/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 324 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 107 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 33 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) TempFilterProof [SOUND, 6 ms] (17) IntTRS (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (19) YES (20) IRSwT (21) IntTRSCompressionProof [EQUIVALENT, 0 ms] (22) IRSwT (23) TempFilterProof [SOUND, 15 ms] (24) IntTRS (25) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (26) 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 PastaB10 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x + y > 0) { if (x > 0) { x--; } else if (y > 0) { y--; } else { continue; } } } } 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 PastaB10 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x + y > 0) { if (x > 0) { x--; } else if (y > 0) { y--; } else { continue; } } } } 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: PastaB10.main([Ljava/lang/String;)V: Graph of 188 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: PastaB10.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: ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 22 IRulesP rules: f582_0_main_Load(EOS(STATIC_582), i87, i48, i87) -> f591_0_main_IntArithmetic(EOS(STATIC_591), i87, i48, i87, i48) :|: TRUE f591_0_main_IntArithmetic(EOS(STATIC_591), i87, i48, i87, i48) -> f601_0_main_LE(EOS(STATIC_601), i87, i48, i87 + i48) :|: i87 >= 0 && i48 >= 0 f601_0_main_LE(EOS(STATIC_601), i87, i48, i97) -> f608_0_main_LE(EOS(STATIC_608), i87, i48, i97) :|: TRUE f608_0_main_LE(EOS(STATIC_608), i87, i48, i97) -> f615_0_main_Load(EOS(STATIC_615), i87, i48) :|: i97 > 0 f615_0_main_Load(EOS(STATIC_615), i87, i48) -> f622_0_main_LE(EOS(STATIC_622), i87, i48, i87) :|: TRUE f622_0_main_LE(EOS(STATIC_622), matching1, i48, matching2) -> f627_0_main_LE(EOS(STATIC_627), 0, i48, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f622_0_main_LE(EOS(STATIC_622), i102, i48, i102) -> f628_0_main_LE(EOS(STATIC_628), i102, i48, i102) :|: TRUE f627_0_main_LE(EOS(STATIC_627), matching1, i48, matching2) -> f631_0_main_Load(EOS(STATIC_631), 0, i48) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 f631_0_main_Load(EOS(STATIC_631), matching1, i48) -> f634_0_main_LE(EOS(STATIC_634), 0, i48, i48) :|: TRUE && matching1 = 0 f634_0_main_LE(EOS(STATIC_634), matching1, matching2, matching3) -> f638_0_main_LE(EOS(STATIC_638), 0, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0 && matching3 = 0 f634_0_main_LE(EOS(STATIC_634), matching1, i105, i105) -> f639_0_main_LE(EOS(STATIC_639), 0, i105, i105) :|: TRUE && matching1 = 0 f638_0_main_LE(EOS(STATIC_638), matching1, matching2, matching3) -> f1645_0_main_Load(EOS(STATIC_1645), 0, 0) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 && matching3 = 0 f1645_0_main_Load(EOS(STATIC_1645), matching1, matching2) -> f565_0_main_Load(EOS(STATIC_565), 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0 f565_0_main_Load(EOS(STATIC_565), i87, i48) -> f582_0_main_Load(EOS(STATIC_582), i87, i48, i87) :|: TRUE f639_0_main_LE(EOS(STATIC_639), matching1, i105, i105) -> f1648_0_main_Inc(EOS(STATIC_1648), 0, i105) :|: i105 > 0 && matching1 = 0 f1648_0_main_Inc(EOS(STATIC_1648), matching1, i105) -> f1652_0_main_JMP(EOS(STATIC_1652), 0, i105 + -1) :|: TRUE && matching1 = 0 f1652_0_main_JMP(EOS(STATIC_1652), matching1, i267) -> f1705_0_main_Load(EOS(STATIC_1705), 0, i267) :|: TRUE && matching1 = 0 f1705_0_main_Load(EOS(STATIC_1705), matching1, i267) -> f565_0_main_Load(EOS(STATIC_565), 0, i267) :|: TRUE && matching1 = 0 f628_0_main_LE(EOS(STATIC_628), i102, i48, i102) -> f633_0_main_Inc(EOS(STATIC_633), i102, i48) :|: i102 > 0 f633_0_main_Inc(EOS(STATIC_633), i102, i48) -> f635_0_main_JMP(EOS(STATIC_635), i102 + -1, i48) :|: TRUE f635_0_main_JMP(EOS(STATIC_635), i104, i48) -> f682_0_main_Load(EOS(STATIC_682), i104, i48) :|: TRUE f682_0_main_Load(EOS(STATIC_682), i104, i48) -> f565_0_main_Load(EOS(STATIC_565), i104, i48) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f582_0_main_Load(EOS(STATIC_582), 0, i48:0, 0) -> f582_0_main_Load(EOS(STATIC_582), 0, i48:0 - 1, 0) :|: i48:0 > 0 f582_0_main_Load(EOS(STATIC_582), i87:0, i48:0, i87:0) -> f582_0_main_Load(EOS(STATIC_582), i87:0 - 1, i48:0, i87:0 - 1) :|: i87:0 > 0 && i87:0 + i48:0 > 0 && i48:0 > -1 Filtered constant ground arguments: f582_0_main_Load(x1, x2, x3, x4) -> f582_0_main_Load(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f582_0_main_Load(x1, x2, x3) -> f582_0_main_Load(x2, x3) Finished conversion. Obtained 2 rules.P rules: f582_0_main_Load(i48:0, cons_0) -> f582_0_main_Load(i48:0 - 1, 0) :|: i48:0 > 0 && cons_0 = 0 f582_0_main_Load(i48:0, i87:0) -> f582_0_main_Load(i48:0, i87:0 - 1) :|: i87:0 + i48:0 > 0 && i48:0 > -1 && i87:0 > 0 ---------------------------------------- (8) Obligation: Rules: f582_0_main_Load(i48:0, cons_0) -> f582_0_main_Load(i48:0 - 1, 0) :|: i48:0 > 0 && cons_0 = 0 f582_0_main_Load(x, x1) -> f582_0_main_Load(x, x1 - 1) :|: x1 + x > 0 && x > -1 && x1 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f582_0_main_Load(i48:0, cons_0) -> f582_0_main_Load(arith, 0) :|: i48:0 > 0 && cons_0 = 0 && arith = i48:0 - 1 f582_0_main_Load(x2, x3) -> f582_0_main_Load(x2, x4) :|: x3 + x2 > 0 && x2 > -1 && x3 > 0 && x4 = x3 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f582_0_main_Load(i48:0, cons_0) -> f582_0_main_Load(arith, 0) :|: i48:0 > 0 && cons_0 = 0 && arith = i48:0 - 1 (2) f582_0_main_Load(x2, x3) -> f582_0_main_Load(x2, x4) :|: x3 + x2 > 0 && x2 > -1 && x3 > 0 && x4 = x3 - 1 Arcs: (1) -> (1) (2) -> (1), (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f582_0_main_Load(x2, x3) -> f582_0_main_Load(x2, x4) :|: x3 + x2 > 0 && x2 > -1 && x3 > 0 && x4 = x3 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f582_0_main_Load(x2:0, x3:0) -> f582_0_main_Load(x2:0, x3:0 - 1) :|: x3:0 + x2:0 > 0 && x2:0 > -1 && x3:0 > 0 ---------------------------------------- (16) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f582_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (17) Obligation: Rules: f582_0_main_Load(x2:0, x3:0) -> f582_0_main_Load(x2:0, c) :|: c = x3:0 - 1 && (x3:0 + x2:0 > 0 && x2:0 > -1 && x3:0 > 0) ---------------------------------------- (18) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f582_0_main_Load(x, x1)] = x + x1 The following rules are decreasing: f582_0_main_Load(x2:0, x3:0) -> f582_0_main_Load(x2:0, c) :|: c = x3:0 - 1 && (x3:0 + x2:0 > 0 && x2:0 > -1 && x3:0 > 0) The following rules are bounded: f582_0_main_Load(x2:0, x3:0) -> f582_0_main_Load(x2:0, c) :|: c = x3:0 - 1 && (x3:0 + x2:0 > 0 && x2:0 > -1 && x3:0 > 0) ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Termination digraph: Nodes: (1) f582_0_main_Load(i48:0, cons_0) -> f582_0_main_Load(arith, 0) :|: i48:0 > 0 && cons_0 = 0 && arith = i48:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f582_0_main_Load(i48:0:0, cons_0) -> f582_0_main_Load(i48:0:0 - 1, 0) :|: i48:0:0 > 0 && cons_0 = 0 ---------------------------------------- (23) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f582_0_main_Load(INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (24) Obligation: Rules: f582_0_main_Load(i48:0:0, c) -> f582_0_main_Load(c1, c2) :|: c2 = 0 && (c1 = i48:0:0 - 1 && c = 0) && (i48:0:0 > 0 && cons_0 = 0) ---------------------------------------- (25) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f582_0_main_Load(x, x1)] = x + c1*x1 The following rules are decreasing: f582_0_main_Load(i48:0:0, c) -> f582_0_main_Load(c1, c2) :|: c2 = 0 && (c1 = i48:0:0 - 1 && c = 0) && (i48:0:0 > 0 && cons_0 = 0) The following rules are bounded: f582_0_main_Load(i48:0:0, c) -> f582_0_main_Load(c1, c2) :|: c2 = 0 && (c1 = i48:0:0 - 1 && c = 0) && (i48:0:0 > 0 && cons_0 = 0) ---------------------------------------- (26) YES