/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern euler2(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToDTProblemTransformerProof [SOUND, 80 ms] (2) TRIPLES (3) TPisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Clauses: euler2(Bound, Result) :- sumEvenFib(0, 1, Bound, Result). sumEvenFib(Fib1, Fib2, Bound, Result) :- ','(nextFib(Fib1, Fib2, NextFib), ','(>(NextFib, Bound), is(Result, 0))). sumEvenFib(Fib1, Fib2, Bound, Result) :- ','(nextFib(Fib1, Fib2, NextFib), ','(=<(NextFib, Bound), ','(=:=(mod(NextFib, 2), 0), ','(sumEvenFib(Fib2, NextFib, Bound, RecursiveResult), is(Result, +(RecursiveResult, NextFib)))))). sumEvenFib(Fib1, Fib2, Bound, Result) :- ','(nextFib(Fib1, Fib2, NextFib), ','(=<(NextFib, Bound), ','(=\=(mod(NextFib, 2), 0), sumEvenFib(Fib2, NextFib, Bound, Result)))). nextFib(Fib1, Fib2, NextFib) :- is(NextFib, +(Fib1, Fib2)). Query: euler2(g,a) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 1, "program": { "directives": [], "clauses": [ [ "(euler2 Bound Result)", "(sumEvenFib (0) (1) Bound Result)" ], [ "(sumEvenFib Fib1 Fib2 Bound Result)", "(',' (nextFib Fib1 Fib2 NextFib) (',' (> NextFib Bound) (is Result (0))))" ], [ "(sumEvenFib Fib1 Fib2 Bound Result)", "(',' (nextFib Fib1 Fib2 NextFib) (',' (=< NextFib Bound) (',' (=:= (mod NextFib (2)) (0)) (',' (sumEvenFib Fib2 NextFib Bound RecursiveResult) (is Result (+ RecursiveResult NextFib))))))" ], [ "(sumEvenFib Fib1 Fib2 Bound Result)", "(',' (nextFib Fib1 Fib2 NextFib) (',' (=< NextFib Bound) (',' (=\\= (mod NextFib (2)) (0)) (sumEvenFib Fib2 NextFib Bound Result))))" ], [ "(nextFib Fib1 Fib2 NextFib)", "(is NextFib (+ Fib1 Fib2))" ] ] }, "graph": { "nodes": { "3244": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (is X103 (+ (0) (1))) (',' (=< X103 T42) 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"PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T42", "T45" ], "free": ["X103"], "exprvars": [ "T42", "T45" ] } }, "900": { "goal": [{ "clause": 3, "scope": 2, "term": "(sumEvenFib (0) (1) T5 T7)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T5"], "free": [], "exprvars": [] } }, "3664": { "goal": [{ "clause": -1, "scope": -1, "term": "(sumEvenFib (1) T45 T42 T44)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T45", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "2" } ], "type": "PlainIntegerOperation", "operation": "mod" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T42", "T45" ], "free": ["X103"], "exprvars": [ "T42", "T45" ] } }, "901": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (nextFib (0) (1) X64) (',' (=< X64 T33) (',' (=:= (mod X64 (2)) (0)) (',' (sumEvenFib (1) X64 T33 X65) (is T35 (+ X65 X64))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T33"], "free": [ "X64", "X65" ], "exprvars": [] } }, "3665": { "goal": [ { "clause": 1, "scope": 6, "term": "(sumEvenFib (1) T45 T42 T44)" }, { "clause": 2, "scope": 6, "term": "(sumEvenFib (1) T45 T42 T44)" }, { "clause": 3, "scope": 6, "term": "(sumEvenFib (1) T45 T42 T44)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T45", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "2" } ], "type": "PlainIntegerOperation", "operation": "mod" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T42", "T45" ], "free": [], "exprvars": [ "T42", "T45" ] } }, "902": { "goal": [{ "clause": 4, "scope": 4, "term": "(',' (nextFib (0) (1) X64) (',' (=< X64 T33) (',' (=:= (mod X64 (2)) (0)) (',' (sumEvenFib (1) X64 T33 X65) (is T35 (+ X65 X64))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T33"], "free": [ "X64", "X65" ], "exprvars": [] } }, "3666": { "goal": [{ "clause": 1, "scope": 6, "term": "(sumEvenFib (1) T45 T42 T44)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T45", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "2" } ], "type": "PlainIntegerOperation", "operation": "mod" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T42", "T45" ], "free": [], "exprvars": [ "T42", "T45" ] } }, "3667": { "goal": [ { "clause": 2, "scope": 6, "term": "(sumEvenFib (1) T45 T42 T44)" }, { "clause": 3, "scope": 6, "term": "(sumEvenFib (1) T45 T42 T44)" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T45", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "2" } ], "type": "PlainIntegerOperation", "operation": "mod" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T42", "T45" ], "free": [], "exprvars": [ "T42", "T45" ] } }, "3668": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (nextFib (1) T63 X131) (',' (> X131 T64) (is T66 (0))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T45", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "2" } ], "type": "PlainIntegerOperation", "operation": "mod" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T64", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T63", "T64" ], "free": ["X131"], "exprvars": [ "T42", "T64", "T63", "T45" ] } }, "3669": { "goal": [{ "clause": 4, "scope": 7, "term": "(',' (nextFib (1) T63 X131) (',' (> X131 T64) (is T66 (0))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T45", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "2" } ], "type": "PlainIntegerOperation", "operation": "mod" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T64", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T63", "T64" ], "free": ["X131"], "exprvars": [ "T42", "T64", "T63", "T45" ] } }, "3702": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (nextFib (1) T100 X195) (',' (=< X195 T101) (',' (=\\= (mod X195 (2)) (0)) (sumEvenFib T100 X195 T101 T103))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T45", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "2" } ], "type": "PlainIntegerOperation", "operation": "mod" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T101", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T100", "T101" ], "free": ["X195"], "exprvars": [ "T42", "T100", "T45", "T101" ] } }, "3703": { "goal": [{ "clause": 4, "scope": 9, "term": "(',' (nextFib (1) T100 X195) (',' (=< X195 T101) (',' (=\\= (mod X195 (2)) (0)) (sumEvenFib T100 X195 T101 T103))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T45", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "2" } ], "type": "PlainIntegerOperation", "operation": "mod" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "!=" }, { "lhs": { "name": "T45", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" }, { "lhs": { "name": "T101", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T42", "type": "PlainIntegerVariable" }, "operation": "<=" } ] }, "ground": [ "T100", "T101" ], "free": ["X195"], "exprvars": [ "T42", "T100", "T45", "T101" ] } } }, "edges": [ { "from": 1, "to": 3, "label": "CASE" }, { "from": 3, "to": 9, "label": "ONLY EVAL with clause\neuler2(X3, X4) :- sumEvenFib(0, 1, X3, X4).\nand substitutionT1 -> T5,\nX3 -> T5,\nT2 -> T7,\nX4 -> T7,\nT6 -> T7" }, { "from": 9, "to": 10, "label": "CASE" }, { "from": 10, "to": 12, "label": "PARALLEL" }, { "from": 10, "to": 13, "label": "PARALLEL" }, { "from": 12, "to": 16, "label": "ONLY EVAL with clause\nsumEvenFib(X23, X24, X25, X26) :- ','(nextFib(X23, X24, X27), ','(>(X27, X25), is(X26, 0))).\nand substitutionX23 -> 0,\nX24 -> 1,\nT5 -> T18,\nX25 -> T18,\nT7 -> T20,\nX26 -> T20,\nT19 -> T20" }, { "from": 13, "to": 899, "label": "PARALLEL" }, { "from": 13, "to": 900, "label": "PARALLEL" }, { "from": 16, "to": 17, "label": "CASE" }, { "from": 17, "to": 20, "label": "ONLY EVAL with clause\nnextFib(X36, X37, X38) :- is(X38, +(X36, X37)).\nand substitutionX36 -> 0,\nX37 -> 1,\nX27 -> X39,\nX38 -> X39" }, { "from": 20, "to": 28, "label": "\nX39 -> T21" }, { "from": 28, "to": 29, "label": "IS ERROR" }, { "from": 28, "to": 811, "label": "ARITHCOMP SUCCESS" }, { "from": 28, "to": 892, "label": "ARITHCOMP FAIL" }, { "from": 811, "to": 893, "label": "\nT20 -> T22" }, { "from": 811, "to": 894, "label": "IS FAIL" }, { "from": 893, "to": 895, "label": "SUCCESS" }, { "from": 899, "to": 901, "label": "ONLY EVAL with clause\nsumEvenFib(X60, X61, X62, X63) :- ','(nextFib(X60, X61, X64), ','(=<(X64, X62), ','(=:=(mod(X64, 2), 0), ','(sumEvenFib(X61, X64, X62, X65), is(X63, +(X65, X64)))))).\nand substitutionX60 -> 0,\nX61 -> 1,\nT5 -> T33,\nX62 -> T33,\nT7 -> T35,\nX63 -> T35,\nT34 -> T35" }, { "from": 900, "to": 3240, "label": "ONLY EVAL with clause\nsumEvenFib(X87, X88, X89, X90) :- ','(nextFib(X87, X88, X91), ','(=<(X91, X89), ','(=\\=(mod(X91, 2), 0), sumEvenFib(X88, X91, X89, X90)))).\nand substitutionX87 -> 0,\nX88 -> 1,\nT5 -> T42,\nX89 -> T42,\nT7 -> T44,\nX90 -> T44,\nT43 -> T44" }, { "from": 901, "to": 902, "label": "CASE" }, { "from": 902, "to": 926, "label": "ONLY EVAL with clause\nnextFib(X74, X75, X76) :- is(X76, +(X74, X75)).\nand substitutionX74 -> 0,\nX75 -> 1,\nX64 -> X77,\nX76 -> X77" }, { "from": 926, "to": 953, "label": "\nX77 -> T36" }, { "from": 953, "to": 968, "label": "IS ERROR" }, { "from": 953, "to": 3161, "label": "ARITHCOMP SUCCESS" }, { "from": 953, "to": 3164, "label": "ARITHCOMP FAIL" }, { "from": 3161, "to": 3238, "label": "ARITHCOMP FAIL" }, { "from": 3240, "to": 3241, "label": "CASE" }, { "from": 3241, "to": 3244, "label": "ONLY EVAL with clause\nnextFib(X100, X101, X102) :- is(X102, +(X100, X101)).\nand substitutionX100 -> 0,\nX101 -> 1,\nX91 -> X103,\nX102 -> X103" }, { "from": 3244, "to": 3245, "label": "\nX103 -> T45" }, { "from": 3245, "to": 3246, "label": "IS ERROR" }, { "from": 3245, "to": 3501, "label": "ARITHCOMP SUCCESS" }, { "from": 3245, "to": 3502, "label": "ARITHCOMP FAIL" }, { "from": 3501, "to": 3664, "label": "ARITHCOMP SUCCESS" }, { "from": 3664, "to": 3665, "label": "CASE" }, { "from": 3665, "to": 3666, "label": "PARALLEL" }, { "from": 3665, "to": 3667, "label": "PARALLEL" }, { "from": 3666, "to": 3668, "label": "ONLY EVAL with clause\nsumEvenFib(X127, X128, X129, X130) :- ','(nextFib(X127, X128, X131), ','(>(X131, X129), is(X130, 0))).\nand substitutionX127 -> 1,\nT45 -> T63,\nX128 -> T63,\nT42 -> T64,\nX129 -> T64,\nT44 -> T66,\nX130 -> T66,\nT65 -> T66" }, { "from": 3667, "to": 3672, "label": "PARALLEL" }, { "from": 3667, "to": 3673, "label": "PARALLEL" }, { "from": 3668, "to": 3669, "label": "CASE" }, { "from": 3669, "to": 3670, "label": "ONLY EVAL with clause\nnextFib(X140, X141, X142) :- is(X142, +(X140, X141)).\nand substitutionX140 -> 1,\nT63 -> T69,\nX141 -> T69,\nX131 -> X143,\nX142 -> X143" }, { "from": 3670, "to": 3671, "label": "\nX143 -> T70" }, { "from": 3672, "to": 3674, "label": "ONLY EVAL with clause\nsumEvenFib(X164, X165, X166, X167) :- ','(nextFib(X164, X165, X168), ','(=<(X168, X166), ','(=:=(mod(X168, 2), 0), ','(sumEvenFib(X165, X168, X166, X169), is(X167, +(X169, X168)))))).\nand substitutionX164 -> 1,\nT45 -> T85,\nX165 -> T85,\nT42 -> T86,\nX166 -> T86,\nT44 -> T88,\nX167 -> T88,\nT87 -> T88" }, { "from": 3673, "to": 3702, "label": "ONLY EVAL with clause\nsumEvenFib(X191, X192, X193, X194) :- ','(nextFib(X191, X192, X195), ','(=<(X195, X193), ','(=\\=(mod(X195, 2), 0), sumEvenFib(X192, X195, X193, X194)))).\nand substitutionX191 -> 1,\nT45 -> T100,\nX192 -> T100,\nT42 -> T101,\nX193 -> T101,\nT44 -> T103,\nX194 -> T103,\nT102 -> T103" }, { "from": 3674, "to": 3675, "label": "CASE" }, { "from": 3675, "to": 3676, "label": "ONLY EVAL with clause\nnextFib(X178, X179, X180) :- is(X180, +(X178, X179)).\nand substitutionX178 -> 1,\nT85 -> T91,\nX179 -> T91,\nX168 -> X181,\nX180 -> X181" }, { "from": 3676, "to": 3677, "label": "\nX181 -> T92" }, { "from": 3702, "to": 3703, "label": "CASE" }, { "from": 3703, "to": 3704, "label": "ONLY EVAL with clause\nnextFib(X204, X205, X206) :- is(X206, +(X204, X205)).\nand substitutionX204 -> 1,\nT100 -> T106,\nX205 -> T106,\nX195 -> X207,\nX206 -> X207" }, { "from": 3704, "to": 3705, "label": "\nX207 -> T107" } ], "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