/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern fib1(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 26 ms] (2) TRUE ---------------------------------------- (0) Obligation: Clauses: fib1(N, F) :- forwardfib(2, N, 1, 1, F). forwardfib(M, N, F1, F2, F2) :- >=(M, N). forwardfib(M, N, F1, F2, F) :- ','(<(M, N), ','(is(NextM, +(M, 1)), ','(is(NextF2, +(F1, F2)), forwardfib(NextM, N, F2, NextF2, F)))). fib2(1, 1) :- !. fib2(2, 1) :- !. fib2(N, F) :- ','(>(N, 2), ','(is(N1, -(N, 1)), ','(fib2(N1, F1), ','(is(N2, -(N, 2)), ','(fib2(N2, F2), is(F, +(F1, F2))))))). Query: fib1(g,a) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 1, "program": { "directives": [], "clauses": [ [ "(fib1 N F)", "(forwardfib (2) N (1) (1) F)" ], [ "(forwardfib M N F1 F2 F2)", "(>= M N)" ], [ "(forwardfib M N F1 F2 F)", "(',' (< M N) (',' (is NextM (+ M (1))) (',' (is NextF2 (+ F1 F2)) (forwardfib NextM N F2 NextF2 F))))" ], [ "(fib2 (1) (1))", "(!)" ], [ "(fib2 (2) (1))", "(!)" ], [ "(fib2 N F)", "(',' (> N (2)) (',' (is N1 (- N (1))) (',' (fib2 N1 F1) (',' (is N2 (- N (2))) (',' (fib2 N2 F2) (is F (+ F1 F2)))))))" ] ] }, "graph": { "nodes": { "22": { "goal": [ { "clause": 1, "scope": 2, "term": "(forwardfib (2) T9 (1) (1) T11)" }, { "clause": 2, "scope": 2, "term": "(forwardfib (2) T9 (1) (1) T11)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T9"], "free": [], "exprvars": [] } }, "23": { "goal": [{ "clause": 1, "scope": 2, "term": "(forwardfib (2) T9 (1) (1) T11)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { 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"PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T23", "T27", "T26" ], "free": [], "exprvars": [ "T23", "T27", "T26" ] } }, "2733": { "goal": [{ "clause": -1, "scope": -1, "term": "(forwardfib T26 T23 (1) T27 T25)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T26", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T27", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T23", "T27", "T26" ], "free": [ "X52", "X53" ], "exprvars": [ "T23", "T27", "T26" ] } }, "2732": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X53 (+ (1) (1))) (forwardfib T26 T23 (1) X53 T25))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T26", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T23", "T26" ], "free": [ "X52", "X53" ], "exprvars": [ "T23", "T26" ] } }, "2731": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": ">=" }] }, "ground": ["T23"], "free": [ "X52", "X53" ], "exprvars": ["T23"] } }, "5": { "goal": [{ "clause": 0, "scope": 1, "term": "(fib1 T1 T2)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": [], "exprvars": [] } }, "2730": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X52 (+ (2) (1))) (',' (is X53 (+ (1) (1))) (forwardfib X52 T23 (1) X53 T25)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" }] }, "ground": ["T23"], "free": [ "X52", "X53" ], "exprvars": ["T23"] } }, "2795": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T26", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T27", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T44", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T44", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T43", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [], "free": [], "exprvars": [ "T23", "T45", "T44", "T27", "T43", "T26" ] } }, "2794": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T26", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T27", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T44", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T44", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T43", "type": "PlainIntegerVariable" }, "operation": ">" } ] }, "ground": [ "T44", "T43" ], "free": [], "exprvars": [ "T23", "T45", "T44", "T27", "T43", "T26" ] } }, "8": { "goal": [{ "clause": -1, "scope": -1, "term": "(forwardfib (2) T9 (1) (1) T11)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T9"], "free": [], "exprvars": [] } }, "2738": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T26", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T27", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [], "free": [], "exprvars": [ "T23", "T27", "T26" ] } }, "2737": { "goal": [{ "clause": -1, "scope": -1, "term": "(>= T43 T44)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T26", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T27", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T44", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T43", "T44" ], "free": [], "exprvars": [ "T23", "T45", "T44", "T27", "T43", "T26" ] } }, "1526": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2736": { "goal": [{ "clause": 2, "scope": 3, "term": "(forwardfib T26 T23 (1) T27 T25)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T26", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T27", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T23", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T23", "T27", "T26" ], "free": [], "exprvars": [ "T23", "T27", "T26" ] } } }, "edges": [ { "from": 1, "to": 5, "label": "CASE" }, { "from": 5, "to": 8, "label": "ONLY EVAL with clause\nfib1(X9, X10) :- forwardfib(2, X9, 1, 1, X10).\nand substitutionT1 -> T9,\nX9 -> T9,\nT2 -> T11,\nX10 -> T11,\nT10 -> T11" }, { "from": 8, "to": 22, "label": "CASE" }, { "from": 22, "to": 23, "label": "PARALLEL" }, { "from": 22, "to": 24, "label": "PARALLEL" }, { "from": 23, "to": 25, "label": "EVAL with clause\nforwardfib(X31, X32, X33, X34, X34) :- >=(X31, X32).\nand substitutionX31 -> 2,\nT9 -> T17,\nX32 -> T17,\nX33 -> 1,\nX34 -> 1,\nT11 -> 1" }, { "from": 23, "to": 26, "label": "EVAL-BACKTRACK" }, { "from": 24, "to": 1516, "label": "ONLY EVAL with clause\nforwardfib(X47, X48, X49, X50, X51) :- ','(<(X47, X48), ','(is(X52, +(X47, 1)), ','(is(X53, +(X49, X50)), forwardfib(X52, X48, X50, X53, X51)))).\nand substitutionX47 -> 2,\nT9 -> T23,\nX48 -> T23,\nX49 -> 1,\nX50 -> 1,\nT11 -> T25,\nX51 -> T25,\nT24 -> T25" }, { "from": 25, "to": 27, "label": "IS ERROR" }, { "from": 25, "to": 1376, "label": "ARITHCOMP SUCCESS" }, { "from": 25, "to": 1378, "label": "ARITHCOMP FAIL" }, { "from": 1376, "to": 1381, "label": "SUCCESS" }, { "from": 1516, "to": 1526, "label": "IS ERROR" }, { "from": 1516, "to": 2730, "label": "ARITHCOMP SUCCESS" }, { "from": 1516, "to": 2731, "label": "ARITHCOMP FAIL" }, { "from": 2730, "to": 2732, "label": "\nX52 -> T26" }, { "from": 2732, "to": 2733, "label": "\nX53 -> T27" }, { "from": 2733, "to": 2734, "label": "CASE" }, { "from": 2734, "to": 2735, "label": "PARALLEL" }, { "from": 2734, "to": 2736, "label": "PARALLEL" }, { "from": 2735, "to": 2737, "label": "EVAL with clause\nforwardfib(X74, X75, X76, X77, X77) :- >=(X74, X75).\nand substitutionT26 -> T43,\nX74 -> T43,\nT23 -> T44,\nX75 -> T44,\nX76 -> 1,\nT27 -> T45,\nX77 -> T45,\nT25 -> T45" }, { "from": 2735, "to": 2738, "label": "EVAL-BACKTRACK" }, { "from": 2736, "to": 2800, "label": "ONLY EVAL with clause\nforwardfib(X90, X91, X92, X93, X94) :- ','(<(X90, X91), ','(is(X95, +(X90, 1)), ','(is(X96, +(X92, X93)), forwardfib(X95, X91, X93, X96, X94)))).\nand substitutionT26 -> T55,\nX90 -> T55,\nT23 -> T56,\nX91 -> T56,\nX92 -> 1,\nT27 -> T57,\nX93 -> T57,\nT25 -> T59,\nX94 -> T59,\nT58 -> T59" }, { "from": 2737, "to": 2793, "label": "ARITHCOMP SUCCESS" }, { "from": 2737, "to": 2794, "label": "ARITHCOMP FAIL" }, { "from": 2793, "to": 2795, "label": "SUCCESS" }, { "from": 2800, "to": 2801, "label": "ARITHCOMP SUCCESS" }, { "from": 2800, "to": 2802, "label": "ARITHCOMP FAIL" }, { "from": 2801, "to": 2803, "label": "\nX95 -> T60" }, { "from": 2803, "to": 2804, "label": "\nX96 -> T61" }, { "from": 2804, "to": 2805, "label": "CASE" }, { "from": 2805, "to": 2806, "label": "PARALLEL" }, { "from": 2805, "to": 2807, "label": "PARALLEL" }, { "from": 2806, "to": 2808, "label": "EVAL with clause\nforwardfib(X117, X118, X119, X120, X120) :- >=(X117, X118).\nand substitutionT60 -> T82,\nX117 -> T82,\nT56 -> T83,\nX118 -> T83,\nT57 -> T84,\nX119 -> T84,\nT61 -> T85,\nX120 -> T85,\nT59 -> T85" }, { "from": 2806, "to": 2809, "label": "EVAL-BACKTRACK" }, { "from": 2807, "to": 2828, "label": "ONLY EVAL with clause\nforwardfib(X133, X134, X135, X136, X137) :- ','(<(X133, X134), ','(is(X138, +(X133, 1)), ','(is(X139, +(X135, X136)), forwardfib(X138, X134, X136, X139, X137)))).\nand substitutionT60 -> T97,\nX133 -> T97,\nT56 -> T98,\nX134 -> T98,\nT57 -> T99,\nX135 -> T99,\nT61 -> T100,\nX136 -> T100,\nT59 -> T102,\nX137 -> T102,\nT101 -> T102" } ], "type": "Graph" } } ---------------------------------------- (2) TRUE