/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 96 ms] (2) JBC problem (3) JBCToGraph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, 328 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, 4 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 53 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class IntRTA { // only wrap a primitive int private int val; // count up to the value // in "limit" public static void count( IntRTA orig, IntRTA limit) { if (orig == null || limit == null) { return; } // introduce sharing IntRTA copy = orig; while (orig.val < limit.val) { copy.val++; } } public static void main(String[] args) { Random.args = args; IntRTA x = new IntRTA(); x.val = Random.random(); IntRTA y = new IntRTA(); y.val = Random.random(); count(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 IntRTA { // only wrap a primitive int private int val; // count up to the value // in "limit" public static void count( IntRTA orig, IntRTA limit) { if (orig == null || limit == null) { return; } // introduce sharing IntRTA copy = orig; while (orig.val < limit.val) { copy.val++; } } public static void main(String[] args) { Random.args = args; IntRTA x = new IntRTA(); x.val = Random.random(); IntRTA y = new IntRTA(); y.val = Random.random(); count(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: IntRTA.main([Ljava/lang/String;)V: Graph of 208 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: IntRTA.main([Ljava/lang/String;)V SCC calls the following helper methods: Performed SCC analyses: *Used field analysis yielded the following read fields: *IntRTA: [val] *Marker field analysis yielded the following relations that could be markers: *IntRTA.val > i48 (Introduced counter i73) ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 14 IRulesP rules: f437_0_count_FieldAccess(EOS(STATIC_437), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i73) -> f438_0_count_Load(EOS(STATIC_438), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i48, i73) :|: TRUE f438_0_count_Load(EOS(STATIC_438), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i48, i73) -> f439_0_count_FieldAccess(EOS(STATIC_439), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i48, java.lang.Object(IntRTA(EOC, i49)), i73) :|: TRUE f439_0_count_FieldAccess(EOS(STATIC_439), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i48, java.lang.Object(IntRTA(EOC, i49)), i73) -> f440_0_count_GE(EOS(STATIC_440), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i48, i49, i73) :|: TRUE f440_0_count_GE(EOS(STATIC_440), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i48, i49, i73) -> f442_0_count_GE(EOS(STATIC_442), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i48, i49, i73) :|: i48 < i49 f442_0_count_GE(EOS(STATIC_442), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i48, i49, i73) -> f449_0_count_Load(EOS(STATIC_449), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i73) :|: i48 < i49 f449_0_count_Load(EOS(STATIC_449), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i73) -> f454_0_count_Duplicate(EOS(STATIC_454), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i73) :|: TRUE f454_0_count_Duplicate(EOS(STATIC_454), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i73) -> f457_0_count_FieldAccess(EOS(STATIC_457), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i73) :|: TRUE f457_0_count_FieldAccess(EOS(STATIC_457), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i73) -> f459_0_count_ConstantStackPush(EOS(STATIC_459), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i48, i73) :|: TRUE f459_0_count_ConstantStackPush(EOS(STATIC_459), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i48, i73) -> f461_0_count_IntArithmetic(EOS(STATIC_461), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i48, 1, i73) :|: TRUE f461_0_count_IntArithmetic(EOS(STATIC_461), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i48, matching1, i73) -> f464_0_count_FieldAccess(EOS(STATIC_464), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i48 + 1, i73) :|: i48 >= 0 && matching1 = 1 f464_0_count_FieldAccess(EOS(STATIC_464), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i56, i73) -> f468_0_count_JMP(EOS(STATIC_468), java.lang.Object(IntRTA(EOC, i56)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i56)), i73 + 1) :|: i73 >= 0 f468_0_count_JMP(EOS(STATIC_468), java.lang.Object(IntRTA(EOC, i56)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i56)), i73) -> f481_0_count_Load(EOS(STATIC_481), java.lang.Object(IntRTA(EOC, i56)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i56)), i73) :|: TRUE f481_0_count_Load(EOS(STATIC_481), java.lang.Object(IntRTA(EOC, i56)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i56)), i73) -> f430_0_count_Load(EOS(STATIC_430), java.lang.Object(IntRTA(EOC, i56)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i56)), i73) :|: TRUE f430_0_count_Load(EOS(STATIC_430), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), i73) -> f437_0_count_FieldAccess(EOS(STATIC_437), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i49)), java.lang.Object(IntRTA(EOC, i48)), java.lang.Object(IntRTA(EOC, i48)), i73) :|: TRUE Combined rules. Obtained 1 IRulesP rules: f437_0_count_FieldAccess(EOS(STATIC_437), java.lang.Object(IntRTA(EOC, i48:0)), java.lang.Object(IntRTA(EOC, i49:0)), java.lang.Object(IntRTA(EOC, i48:0)), java.lang.Object(IntRTA(EOC, i48:0)), i73:0) -> f437_0_count_FieldAccess(EOS(STATIC_437), java.lang.Object(IntRTA(EOC, i48:0 + 1)), java.lang.Object(IntRTA(EOC, i49:0)), java.lang.Object(IntRTA(EOC, i48:0 + 1)), java.lang.Object(IntRTA(EOC, i48:0 + 1)), i73:0 + 1) :|: i49:0 > i48:0 && i73:0 > -1 && i48:0 > -1 Filtered constant ground arguments: f437_0_count_FieldAccess(x1, x2, x3, x4, x5, x6) -> f437_0_count_FieldAccess(x2, x3, x4, x5, x6) EOS(x1) -> EOS IntRTA(x1, x2) -> IntRTA(x2) Filtered duplicate arguments: f437_0_count_FieldAccess(x1, x2, x3, x4, x5) -> f437_0_count_FieldAccess(x2, x4, x5) Finished conversion. Obtained 1 rules.P rules: f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(i48:0)), i73:0, i49:0, i48:0) -> f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(i48:0 + 1)), i73:0 + 1, i49:0, i48:0 + 1) :|: i73:0 > -1 && i48:0 > -1 && i49:0 > i48:0 ---------------------------------------- (8) Obligation: Rules: f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(i48:0)), i73:0, i49:0, i48:0) -> f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(i48:0 + 1)), i73:0 + 1, i49:0, i48:0 + 1) :|: i73:0 > -1 && i48:0 > -1 && i49:0 > i48:0 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(i48:0)), i73:0, i49:0, i48:0) -> f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(arith1)), arith, i49:0, arith1) :|: i73:0 > -1 && i48:0 > -1 && i49:0 > i48:0 && arith = i73:0 + 1 && arith1 = i48:0 + 1 && arith1 = i48:0 + 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(i48:0)), i73:0, i49:0, i48:0) -> f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(arith1)), arith, i49:0, arith1) :|: i73:0 > -1 && i48:0 > -1 && i49:0 > i48:0 && arith = i73:0 + 1 && arith1 = i48:0 + 1 && arith1 = i48:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(i48:0)), i73:0, i49:0, i48:0) -> f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0)), java.lang.Object(IntRTA(arith1)), arith, i49:0, arith1) :|: i73:0 > -1 && i48:0 > -1 && i49:0 > i48:0 && arith = i73:0 + 1 && arith1 = i48:0 + 1 && arith1 = i48:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0:0)), java.lang.Object(IntRTA(i48:0:0)), i73:0:0, i49:0:0, i48:0:0) -> f437_0_count_FieldAccess(java.lang.Object(IntRTA(i49:0:0)), java.lang.Object(IntRTA(i48:0:0 + 1)), i73:0:0 + 1, i49:0:0, i48:0:0 + 1) :|: i73:0:0 > -1 && i48:0:0 > -1 && i49:0:0 > i48:0:0 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f437_0_count_FieldAccess(VARIABLE, VARIABLE, INTEGER, INTEGER, INTEGER) java.lang.Object(VARIABLE) IntRTA(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f437_0_count_FieldAccess(c, c1, i73:0:0, i49:0:0, i48:0:0) -> f437_0_count_FieldAccess(c2, c3, c4, i49:0:0, c5) :|: c5 = i48:0:0 + 1 && (c4 = i73:0:0 + 1 && (c3 = 0 && (c2 = 0 && (c1 = 0 && c = 0)))) && (i73:0:0 > -1 && i48:0:0 > -1 && i49:0:0 > i48:0:0) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f437_0_count_FieldAccess(x, x1, x2, x3, x4)] = c*x + c1*x1 + x3 - x4 The following rules are decreasing: f437_0_count_FieldAccess(c, c1, i73:0:0, i49:0:0, i48:0:0) -> f437_0_count_FieldAccess(c2, c3, c4, i49:0:0, c5) :|: c5 = i48:0:0 + 1 && (c4 = i73:0:0 + 1 && (c3 = 0 && (c2 = 0 && (c1 = 0 && c = 0)))) && (i73:0:0 > -1 && i48:0:0 > -1 && i49:0:0 > i48:0:0) The following rules are bounded: f437_0_count_FieldAccess(c, c1, i73:0:0, i49:0:0, i48:0:0) -> f437_0_count_FieldAccess(c2, c3, c4, i49:0:0, c5) :|: c5 = i48:0:0 + 1 && (c4 = i73:0:0 + 1 && (c3 = 0 && (c2 = 0 && (c1 = 0 && c = 0)))) && (i73:0:0 > -1 && i48:0:0 > -1 && i49:0:0 > i48:0:0) ---------------------------------------- (18) YES