/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern fib1(a,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToDTProblemTransformerProof [SOUND, 75 ms] (2) TRIPLES (3) TPisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (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(a,g) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "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": { "25": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "type": "Nodes", "2768": { "goal": [{ "clause": 2, "scope": 3, "term": "(forwardfib T22 T21 (1) T23 T20)" }], "kb": { "nonunifying": [], "intvars": {}, 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"arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T23", "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": "T21", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T20", "T23", "T22", "T21" ], "free": [], "exprvars": [ "T23", "T22", "T21" ] } }, "2930": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (< T90 T91) (',' (is X128 (+ T90 (1))) (',' (is X129 (+ T92 T93)) (forwardfib X128 T91 T93 X129 T94))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T22", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T23", "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": { "name": "T54", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T50", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T55", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "name": "T52", "type": "PlainIntegerVariable" } ], "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": { "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": { "arguments": [ { "name": "T50", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T50", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "name": "T92", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "1" }, { "name": "T52", "type": "PlainIntegerVariable" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "2" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T51", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T50", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T51", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T21", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T21", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T91", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T51", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T90", "T91", "T92", "T93", "T94" ], "free": [ "X128", "X129" ], "exprvars": [ "T92", "T91", "T52", "T90", "T51", "T23", "T50", "T22", "T55", "T93", "T21", "T54" ] } }, "7": { "goal": [{ "clause": -1, "scope": -1, "term": "(forwardfib (2) T7 (1) (1) T6)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": [], "exprvars": [] } }, "2794": { "goal": [{ "clause": -1, "scope": -1, "term": "(>= T39 T40)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T22", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T23", "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": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T39", "T40" ], "free": [], "exprvars": [ "T41", "T40", "T23", "T39", "T22", "T21" ] } }, "8": { "goal": [ { "clause": 1, "scope": 2, "term": "(forwardfib (2) T7 (1) (1) T6)" }, { "clause": 2, "scope": 2, "term": "(forwardfib (2) T7 (1) (1) T6)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": [], "exprvars": [] } }, "2737": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X43 (+ (1) (1))) (forwardfib T22 T21 (1) X43 T20))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T22", "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": "T21", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T20", "T22", "T21" ], "free": [ "X42", "X43" ], "exprvars": [ "T22", "T21" ] } }, "21": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2857": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (< T50 T51) (',' (is X85 (+ T50 (1))) (',' (is X86 (+ (1) T52)) (forwardfib X85 T51 T52 X86 T53))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T22", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "2" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T23", "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": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T51", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T50", "T51", "T52", "T53" ], "free": [ "X85", "X86" ], "exprvars": [ "T52", "T51", "T23", "T50", "T22", "T21" ] } } }, "edges": [ { "from": 1, "to": 3, "label": "CASE" }, { "from": 3, "to": 7, "label": "ONLY EVAL with clause\nfib1(X3, X4) :- forwardfib(2, X3, 1, 1, X4).\nand substitutionT1 -> T7,\nX3 -> T7,\nT2 -> T6,\nX4 -> T6,\nT5 -> T7" }, { "from": 7, "to": 8, "label": "CASE" }, { "from": 8, "to": 10, "label": "PARALLEL" }, { "from": 8, "to": 11, "label": "PARALLEL" }, { "from": 10, "to": 19, "label": "EVAL with clause\nforwardfib(X21, X22, X23, X24, X24) :- >=(X21, X22).\nand substitutionX21 -> 2,\nT7 -> T13,\nX22 -> T13,\nX23 -> 1,\nX24 -> 1,\nT6 -> 1,\nT12 -> T13" }, { "from": 10, "to": 21, "label": "EVAL-BACKTRACK" }, { "from": 11, "to": 2626, "label": "ONLY EVAL with clause\nforwardfib(X37, X38, X39, X40, X41) :- ','(<(X37, X38), ','(is(X42, +(X37, 1)), ','(is(X43, +(X39, X40)), forwardfib(X42, X38, X40, X43, X41)))).\nand substitutionX37 -> 2,\nT7 -> T21,\nX38 -> T21,\nX39 -> 1,\nX40 -> 1,\nT6 -> T20,\nX41 -> T20,\nT19 -> T21" }, { "from": 19, "to": 25, "label": "IS ERROR" }, { "from": 19, "to": 2621, "label": "ARITHCOMP SUCCESS" }, { "from": 19, "to": 2622, "label": "ARITHCOMP FAIL" }, { "from": 2621, "to": 2623, "label": "SUCCESS" }, { "from": 2626, "to": 2627, "label": "IS ERROR" }, { "from": 2626, "to": 2721, "label": "ARITHCOMP SUCCESS" }, { "from": 2626, "to": 2723, "label": "ARITHCOMP FAIL" }, { "from": 2721, "to": 2737, "label": "\nX42 -> T22" }, { "from": 2737, "to": 2742, "label": "\nX43 -> T23" }, { "from": 2742, "to": 2754, "label": "CASE" }, { "from": 2754, "to": 2767, "label": "PARALLEL" }, { "from": 2754, "to": 2768, "label": "PARALLEL" }, { "from": 2767, "to": 2794, "label": "EVAL with clause\nforwardfib(X64, X65, X66, X67, X67) :- >=(X64, X65).\nand substitutionT22 -> T39,\nX64 -> T39,\nT21 -> T40,\nX65 -> T40,\nX66 -> 1,\nT23 -> T41,\nX67 -> T41,\nT20 -> T41" }, { "from": 2767, "to": 2799, "label": "EVAL-BACKTRACK" }, { "from": 2768, "to": 2857, "label": "ONLY EVAL with clause\nforwardfib(X80, X81, X82, X83, X84) :- ','(<(X80, X81), ','(is(X85, +(X80, 1)), ','(is(X86, +(X82, X83)), forwardfib(X85, X81, X83, X86, X84)))).\nand substitutionT22 -> T50,\nX80 -> T50,\nT21 -> T51,\nX81 -> T51,\nX82 -> 1,\nT23 -> T52,\nX83 -> T52,\nT20 -> T53,\nX84 -> T53" }, { "from": 2794, "to": 2854, "label": "ARITHCOMP SUCCESS" }, { "from": 2794, "to": 2855, "label": "ARITHCOMP FAIL" }, { "from": 2854, "to": 2856, "label": "SUCCESS" }, { "from": 2857, "to": 2920, "label": "ARITHCOMP SUCCESS" }, { "from": 2857, "to": 2921, "label": "ARITHCOMP FAIL" }, { "from": 2920, "to": 2922, "label": "\nX85 -> T54" }, { "from": 2922, "to": 2923, "label": "\nX86 -> T55" }, { "from": 2923, "to": 2924, "label": "CASE" }, { "from": 2924, "to": 2925, "label": "PARALLEL" }, { "from": 2924, "to": 2926, "label": "PARALLEL" }, { "from": 2925, "to": 2927, "label": "EVAL with clause\nforwardfib(X107, X108, X109, X110, X110) :- >=(X107, X108).\nand substitutionT54 -> T76,\nX107 -> T76,\nT51 -> T77,\nX108 -> T77,\nT52 -> T78,\nX109 -> T78,\nT55 -> T79,\nX110 -> T79,\nT53 -> T79" }, { "from": 2925, "to": 2928, "label": "EVAL-BACKTRACK" }, { "from": 2926, "to": 2930, "label": "ONLY EVAL with clause\nforwardfib(X123, X124, X125, X126, X127) :- ','(<(X123, X124), ','(is(X128, +(X123, 1)), ','(is(X129, +(X125, X126)), forwardfib(X128, X124, X126, X129, X127)))).\nand substitutionT54 -> T90,\nX123 -> T90,\nT51 -> T91,\nX124 -> T91,\nT52 -> T92,\nX125 -> T92,\nT55 -> T93,\nX126 -> T93,\nT53 -> T94,\nX127 -> T94" } ], "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