/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 377 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) AND (7) JBCTerminationSCC (8) SCCToQDPProof [SOUND, 77 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) JBCTerminationSCC (13) SCCToIRSProof [SOUND, 93 ms] (14) IRSwT (15) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (16) IRSwT (17) IRSwTTerminationDigraphProof [EQUIVALENT, 26 ms] (18) IRSwT (19) IntTRSCompressionProof [EQUIVALENT, 0 ms] (20) IRSwT (21) TempFilterProof [SOUND, 24 ms] (22) IntTRS (23) PolynomialOrderProcessor [EQUIVALENT, 2 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: f1514_0_length_Load(EOS(STATIC_1514), java.lang.Object(o186sub)) -> f1515_0_length_FieldAccess(EOS(STATIC_1515), java.lang.Object(o186sub)) :|: TRUE f1515_0_length_FieldAccess(EOS(STATIC_1515), java.lang.Object(List1(EOC, o191))) -> f1516_0_length_FieldAccess(EOS(STATIC_1516), java.lang.Object(List1(EOC, o191))) :|: TRUE f1516_0_length_FieldAccess(EOS(STATIC_1516), java.lang.Object(List1(EOC, o191))) -> f1517_0_length_Duplicate(EOS(STATIC_1517), o191) :|: TRUE f1517_0_length_Duplicate(EOS(STATIC_1517), o191) -> f1518_0_length_Store(EOS(STATIC_1518), o191, o191) :|: TRUE f1518_0_length_Store(EOS(STATIC_1518), o191, o191) -> f1519_0_length_EQ(EOS(STATIC_1519), o191, o191) :|: TRUE f1519_0_length_EQ(EOS(STATIC_1519), java.lang.Object(o192sub), java.lang.Object(o192sub)) -> f1520_0_length_EQ(EOS(STATIC_1520), java.lang.Object(o192sub), java.lang.Object(o192sub)) :|: TRUE f1520_0_length_EQ(EOS(STATIC_1520), java.lang.Object(o192sub), java.lang.Object(o192sub)) -> f1522_0_length_Inc(EOS(STATIC_1522), java.lang.Object(o192sub)) :|: TRUE f1522_0_length_Inc(EOS(STATIC_1522), java.lang.Object(o192sub)) -> f1524_0_length_JMP(EOS(STATIC_1524), java.lang.Object(o192sub)) :|: TRUE f1524_0_length_JMP(EOS(STATIC_1524), java.lang.Object(o192sub)) -> f1537_0_length_ConstantStackPush(EOS(STATIC_1537), java.lang.Object(o192sub)) :|: TRUE f1537_0_length_ConstantStackPush(EOS(STATIC_1537), java.lang.Object(o192sub)) -> f1513_0_length_ConstantStackPush(EOS(STATIC_1513), java.lang.Object(o192sub)) :|: TRUE f1513_0_length_ConstantStackPush(EOS(STATIC_1513), java.lang.Object(o186sub)) -> f1514_0_length_Load(EOS(STATIC_1514), java.lang.Object(o186sub)) :|: TRUE R rules: Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules: f1514_0_length_Load(EOS(STATIC_1514), java.lang.Object(List1(EOC, java.lang.Object(o192sub:0)))) -> f1514_0_length_Load(EOS(STATIC_1514), java.lang.Object(o192sub:0)) :|: TRUE R rules: Filtered ground terms: f1514_0_length_Load(x1, x2) -> f1514_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: F1514_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o192sub:0:0)))) -> F1514_0_LENGTH_LOAD(java.lang.Object(o192sub:0:0)) :|: TRUE R rules: ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: F1514_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o192sub:0:0)))) -> F1514_0_LENGTH_LOAD(java.lang.Object(o192sub: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: *F1514_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o192sub:0:0)))) -> F1514_0_LENGTH_LOAD(java.lang.Object(o192sub: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: f1113_0_main_Inc(EOS(STATIC_1113), i80, i80, o120[List1.next]o118) -> f1115_0_main_LE(EOS(STATIC_1115), i80 + -1, i80, o120[List1.next]o118) :|: TRUE f1115_0_main_LE(EOS(STATIC_1115), i89, i95, o120[List1.next]o118) -> f1121_0_main_LE(EOS(STATIC_1121), i89, i95, o120[List1.next]o118) :|: TRUE f1121_0_main_LE(EOS(STATIC_1121), i89, i95, o120[List1.next]o118) -> f1128_0_main_New(EOS(STATIC_1128), i89, o120[List1.next]o118) :|: i95 > 0 f1128_0_main_New(EOS(STATIC_1128), i89, o120[List1.next]o118) -> f1133_0_main_Duplicate(EOS(STATIC_1133), i89, o120[List1.next]o118) :|: TRUE f1133_0_main_Duplicate(EOS(STATIC_1133), i89, o120[List1.next]o118) -> f1149_0_main_Load(EOS(STATIC_1149), i89, o120[List1.next]o118) :|: TRUE f1149_0_main_Load(EOS(STATIC_1149), i89, o120[List1.next]o118) -> f1151_0_main_InvokeMethod(EOS(STATIC_1151), i89, o120[List1.next]o118) :|: TRUE f1151_0_main_InvokeMethod(EOS(STATIC_1151), i89, o120[List1.next]o118) -> f1156_0__init__Load(EOS(STATIC_1156), i89, o120[List1.next]o118) :|: TRUE f1156_0__init__Load(EOS(STATIC_1156), i89, o120[List1.next]o118) -> f1161_0__init__InvokeMethod(EOS(STATIC_1161), i89, o120[List1.next]o118) :|: TRUE f1161_0__init__InvokeMethod(EOS(STATIC_1161), i89, o120[List1.next]o118) -> f1168_0__init__Load(EOS(STATIC_1168), i89, o120[List1.next]o118) :|: TRUE f1168_0__init__Load(EOS(STATIC_1168), i89, o120[List1.next]o118) -> f1197_0__init__NULL(EOS(STATIC_1197), i89, o120[List1.next]o118) :|: TRUE f1197_0__init__NULL(EOS(STATIC_1197), i89, o120[List1.next]o118) -> f1199_0__init__Load(EOS(STATIC_1199), i89, o120[List1.next]o118) :|: TRUE f1199_0__init__Load(EOS(STATIC_1199), i89, o120[List1.next]o118) -> f1204_0__init__Load(EOS(STATIC_1204), i89, o120[List1.next]o118) :|: TRUE f1204_0__init__Load(EOS(STATIC_1204), i89, o120[List1.next]o118) -> f1209_0__init__FieldAccess(EOS(STATIC_1209), i89, o120[List1.next]o118) :|: TRUE f1209_0__init__FieldAccess(EOS(STATIC_1209), i89, o120[List1.next]o118) -> f1225_0__init__FieldAccess(EOS(STATIC_1225), i89, o120[List1.next]o118) :|: o120[List1.next]o118 > 0 f1209_0__init__FieldAccess(EOS(STATIC_1209), i89, o138[List1.next]o138) -> f1226_0__init__FieldAccess(EOS(STATIC_1226), i89) :|: TRUE f1225_0__init__FieldAccess(EOS(STATIC_1225), i89, o120[List1.next]o118) -> f1270_0__init__Load(EOS(STATIC_1270), i89, o120[List1.next]o118) :|: TRUE f1270_0__init__Load(EOS(STATIC_1270), i89, o120[List1.next]o118) -> f1274_0__init__Load(EOS(STATIC_1274), i89, o120[List1.next]o118) :|: TRUE f1274_0__init__Load(EOS(STATIC_1274), i89, o120[List1.next]o118) -> f1282_0__init__FieldAccess(EOS(STATIC_1282), i89, o120[List1.next]o118) :|: TRUE f1282_0__init__FieldAccess(EOS(STATIC_1282), i89, o120[List1.next]o118) -> f1312_0__init__Return(EOS(STATIC_1312), i89, o120[List1.next]o118) :|: TRUE f1312_0__init__Return(EOS(STATIC_1312), i89, o120[List1.next]o118) -> f1322_0_main_Store(EOS(STATIC_1322), i89, o120[List1.next]o118) :|: TRUE f1322_0_main_Store(EOS(STATIC_1322), i89, o120[List1.next]o118) -> f1339_0_main_JMP(EOS(STATIC_1339), i89, o120[List1.next]o118) :|: TRUE f1339_0_main_JMP(EOS(STATIC_1339), i89, o120[List1.next]o118) -> f1392_0_main_Load(EOS(STATIC_1392), i89, o120[List1.next]o118) :|: TRUE f1392_0_main_Load(EOS(STATIC_1392), i89, o120[List1.next]o118) -> f1083_0_main_Load(EOS(STATIC_1083), i89, o120[List1.next]o126) :|: TRUE f1083_0_main_Load(EOS(STATIC_1083), i80, o120[List1.next]o118) -> f1113_0_main_Inc(EOS(STATIC_1113), i80, i80, o120[List1.next]o118) :|: TRUE f1226_0__init__FieldAccess(EOS(STATIC_1226), i89) -> f1271_0__init__FieldAccess(EOS(STATIC_1271), i89) :|: TRUE f1271_0__init__FieldAccess(EOS(STATIC_1271), i89) -> f1275_0__init__Load(EOS(STATIC_1275), i89) :|: TRUE f1275_0__init__Load(EOS(STATIC_1275), i89) -> f1283_0__init__Load(EOS(STATIC_1283), i89) :|: TRUE f1283_0__init__Load(EOS(STATIC_1283), i89) -> f1317_0__init__FieldAccess(EOS(STATIC_1317), i89) :|: TRUE f1317_0__init__FieldAccess(EOS(STATIC_1317), i89) -> f1331_0__init__Return(EOS(STATIC_1331), i89) :|: TRUE f1331_0__init__Return(EOS(STATIC_1331), i89) -> f1343_0_main_Store(EOS(STATIC_1343), i89) :|: TRUE f1343_0_main_Store(EOS(STATIC_1343), i89) -> f1393_0_main_JMP(EOS(STATIC_1393), i89) :|: TRUE f1393_0_main_JMP(EOS(STATIC_1393), i89) -> f1457_0_main_Load(EOS(STATIC_1457), i89) :|: TRUE f1457_0_main_Load(EOS(STATIC_1457), i89) -> f1083_0_main_Load(EOS(STATIC_1083), i89, o142[List1.next]o126) :|: o142[List1.next]o126 = 1 Combined rules. Obtained 2 IRulesP rules: f1113_0_main_Inc(EOS(STATIC_1113), i80:0, i80:0, o120[List1.next]o118:0) -> f1113_0_main_Inc(EOS(STATIC_1113), i80:0 - 1, i80:0 - 1, 1) :|: i80:0 > 0 f1113_0_main_Inc(EOS(STATIC_1113), i80:0, i80:0, o120[List1.next]o118:0) -> f1113_0_main_Inc(EOS(STATIC_1113), i80:0 - 1, i80:0 - 1, o120[List1.next]o126:0) :|: o120[List1.next]o118:0 > 0 && i80:0 > 0 Filtered constant ground arguments: f1113_0_main_Inc(x1, x2, x3, x4) -> f1113_0_main_Inc(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f1113_0_main_Inc(x1, x2, x3) -> f1113_0_main_Inc(x2, x3) Finished conversion. Obtained 2 rules.P rules: f1113_0_main_Inc(i80:0, o120[List1.next]o118:0) -> f1113_0_main_Inc(i80:0 - 1, 1) :|: i80:0 > 0 f1113_0_main_Inc(i80:0, o120[List1.next]o118:0) -> f1113_0_main_Inc(i80:0 - 1, o120[List1.next]o126:0) :|: o120[List1.next]o118:0 > 0 && i80:0 > 0 ---------------------------------------- (14) Obligation: Rules: f1113_0_main_Inc(i80:0, o120[List1.next]o118:0) -> f1113_0_main_Inc(i80:0 - 1, 1) :|: i80:0 > 0 f1113_0_main_Inc(x, x1) -> f1113_0_main_Inc(x - 1, x2) :|: x1 > 0 && x > 0 ---------------------------------------- (15) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (16) Obligation: Rules: f1113_0_main_Inc(i80:0, o120[List1.next]o118:0) -> f1113_0_main_Inc(arith, 1) :|: i80:0 > 0 && arith = i80:0 - 1 f1113_0_main_Inc(x3, x4) -> f1113_0_main_Inc(x5, x6) :|: x4 > 0 && x3 > 0 && x5 = x3 - 1 ---------------------------------------- (17) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1113_0_main_Inc(i80:0, o120[List1.next]o118:0) -> f1113_0_main_Inc(arith, 1) :|: i80:0 > 0 && arith = i80:0 - 1 (2) f1113_0_main_Inc(x3, x4) -> f1113_0_main_Inc(x5, x6) :|: x4 > 0 && x3 > 0 && x5 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (18) Obligation: Termination digraph: Nodes: (1) f1113_0_main_Inc(i80:0, o120[List1.next]o118:0) -> f1113_0_main_Inc(arith, 1) :|: i80:0 > 0 && arith = i80:0 - 1 (2) f1113_0_main_Inc(x3, x4) -> f1113_0_main_Inc(x5, x6) :|: x4 > 0 && x3 > 0 && x5 = x3 - 1 Arcs: (1) -> (1), (2) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (19) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (20) Obligation: Rules: f1113_0_main_Inc(i80:0:0, o120[List1.next]o118:0:0) -> f1113_0_main_Inc(i80:0:0 - 1, 1) :|: i80:0:0 > 0 f1113_0_main_Inc(x3:0, x4:0) -> f1113_0_main_Inc(x3:0 - 1, x6:0) :|: x4:0 > 0 && x3:0 > 0 ---------------------------------------- (21) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1113_0_main_Inc(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (22) Obligation: Rules: f1113_0_main_Inc(i80:0:0, o120[List1.next]o118:0:0) -> f1113_0_main_Inc(c, c1) :|: c1 = 1 && c = i80:0:0 - 1 && i80:0:0 > 0 f1113_0_main_Inc(x3:0, x4:0) -> f1113_0_main_Inc(c2, x6:0) :|: c2 = x3:0 - 1 && (x4:0 > 0 && x3:0 > 0) ---------------------------------------- (23) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1113_0_main_Inc(x, x1)] = x The following rules are decreasing: f1113_0_main_Inc(i80:0:0, o120[List1.next]o118:0:0) -> f1113_0_main_Inc(c, c1) :|: c1 = 1 && c = i80:0:0 - 1 && i80:0:0 > 0 f1113_0_main_Inc(x3:0, x4:0) -> f1113_0_main_Inc(c2, x6:0) :|: c2 = x3:0 - 1 && (x4:0 > 0 && x3:0 > 0) The following rules are bounded: f1113_0_main_Inc(i80:0:0, o120[List1.next]o118:0:0) -> f1113_0_main_Inc(c, c1) :|: c1 = 1 && c = i80:0:0 - 1 && i80:0:0 > 0 f1113_0_main_Inc(x3:0, x4:0) -> f1113_0_main_Inc(c2, x6:0) :|: c2 = x3:0 - 1 && (x4:0 > 0 && x3:0 > 0) ---------------------------------------- (24) YES