4.01/1.84 YES 4.01/1.88 proof of /export/starexec/sandbox/benchmark/theBenchmark.pl 4.01/1.88 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.01/1.88 4.01/1.88 4.01/1.88 Left Termination of the query pattern 4.01/1.88 4.01/1.88 g(a) 4.01/1.88 4.01/1.88 w.r.t. the given Prolog program could successfully be proven: 4.01/1.88 4.01/1.88 (0) Prolog 4.01/1.88 (1) PrologToIRSwTTransformerProof [SOUND, 81 ms] 4.01/1.88 (2) IRSwT 4.01/1.88 (3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] 4.01/1.88 (4) TRUE 4.01/1.88 4.01/1.88 4.01/1.88 ---------------------------------------- 4.01/1.88 4.01/1.88 (0) 4.01/1.88 Obligation: 4.01/1.88 Clauses: 4.01/1.88 4.01/1.88 g(W) :- ','(eq(X, .(.(a, []), .(.(R, []), []))), ','(eq(Y, .(.(S, .(c, [])), .([], []))), ','(app_1(X, Y, Z), ','(eq(Z, .(U, V)), app_2(U, U, W))))). 4.01/1.88 app_1([], X, X). 4.01/1.88 app_1(.(X, Xs), Ys, .(X, Zs)) :- app_1(Xs, Ys, Zs). 4.01/1.88 app_2([], X, X). 4.01/1.88 app_2(.(X, Xs), Ys, .(X, Zs)) :- app_2(Xs, Ys, Zs). 4.01/1.88 eq(X, X). 4.01/1.88 4.01/1.88 4.01/1.88 Query: g(a) 4.01/1.88 ---------------------------------------- 4.01/1.88 4.01/1.88 (1) PrologToIRSwTTransformerProof (SOUND) 4.01/1.88 Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert 4.01/1.88 4.01/1.88 { 4.01/1.88 "root": 1, 4.01/1.88 "program": { 4.01/1.88 "directives": [], 4.01/1.88 "clauses": [ 4.01/1.88 [ 4.01/1.88 "(g W)", 4.01/1.88 "(',' (eq X (. (. (a) ([])) (. (. R ([])) ([])))) (',' (eq Y (. (. S (. (c) ([]))) (. ([]) ([])))) (',' (app_1 X Y Z) (',' (eq Z (. U V)) (app_2 U U W)))))" 4.01/1.88 ], 4.01/1.88 [ 4.01/1.88 "(app_1 ([]) X X)", 4.01/1.88 null 4.01/1.88 ], 4.01/1.88 [ 4.01/1.88 "(app_1 (. X Xs) Ys (. X Zs))", 4.01/1.88 "(app_1 Xs Ys Zs)" 4.01/1.88 ], 4.01/1.88 [ 4.01/1.88 "(app_2 ([]) X X)", 4.01/1.88 null 4.01/1.88 ], 4.01/1.88 [ 4.01/1.88 "(app_2 (. X Xs) Ys (. X Zs))", 4.01/1.88 "(app_2 Xs Ys Zs)" 4.01/1.88 ], 4.01/1.88 [ 4.01/1.88 "(eq X X)", 4.01/1.88 null 4.01/1.88 ] 4.01/1.88 ] 4.01/1.88 }, 4.01/1.88 "graph": { 4.01/1.88 "nodes": { 4.01/1.88 "type": "Nodes", 4.01/1.88 "470": { 4.01/1.88 "goal": [], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "351": { 4.01/1.88 "goal": [], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "593": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": -1, 4.01/1.88 "scope": -1, 4.01/1.88 "term": "(app_2 T470 (. T472 T473) T471)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "352": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": 5, 4.01/1.88 "scope": 7, 4.01/1.88 "term": "(',' (eq T7 (. X20 X21)) (app_2 X20 X20 T8))" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [ 4.01/1.88 "X20", 4.01/1.88 "X21" 4.01/1.88 ], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "594": { 4.01/1.88 "goal": [], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "474": { 4.01/1.88 "goal": [ 4.01/1.88 { 4.01/1.88 "clause": 3, 4.01/1.88 "scope": 12, 4.01/1.88 "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" 4.01/1.88 }, 4.01/1.88 { 4.01/1.88 "clause": 4, 4.01/1.88 "scope": 12, 4.01/1.88 "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" 4.01/1.88 } 4.01/1.88 ], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "475": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": 3, 4.01/1.88 "scope": 12, 4.01/1.88 "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "476": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": 4, 4.01/1.88 "scope": 12, 4.01/1.88 "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "510": { 4.01/1.88 "goal": [ 4.01/1.88 { 4.01/1.88 "clause": 3, 4.01/1.88 "scope": 13, 4.01/1.88 "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. T189 T183))))) T184)" 4.01/1.88 }, 4.01/1.88 { 4.01/1.88 "clause": 4, 4.01/1.88 "scope": 13, 4.01/1.88 "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. T189 T183))))) T184)" 4.01/1.88 } 4.01/1.88 ], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "511": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": 3, 4.01/1.88 "scope": 13, 4.01/1.88 "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. T189 T183))))) T184)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "512": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": 4, 4.01/1.88 "scope": 13, 4.01/1.88 "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. T189 T183))))) T184)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "359": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": -1, 4.01/1.88 "scope": -1, 4.01/1.88 "term": "(app_2 T18 T18 T19)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "515": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": -1, 4.01/1.88 "scope": -1, 4.01/1.88 "term": "(true)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "516": { 4.01/1.88 "goal": [], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "518": { 4.01/1.88 "goal": [], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "480": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": -1, 4.01/1.88 "scope": -1, 4.01/1.88 "term": "(true)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "360": { 4.01/1.88 "goal": [], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "481": { 4.01/1.88 "goal": [], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "240": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": -1, 4.01/1.88 "scope": -1, 4.01/1.88 "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": ["X19"], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "361": { 4.01/1.88 "goal": [ 4.01/1.88 { 4.01/1.88 "clause": 3, 4.01/1.88 "scope": 8, 4.01/1.88 "term": "(app_2 T18 T18 T19)" 4.01/1.88 }, 4.01/1.88 { 4.01/1.88 "clause": 4, 4.01/1.88 "scope": 8, 4.01/1.88 "term": "(app_2 T18 T18 T19)" 4.01/1.88 } 4.01/1.88 ], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "482": { 4.01/1.88 "goal": [], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.88 "arithmetic": { 4.01/1.88 "type": "PlainIntegerRelationState", 4.01/1.88 "relations": [] 4.01/1.88 }, 4.01/1.88 "ground": [], 4.01/1.88 "free": [], 4.01/1.88 "exprvars": [] 4.01/1.88 } 4.01/1.88 }, 4.01/1.88 "241": { 4.01/1.88 "goal": [{ 4.01/1.88 "clause": -1, 4.01/1.88 "scope": -1, 4.01/1.88 "term": "(',' (eq T7 (. X20 X21)) (app_2 X20 X20 T8))" 4.01/1.88 }], 4.01/1.88 "kb": { 4.01/1.88 "nonunifying": [], 4.01/1.88 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [ 4.01/1.89 "X20", 4.01/1.89 "X21" 4.01/1.89 ], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "362": { 4.01/1.89 "goal": [{ 4.01/1.89 "clause": 3, 4.01/1.89 "scope": 8, 4.01/1.89 "term": "(app_2 T18 T18 T19)" 4.01/1.89 }], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "363": { 4.01/1.89 "goal": [{ 4.01/1.89 "clause": 4, 4.01/1.89 "scope": 8, 4.01/1.89 "term": "(app_2 T18 T18 T19)" 4.01/1.89 }], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "1": { 4.01/1.89 "goal": [{ 4.01/1.89 "clause": -1, 4.01/1.89 "scope": -1, 4.01/1.89 "term": "(g T1)" 4.01/1.89 }], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "364": { 4.01/1.89 "goal": [{ 4.01/1.89 "clause": -1, 4.01/1.89 "scope": -1, 4.01/1.89 "term": "(true)" 4.01/1.89 }], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "485": { 4.01/1.89 "goal": [{ 4.01/1.89 "clause": -1, 4.01/1.89 "scope": -1, 4.01/1.89 "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. 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T416 T440) T415)" 4.01/1.89 }], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "465": { 4.01/1.89 "goal": [], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "586": { 4.01/1.89 "goal": [{ 4.01/1.89 "clause": 4, 4.01/1.89 "scope": 16, 4.01/1.89 "term": "(app_2 T414 (. T416 T440) T415)" 4.01/1.89 }], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "466": { 4.01/1.89 "goal": [], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "587": { 4.01/1.89 "goal": [{ 4.01/1.89 "clause": -1, 4.01/1.89 "scope": -1, 4.01/1.89 "term": "(true)" 4.01/1.89 }], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "588": { 4.01/1.89 "goal": [], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "589": { 4.01/1.89 "goal": [], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "469": { 4.01/1.89 "goal": [{ 4.01/1.89 "clause": -1, 4.01/1.89 "scope": -1, 4.01/1.89 "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)" 4.01/1.89 }], 4.01/1.89 "kb": { 4.01/1.89 "nonunifying": [], 4.01/1.89 "intvars": {}, 4.01/1.89 "arithmetic": { 4.01/1.89 "type": "PlainIntegerRelationState", 4.01/1.89 "relations": [] 4.01/1.89 }, 4.01/1.89 "ground": [], 4.01/1.89 "free": [], 4.01/1.89 "exprvars": [] 4.01/1.89 } 4.01/1.89 } 4.01/1.89 }, 4.01/1.89 "edges": [ 4.01/1.89 { 4.01/1.89 "from": 1, 4.01/1.89 "to": 34, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 34, 4.01/1.89 "to": 35, 4.01/1.89 "label": "ONLY EVAL with clause\ng(X14) :- ','(eq(X15, .(.(a, []), .(.(X16, []), []))), ','(eq(X17, .(.(X18, .(c, [])), .([], []))), ','(app_1(X15, X17, X19), ','(eq(X19, .(X20, X21)), app_2(X20, X20, X14))))).\nand substitutionT1 -> T6,\nX14 -> T6,\nT5 -> T6" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 35, 4.01/1.89 "to": 36, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 36, 4.01/1.89 "to": 141, 4.01/1.89 "label": "ONLY EVAL with clause\neq(X34, X34).\nand substitutionX15 -> .(.(a, []), .(.(X36, []), [])),\nX34 -> .(.(a, []), .(.(X36, []), [])),\nX16 -> X36,\nX35 -> .(.(a, []), .(.(X36, []), []))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 141, 4.01/1.89 "to": 143, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 143, 4.01/1.89 "to": 177, 4.01/1.89 "label": "ONLY EVAL with clause\neq(X47, X47).\nand substitutionX17 -> .(.(X49, .(c, [])), .([], [])),\nX47 -> .(.(X49, .(c, [])), .([], [])),\nX18 -> X49,\nX48 -> .(.(X49, .(c, [])), .([], []))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 177, 4.01/1.89 "to": 240, 4.01/1.89 "label": "SPLIT 1" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 177, 4.01/1.89 "to": 241, 4.01/1.89 "label": "SPLIT 2\nreplacements:X19 -> T7,\nT6 -> T8" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 240, 4.01/1.89 "to": 251, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 241, 4.01/1.89 "to": 352, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 251, 4.01/1.89 "to": 252, 4.01/1.89 "label": "BACKTRACK\nfor clause: app_1([], X, X)because of non-unification" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 252, 4.01/1.89 "to": 319, 4.01/1.89 "label": "ONLY EVAL with clause\napp_1(.(X71, X72), X73, .(X71, X74)) :- app_1(X72, X73, X74).\nand substitutionX71 -> .(a, []),\nX36 -> X75,\nX72 -> .(.(X75, []), []),\nX49 -> X76,\nX73 -> .(.(X76, .(c, [])), .([], [])),\nX74 -> X77,\nX19 -> .(.(a, []), X77)" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 319, 4.01/1.89 "to": 320, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 320, 4.01/1.89 "to": 321, 4.01/1.89 "label": "BACKTRACK\nfor clause: app_1([], X, X)because of non-unification" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 321, 4.01/1.89 "to": 323, 4.01/1.89 "label": "ONLY EVAL with clause\napp_1(.(X97, X98), X99, .(X97, X100)) :- app_1(X98, X99, X100).\nand substitutionX75 -> X101,\nX97 -> .(X101, []),\nX98 -> [],\nX76 -> X102,\nX99 -> .(.(X102, .(c, [])), .([], [])),\nX100 -> X103,\nX77 -> .(.(X101, []), X103)" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 323, 4.01/1.89 "to": 328, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 328, 4.01/1.89 "to": 330, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 328, 4.01/1.89 "to": 331, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 330, 4.01/1.89 "to": 338, 4.01/1.89 "label": "ONLY EVAL with clause\napp_1([], X114, X114).\nand substitutionX102 -> X115,\nX114 -> .(.(X115, .(c, [])), .([], [])),\nX103 -> .(.(X115, .(c, [])), .([], []))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 331, 4.01/1.89 "to": 351, 4.01/1.89 "label": "BACKTRACK\nfor clause: app_1(.(X, Xs), Ys, .(X, Zs)) :- app_1(Xs, Ys, Zs)because of non-unification" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 338, 4.01/1.89 "to": 340, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 352, 4.01/1.89 "to": 359, 4.01/1.89 "label": "EVAL with clause\neq(X124, X124).\nand substitutionT7 -> .(T18, T17),\nX124 -> .(T18, T17),\nX20 -> T18,\nX21 -> T17,\nT15 -> .(T18, T17),\nT16 -> T18,\nT8 -> T19" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 352, 4.01/1.89 "to": 360, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 359, 4.01/1.89 "to": 361, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 361, 4.01/1.89 "to": 362, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 361, 4.01/1.89 "to": 363, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 362, 4.01/1.89 "to": 364, 4.01/1.89 "label": "EVAL with clause\napp_2([], X131, X131).\nand substitutionT18 -> [],\nX131 -> [],\nT19 -> []" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 362, 4.01/1.89 "to": 366, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 363, 4.01/1.89 "to": 377, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X140, X141), X142, .(X140, X143)) :- app_2(X141, X142, X143).\nand substitutionX140 -> T31,\nX141 -> T29,\nT18 -> .(T31, T29),\nX142 -> .(T31, T29),\nX143 -> T30,\nT19 -> .(T31, T30),\nT27 -> T29,\nT28 -> T30,\nT26 -> T31" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 363, 4.01/1.89 "to": 379, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 364, 4.01/1.89 "to": 368, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 377, 4.01/1.89 "to": 383, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 383, 4.01/1.89 "to": 384, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 383, 4.01/1.89 "to": 385, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 384, 4.01/1.89 "to": 388, 4.01/1.89 "label": "EVAL with clause\napp_2([], X150, X150).\nand substitutionT29 -> [],\nT31 -> T38,\nX150 -> .(T38, []),\nT30 -> .(T38, [])" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 384, 4.01/1.89 "to": 389, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 385, 4.01/1.89 "to": 396, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X159, X160), X161, .(X159, X162)) :- app_2(X160, X161, X162).\nand substitutionX159 -> T54,\nX160 -> T51,\nT29 -> .(T54, T51),\nT31 -> T53,\nX161 -> .(T53, .(T54, T51)),\nX162 -> T52,\nT30 -> .(T54, T52),\nT48 -> T51,\nT50 -> T52,\nT49 -> T53,\nT47 -> T54" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 385, 4.01/1.89 "to": 397, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 388, 4.01/1.89 "to": 390, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 396, 4.01/1.89 "to": 430, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 430, 4.01/1.89 "to": 431, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 430, 4.01/1.89 "to": 432, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 431, 4.01/1.89 "to": 453, 4.01/1.89 "label": "EVAL with clause\napp_2([], X169, X169).\nand substitutionT51 -> [],\nT53 -> T67,\nT54 -> T68,\nX169 -> .(T67, .(T68, [])),\nT52 -> .(T67, .(T68, []))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 431, 4.01/1.89 "to": 454, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 432, 4.01/1.89 "to": 456, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X178, X179), X180, .(X178, X181)) :- app_2(X179, X180, X181).\nand substitutionX178 -> T88,\nX179 -> T84,\nT51 -> .(T88, T84),\nT53 -> T86,\nT54 -> T87,\nX180 -> .(T86, .(T87, .(T88, T84))),\nX181 -> T85,\nT52 -> .(T88, T85),\nT80 -> T84,\nT83 -> T85,\nT81 -> T86,\nT82 -> T87,\nT79 -> T88" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 432, 4.01/1.89 "to": 457, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 453, 4.01/1.89 "to": 455, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 456, 4.01/1.89 "to": 458, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 458, 4.01/1.89 "to": 462, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 458, 4.01/1.89 "to": 463, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 462, 4.01/1.89 "to": 464, 4.01/1.89 "label": "EVAL with clause\napp_2([], X188, X188).\nand substitutionT84 -> [],\nT86 -> T107,\nT87 -> T108,\nT88 -> T109,\nX188 -> .(T107, .(T108, .(T109, []))),\nT85 -> .(T107, .(T108, .(T109, [])))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 462, 4.01/1.89 "to": 465, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 463, 4.01/1.89 "to": 469, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X197, X198), X199, .(X197, X200)) :- app_2(X198, X199, X200).\nand substitutionX197 -> T133,\nX198 -> T128,\nT84 -> .(T133, T128),\nT86 -> T130,\nT87 -> T131,\nT88 -> T132,\nX199 -> .(T130, .(T131, .(T132, .(T133, T128)))),\nX200 -> T129,\nT85 -> .(T133, T129),\nT123 -> T128,\nT127 -> T129,\nT124 -> T130,\nT125 -> T131,\nT126 -> T132,\nT122 -> T133" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 463, 4.01/1.89 "to": 470, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 464, 4.01/1.89 "to": 466, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 469, 4.01/1.89 "to": 474, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 474, 4.01/1.89 "to": 475, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 474, 4.01/1.89 "to": 476, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 475, 4.01/1.89 "to": 480, 4.01/1.89 "label": "EVAL with clause\napp_2([], X207, X207).\nand substitutionT128 -> [],\nT130 -> T158,\nT131 -> T159,\nT132 -> T160,\nT133 -> T161,\nX207 -> .(T158, .(T159, .(T160, .(T161, [])))),\nT129 -> .(T158, .(T159, .(T160, .(T161, []))))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 475, 4.01/1.89 "to": 481, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 476, 4.01/1.89 "to": 485, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X216, X217), X218, .(X216, X219)) :- app_2(X217, X218, X219).\nand substitutionX216 -> T189,\nX217 -> T183,\nT128 -> .(T189, T183),\nT130 -> T185,\nT131 -> T186,\nT132 -> T187,\nT133 -> T188,\nX218 -> .(T185, .(T186, .(T187, .(T188, .(T189, T183))))),\nX219 -> T184,\nT129 -> .(T189, T184),\nT177 -> T183,\nT182 -> T184,\nT178 -> T185,\nT179 -> T186,\nT180 -> T187,\nT181 -> T188,\nT176 -> T189" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 476, 4.01/1.89 "to": 486, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 480, 4.01/1.89 "to": 482, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 485, 4.01/1.89 "to": 510, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 510, 4.01/1.89 "to": 511, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 510, 4.01/1.89 "to": 512, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 511, 4.01/1.89 "to": 515, 4.01/1.89 "label": "EVAL with clause\napp_2([], X226, X226).\nand substitutionT183 -> [],\nT185 -> T220,\nT186 -> T221,\nT187 -> T222,\nT188 -> T223,\nT189 -> T224,\nX226 -> .(T220, .(T221, .(T222, .(T223, .(T224, []))))),\nT184 -> .(T220, .(T221, .(T222, .(T223, .(T224, [])))))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 511, 4.01/1.89 "to": 516, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 512, 4.01/1.89 "to": 524, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X235, X236), X237, .(X235, X238)) :- app_2(X236, X237, X238).\nand substitutionX235 -> T256,\nX236 -> T249,\nT183 -> .(T256, T249),\nT185 -> T251,\nT186 -> T252,\nT187 -> T253,\nT188 -> T254,\nT189 -> T255,\nX237 -> .(T251, .(T252, .(T253, .(T254, .(T255, .(T256, T249)))))),\nX238 -> T250,\nT184 -> .(T256, T250),\nT242 -> T249,\nT248 -> T250,\nT243 -> T251,\nT244 -> T252,\nT245 -> T253,\nT246 -> T254,\nT247 -> T255,\nT241 -> T256" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 512, 4.01/1.89 "to": 525, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 515, 4.01/1.89 "to": 518, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 524, 4.01/1.89 "to": 528, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 528, 4.01/1.89 "to": 529, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 528, 4.01/1.89 "to": 530, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 529, 4.01/1.89 "to": 554, 4.01/1.89 "label": "EVAL with clause\napp_2([], X245, X245).\nand substitutionT249 -> [],\nT251 -> T293,\nT252 -> T294,\nT253 -> T295,\nT254 -> T296,\nT255 -> T297,\nT256 -> T298,\nX245 -> .(T293, .(T294, .(T295, .(T296, .(T297, .(T298, [])))))),\nT250 -> .(T293, .(T294, .(T295, .(T296, .(T297, .(T298, []))))))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 529, 4.01/1.89 "to": 555, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 530, 4.01/1.89 "to": 560, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X254, X255), X256, .(X254, X257)) :- app_2(X255, X256, X257).\nand substitutionX254 -> T334,\nX255 -> T326,\nT249 -> .(T334, T326),\nT251 -> T328,\nT252 -> T329,\nT253 -> T330,\nT254 -> T331,\nT255 -> T332,\nT256 -> T333,\nX256 -> .(T328, .(T329, .(T330, .(T331, .(T332, .(T333, .(T334, T326))))))),\nX257 -> T327,\nT250 -> .(T334, T327),\nT318 -> T326,\nT325 -> T327,\nT319 -> T328,\nT320 -> T329,\nT321 -> T330,\nT322 -> T331,\nT323 -> T332,\nT324 -> T333,\nT317 -> T334" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 530, 4.01/1.89 "to": 561, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 554, 4.01/1.89 "to": 556, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 560, 4.01/1.89 "to": 565, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 565, 4.01/1.89 "to": 569, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 565, 4.01/1.89 "to": 570, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 569, 4.01/1.89 "to": 575, 4.01/1.89 "label": "EVAL with clause\napp_2([], X264, X264).\nand substitutionT326 -> [],\nT328 -> T377,\nT329 -> T378,\nT330 -> T379,\nT331 -> T380,\nT332 -> T381,\nT333 -> T382,\nT334 -> T383,\nX264 -> .(T377, .(T378, .(T379, .(T380, .(T381, .(T382, .(T383, []))))))),\nT327 -> .(T377, .(T378, .(T379, .(T380, .(T381, .(T382, .(T383, [])))))))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 569, 4.01/1.89 "to": 576, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 570, 4.01/1.89 "to": 578, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X273, X274), X275, .(X273, X276)) :- app_2(X274, X275, X276).\nand substitutionX273 -> T423,\nX274 -> T414,\nT326 -> .(T423, T414),\nT328 -> T416,\nT329 -> T417,\nT330 -> T418,\nT331 -> T419,\nT332 -> T420,\nT333 -> T421,\nT334 -> T422,\nX275 -> .(T416, .(T417, .(T418, .(T419, .(T420, .(T421, .(T422, .(T423, T414)))))))),\nX276 -> T415,\nT327 -> .(T423, T415),\nT405 -> T414,\nT413 -> T415,\nT406 -> T416,\nT407 -> T417,\nT408 -> T418,\nT409 -> T419,\nT410 -> T420,\nT411 -> T421,\nT412 -> T422,\nT404 -> T423" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 570, 4.01/1.89 "to": 579, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 575, 4.01/1.89 "to": 577, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 578, 4.01/1.89 "to": 581, 4.01/1.89 "label": "GENERALIZATION\nT440 <-- .(T417, .(T418, .(T419, .(T420, .(T421, .(T422, .(T423, T414)))))))" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 581, 4.01/1.89 "to": 583, 4.01/1.89 "label": "CASE" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 583, 4.01/1.89 "to": 585, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 583, 4.01/1.89 "to": 586, 4.01/1.89 "label": "PARALLEL" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 585, 4.01/1.89 "to": 587, 4.01/1.89 "label": "EVAL with clause\napp_2([], X285, X285).\nand substitutionT414 -> [],\nT416 -> T453,\nT440 -> T454,\nX285 -> .(T453, T454),\nT415 -> .(T453, T454)" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 585, 4.01/1.89 "to": 588, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 586, 4.01/1.89 "to": 593, 4.01/1.89 "label": "EVAL with clause\napp_2(.(X294, X295), X296, .(X294, X297)) :- app_2(X295, X296, X297).\nand substitutionX294 -> T465,\nX295 -> T470,\nT414 -> .(T465, T470),\nT416 -> T472,\nT440 -> T473,\nX296 -> .(T472, T473),\nX297 -> T471,\nT415 -> .(T465, T471),\nT466 -> T470,\nT469 -> T471,\nT467 -> T472,\nT468 -> T473" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 586, 4.01/1.89 "to": 594, 4.01/1.89 "label": "EVAL-BACKTRACK" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 587, 4.01/1.89 "to": 589, 4.01/1.89 "label": "SUCCESS" 4.01/1.89 }, 4.01/1.89 { 4.01/1.89 "from": 593, 4.01/1.89 "to": 581, 4.01/1.89 "label": "INSTANCE with matching:\nT414 -> T470\nT416 -> T472\nT440 -> T473\nT415 -> T471" 4.01/1.89 } 4.01/1.89 ], 4.01/1.89 "type": "Graph" 4.01/1.89 } 4.01/1.89 } 4.01/1.89 4.01/1.89 ---------------------------------------- 4.01/1.89 4.01/1.89 (2) 4.01/1.89 Obligation: 4.01/1.89 Rules: 4.01/1.89 f593_in -> f581_in :|: TRUE 4.01/1.89 f581_out -> f593_out :|: TRUE 4.01/1.89 f583_in -> f585_in :|: TRUE 4.01/1.89 f583_in -> f586_in :|: TRUE 4.01/1.89 f586_out -> f583_out :|: TRUE 4.01/1.89 f585_out -> f583_out :|: TRUE 4.01/1.89 f581_in -> f583_in :|: TRUE 4.01/1.89 f583_out -> f581_out :|: TRUE 4.01/1.89 f593_out -> f586_out :|: TRUE 4.01/1.89 f594_out -> f586_out :|: TRUE 4.01/1.89 f586_in -> f593_in :|: TRUE 4.01/1.89 f586_in -> f594_in :|: TRUE 4.01/1.89 f1_in -> f34_in :|: TRUE 4.01/1.89 f34_out -> f1_out :|: TRUE 4.01/1.89 f34_in -> f35_in :|: TRUE 4.01/1.89 f35_out -> f34_out :|: TRUE 4.01/1.89 f35_in -> f36_in :|: TRUE 4.01/1.89 f36_out -> f35_out :|: TRUE 4.01/1.89 f36_in -> f141_in :|: TRUE 4.01/1.89 f141_out -> f36_out :|: TRUE 4.01/1.89 f143_out -> f141_out :|: TRUE 4.01/1.89 f141_in -> f143_in :|: TRUE 4.01/1.89 f177_out -> f143_out :|: TRUE 4.01/1.89 f143_in -> f177_in :|: TRUE 4.01/1.89 f240_out -> f241_in :|: TRUE 4.01/1.89 f177_in -> f240_in :|: TRUE 4.01/1.89 f241_out -> f177_out :|: TRUE 4.01/1.89 f241_in -> f352_in :|: TRUE 4.01/1.89 f352_out -> f241_out :|: TRUE 4.01/1.89 f352_in -> f360_in :|: TRUE 4.01/1.89 f359_out -> f352_out :|: TRUE 4.01/1.89 f352_in -> f359_in :|: TRUE 4.01/1.89 f360_out -> f352_out :|: TRUE 4.01/1.89 f359_in -> f361_in :|: TRUE 4.01/1.89 f361_out -> f359_out :|: TRUE 4.01/1.89 f361_in -> f362_in :|: TRUE 4.01/1.89 f362_out -> f361_out :|: TRUE 4.01/1.89 f361_in -> f363_in :|: TRUE 4.01/1.89 f363_out -> f361_out :|: TRUE 4.01/1.89 f363_in -> f377_in :|: TRUE 4.01/1.89 f377_out -> f363_out :|: TRUE 4.01/1.89 f379_out -> f363_out :|: TRUE 4.01/1.89 f363_in -> f379_in :|: TRUE 4.01/1.89 f377_in -> f383_in :|: TRUE 4.01/1.89 f383_out -> f377_out :|: TRUE 4.01/1.89 f385_out -> f383_out :|: TRUE 4.01/1.89 f384_out -> f383_out :|: TRUE 4.01/1.89 f383_in -> f384_in :|: TRUE 4.01/1.89 f383_in -> f385_in :|: TRUE 4.01/1.89 f385_in -> f397_in :|: TRUE 4.01/1.89 f397_out -> f385_out :|: TRUE 4.01/1.89 f385_in -> f396_in :|: TRUE 4.01/1.89 f396_out -> f385_out :|: TRUE 4.01/1.89 f430_out -> f396_out :|: TRUE 4.01/1.89 f396_in -> f430_in :|: TRUE 4.01/1.89 f430_in -> f432_in :|: TRUE 4.01/1.89 f431_out -> f430_out :|: TRUE 4.01/1.89 f432_out -> f430_out :|: TRUE 4.01/1.89 f430_in -> f431_in :|: TRUE 4.01/1.89 f457_out -> f432_out :|: TRUE 4.01/1.89 f432_in -> f456_in :|: TRUE 4.01/1.89 f432_in -> f457_in :|: TRUE 4.01/1.89 f456_out -> f432_out :|: TRUE 4.01/1.89 f458_out -> f456_out :|: TRUE 4.01/1.89 f456_in -> f458_in :|: TRUE 4.01/1.89 f462_out -> f458_out :|: TRUE 4.01/1.89 f463_out -> f458_out :|: TRUE 4.01/1.89 f458_in -> f463_in :|: TRUE 4.01/1.89 f458_in -> f462_in :|: TRUE 4.01/1.89 f463_in -> f469_in :|: TRUE 4.01/1.89 f470_out -> f463_out :|: TRUE 4.01/1.89 f469_out -> f463_out :|: TRUE 4.01/1.89 f463_in -> f470_in :|: TRUE 4.01/1.89 f469_in -> f474_in :|: TRUE 4.01/1.89 f474_out -> f469_out :|: TRUE 4.01/1.89 f476_out -> f474_out :|: TRUE 4.01/1.89 f475_out -> f474_out :|: TRUE 4.01/1.89 f474_in -> f476_in :|: TRUE 4.01/1.89 f474_in -> f475_in :|: TRUE 4.01/1.89 f476_in -> f485_in :|: TRUE 4.01/1.89 f485_out -> f476_out :|: TRUE 4.01/1.89 f476_in -> f486_in :|: TRUE 4.01/1.89 f486_out -> f476_out :|: TRUE 4.01/1.89 f510_out -> f485_out :|: TRUE 4.01/1.89 f485_in -> f510_in :|: TRUE 4.01/1.89 f511_out -> f510_out :|: TRUE 4.01/1.89 f510_in -> f512_in :|: TRUE 4.01/1.89 f510_in -> f511_in :|: TRUE 4.01/1.89 f512_out -> f510_out :|: TRUE 4.01/1.89 f512_in -> f524_in :|: TRUE 4.01/1.89 f512_in -> f525_in :|: TRUE 4.01/1.89 f524_out -> f512_out :|: TRUE 4.01/1.89 f525_out -> f512_out :|: TRUE 4.01/1.89 f528_out -> f524_out :|: TRUE 4.01/1.89 f524_in -> f528_in :|: TRUE 4.01/1.89 f528_in -> f530_in :|: TRUE 4.01/1.89 f529_out -> f528_out :|: TRUE 4.01/1.89 f530_out -> f528_out :|: TRUE 4.01/1.89 f528_in -> f529_in :|: TRUE 4.01/1.89 f530_in -> f560_in :|: TRUE 4.01/1.89 f560_out -> f530_out :|: TRUE 4.01/1.89 f530_in -> f561_in :|: TRUE 4.01/1.89 f561_out -> f530_out :|: TRUE 4.01/1.89 f565_out -> f560_out :|: TRUE 4.01/1.89 f560_in -> f565_in :|: TRUE 4.01/1.89 f565_in -> f569_in :|: TRUE 4.01/1.89 f569_out -> f565_out :|: TRUE 4.01/1.89 f570_out -> f565_out :|: TRUE 4.01/1.89 f565_in -> f570_in :|: TRUE 4.01/1.89 f570_in -> f579_in :|: TRUE 4.01/1.89 f579_out -> f570_out :|: TRUE 4.01/1.89 f570_in -> f578_in :|: TRUE 4.01/1.89 f578_out -> f570_out :|: TRUE 4.01/1.89 f578_in -> f581_in :|: TRUE 4.01/1.89 f581_out -> f578_out :|: TRUE 4.01/1.89 Start term: f1_in 4.01/1.89 4.01/1.89 ---------------------------------------- 4.01/1.89 4.01/1.89 (3) IRSwTSimpleDependencyGraphProof (EQUIVALENT) 4.01/1.89 Constructed simple dependency graph. 4.01/1.89 4.01/1.89 Simplified to the following IRSwTs: 4.01/1.89 4.01/1.89 4.01/1.89 ---------------------------------------- 4.01/1.89 4.01/1.89 (4) 4.01/1.89 TRUE 4.27/1.93 EOF