = i77:0:0 - 1 && (o119[List1.next]o117:0:0 > 0 && i77:0:0 > 0) ---------------------------------------- (23) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f965_0_main_Inc(x, x1)] = x The following rules are decreasing: f965_0_main_Inc(x2:0, x3:0) -> f965_0_main_Inc(c, c1) :|: c1 = 1 && c = x2:0 - 1 && x2:0 > 0 f965_0_main_Inc(i77:0:0, o119[List1.next]o117:0:0) -> f965_0_main_Inc(c2, o119[List1.next]o124:0:0) :|: c2 = i77:0:0 - 1 && (o119[List1.next]o117:0:0 > 0 && i77:0:0 > 0) The following rules are bounded: f965_0_main_Inc(x2:0, x3:0) -> f965_0_main_Inc(c, c1) :|: c1 = 1 && c = x2:0 - 1 && x2:0 > 0 f965_0_main_Inc(i77:0:0, o119[List1.next]o117:0:0) -> f965_0_main_Inc(c2, o119[List1.next]o124:0:0) :|: c2 = i77:0:0 - 1 && (o119[List1.next]o117:0:0 > 0 && i77:0:0 > 0) ---------------------------------------- (24) YES