/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern list(g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToDTProblemTransformerProof [SOUND, 0 ms] (2) TRIPLES (3) TPisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Clauses: list([]). list(X) :- ','(no(empty(X)), ','(tail(X, T), list(T))). tail([], []). tail(.(X, Xs), Xs). empty(X). no(X) :- ','(X, ','(!, failure(a))). no(X1). failure(b). Query: list(g) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 1, "program": { "directives": [], "clauses": [ [ "(list ([]))", null ], [ "(list X)", "(',' (no (empty X)) (',' (tail X T) (list T)))" ], [ "(tail ([]) ([]))", null ], [ "(tail (. X Xs) Xs)", null ], [ "(empty X)", null ], [ "(no X)", "(',' X (',' (!) (failure (a))))" ], [ "(no X1)", null ], [ "(failure (b))", null ] ] }, "graph": { "nodes": { "33": { "goal": [{ "clause": 7, "scope": 5, "term": "(',' (failure (a)) (',' (tail ([]) X4) (list X4)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X4"], "exprvars": [] } }, "23": { "goal": [ { "clause": -1, "scope": -1, "term": "(',' (empty ([])) (',' (',' (!_2) (failure (a))) (',' (tail ([]) X4) (list X4))))" }, { "clause": -1, "scope": 3, "term": null }, { "clause": 6, "scope": 2, "term": "(',' (no (empty ([]))) (',' (tail ([]) X4) (list X4)))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X4"], "exprvars": [] } }, "34": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "13": { "goal": [ { "clause": -1, "scope": -1, "term": "(true)" }, { "clause": 1, "scope": 1, "term": "(list ([]))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "35": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (no (empty T3)) (',' (tail T3 X13) (list X13)))" }], "kb": { "nonunifying": [[ "(list T3)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T3"], "free": ["X13"], "exprvars": [] } }, "14": { "goal": [{ "clause": 1, "scope": 1, "term": "(list T1)" }], "kb": { "nonunifying": [[ "(list T1)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": [], "exprvars": [] } }, "25": { "goal": [ { "clause": 4, "scope": 4, "term": "(',' (empty ([])) (',' (',' (!_2) (failure (a))) (',' (tail ([]) X4) (list X4))))" }, { "clause": -1, "scope": 4, "term": null }, { "clause": -1, "scope": 3, "term": null }, { "clause": 6, "scope": 2, "term": "(',' (no (empty ([]))) (',' (tail ([]) X4) (list X4)))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X4"], "exprvars": [] } }, "36": { "goal": [ { "clause": 5, "scope": 6, "term": "(',' (no (empty T3)) (',' (tail T3 X13) (list X13)))" }, { "clause": 6, "scope": 6, "term": "(',' (no (empty T3)) (',' (tail T3 X13) (list X13)))" } ], "kb": { "nonunifying": [[ "(list T3)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T3"], "free": ["X13"], "exprvars": [] } }, "37": { "goal": [ { "clause": -1, "scope": -1, "term": "(',' (',' (call (empty T6)) (',' (!_6) (failure (a)))) (',' (tail T6 X13) (list X13)))" }, { "clause": 6, "scope": 6, "term": "(',' (no (empty T6)) (',' (tail T6 X13) (list X13)))" } ], "kb": { "nonunifying": [[ "(list T6)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": ["X13"], "exprvars": [] } }, "16": { "goal": [{ "clause": 1, "scope": 1, "term": "(list ([]))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "27": { "goal": [ { "clause": -1, "scope": -1, "term": "(',' (',' (!_2) (failure (a))) (',' (tail ([]) X4) (list X4)))" }, { "clause": -1, "scope": 4, "term": null }, { "clause": -1, "scope": 3, "term": null }, { "clause": 6, "scope": 2, "term": "(',' (no (empty ([]))) (',' (tail ([]) X4) (list X4)))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X4"], "exprvars": [] } }, "38": { "goal": [ { "clause": -1, "scope": -1, "term": "(',' (empty T6) (',' (',' (!_6) (failure (a))) (',' (tail T6 X13) (list X13))))" }, { "clause": -1, "scope": 7, "term": null }, { "clause": 6, "scope": 6, "term": "(',' (no (empty T6)) (',' (tail T6 X13) (list X13)))" } ], "kb": { "nonunifying": [[ "(list T6)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": ["X13"], "exprvars": [] } }, "17": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (no (empty ([]))) (',' (tail ([]) X4) (list X4)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X4"], "exprvars": [] } }, "39": { "goal": [ { "clause": 4, "scope": 8, "term": "(',' (empty T6) (',' (',' (!_6) (failure (a))) (',' (tail T6 X13) (list X13))))" }, { "clause": -1, "scope": 8, "term": null }, { "clause": -1, "scope": 7, "term": null }, { "clause": 6, "scope": 6, "term": "(',' (no (empty T6)) (',' (tail T6 X13) (list X13)))" } ], "kb": { "nonunifying": [[ "(list T6)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T6"], "free": ["X13"], "exprvars": [] } }, "29": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (failure (a)) (',' (tail ([]) X4) (list X4)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X4"], "exprvars": [] } }, "19": { "goal": [ { "clause": 5, "scope": 2, "term": "(',' (no (empty ([]))) (',' (tail ([]) X4) (list X4)))" }, { "clause": 6, "scope": 2, "term": "(',' (no (empty ([]))) (',' (tail ([]) X4) (list X4)))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X4"], "exprvars": [] } }, "type": "Nodes", "1": { "goal": [{ "clause": -1, "scope": -1, "term": "(list T1)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": [], "exprvars": [] } }, "5": { "goal": [ { "clause": 0, "scope": 1, "term": "(list T1)" }, { "clause": 1, "scope": 1, "term": "(list T1)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T1"], "free": [], "exprvars": [] } }, "40": { "goal": [ { "clause": -1, "scope": -1, "term": "(',' (',' (!_6) (failure (a))) (',' (tail T9 X13) (list X13)))" }, { "clause": -1, "scope": 8, "term": null }, { "clause": -1, "scope": 7, "term": null }, { "clause": 6, "scope": 6, "term": "(',' (no (empty T9)) (',' (tail T9 X13) (list X13)))" } ], "kb": { "nonunifying": [[ "(list T9)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T9"], "free": ["X13"], "exprvars": [] } }, "41": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (failure (a)) (',' (tail T9 X13) (list X13)))" }], "kb": { "nonunifying": [[ "(list T9)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T9"], "free": ["X13"], "exprvars": [] } }, "42": { "goal": [{ "clause": 7, "scope": 9, "term": "(',' (failure (a)) (',' (tail T9 X13) (list X13)))" }], "kb": { "nonunifying": [[ "(list T9)", "(list ([]))" ]], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T9"], "free": ["X13"], "exprvars": [] } }, "21": { "goal": [ { "clause": -1, "scope": -1, "term": "(',' (',' (call (empty ([]))) (',' (!_2) (failure (a)))) (',' (tail ([]) X4) (list X4)))" }, { "clause": 6, "scope": 2, "term": "(',' (no (empty ([]))) (',' (tail ([]) X4) (list X4)))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X4"], "exprvars": [] } }, "43": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 1, "to": 5, "label": "CASE" }, { "from": 5, "to": 13, "label": "EVAL with clause\nlist([]).\nand substitutionT1 -> []" }, { "from": 5, "to": 14, "label": "EVAL-BACKTRACK" }, { "from": 13, "to": 16, "label": "SUCCESS" }, { "from": 14, "to": 35, "label": "ONLY EVAL with clause\nlist(X12) :- ','(no(empty(X12)), ','(tail(X12, X13), list(X13))).\nand substitutionT1 -> T3,\nX12 -> T3" }, { "from": 16, "to": 17, "label": "ONLY EVAL with clause\nlist(X3) :- ','(no(empty(X3)), ','(tail(X3, X4), list(X4))).\nand substitutionX3 -> []" }, { "from": 17, "to": 19, "label": "CASE" }, { "from": 19, "to": 21, "label": "ONLY EVAL with clause\nno(X7) :- ','(call(X7), ','(!_2, failure(a))).\nand substitutionX7 -> empty([])" }, { "from": 21, "to": 23, "label": "CALL" }, { "from": 23, "to": 25, "label": "CASE" }, { "from": 25, "to": 27, "label": "ONLY EVAL with clause\nempty(X10).\nand substitutionX10 -> []" }, { "from": 27, "to": 29, "label": "CUT" }, { "from": 29, "to": 33, "label": "CASE" }, { "from": 33, "to": 34, "label": "BACKTRACK\nfor clause: failure(b)because of non-unification" }, { "from": 35, "to": 36, "label": "CASE" }, { "from": 36, "to": 37, "label": "ONLY EVAL with clause\nno(X16) :- ','(call(X16), ','(!_6, failure(a))).\nand substitutionT3 -> T6,\nX16 -> empty(T6)" }, { "from": 37, "to": 38, "label": "CALL" }, { "from": 38, "to": 39, "label": "CASE" }, { "from": 39, "to": 40, "label": "ONLY EVAL with clause\nempty(X19).\nand substitutionT6 -> T9,\nX19 -> T9" }, { "from": 40, "to": 41, "label": "CUT" }, { "from": 41, "to": 42, "label": "CASE" }, { "from": 42, "to": 43, "label": "BACKTRACK\nfor clause: failure(b)because of non-unification" } ], "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