/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 331 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 75 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 33 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 14 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class Duplicate{ public static int round (int x) { if (x % 2 == 0) return x; else return x+1; } public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while ((x > y) && (y > 2)) { x++; y = 2*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: public class Duplicate{ public static int round (int x) { if (x % 2 == 0) return x; else return x+1; } public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); while ((x > y) && (y > 2)) { x++; y = 2*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: Duplicate.main([Ljava/lang/String;)V: Graph of 185 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: Duplicate.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 15 IRulesP rules: f404_0_main_Load(EOS(STATIC_404), i56, i57, i56) -> f406_0_main_LE(EOS(STATIC_406), i56, i57, i56, i57) :|: TRUE f406_0_main_LE(EOS(STATIC_406), i56, i57, i56, i57) -> f411_0_main_LE(EOS(STATIC_411), i56, i57, i56, i57) :|: i56 > i57 f411_0_main_LE(EOS(STATIC_411), i56, i57, i56, i57) -> f418_0_main_Load(EOS(STATIC_418), i56, i57) :|: i56 > i57 f418_0_main_Load(EOS(STATIC_418), i56, i57) -> f420_0_main_ConstantStackPush(EOS(STATIC_420), i56, i57, i57) :|: TRUE f420_0_main_ConstantStackPush(EOS(STATIC_420), i56, i57, i57) -> f421_0_main_LE(EOS(STATIC_421), i56, i57, i57, 2) :|: TRUE f421_0_main_LE(EOS(STATIC_421), i66, i65, i65, matching1) -> f432_0_main_LE(EOS(STATIC_432), i66, i65, i65, 2) :|: TRUE && matching1 = 2 f432_0_main_LE(EOS(STATIC_432), i66, i65, i65, matching1) -> f434_0_main_Inc(EOS(STATIC_434), i66, i65) :|: i65 > 2 && matching1 = 2 f434_0_main_Inc(EOS(STATIC_434), i66, i65) -> f435_0_main_ConstantStackPush(EOS(STATIC_435), i66 + 1, i65) :|: TRUE f435_0_main_ConstantStackPush(EOS(STATIC_435), i67, i65) -> f436_0_main_Load(EOS(STATIC_436), i67, i65, 2) :|: TRUE f436_0_main_Load(EOS(STATIC_436), i67, i65, matching1) -> f437_0_main_IntArithmetic(EOS(STATIC_437), i67, 2, i65) :|: TRUE && matching1 = 2 f437_0_main_IntArithmetic(EOS(STATIC_437), i67, matching1, i65) -> f438_0_main_Store(EOS(STATIC_438), i67, 2 * i65) :|: i65 > 1 && matching1 = 2 f438_0_main_Store(EOS(STATIC_438), i67, i68) -> f439_0_main_JMP(EOS(STATIC_439), i67, i68) :|: TRUE f439_0_main_JMP(EOS(STATIC_439), i67, i68) -> f446_0_main_Load(EOS(STATIC_446), i67, i68) :|: TRUE f446_0_main_Load(EOS(STATIC_446), i67, i68) -> f394_0_main_Load(EOS(STATIC_394), i67, i68) :|: TRUE f394_0_main_Load(EOS(STATIC_394), i56, i57) -> f404_0_main_Load(EOS(STATIC_404), i56, i57, i56) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f404_0_main_Load(EOS(STATIC_404), i56:0, i57:0, i56:0) -> f404_0_main_Load(EOS(STATIC_404), i56:0 + 1, 2 * i57:0, i56:0 + 1) :|: i57:0 > 2 && i57:0 < i56:0 Filtered constant ground arguments: f404_0_main_Load(x1, x2, x3, x4) -> f404_0_main_Load(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f404_0_main_Load(x1, x2, x3) -> f404_0_main_Load(x2, x3) Finished conversion. Obtained 1 rules.P rules: f404_0_main_Load(i57:0, i56:0) -> f404_0_main_Load(2 * i57:0, i56:0 + 1) :|: i57:0 > 2 && i57:0 < i56:0 ---------------------------------------- (8) Obligation: Rules: f404_0_main_Load(i57:0, i56:0) -> f404_0_main_Load(2 * i57:0, i56:0 + 1) :|: i57:0 > 2 && i57:0 < i56:0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f404_0_main_Load(i57:0, i56:0) -> f404_0_main_Load(arith, arith1) :|: i57:0 > 2 && i57:0 < i56:0 && arith = 2 * i57:0 && arith1 = i56:0 + 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f404_0_main_Load(i57:0, i56:0) -> f404_0_main_Load(arith, arith1) :|: i57:0 > 2 && i57:0 < i56:0 && arith = 2 * i57:0 && arith1 = i56:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f404_0_main_Load(i57:0, i56:0) -> f404_0_main_Load(arith, arith1) :|: i57:0 > 2 && i57:0 < i56:0 && arith = 2 * i57:0 && arith1 = i56:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f404_0_main_Load(i57:0:0, i56:0:0) -> f404_0_main_Load(2 * i57:0:0, i56:0:0 + 1) :|: i57:0:0 > 2 && i57:0:0 < i56:0:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f404_0_main_Load(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f404_0_main_Load(i57:0:0, i56:0:0) -> f404_0_main_Load(c, c1) :|: c1 = i56:0:0 + 1 && c = 2 * i57:0:0 && (i57:0:0 > 2 && i57:0:0 < i56:0:0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f404_0_main_Load(x, x1)] = -x + x1 The following rules are decreasing: f404_0_main_Load(i57:0:0, i56:0:0) -> f404_0_main_Load(c, c1) :|: c1 = i56:0:0 + 1 && c = 2 * i57:0:0 && (i57:0:0 > 2 && i57:0:0 < i56:0:0) The following rules are bounded: f404_0_main_Load(i57:0:0, i56:0:0) -> f404_0_main_Load(c, c1) :|: c1 = i56:0:0 + 1 && c = 2 * i57:0:0 && (i57:0:0 > 2 && i57:0:0 < i56:0:0) ---------------------------------------- (18) YES