/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern test_fun(g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 39 ms] (2) TRUE ---------------------------------------- (0) Obligation: Clauses: test_fun(X, Y) :- loop1(X, Y, 0). loop1(X, Y, C) :- ','(>(X, 0), loop2(X, Y, C)). loop1(X, Y, C) :- =<(X, 0). loop2(X, Y, C) :- ','(>(Y, 0), ','(is(Y1, -(Y, 1)), ','(is(C1, +(C, 1)), loop2(X, Y1, C1)))). loop2(X, Y, C) :- ','(=<(Y, 0), ','(is(X1, -(X, 1)), ','(is(C1, +(C, 1)), loop1(X1, Y, C1)))). Query: test_fun(g,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 3, "program": { "directives": [], "clauses": [ [ "(test_fun X Y)", "(loop1 X Y (0))" ], [ "(loop1 X Y C)", "(',' (> X (0)) (loop2 X Y C))" ], [ "(loop1 X Y C)", "(=< X (0))" ], [ "(loop2 X Y C)", "(',' (> Y (0)) (',' (is Y1 (- Y (1))) (',' (is C1 (+ C (1))) (loop2 X Y1 C1))))" ], [ "(loop2 X Y C)", "(',' (=< Y (0)) (',' (is X1 (- X (1))) (',' (is C1 (+ C (1))) (loop1 X1 Y C1))))" ] ] }, "graph": { "nodes": { "22": { "goal": [{ "clause": 2, "scope": 2, "term": "(loop1 T9 T10 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T9", "T10" ], "free": [], "exprvars": [] } }, "3060": { "goal": [{ "clause": -1, "scope": -1, "term": "(=< T103 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T103"], "free": [], "exprvars": [] } }, "23": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (> T21 (0)) (loop2 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[] }, "ground": [], "free": [], "exprvars": [] } }, "21": { "goal": [{ "clause": 1, "scope": 2, "term": "(loop1 T9 T10 (0))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T9", "T10" ], "free": [], "exprvars": [] } }, "2516": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (> T34 (0)) (',' (is X53 (- T34 (1))) (',' (is X54 (+ (0) (1))) (loop2 T33 X53 X54))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T33", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T21", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": [ "T33", "T34" ], "free": [ "X53", "X54" ], "exprvars": [ "T33", "T21" ] } } }, "edges": [ { "from": 3, "to": 6, "label": "CASE" }, { "from": 6, "to": 8, "label": "ONLY EVAL with clause\ntest_fun(X9, X10) :- loop1(X9, X10, 0).\nand substitutionT1 -> T9,\nX9 -> T9,\nT2 -> T10,\nX10 -> T10" }, { "from": 8, "to": 11, "label": "CASE" }, { "from": 11, "to": 21, "label": "PARALLEL" }, { "from": 11, "to": 22, "label": "PARALLEL" }, { "from": 21, "to": 23, "label": "ONLY EVAL with clause\nloop1(X26, X27, X28) :- ','(>(X26, 0), loop2(X26, X27, X28)).\nand substitutionT9 -> T21,\nX26 -> T21,\nT10 -> T22,\nX27 -> T22,\nX28 -> 0" }, { "from": 22, "to": 3060, "label": "ONLY EVAL with clause\nloop1(X140, X141, X142) :- =<(X140, 0).\nand substitutionT9 -> T103,\nX140 -> T103,\nT10 -> T104,\nX141 -> T104,\nX142 -> 0" }, { "from": 23, "to": 24, "label": "IS ERROR" }, { "from": 23, "to": 2511, "label": "ARITHCOMP SUCCESS" }, { "from": 23, "to": 2512, "label": "ARITHCOMP FAIL" }, { "from": 2511, "to": 2513, "label": "CASE" }, { "from": 2513, "to": 2514, "label": "PARALLEL" }, { "from": 2513, "to": 2515, "label": "PARALLEL" }, { "from": 2514, "to": 2516, "label": "ONLY EVAL with clause\nloop2(X50, X51, X52) :- ','(>(X51, 0), ','(is(X53, -(X51, 1)), ','(is(X54, +(X52, 1)), loop2(X50, X53, X54)))).\nand substitutionT21 -> T33,\nX50 -> T33,\nT22 -> T34,\nX51 -> T34,\nX52 -> 0" }, { "from": 2515, "to": 3027, "label": "ONLY EVAL with clause\nloop2(X102, X103, X104) :- ','(=<(X103, 0), ','(is(X105, -(X102, 1)), ','(is(X106, +(X104, 1)), loop1(X105, X103, X106)))).\nand substitutionT21 -> T68,\nX102 -> T68,\nT22 -> T69,\nX103 -> T69,\nX104 -> 0" }, { "from": 2516, "to": 2517, "label": "IS ERROR" }, { "from": 2516, "to": 2662, "label": "ARITHCOMP SUCCESS" }, { "from": 2516, "to": 2663, "label": "ARITHCOMP FAIL" }, { "from": 2662, "to": 3004, "label": "\nX53 -> T35" }, { "from": 3004, "to": 3013, "label": "\nX54 -> T36" }, { "from": 3013, "to": 3016, "label": "CASE" }, { "from": 3016, "to": 3017, "label": "PARALLEL" }, { "from": 3016, "to": 3018, "label": "PARALLEL" }, { "from": 3017, "to": 3020, "label": "ONLY EVAL with clause\nloop2(X76, X77, X78) :- ','(>(X77, 0), ','(is(X79, -(X77, 1)), ','(is(X80, +(X78, 1)), loop2(X76, X79, X80)))).\nand substitutionT33 -> T52,\nX76 -> T52,\nT35 -> T53,\nX77 -> T53,\nT36 -> T54,\nX78 -> T54" }, { "from": 3018, "to": 3022, "label": "ONLY EVAL with clause\nloop2(X89, X90, X91) :- ','(=<(X90, 0), ','(is(X92, -(X89, 1)), ','(is(X93, +(X91, 1)), loop1(X92, X90, X93)))).\nand substitutionT33 -> T61,\nX89 -> T61,\nT35 -> T62,\nX90 -> T62,\nT36 -> T63,\nX91 -> T63" }, { "from": 3027, "to": 3028, "label": "IS ERROR" }, { "from": 3027, "to": 3029, "label": "ARITHCOMP SUCCESS" }, { "from": 3027, "to": 3030, "label": "ARITHCOMP FAIL" }, { "from": 3029, "to": 3031, "label": "\nX105 -> T70" }, { "from": 3031, "to": 3032, "label": "\nX106 -> T71" }, { "from": 3032, "to": 3033, "label": "CASE" }, { "from": 3033, "to": 3034, "label": "PARALLEL" }, { "from": 3033, "to": 3035, "label": "PARALLEL" }, { "from": 3034, "to": 3036, "label": "ONLY EVAL with clause\nloop1(X122, X123, X124) :- ','(>(X122, 0), loop2(X122, X123, X124)).\nand substitutionT70 -> T87,\nX122 -> T87,\nT69 -> T88,\nX123 -> T88,\nT71 -> T89,\nX124 -> T89" }, { "from": 3035, "to": 3044, "label": "ONLY EVAL with clause\nloop1(X131, X132, X133) :- =<(X131, 0).\nand substitutionT70 -> T96,\nX131 -> T96,\nT69 -> T97,\nX132 -> T97,\nT71 -> T98,\nX133 -> T98" }, { "from": 3060, "to": 3061, "label": "IS ERROR" }, { "from": 3060, "to": 3067, "label": "ARITHCOMP SUCCESS" }, { "from": 3060, "to": 3068, "label": "ARITHCOMP FAIL" }, { "from": 3067, "to": 3069, "label": "SUCCESS" } ], "type": "Graph" } } ---------------------------------------- (2) TRUE