/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern power(g,g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToDTProblemTransformerProof [SOUND, 72 ms] (2) TRIPLES (3) TPisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Clauses: power(0, N, 0) :- >(N, 0). power(X, 0, 1) :- >(X, 0). power(X, N, V) :- ','(>(X, 0), ','(>(N, 0), ','(is(N1, -(N, 1)), ','(power(X, N1, V1), is(V, *(V1, X)))))). Query: power(g,g,a) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 1, "program": { "directives": [], "clauses": [ [ "(power (0) N (0))", "(> N (0))" ], [ "(power X (0) (1))", "(> X (0))" ], [ "(power X N V)", "(',' (> X (0)) (',' (> N (0)) (',' (is N1 (- N (1))) (',' (power X N1 V1) (is V (* V1 X))))))" ] ] }, "graph": { "nodes": { "type": "Nodes", "2504": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T5", "type": "PlainIntegerVariable" }, "operation": ">=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T5", "type": "PlainIntegerVariable" }, "operation": ">=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": 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"(',' (> T31 (0)) (',' (> (0) (0)) (',' (is X55 (- (0) (1))) (',' (power T31 X55 X56) (is T33 (* X56 T31))))))" }], "kb": { "nonunifying": [[ "(power T31 (0) T3)", "(power (0) X2 (0))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": ">=" }, { "lhs": { "name": "T31", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": ">=" } ] }, "ground": ["T31"], "free": [ "X2", "X55", "X56" ], "exprvars": [ "T31", "T23" ] } }, "2538": { "goal": [], "kb": { "nonunifying": [[ "(power T26 (0) T3)", "(power (0) X2 (0))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T26", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T26", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": ">=" } ] }, "ground": ["T26"], "free": [ "X2", "X47", "X48" ], "exprvars": [ "T23", "T26" ] } } }, "edges": [ { "from": 1, "to": 4, "label": "CASE" }, { "from": 4, "to": 17, "label": "EVAL with clause\npower(0, X2, 0) :- >(X2, 0).\nand substitutionT1 -> 0,\nT2 -> T5,\nX2 -> T5,\nT3 -> 0" }, { "from": 4, "to": 18, "label": "EVAL-BACKTRACK" }, { "from": 17, "to": 19, "label": "IS ERROR" }, { "from": 17, "to": 783, "label": "ARITHCOMP SUCCESS" }, { "from": 17, "to": 784, "label": "ARITHCOMP FAIL" }, { "from": 18, "to": 2507, "label": "EVAL with clause\npower(X40, 0, 1) :- >(X40, 0).\nand substitutionT1 -> T23,\nX40 -> T23,\nT2 -> 0,\nT3 -> 1" }, { "from": 18, "to": 2508, "label": "EVAL-BACKTRACK" }, { "from": 783, "to": 785, "label": "SUCCESS" }, { "from": 784, "to": 2244, "label": "EVAL with clause\npower(X22, 0, 1) :- >(X22, 0).\nand substitutionX22 -> 0,\nT5 -> 0,\nT3 -> 1" }, { "from": 784, "to": 2245, "label": "EVAL-BACKTRACK" }, { "from": 785, "to": 786, "label": "EVAL with clause\npower(X4, 0, 1) :- >(X4, 0).\nand substitutionX4 -> 0,\nT5 -> 0,\nT3 -> 1" }, { "from": 785, "to": 787, "label": "EVAL-BACKTRACK" }, { "from": 786, "to": 793, "label": "ARITHCOMP FAIL" }, { "from": 787, "to": 1367, "label": "ONLY EVAL with clause\npower(X16, X17, X18) :- ','(>(X16, 0), ','(>(X17, 0), ','(is(X19, -(X17, 1)), ','(power(X16, X19, X20), is(X18, *(X20, X16)))))).\nand substitutionX16 -> 0,\nT5 -> T11,\nX17 -> T11,\nT3 -> T13,\nX18 -> T13,\nT12 -> T13" }, { "from": 793, "to": 794, "label": "ONLY EVAL with clause\npower(X8, X9, X10) :- ','(>(X8, 0), ','(>(X9, 0), ','(is(X11, -(X9, 1)), ','(power(X8, X11, X12), is(X10, *(X12, X8)))))).\nand substitutionX8 -> 0,\nX9 -> 0,\nT3 -> T8,\nX10 -> T8,\nT7 -> T8" }, { "from": 1367, "to": 2243, "label": "ARITHCOMP FAIL" }, { "from": 2244, "to": 2362, "label": "ARITHCOMP FAIL" }, { "from": 2245, "to": 2505, "label": "ONLY EVAL with clause\npower(X34, X35, X36) :- ','(>(X34, 0), ','(>(X35, 0), ','(is(X37, -(X35, 1)), ','(power(X34, X37, X38), is(X36, *(X38, X34)))))).\nand substitutionX34 -> 0,\nT5 -> T19,\nX35 -> T19,\nT3 -> T21,\nX36 -> T21,\nT20 -> T21" }, { "from": 2362, "to": 2363, "label": "ONLY EVAL with clause\npower(X26, X27, X28) :- ','(>(X26, 0), ','(>(X27, 0), ','(is(X29, -(X27, 1)), ','(power(X26, X29, X30), is(X28, *(X30, X26)))))).\nand substitutionX26 -> 0,\nX27 -> 0,\nT3 -> T16,\nX28 -> T16,\nT15 -> T16" }, { "from": 2363, "to": 2504, "label": "ARITHCOMP FAIL" }, { "from": 2505, "to": 2506, "label": "ARITHCOMP FAIL" }, { "from": 2507, "to": 2509, "label": "IS ERROR" }, { "from": 2507, "to": 2532, "label": "ARITHCOMP SUCCESS" }, { "from": 2507, "to": 2533, "label": "ARITHCOMP FAIL" }, { "from": 2508, "to": 2543, "label": "ONLY EVAL with clause\npower(X60, X61, X62) :- ','(>(X60, 0), ','(>(X61, 0), ','(is(X63, -(X61, 1)), ','(power(X60, X63, X64), is(X62, *(X64, X60)))))).\nand substitutionT1 -> T37,\nX60 -> T37,\nT2 -> T38,\nX61 -> T38,\nT3 -> T40,\nX62 -> T40,\nT39 -> T40" }, { "from": 2532, "to": 2534, "label": "SUCCESS" }, { "from": 2533, "to": 2539, "label": "ONLY EVAL with clause\npower(X52, X53, X54) :- ','(>(X52, 0), ','(>(X53, 0), ','(is(X55, -(X53, 1)), ','(power(X52, X55, X56), is(X54, *(X56, X52)))))).\nand substitutionT23 -> T31,\nX52 -> T31,\nX53 -> 0,\nT3 -> T33,\nX54 -> T33,\nT32 -> T33" }, { "from": 2534, "to": 2535, "label": "ONLY EVAL with clause\npower(X44, X45, X46) :- ','(>(X44, 0), ','(>(X45, 0), ','(is(X47, -(X45, 1)), ','(power(X44, X47, X48), is(X46, *(X48, X44)))))).\nand substitutionT23 -> T26,\nX44 -> T26,\nX45 -> 0,\nT3 -> T28,\nX46 -> T28,\nT27 -> T28" }, { "from": 2535, "to": 2536, "label": "ARITHCOMP SUCCESS" }, { "from": 2535, "to": 2537, "label": "ARITHCOMP FAIL" }, { "from": 2536, "to": 2538, "label": "ARITHCOMP FAIL" }, { "from": 2539, "to": 2540, "label": "ARITHCOMP SUCCESS" }, { "from": 2539, "to": 2541, "label": "ARITHCOMP FAIL" }, { "from": 2540, "to": 2542, "label": "ARITHCOMP FAIL" }, { "from": 2543, "to": 2544, "label": "IS ERROR" }, { "from": 2543, "to": 2545, "label": "ARITHCOMP SUCCESS" }, { "from": 2543, "to": 2546, "label": "ARITHCOMP FAIL" }, { "from": 2545, "to": 2547, "label": "IS ERROR" }, { "from": 2545, "to": 2548, "label": "ARITHCOMP SUCCESS" }, { "from": 2545, "to": 2549, "label": "ARITHCOMP FAIL" }, { "from": 2548, "to": 2596, "label": "\nX63 -> T41" }, { "from": 2596, "to": 2597, "label": "CASE" }, { "from": 2597, "to": 2598, "label": "PARALLEL" }, { "from": 2597, "to": 2599, "label": "PARALLEL" }, { "from": 2598, "to": 2600, "label": "EVAL with clause\npower(0, X69, 0) :- >(X69, 0).\nand substitutionT37 -> 0,\nT41 -> T46,\nX69 -> T46,\nX64 -> 0" }, { "from": 2598, "to": 2601, "label": "EVAL-BACKTRACK" }, { "from": 2599, "to": 2602, "label": "PARALLEL" }, { "from": 2599, "to": 2603, "label": "PARALLEL" }, { "from": 2602, "to": 2604, "label": "EVAL with clause\npower(X74, 0, 1) :- >(X74, 0).\nand substitutionT37 -> T51,\nX74 -> T51,\nT41 -> 0,\nX64 -> 1" }, { "from": 2602, "to": 2605, "label": "EVAL-BACKTRACK" }, { "from": 2603, "to": 2606, "label": "ONLY EVAL with clause\npower(X85, X86, X87) :- ','(>(X85, 0), ','(>(X86, 0), ','(is(X88, -(X86, 1)), ','(power(X85, X88, X89), is(X87, *(X89, X85)))))).\nand substitutionT37 -> T56,\nX85 -> T56,\nT41 -> T57,\nX86 -> T57,\nX64 -> X90,\nX87 -> X90" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Triples: Clauses: Afs: ---------------------------------------- (3) TPisEmptyProof (EQUIVALENT) There are no more dependency triples. Hence, the dependency triple problem trivially terminates. ---------------------------------------- (4) YES