/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 383 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 105 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 82 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) TempFilterProof [SOUND, 8 ms] (17) IntTRS (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (19) YES (20) IRSwT (21) IntTRSCompressionProof [EQUIVALENT, 0 ms] (22) IRSwT (23) TempFilterProof [SOUND, 37 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 PastaB11 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x + y > 0) { if (x > y) { x--; } else if (x == y) { x--; } else { y--; } } } } 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 PastaB11 { public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while (x + y > 0) { if (x > y) { x--; } else if (x == y) { x--; } else { y--; } } } } 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: PastaB11.main([Ljava/lang/String;)V: Graph of 198 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: PastaB11.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 26 IRulesP rules: f1048_0_main_Load(EOS(STATIC_1048), i219, i207, i219) -> f1049_0_main_IntArithmetic(EOS(STATIC_1049), i219, i207, i219, i207) :|: TRUE f1049_0_main_IntArithmetic(EOS(STATIC_1049), i219, i207, i219, i207) -> f1051_0_main_LE(EOS(STATIC_1051), i219, i207, i219 + i207) :|: TRUE f1051_0_main_LE(EOS(STATIC_1051), i219, i207, i223) -> f1053_0_main_LE(EOS(STATIC_1053), i219, i207, i223) :|: TRUE f1053_0_main_LE(EOS(STATIC_1053), i219, i207, i223) -> f1055_0_main_Load(EOS(STATIC_1055), i219, i207) :|: i223 > 0 f1055_0_main_Load(EOS(STATIC_1055), i219, i207) -> f1057_0_main_Load(EOS(STATIC_1057), i219, i207, i219) :|: TRUE f1057_0_main_Load(EOS(STATIC_1057), i219, i207, i219) -> f1058_0_main_LE(EOS(STATIC_1058), i219, i207, i219, i207) :|: TRUE f1058_0_main_LE(EOS(STATIC_1058), i219, i207, i219, i207) -> f1061_0_main_LE(EOS(STATIC_1061), i219, i207, i219, i207) :|: i219 <= i207 f1058_0_main_LE(EOS(STATIC_1058), i219, i207, i219, i207) -> f1062_0_main_LE(EOS(STATIC_1062), i219, i207, i219, i207) :|: i219 > i207 f1061_0_main_LE(EOS(STATIC_1061), i219, i207, i219, i207) -> f1065_0_main_Load(EOS(STATIC_1065), i219, i207) :|: i219 <= i207 f1065_0_main_Load(EOS(STATIC_1065), i219, i207) -> f1067_0_main_Load(EOS(STATIC_1067), i219, i207, i219) :|: TRUE f1067_0_main_Load(EOS(STATIC_1067), i219, i207, i219) -> f1069_0_main_NE(EOS(STATIC_1069), i219, i207, i219, i207) :|: TRUE f1069_0_main_NE(EOS(STATIC_1069), i219, i207, i219, i207) -> f1081_0_main_NE(EOS(STATIC_1081), i219, i207, i219, i207) :|: !(i219 = i207) f1069_0_main_NE(EOS(STATIC_1069), i207, i207, i207, i207) -> f1082_0_main_NE(EOS(STATIC_1082), i207, i207, i207, i207) :|: i219 = i207 f1081_0_main_NE(EOS(STATIC_1081), i219, i207, i219, i207) -> f1084_0_main_Inc(EOS(STATIC_1084), i219, i207) :|: i219 < i207 f1084_0_main_Inc(EOS(STATIC_1084), i219, i207) -> f1087_0_main_JMP(EOS(STATIC_1087), i219, i207 + -1) :|: TRUE f1087_0_main_JMP(EOS(STATIC_1087), i219, i226) -> f1092_0_main_Load(EOS(STATIC_1092), i219, i226) :|: TRUE f1092_0_main_Load(EOS(STATIC_1092), i219, i226) -> f1047_0_main_Load(EOS(STATIC_1047), i219, i226) :|: TRUE f1047_0_main_Load(EOS(STATIC_1047), i219, i207) -> f1048_0_main_Load(EOS(STATIC_1048), i219, i207, i219) :|: TRUE f1082_0_main_NE(EOS(STATIC_1082), i207, i207, i207, i207) -> f1085_0_main_Inc(EOS(STATIC_1085), i207, i207) :|: TRUE f1085_0_main_Inc(EOS(STATIC_1085), i207, i207) -> f1088_0_main_JMP(EOS(STATIC_1088), i207 + -1, i207) :|: TRUE f1088_0_main_JMP(EOS(STATIC_1088), i227, i207) -> f1097_0_main_Load(EOS(STATIC_1097), i227, i207) :|: TRUE f1097_0_main_Load(EOS(STATIC_1097), i227, i207) -> f1047_0_main_Load(EOS(STATIC_1047), i227, i207) :|: TRUE f1062_0_main_LE(EOS(STATIC_1062), i219, i207, i219, i207) -> f1066_0_main_Inc(EOS(STATIC_1066), i219, i207) :|: i219 > i207 f1066_0_main_Inc(EOS(STATIC_1066), i219, i207) -> f1068_0_main_JMP(EOS(STATIC_1068), i219 + -1, i207) :|: TRUE f1068_0_main_JMP(EOS(STATIC_1068), i224, i207) -> f1080_0_main_Load(EOS(STATIC_1080), i224, i207) :|: TRUE f1080_0_main_Load(EOS(STATIC_1080), i224, i207) -> f1047_0_main_Load(EOS(STATIC_1047), i224, i207) :|: TRUE Combined rules. Obtained 3 IRulesP rules: f1048_0_main_Load(EOS(STATIC_1048), i219:0, i207:0, i219:0) -> f1048_0_main_Load(EOS(STATIC_1048), i219:0, i207:0 - 1, i219:0) :|: i219:0 < i207:0 && i219:0 + i207:0 > 0 f1048_0_main_Load(EOS(STATIC_1048), i219:0, i207:0, i219:0) -> f1048_0_main_Load(EOS(STATIC_1048), i219:0 - 1, i207:0, i219:0 - 1) :|: i219:0 + i207:0 > 0 && i219:0 > i207:0 f1048_0_main_Load(EOS(STATIC_1048), i219:0, i219:0, i219:0) -> f1048_0_main_Load(EOS(STATIC_1048), i219:0 - 1, i219:0, i219:0 - 1) :|: i219:0 + i219:0 > 0 Filtered constant ground arguments: f1048_0_main_Load(x1, x2, x3, x4) -> f1048_0_main_Load(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f1048_0_main_Load(x1, x2, x3) -> f1048_0_main_Load(x2, x3) Finished conversion. Obtained 3 rules.P rules: f1048_0_main_Load(i207:0, i219:0) -> f1048_0_main_Load(i207:0 - 1, i219:0) :|: i219:0 < i207:0 && i219:0 + i207:0 > 0 f1048_0_main_Load(i207:0, i219:0) -> f1048_0_main_Load(i207:0, i219:0 - 1) :|: i219:0 + i207:0 > 0 && i219:0 > i207:0 f1048_0_main_Load(i219:0, i219:0) -> f1048_0_main_Load(i219:0, i219:0 - 1) :|: i219:0 + i219:0 > 0 ---------------------------------------- (8) Obligation: Rules: f1048_0_main_Load(i207:0, i219:0) -> f1048_0_main_Load(i207:0 - 1, i219:0) :|: i219:0 < i207:0 && i219:0 + i207:0 > 0 f1048_0_main_Load(x, x1) -> f1048_0_main_Load(x, x1 - 1) :|: x1 + x > 0 && x1 > x f1048_0_main_Load(x2, x2) -> f1048_0_main_Load(x2, x2 - 1) :|: x2 + x2 > 0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f1048_0_main_Load(i207:0, i219:0) -> f1048_0_main_Load(arith, i219:0) :|: i219:0 < i207:0 && i219:0 + i207:0 > 0 && arith = i207:0 - 1 f1048_0_main_Load(x3, x4) -> f1048_0_main_Load(x3, x5) :|: x4 + x3 > 0 && x4 > x3 && x5 = x4 - 1 f1048_0_main_Load(x6, x6) -> f1048_0_main_Load(x6, x7) :|: x6 + x6 > 0 && x7 = x6 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f1048_0_main_Load(i207:0, i219:0) -> f1048_0_main_Load(arith, i219:0) :|: i219:0 < i207:0 && i219:0 + i207:0 > 0 && arith = i207:0 - 1 (2) f1048_0_main_Load(x3, x4) -> f1048_0_main_Load(x3, x5) :|: x4 + x3 > 0 && x4 > x3 && x5 = x4 - 1 (3) f1048_0_main_Load(x6, x6) -> f1048_0_main_Load(x6, x7) :|: x6 + x6 > 0 && x7 = x6 - 1 Arcs: (1) -> (1), (3) (2) -> (2), (3) (3) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) f1048_0_main_Load(x3, x4) -> f1048_0_main_Load(x3, x5) :|: x4 + x3 > 0 && x4 > x3 && x5 = x4 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: f1048_0_main_Load(x3:0, x4:0) -> f1048_0_main_Load(x3:0, x4:0 - 1) :|: x4:0 + x3:0 > 0 && x4:0 > x3:0 ---------------------------------------- (16) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1048_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (17) Obligation: Rules: f1048_0_main_Load(x3:0, x4:0) -> f1048_0_main_Load(x3:0, c) :|: c = x4:0 - 1 && (x4:0 + x3:0 > 0 && x4:0 > x3:0) ---------------------------------------- (18) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1048_0_main_Load(x, x1)] = -x + x1 The following rules are decreasing: f1048_0_main_Load(x3:0, x4:0) -> f1048_0_main_Load(x3:0, c) :|: c = x4:0 - 1 && (x4:0 + x3:0 > 0 && x4:0 > x3:0) The following rules are bounded: f1048_0_main_Load(x3:0, x4:0) -> f1048_0_main_Load(x3:0, c) :|: c = x4:0 - 1 && (x4:0 + x3:0 > 0 && x4:0 > x3:0) ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Termination digraph: Nodes: (1) f1048_0_main_Load(i207:0, i219:0) -> f1048_0_main_Load(arith, i219:0) :|: i219:0 < i207:0 && i219:0 + i207:0 > 0 && arith = i207:0 - 1 (2) f1048_0_main_Load(x6, x6) -> f1048_0_main_Load(x6, x7) :|: x6 + x6 > 0 && x7 = x6 - 1 Arcs: (1) -> (1), (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (21) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (22) Obligation: Rules: f1048_0_main_Load(x6:0, x6:0) -> f1048_0_main_Load(x6:0, x6:0 - 1) :|: x6:0 + x6:0 > 0 f1048_0_main_Load(i207:0:0, i219:0:0) -> f1048_0_main_Load(i207:0:0 - 1, i219:0:0) :|: i219:0:0 < i207:0:0 && i219:0:0 + i207:0:0 > 0 ---------------------------------------- (23) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f1048_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (24) Obligation: Rules: f1048_0_main_Load(x6:0, x6:0) -> f1048_0_main_Load(x6:0, c) :|: c = x6:0 - 1 && x6:0 + x6:0 > 0 f1048_0_main_Load(i207:0:0, i219:0:0) -> f1048_0_main_Load(c1, i219:0:0) :|: c1 = i207:0:0 - 1 && (i219:0:0 < i207:0:0 && i219:0:0 + i207:0:0 > 0) ---------------------------------------- (25) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f1048_0_main_Load(x, x1)] = x + x1 The following rules are decreasing: f1048_0_main_Load(x6:0, x6:0) -> f1048_0_main_Load(x6:0, c) :|: c = x6:0 - 1 && x6:0 + x6:0 > 0 f1048_0_main_Load(i207:0:0, i219:0:0) -> f1048_0_main_Load(c1, i219:0:0) :|: c1 = i207:0:0 - 1 && (i219:0:0 < i207:0:0 && i219:0:0 + i207:0:0 > 0) The following rules are bounded: f1048_0_main_Load(x6:0, x6:0) -> f1048_0_main_Load(x6:0, c) :|: c = x6:0 - 1 && x6:0 + x6:0 > 0 f1048_0_main_Load(i207:0:0, i219:0:0) -> f1048_0_main_Load(c1, i219:0:0) :|: c1 = i207:0:0 - 1 && (i219:0:0 < i207:0:0 && i219:0:0 + i207:0:0 > 0) ---------------------------------------- (26) YES