/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern test_fun(g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToDTProblemTransformerProof [SOUND, 79 ms] (2) TRIPLES (3) TPisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Clauses: test_fun(X, Y) :- loop(X, Y, 0). loop(X, Y, C) :- ','(=\=(X, Y), loop_body(X, Y, C)). loop(X, Y, C) :- =:=(X, Y). loop_body(X, Y, C) :- ','(>(X, Y), ','(!, ','(is(Y1, +(Y, 1)), ','(is(C1, +(C, 1)), loop(X, Y1, C1))))). loop_body(X, Y, C) :- ','(=<(X, Y), ','(!, ','(is(X1, +(X, 1)), ','(is(C1, +(C, 1)), loop(X1, Y, C1))))). Query: test_fun(g,g) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 3, "program": { "directives": [], "clauses": [ [ "(test_fun X Y)", "(loop X Y (0))" ], [ "(loop X Y C)", "(',' (=\\= X Y) (loop_body X Y C))" ], [ "(loop X Y C)", "(=:= X Y)" ], [ "(loop_body X Y C)", "(',' (> X Y) (',' (!) (',' (is Y1 (+ Y (1))) (',' (is C1 (+ C (1))) (loop X Y1 C1)))))" ], [ "(loop_body X Y C)", "(',' (=< X Y) (',' (!) (',' (is X1 (+ X (1))) (',' (is C1 (+ C (1))) (loop X1 Y C1)))))" ] ] }, "graph": { "nodes": { "3266": { "goal": [{ "clause": -1, "scope": -1, "term": "(true)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T97", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T98", "type": "PlainIntegerVariable" }, "operation": "=" }] }, "ground": [ "T97", "T98" ], "free": [], "exprvars": [ "T97", "T98" ] } }, "type": "Nodes", "470": { "goal": [ { "clause": 3, "scope": 3, "term": "(loop_body T15 T16 (0))" }, { "clause": 4, "scope": 3, "term": "(loop_body T15 T16 (0))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }] }, "ground": [ "T16", "T15" ], "free": [], "exprvars": [ "T16", "T15" ] } }, "475": { "goal": [{ "clause": 3, "scope": 3, "term": "(loop_body T15 T16 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }] }, "ground": [ "T16", "T15" ], "free": [], "exprvars": [ "T16", "T15" ] } }, "476": { "goal": [{ "clause": 4, "scope": 3, "term": "(loop_body T15 T16 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }] }, "ground": [ "T16", "T15" ], "free": [], "exprvars": [ "T16", "T15" ] } }, "3236": { "goal": [{ "clause": -1, "scope": -1, "term": "(loop T64 T63 T65)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T64", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T62", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T65", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }, { "lhs": { "name": "T63", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }, { "lhs": { "name": "T62", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T63", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T64", "T63", "T62", "T65" ], "free": [ "X85", "X86" ], "exprvars": [ "T64", "T63", "T62", "T16", "T65", "T15" ] } }, "1079": { "goal": [{ "clause": -1, "scope": -1, "term": "(loop T27 T29 T30)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T29", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T28", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T30", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }, { "lhs": { "name": "T28", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }, { "lhs": { "name": "T28", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T27", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T30", "T29", "T28", "T27" ], "free": [ "X45", "X46" ], "exprvars": [ "T30", "T29", "T28", "T16", "T27", "T15" ] } }, "3235": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X86 (+ (0) (1))) (loop T64 T63 X86))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T64", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T62", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T15", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }, { "lhs": { "name": "T63", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }, { "lhs": { "name": "T62", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T63", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T64", "T63", "T62" ], "free": [ "X85", "X86" ], "exprvars": [ "T64", "T63", "T62", "T16", "T15" ] } }, "3257": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { 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}, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }, { "lhs": { "name": "T28", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T16", "type": "PlainIntegerVariable" }, "operation": "!=" }, { "lhs": { "name": "T28", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T27", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T30", "T29", "T27" ], "free": [], "exprvars": [ "T30", "T29", "T28", "T16", "T27", "T15" ] } }, "3267": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "name": "T97", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T98", "type": "PlainIntegerVariable" }, "operation": "!=" }] }, "ground": [ "T97", "T98" ], "free": [], "exprvars": [ "T97", "T98" ] } }, "9": { "goal": [{ "clause": -1, "scope": -1, "term": "(loop T5 T6 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T5", "T6" ], "free": [], "exprvars": [] } } }, "edges": [ { "from": 3, "to": 4, "label": "CASE" }, { "from": 4, "to": 9, "label": "ONLY EVAL with clause\ntest_fun(X4, X5) :- loop(X4, X5, 0).\nand substitutionT1 -> T5,\nX4 -> T5,\nT2 -> T6,\nX5 -> T6" }, { "from": 9, "to": 10, "label": "CASE" }, { "from": 10, "to": 11, "label": "PARALLEL" }, { "from": 10, "to": 12, "label": "PARALLEL" }, { "from": 11, "to": 13, "label": "ONLY EVAL with clause\nloop(X18, X19, X20) :- ','(=\\=(X18, X19), loop_body(X18, X19, X20)).\nand substitutionT5 -> T15,\nX18 -> T15,\nT6 -> T16,\nX19 -> T16,\nX20 -> 0" }, { "from": 12, "to": 3256, "label": "ONLY EVAL with clause\nloop(X120, X121, X122) :- =:=(X120, X121).\nand substitutionT5 -> T97,\nX120 -> T97,\nT6 -> T98,\nX121 -> T98,\nX122 -> 0" }, { "from": 13, "to": 14, "label": "IS ERROR" }, { "from": 13, "to": 460, "label": "ARITHCOMP SUCCESS" }, { "from": 13, "to": 461, "label": "ARITHCOMP FAIL" }, { "from": 460, "to": 470, "label": "CASE" }, { "from": 470, "to": 475, "label": "PARALLEL" }, { "from": 470, "to": 476, "label": "PARALLEL" }, { "from": 475, "to": 489, "label": "ONLY EVAL with clause\nloop_body(X42, X43, X44) :- ','(>(X42, X43), ','(!_3, ','(is(X45, +(X43, 1)), ','(is(X46, +(X44, 1)), loop(X42, X45, X46))))).\nand substitutionT15 -> T27,\nX42 -> T27,\nT16 -> T28,\nX43 -> T28,\nX44 -> 0" }, { "from": 476, "to": 3229, "label": "ONLY EVAL with clause\nloop_body(X82, X83, X84) :- ','(=<(X82, X83), ','(!_3, ','(is(X85, +(X82, 1)), ','(is(X86, +(X84, 1)), loop(X85, X83, X86))))).\nand substitutionT15 -> T62,\nX82 -> T62,\nT16 -> T63,\nX83 -> T63,\nX84 -> 0" }, { "from": 489, "to": 712, "label": "ARITHCOMP SUCCESS" }, { "from": 489, "to": 713, "label": "ARITHCOMP FAIL" }, { "from": 712, "to": 714, "label": "CUT" }, { "from": 714, "to": 1003, "label": "\nX45 -> T29" }, { "from": 1003, "to": 1079, "label": "\nX46 -> T30" }, { "from": 1079, "to": 1166, "label": "CASE" }, { "from": 1166, "to": 1266, "label": "PARALLEL" }, { "from": 1166, "to": 1269, "label": "PARALLEL" }, { "from": 1266, "to": 1352, "label": "ONLY EVAL with clause\nloop(X62, X63, X64) :- ','(=\\=(X62, X63), loop_body(X62, X63, X64)).\nand substitutionT27 -> T46,\nX62 -> T46,\nT29 -> T47,\nX63 -> T47,\nT30 -> T48,\nX64 -> T48" }, { "from": 1269, "to": 3005, "label": "ONLY EVAL with clause\nloop(X71, X72, X73) :- =:=(X71, X72).\nand substitutionT27 -> T55,\nX71 -> T55,\nT29 -> T56,\nX72 -> T56,\nT30 -> T57,\nX73 -> T57" }, { "from": 3229, "to": 3232, "label": "ARITHCOMP SUCCESS" }, { "from": 3229, "to": 3233, "label": "ARITHCOMP FAIL" }, { "from": 3232, "to": 3234, "label": "CUT" }, { "from": 3234, "to": 3235, "label": "\nX85 -> T64" }, { "from": 3235, "to": 3236, "label": "\nX86 -> T65" }, { "from": 3236, "to": 3247, "label": "CASE" }, { "from": 3247, "to": 3248, "label": "PARALLEL" }, { "from": 3247, "to": 3249, "label": "PARALLEL" }, { "from": 3248, "to": 3250, "label": "ONLY EVAL with clause\nloop(X102, X103, X104) :- ','(=\\=(X102, X103), loop_body(X102, X103, X104)).\nand substitutionT64 -> T81,\nX102 -> T81,\nT63 -> T82,\nX103 -> T82,\nT65 -> T83,\nX104 -> T83" }, { "from": 3249, "to": 3255, "label": "ONLY EVAL with clause\nloop(X111, X112, X113) :- =:=(X111, X112).\nand substitutionT64 -> T90,\nX111 -> T90,\nT63 -> T91,\nX112 -> T91,\nT65 -> T92,\nX113 -> T92" }, { "from": 3256, "to": 3257, "label": "IS ERROR" }, { "from": 3256, "to": 3266, "label": "ARITHCOMP SUCCESS" }, { "from": 3256, "to": 3267, "label": "ARITHCOMP FAIL" }, { "from": 3266, "to": 3268, "label": "SUCCESS" } ], "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