/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern test_fun(g,g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToDTProblemTransformerProof [SOUND, 99 ms] (2) TRIPLES (3) TPisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Clauses: test_fun(X, Y, Z) :- loop1(X, Y, Z, 0). loop1(X, Y, Z, C) :- ','(>(X, Z), loop2(X, Y, Z, C)). loop1(X, Y, Z, C) :- =<(X, Z). loop2(X, Y, Z, C) :- ','(>(Y, Z), ','(is(Y1, -(Y, 1)), ','(is(C1, +(C, 1)), loop2(X, Y1, Z, C1)))). loop2(X, Y, Z, C) :- ','(=<(Y, Z), ','(is(X1, -(X, 1)), ','(is(C1, +(C, 1)), loop1(X1, Y, Z, C1)))). Query: test_fun(g,g,g) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 1, "program": { "directives": [], "clauses": [ [ "(test_fun X Y Z)", "(loop1 X Y Z (0))" ], [ "(loop1 X Y Z C)", "(',' (> X Z) (loop2 X Y Z C))" ], [ "(loop1 X Y Z C)", "(=< X Z)" ], [ "(loop2 X Y Z C)", "(',' (> Y Z) (',' (is Y1 (- Y (1))) (',' (is C1 (+ C (1))) (loop2 X Y1 Z C1))))" ], [ "(loop2 X Y Z C)", "(',' (=< Y Z) (',' (is X1 (- X (1))) (',' (is C1 (+ C (1))) (loop1 X1 Y Z C1))))" ] ] }, "graph": { "nodes": { "3244": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T24", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T22", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T87", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T22", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T88", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T89", "type": "PlainIntegerVariable" }, "operation": ">" } ] }, "ground": [ "T89", "T88", "T87" ], "free": [ "X122", "X123" ], "exprvars": [ "T24", "T89", "T22", "T88", "T87" ] } }, "3243": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X122 (- T87 (1))) (',' (is X123 (+ (0) (1))) (loop1 X122 T88 T89 X123)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T24", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T22", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T87", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T22", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T88", "type": 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"PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T24", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T22", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T40", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T22", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T42", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T41", "type": "PlainIntegerVariable" }, "operation": ">=" } ] }, "ground": [ "T42", "T41", "T40" ], "free": [ "X58", "X59" ], "exprvars": [ "T42", "T41", "T24", "T40", "T22" ] } }, "3238": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "3215": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X58 (- T41 (1))) (',' (is X59 (+ (0) (1))) (loop2 T40 X58 T42 X59)))" }], 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"name": "T22", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T22", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T88", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T89", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T126", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T89", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T124", "T126" ], "free": [], "exprvars": [ "T126", "T91", "T125", "T24", "T127", "T90", "T89", "T22", "T88", "T87", "T124" ] } }, "8": { "goal": [ { "clause": 1, "scope": 2, "term": "(loop1 T7 T8 T9 (0))" }, { "clause": 2, "scope": 2, "term": "(loop1 T7 T8 T9 (0))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T7", "T8", "T9" ], "free": [], "exprvars": [] } } }, "edges": [ { "from": 1, "to": 5, "label": "CASE" }, { "from": 5, "to": 7, "label": "ONLY EVAL with clause\ntest_fun(X5, X6, X7) :- loop1(X5, X6, X7, 0).\nand substitutionT1 -> T7,\nX5 -> T7,\nT2 -> T8,\nX6 -> T8,\nT3 -> T9,\nX7 -> T9" }, { "from": 7, "to": 8, "label": "CASE" }, { "from": 8, "to": 10, "label": "PARALLEL" }, { "from": 8, "to": 11, "label": "PARALLEL" }, { "from": 10, "to": 15, "label": "ONLY EVAL with clause\nloop1(X24, X25, X26, X27) :- ','(>(X24, X26), loop2(X24, X25, X26, X27)).\nand substitutionT7 -> T22,\nX24 -> T22,\nT8 -> T23,\nX25 -> T23,\nT9 -> T24,\nX26 -> T24,\nX27 -> 0" }, { "from": 11, "to": 3270, "label": "ONLY EVAL with clause\nloop1(X168, X169, X170, X171) :- =<(X168, X170).\nand substitutionT7 -> T134,\nX168 -> T134,\nT8 -> T135,\nX169 -> T135,\nT9 -> T136,\nX170 -> T136,\nX171 -> 0" }, { "from": 15, "to": 16, "label": "IS ERROR" }, { "from": 15, "to": 3104, "label": "ARITHCOMP SUCCESS" }, { "from": 15, "to": 3106, "label": "ARITHCOMP FAIL" }, { "from": 3104, "to": 3107, "label": "CASE" }, { "from": 3107, "to": 3109, "label": "PARALLEL" }, { "from": 3107, "to": 3110, "label": "PARALLEL" }, { "from": 3109, "to": 3113, "label": "ONLY EVAL with clause\nloop2(X54, X55, X56, X57) :- ','(>(X55, X56), ','(is(X58, -(X55, 1)), ','(is(X59, +(X57, 1)), loop2(X54, X58, X56, X59)))).\nand substitutionT22 -> T40,\nX54 -> T40,\nT23 -> T41,\nX55 -> T41,\nT24 -> T42,\nX56 -> T42,\nX57 -> 0" }, { "from": 3110, "to": 3237, "label": "ONLY EVAL with clause\nloop2(X118, X119, X120, X121) :- ','(=<(X119, X120), ','(is(X122, -(X118, 1)), ','(is(X123, +(X121, 1)), loop1(X122, X119, X120, X123)))).\nand substitutionT22 -> T87,\nX118 -> T87,\nT23 -> T88,\nX119 -> T88,\nT24 -> T89,\nX120 -> T89,\nX121 -> 0" }, { "from": 3113, "to": 3114, "label": "IS ERROR" }, { "from": 3113, "to": 3215, "label": "ARITHCOMP SUCCESS" }, { "from": 3113, "to": 3216, "label": "ARITHCOMP FAIL" }, { "from": 3215, "to": 3217, "label": "\nX58 -> T43" }, { "from": 3217, "to": 3218, "label": "\nX59 -> T44" }, { "from": 3218, "to": 3223, "label": "CASE" }, { "from": 3223, "to": 3225, "label": "PARALLEL" }, { "from": 3223, "to": 3226, "label": "PARALLEL" }, { "from": 3225, "to": 3229, "label": "ONLY EVAL with clause\nloop2(X86, X87, X88, X89) :- ','(>(X87, X88), ','(is(X90, -(X87, 1)), ','(is(X91, +(X89, 1)), loop2(X86, X90, X88, X91)))).\nand substitutionT40 -> T65,\nX86 -> T65,\nT43 -> T66,\nX87 -> T66,\nT42 -> T67,\nX88 -> T67,\nT44 -> T68,\nX89 -> T68" }, { "from": 3226, "to": 3234, "label": "ONLY EVAL with clause\nloop2(X102, X103, X104, X105) :- ','(=<(X103, X104), ','(is(X106, -(X102, 1)), ','(is(X107, +(X105, 1)), loop1(X106, X103, X104, X107)))).\nand substitutionT40 -> T77,\nX102 -> T77,\nT43 -> T78,\nX103 -> T78,\nT42 -> T79,\nX104 -> T79,\nT44 -> T80,\nX105 -> T80" }, { "from": 3237, "to": 3238, "label": "IS ERROR" }, { "from": 3237, "to": 3243, "label": "ARITHCOMP SUCCESS" }, { "from": 3237, "to": 3244, "label": "ARITHCOMP FAIL" }, { "from": 3243, "to": 3245, "label": "\nX122 -> T90" }, { "from": 3245, "to": 3246, "label": "\nX123 -> T91" }, { "from": 3246, "to": 3247, "label": "CASE" }, { "from": 3247, "to": 3256, "label": "PARALLEL" }, { "from": 3247, "to": 3257, "label": "PARALLEL" }, { "from": 3256, "to": 3258, "label": "ONLY EVAL with clause\nloop1(X144, X145, X146, X147) :- ','(>(X144, X146), loop2(X144, X145, X146, X147)).\nand substitutionT90 -> T112,\nX144 -> T112,\nT88 -> T113,\nX145 -> T113,\nT89 -> T114,\nX146 -> T114,\nT91 -> T115,\nX147 -> T115" }, { "from": 3257, "to": 3267, "label": "ONLY EVAL with clause\nloop1(X156, X157, X158, X159) :- =<(X156, X158).\nand substitutionT90 -> T124,\nX156 -> T124,\nT88 -> T125,\nX157 -> T125,\nT89 -> T126,\nX158 -> T126,\nT91 -> T127,\nX159 -> T127" }, { "from": 3270, "to": 3271, "label": "IS ERROR" }, { "from": 3270, "to": 3274, "label": "ARITHCOMP SUCCESS" }, { "from": 3270, "to": 3275, "label": "ARITHCOMP FAIL" }, { "from": 3274, "to": 3276, "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