/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 178 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 113 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 53 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 51 ms] (16) IntTRS (17) RankingReductionPairProof [EQUIVALENT, 27 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class GCD5 { public static int gcd(int a, int b) { int tmp; while(b > 0 && a > 0) { tmp = b; b = a % b; a = tmp; } return a; } public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); gcd(x, 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 GCD5 { public static int gcd(int a, int b) { int tmp; while(b > 0 && a > 0) { tmp = b; b = a % b; a = tmp; } return a; } public static void main(String[] args) { Random.args = args; int x = Random.random(); int y = Random.random(); gcd(x, 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: GCD5.main([Ljava/lang/String;)V: Graph of 194 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: GCD5.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 16 IRulesP rules: f401_0_gcd_LE(EOS(STATIC_401), i19, i54, i54) -> f417_0_gcd_LE(EOS(STATIC_417), i19, i54, i54) :|: TRUE f417_0_gcd_LE(EOS(STATIC_417), i19, i54, i54) -> f427_0_gcd_Load(EOS(STATIC_427), i19, i54) :|: i54 > 0 f427_0_gcd_Load(EOS(STATIC_427), i19, i54) -> f481_0_gcd_LE(EOS(STATIC_481), i19, i54, i19) :|: TRUE f481_0_gcd_LE(EOS(STATIC_481), i64, i54, i64) -> f519_0_gcd_LE(EOS(STATIC_519), i64, i54, i64) :|: TRUE f519_0_gcd_LE(EOS(STATIC_519), i64, i54, i64) -> f537_0_gcd_Load(EOS(STATIC_537), i64, i54) :|: i64 > 0 f537_0_gcd_Load(EOS(STATIC_537), i64, i54) -> f544_0_gcd_Store(EOS(STATIC_544), i64, i54, i54) :|: TRUE f544_0_gcd_Store(EOS(STATIC_544), i64, i54, i54) -> f558_0_gcd_Load(EOS(STATIC_558), i64, i54, i54) :|: TRUE f558_0_gcd_Load(EOS(STATIC_558), i64, i54, i54) -> f587_0_gcd_Load(EOS(STATIC_587), i54, i54, i64) :|: TRUE f587_0_gcd_Load(EOS(STATIC_587), i54, i54, i64) -> f593_0_gcd_IntArithmetic(EOS(STATIC_593), i54, i64, i54) :|: TRUE f593_0_gcd_IntArithmetic(EOS(STATIC_593), i54, i64, i54) -> f599_0_gcd_Store(EOS(STATIC_599), i54, i64 % i54) :|: TRUE f599_0_gcd_Store(EOS(STATIC_599), i54, i70) -> f604_0_gcd_Load(EOS(STATIC_604), i70, i54) :|: TRUE f604_0_gcd_Load(EOS(STATIC_604), i70, i54) -> f608_0_gcd_Store(EOS(STATIC_608), i70, i54) :|: TRUE f608_0_gcd_Store(EOS(STATIC_608), i70, i54) -> f611_0_gcd_JMP(EOS(STATIC_611), i54, i70) :|: TRUE f611_0_gcd_JMP(EOS(STATIC_611), i54, i70) -> f672_0_gcd_Load(EOS(STATIC_672), i54, i70) :|: TRUE f672_0_gcd_Load(EOS(STATIC_672), i54, i70) -> f381_0_gcd_Load(EOS(STATIC_381), i54, i70) :|: TRUE f381_0_gcd_Load(EOS(STATIC_381), i19, i45) -> f401_0_gcd_LE(EOS(STATIC_401), i19, i45, i45) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f401_0_gcd_LE(EOS(STATIC_401), i19:0, i54:0, i54:0) -> f401_0_gcd_LE'(EOS(STATIC_401), i19:0, i54:0, i54:0) :|: i19:0 > 0 && i54:0 > 0 f401_0_gcd_LE'(EOS(STATIC_401), i19:0, i54:0, i54:0) -> f401_0_gcd_LE(EOS(STATIC_401), i54:0, i19:0 - i54:0 * div, i19:0 - i54:0 * div1) :|: i54:0 > 0 && i19:0 > 0 && i19:0 - i54:0 * div + i54:0 > 0 && i54:0 > i19:0 - i54:0 * div && i54:0 > i19:0 - i54:0 * div1 && i19:0 - i54:0 * div1 + i54:0 > 0 Filtered constant ground arguments: f401_0_gcd_LE(x1, x2, x3, x4) -> f401_0_gcd_LE(x2, x3, x4) f401_0_gcd_LE'(x1, x2, x3, x4) -> f401_0_gcd_LE'(x2, x3, x4) EOS(x1) -> EOS Filtered duplicate arguments: f401_0_gcd_LE'(x1, x2, x3) -> f401_0_gcd_LE'(x1, x3) Finished conversion. Obtained 2 rules.P rules: f401_0_gcd_LE(i19:0, i54:0, i54:0) -> f401_0_gcd_LE'(i19:0, i54:0) :|: i19:0 > 0 && i54:0 > 0 f401_0_gcd_LE'(i19:0, i54:0) -> f401_0_gcd_LE(i54:0, i19:0 - i54:0 * div, i19:0 - i54:0 * div1) :|: i19:0 > 0 && i54:0 > 0 && i19:0 - i54:0 * div + i54:0 > 0 && i54:0 > i19:0 - i54:0 * div && i19:0 - i54:0 * div1 + i54:0 > 0 && i54:0 > i19:0 - i54:0 * div1 ---------------------------------------- (8) Obligation: Rules: f401_0_gcd_LE(i19:0, i54:0, i54:0) -> f401_0_gcd_LE'(i19:0, i54:0) :|: i19:0 > 0 && i54:0 > 0 f401_0_gcd_LE'(x, x1) -> f401_0_gcd_LE(x1, x - x1 * x2, x - x1 * x3) :|: x > 0 && x1 > 0 && x - x1 * x2 + x1 > 0 && x1 > x - x1 * x2 && x - x1 * x3 + x1 > 0 && x1 > x - x1 * x3 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f401_0_gcd_LE(i19:0, i54:0, i54:0) -> f401_0_gcd_LE'(i19:0, i54:0) :|: i19:0 > 0 && i54:0 > 0 f401_0_gcd_LE'(x, x1) -> f401_0_gcd_LE(x1, arith, arith1) :|: x > 0 && x1 > 0 && x - x1 * x2 + x1 > 0 && x1 > x - x1 * x2 && x - x1 * x3 + x1 > 0 && x1 > x - x1 * x3 && arith = x - x1 * x2 && arith1 = x - x1 * x3 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f401_0_gcd_LE(i19:0, i54:0, i54:0) -> f401_0_gcd_LE'(i19:0, i54:0) :|: i19:0 > 0 && i54:0 > 0 (2) f401_0_gcd_LE'(x, x1) -> f401_0_gcd_LE(x1, arith, arith1) :|: x > 0 && x1 > 0 && x - x1 * x2 + x1 > 0 && x1 > x - x1 * x2 && x - x1 * x3 + x1 > 0 && x1 > x - x1 * x3 && arith = x - x1 * x2 && arith1 = x - x1 * x3 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f401_0_gcd_LE(i19:0, i54:0, i54:0) -> f401_0_gcd_LE'(i19:0, i54:0) :|: i19:0 > 0 && i54:0 > 0 (2) f401_0_gcd_LE'(x, x1) -> f401_0_gcd_LE(x1, arith, arith1) :|: x > 0 && x1 > 0 && x - x1 * x2 + x1 > 0 && x1 > x - x1 * x2 && x - x1 * x3 + x1 > 0 && x1 > x - x1 * x3 && arith = x - x1 * x2 && arith1 = x - x1 * x3 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f401_0_gcd_LE(i19:0:0, i54:0:0, i54:0:0) -> f401_0_gcd_LE(i54:0:0, i19:0:0 - i54:0:0 * x2:0, i19:0:0 - i54:0:0 * x3:0) :|: i54:0:0 > i19:0:0 - i54:0:0 * x3:0 && i19:0:0 - i54:0:0 * x3:0 + i54:0:0 > 0 && i54:0:0 > i19:0:0 - i54:0:0 * x2:0 && i19:0:0 - i54:0:0 * x2:0 + i54:0:0 > 0 && i54:0:0 > 0 && i19:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f401_0_gcd_LE(INTEGER, INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f401_0_gcd_LE(i19:0:0, i54:0:0, i54:0:0) -> f401_0_gcd_LE(i54:0:0, c, c1) :|: c1 = i19:0:0 - i54:0:0 * x3:0 && c = i19:0:0 - i54:0:0 * x2:0 && (i54:0:0 > i19:0:0 - i54:0:0 * x3:0 && i19:0:0 - i54:0:0 * x3:0 + i54:0:0 > 0 && i54:0:0 > i19:0:0 - i54:0:0 * x2:0 && i19:0:0 - i54:0:0 * x2:0 + i54:0:0 > 0 && i54:0:0 > 0 && i19:0:0 > 0) ---------------------------------------- (17) RankingReductionPairProof (EQUIVALENT) Interpretation: [ f401_0_gcd_LE ] = f401_0_gcd_LE_3 The following rules are decreasing: f401_0_gcd_LE(i19:0:0, i54:0:0, i54:0:0) -> f401_0_gcd_LE(i54:0:0, c, c1) :|: c1 = i19:0:0 - i54:0:0 * x3:0 && c = i19:0:0 - i54:0:0 * x2:0 && (i54:0:0 > i19:0:0 - i54:0:0 * x3:0 && i19:0:0 - i54:0:0 * x3:0 + i54:0:0 > 0 && i54:0:0 > i19:0:0 - i54:0:0 * x2:0 && i19:0:0 - i54:0:0 * x2:0 + i54:0:0 > 0 && i54:0:0 > 0 && i19:0:0 > 0) The following rules are bounded: f401_0_gcd_LE(i19:0:0, i54:0:0, i54:0:0) -> f401_0_gcd_LE(i54:0:0, c, c1) :|: c1 = i19:0:0 - i54:0:0 * x3:0 && c = i19:0:0 - i54:0:0 * x2:0 && (i54:0:0 > i19:0:0 - i54:0:0 * x3:0 && i19:0:0 - i54:0:0 * x3:0 + i54:0:0 > 0 && i54:0:0 > i19:0:0 - i54:0:0 * x2:0 && i19:0:0 - i54:0:0 * x2:0 + i54:0:0 > 0 && i54:0:0 > 0 && i19:0:0 > 0) ---------------------------------------- (18) YES