/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph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, 342 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 137 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 16 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class EqUserDefRec { public static void main(String[] args) { int x = args[0].length(); int y = args[1].length(); eq(x, y); } public static boolean eq(int x, int y) { if (x > 0 && y > 0) { return eq(x-1, y-1); } else { return (x == 0 && y == 0); } } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class EqUserDefRec { public static void main(String[] args) { int x = args[0].length(); int y = args[1].length(); eq(x, y); } public static boolean eq(int x, int y) { if (x > 0 && y > 0) { return eq(x-1, y-1); } else { return (x == 0 && y == 0); } } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: EqUserDefRec.main([Ljava/lang/String;)V: Graph of 129 nodes with 0 SCCs. EqUserDefRec.eq(II)Z: Graph of 43 nodes with 0 SCCs. ---------------------------------------- (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: EqUserDefRec.eq(II)Z SCC calls the following helper methods: EqUserDefRec.eq(II)Z 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: f310_0_eq_LE(EOS(STATIC_310), i46, i30, i46, i30, i46) -> f325_0_eq_LE(EOS(STATIC_325), i46, i30, i46, i30, i46) :|: TRUE f325_0_eq_LE(EOS(STATIC_325), i46, i30, i46, i30, i46) -> f335_0_eq_Load(EOS(STATIC_335), i46, i30, i46, i30) :|: i46 > 0 f335_0_eq_Load(EOS(STATIC_335), i46, i30, i46, i30) -> f350_0_eq_LE(EOS(STATIC_350), i46, i30, i46, i30, i30) :|: TRUE f350_0_eq_LE(EOS(STATIC_350), i46, i49, i46, i49, i49) -> f360_0_eq_LE(EOS(STATIC_360), i46, i49, i46, i49, i49) :|: TRUE f360_0_eq_LE(EOS(STATIC_360), i46, i49, i46, i49, i49) -> f365_0_eq_Load(EOS(STATIC_365), i46, i49, i46, i49) :|: i49 > 0 f365_0_eq_Load(EOS(STATIC_365), i46, i49, i46, i49) -> f391_0_eq_ConstantStackPush(EOS(STATIC_391), i46, i49, i49, i46) :|: TRUE f391_0_eq_ConstantStackPush(EOS(STATIC_391), i46, i49, i49, i46) -> f407_0_eq_IntArithmetic(EOS(STATIC_407), i46, i49, i49, i46, 1) :|: TRUE f407_0_eq_IntArithmetic(EOS(STATIC_407), i46, i49, i49, i46, matching1) -> f422_0_eq_Load(EOS(STATIC_422), i46, i49, i49, i46 - 1) :|: i46 > 0 && matching1 = 1 f422_0_eq_Load(EOS(STATIC_422), i46, i49, i49, i55) -> f440_0_eq_ConstantStackPush(EOS(STATIC_440), i46, i49, i55, i49) :|: TRUE f440_0_eq_ConstantStackPush(EOS(STATIC_440), i46, i49, i55, i49) -> f516_0_eq_IntArithmetic(EOS(STATIC_516), i46, i49, i55, i49, 1) :|: TRUE f516_0_eq_IntArithmetic(EOS(STATIC_516), i46, i49, i55, i49, matching1) -> f550_0_eq_InvokeMethod(EOS(STATIC_550), i46, i49, i55, i49 - 1) :|: i49 > 0 && matching1 = 1 f550_0_eq_InvokeMethod(EOS(STATIC_550), i46, i49, i55, i73) -> f568_0_eq_Load(EOS(STATIC_568), i55, i73, i55, i73) :|: i46 >= 1 && i49 >= 1 && i55 < i46 && i73 < i49 f550_0_eq_InvokeMethod(EOS(STATIC_550), i46, i49, i55, i73) -> f568_1_eq_Load(EOS(STATIC_568), i46, i49, i55, i73) :|: i46 >= 1 && i49 >= 1 && i55 < i46 && i73 < i49 f568_0_eq_Load(EOS(STATIC_568), i55, i73, i55, i73) -> f570_0_eq_Load(EOS(STATIC_570), i55, i73, i55, i73) :|: TRUE f570_0_eq_Load(EOS(STATIC_570), i55, i73, i55, i73) -> f294_0_eq_Load(EOS(STATIC_294), i55, i73, i55, i73) :|: TRUE f294_0_eq_Load(EOS(STATIC_294), i11, i30, i11, i30) -> f310_0_eq_LE(EOS(STATIC_310), i11, i30, i11, i30, i11) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f310_0_eq_LE(EOS(STATIC_310), i46:0, i30:0, i46:0, i30:0, i46:0) -> f310_0_eq_LE(EOS(STATIC_310), i46:0 - 1, i30:0 - 1, i46:0 - 1, i30:0 - 1, i46:0 - 1) :|: i46:0 > 0 && i30:0 > 0 && i46:0 - 1 < i46:0 && i30:0 - 1 < i30:0 Removed following non-SCC rules: f310_0_eq_LE(EOS(STATIC_310), i46:0, i30:0, i46:0, i30:0, i46:0) -> f568_1_eq_Load(EOS(STATIC_568), i46:0, i30:0, i46:0 - 1, i30:0 - 1) :|: i46:0 > 0 && i30:0 > 0 && i46:0 - 1 < i46:0 && i30:0 - 1 < i30:0 Filtered constant ground arguments: f310_0_eq_LE(x1, x2, x3, x4, x5, x6) -> f310_0_eq_LE(x2, x3, x4, x5, x6) EOS(x1) -> EOS Filtered duplicate arguments: f310_0_eq_LE(x1, x2, x3, x4, x5) -> f310_0_eq_LE(x4, x5) Finished conversion. Obtained 1 rules.P rules: f310_0_eq_LE(i30:0, i46:0) -> f310_0_eq_LE(i30:0 - 1, i46:0 - 1) :|: i30:0 > 0 && i46:0 > 0 && i30:0 - 1 < i30:0 && i46:0 - 1 < i46:0 ---------------------------------------- (8) Obligation: Rules: f310_0_eq_LE(i30:0, i46:0) -> f310_0_eq_LE(i30:0 - 1, i46:0 - 1) :|: i30:0 > 0 && i46:0 > 0 && i30:0 - 1 < i30:0 && i46:0 - 1 < i46:0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f310_0_eq_LE(i30:0, i46:0) -> f310_0_eq_LE(arith, arith1) :|: i30:0 > 0 && i46:0 > 0 && i30:0 - 1 < i30:0 && i46:0 - 1 < i46:0 && arith = i30:0 - 1 && arith1 = i46:0 - 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f310_0_eq_LE(i30:0, i46:0) -> f310_0_eq_LE(arith, arith1) :|: i30:0 > 0 && i46:0 > 0 && i30:0 - 1 < i30:0 && i46:0 - 1 < i46:0 && arith = i30:0 - 1 && arith1 = i46:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f310_0_eq_LE(i30:0, i46:0) -> f310_0_eq_LE(arith, arith1) :|: i30:0 > 0 && i46:0 > 0 && i30:0 - 1 < i30:0 && i46:0 - 1 < i46:0 && arith = i30:0 - 1 && arith1 = i46:0 - 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f310_0_eq_LE(i30:0:0, i46:0:0) -> f310_0_eq_LE(i30:0:0 - 1, i46:0:0 - 1) :|: i30:0:0 - 1 < i30:0:0 && i46:0:0 - 1 < i46:0:0 && i46:0:0 > 0 && i30:0:0 > 0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f310_0_eq_LE(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f310_0_eq_LE(i30:0:0, i46:0:0) -> f310_0_eq_LE(c, c1) :|: c1 = i46:0:0 - 1 && c = i30:0:0 - 1 && (i30:0:0 - 1 < i30:0:0 && i46:0:0 - 1 < i46:0:0 && i46:0:0 > 0 && i30:0:0 > 0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f310_0_eq_LE(x, x1)] = x1 The following rules are decreasing: f310_0_eq_LE(i30:0:0, i46:0:0) -> f310_0_eq_LE(c, c1) :|: c1 = i46:0:0 - 1 && c = i30:0:0 - 1 && (i30:0:0 - 1 < i30:0:0 && i46:0:0 - 1 < i46:0:0 && i46:0:0 > 0 && i30:0:0 > 0) The following rules are bounded: f310_0_eq_LE(i30:0:0, i46:0:0) -> f310_0_eq_LE(c, c1) :|: c1 = i46:0:0 - 1 && c = i30:0:0 - 1 && (i30:0:0 - 1 < i30:0:0 && i46:0:0 - 1 < i46:0:0 && i46:0:0 > 0 && i30:0:0 > 0) ---------------------------------------- (18) YES