20.04/6.02 YES 20.04/6.09 proof of /export/starexec/sandbox/benchmark/theBenchmark.pl 20.04/6.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.04/6.09 20.04/6.09 20.04/6.09 Left Termination of the query pattern 20.04/6.09 20.04/6.09 mergesort(g,a,a) 20.04/6.09 20.04/6.09 w.r.t. the given Prolog program could successfully be proven: 20.04/6.09 20.04/6.09 (0) Prolog 20.04/6.09 (1) PrologToTRSTransformerProof [SOUND, 81 ms] 20.04/6.09 (2) QTRS 20.04/6.09 (3) DependencyPairsProof [EQUIVALENT, 0 ms] 20.04/6.09 (4) QDP 20.04/6.09 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 20.04/6.09 (6) AND 20.04/6.09 (7) QDP 20.04/6.09 (8) UsableRulesProof [EQUIVALENT, 0 ms] 20.04/6.09 (9) QDP 20.04/6.09 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.04/6.09 (11) YES 20.04/6.09 (12) QDP 20.04/6.09 (13) UsableRulesProof [EQUIVALENT, 0 ms] 20.04/6.09 (14) QDP 20.04/6.09 (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.04/6.09 (16) YES 20.04/6.09 (17) QDP 20.04/6.09 (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.04/6.09 (19) YES 20.04/6.09 (20) QDP 20.04/6.09 (21) UsableRulesProof [EQUIVALENT, 0 ms] 20.04/6.09 (22) QDP 20.04/6.09 (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] 20.04/6.09 (24) YES 20.04/6.09 (25) QDP 20.04/6.09 (26) QDPOrderProof [EQUIVALENT, 204 ms] 20.04/6.09 (27) QDP 20.04/6.09 (28) DependencyGraphProof [EQUIVALENT, 0 ms] 20.04/6.09 (29) TRUE 20.04/6.09 20.04/6.09 20.04/6.09 ---------------------------------------- 20.04/6.09 20.04/6.09 (0) 20.04/6.09 Obligation: 20.04/6.09 Clauses: 20.04/6.09 20.04/6.09 mergesort([], [], Ls). 20.04/6.09 mergesort(.(X, []), .(X, []), Ls). 20.04/6.09 mergesort(.(X, .(Y, Xs)), Ys, .(H, Ls)) :- ','(split(.(X, .(Y, Xs)), X1s, X2s, .(H, Ls)), ','(mergesort(X1s, Y1s, Ls), ','(mergesort(X2s, Y2s, Ls), merge(Y1s, Y2s, Ys, .(H, Ls))))). 20.04/6.09 split([], [], [], Ls). 20.04/6.09 split(.(X, Xs), .(X, Ys), Zs, .(H, Ls)) :- split(Xs, Zs, Ys, Ls). 20.04/6.09 merge([], Xs, Xs, Ls). 20.04/6.09 merge(Xs, [], Xs, Ls). 20.04/6.09 merge(.(X, Xs), .(Y, Ys), .(X, Zs), .(H, Ls)) :- ','(le(X, Y), merge(Xs, .(Y, Ys), Zs, Ls)). 20.04/6.09 merge(.(X, Xs), .(Y, Ys), .(Y, Zs), .(H, Ls)) :- ','(gt(X, Y), merge(.(X, Xs), Ys, Zs, Ls)). 20.04/6.09 gt(s(X), s(Y)) :- gt(X, Y). 20.04/6.09 gt(s(0), 0). 20.04/6.09 le(s(X), s(Y)) :- le(X, Y). 20.04/6.09 le(0, s(0)). 20.04/6.09 le(0, 0). 20.04/6.09 20.04/6.09 20.04/6.09 Query: mergesort(g,a,a) 20.04/6.09 ---------------------------------------- 20.04/6.09 20.04/6.09 (1) PrologToTRSTransformerProof (SOUND) 20.04/6.09 Transformed Prolog program to TRS. 20.04/6.09 20.04/6.09 { 20.04/6.09 "root": 2, 20.04/6.09 "program": { 20.04/6.09 "directives": [], 20.04/6.09 "clauses": [ 20.04/6.09 [ 20.04/6.09 "(mergesort ([]) ([]) Ls)", 20.04/6.09 null 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(mergesort (. X ([])) (. X ([])) Ls)", 20.04/6.09 null 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(mergesort (. X (. Y Xs)) Ys (. H Ls))", 20.04/6.09 "(',' (split (. X (. Y Xs)) X1s X2s (. H Ls)) (',' (mergesort X1s Y1s Ls) (',' (mergesort X2s Y2s Ls) (merge Y1s Y2s Ys (. H Ls)))))" 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(split ([]) ([]) ([]) Ls)", 20.04/6.09 null 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(split (. X Xs) (. X Ys) Zs (. H Ls))", 20.04/6.09 "(split Xs Zs Ys Ls)" 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(merge ([]) Xs Xs Ls)", 20.04/6.09 null 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(merge Xs ([]) Xs Ls)", 20.04/6.09 null 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(merge (. X Xs) (. Y Ys) (. X Zs) (. H Ls))", 20.04/6.09 "(',' (le X Y) (merge Xs (. Y Ys) Zs Ls))" 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(merge (. X Xs) (. Y Ys) (. Y Zs) (. H Ls))", 20.04/6.09 "(',' (gt X Y) (merge (. X Xs) Ys Zs Ls))" 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(gt (s X) (s Y))", 20.04/6.09 "(gt X Y)" 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(gt (s (0)) (0))", 20.04/6.09 null 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(le (s X) (s Y))", 20.04/6.09 "(le X Y)" 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(le (0) (s (0)))", 20.04/6.09 null 20.04/6.09 ], 20.04/6.09 [ 20.04/6.09 "(le (0) (0))", 20.04/6.09 null 20.04/6.09 ] 20.04/6.09 ] 20.04/6.09 }, 20.04/6.09 "graph": { 20.04/6.09 "nodes": { 20.04/6.09 "type": "Nodes", 20.04/6.09 "472": { 20.04/6.09 "goal": [{ 20.04/6.09 "clause": -1, 20.04/6.09 "scope": -1, 20.04/6.09 "term": "(mergesort T40 X40 T42)" 20.04/6.09 }], 20.04/6.09 "kb": { 20.04/6.09 "nonunifying": [], 20.04/6.09 "intvars": {}, 20.04/6.09 "arithmetic": { 20.04/6.09 "type": "PlainIntegerRelationState", 20.04/6.09 "relations": [] 20.04/6.09 }, 20.04/6.09 "ground": ["T40"], 20.04/6.09 "free": ["X40"], 20.04/6.09 "exprvars": [] 20.04/6.09 } 20.04/6.09 }, 20.04/6.09 "110": { 20.04/6.09 "goal": [ 20.04/6.09 { 20.04/6.09 "clause": 3, 20.04/6.09 "scope": 4, 20.04/6.09 "term": "(split T71 X99 X98 T74)" 20.04/6.09 }, 20.04/6.09 { 20.04/6.09 "clause": 4, 20.04/6.09 "scope": 4, 20.04/6.09 "term": "(split T71 X99 X98 T74)" 20.04/6.09 } 20.04/6.09 ], 20.04/6.09 "kb": { 20.04/6.09 "nonunifying": [], 20.04/6.09 "intvars": {}, 20.04/6.09 "arithmetic": { 20.04/6.09 "type": "PlainIntegerRelationState", 20.04/6.09 "relations": [] 20.04/6.09 }, 20.04/6.09 "ground": ["T71"], 20.04/6.09 "free": [ 20.04/6.09 "X98", 20.04/6.09 "X99" 20.04/6.09 ], 20.04/6.09 "exprvars": [] 20.04/6.09 } 20.04/6.09 }, 20.04/6.09 "473": { 20.04/6.09 "goal": [{ 20.04/6.09 "clause": -1, 20.04/6.09 "scope": -1, 20.04/6.09 "term": "(',' (mergesort T41 X41 T100) (merge T99 X41 T101 (. 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"PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "76": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": 1, 20.04/6.10 "scope": 1, 20.04/6.10 "term": "(mergesort T1 T2 T3)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": ["T1"], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "77": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": 2, 20.04/6.10 "scope": 1, 20.04/6.10 "term": "(mergesort T1 T2 T3)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": ["T1"], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "78": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": -1, 20.04/6.10 "scope": -1, 20.04/6.10 "term": "(true)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "79": { 20.04/6.10 "goal": [], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "100": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": -1, 20.04/6.10 "scope": -1, 20.04/6.10 "term": "(split (. T57 T58) X72 X71 T61)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [ 20.04/6.10 "T57", 20.04/6.10 "T58" 20.04/6.10 ], 20.04/6.10 "free": [ 20.04/6.10 "X71", 20.04/6.10 "X72" 20.04/6.10 ], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "740": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": 12, 20.04/6.10 "scope": 6, 20.04/6.10 "term": "(le T177 T179)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [ 20.04/6.10 "T177", 20.04/6.10 "T179" 20.04/6.10 ], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "741": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": 13, 20.04/6.10 "scope": 6, 20.04/6.10 "term": "(le T177 T179)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [ 20.04/6.10 "T177", 20.04/6.10 "T179" 20.04/6.10 ], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "500": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": -1, 20.04/6.10 "scope": -1, 20.04/6.10 "term": "(true)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "106": { 20.04/6.10 "goal": [ 20.04/6.10 { 20.04/6.10 "clause": 3, 20.04/6.10 "scope": 3, 20.04/6.10 "term": "(split (. T57 T58) X72 X71 T61)" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "clause": 4, 20.04/6.10 "scope": 3, 20.04/6.10 "term": "(split (. T57 T58) X72 X71 T61)" 20.04/6.10 } 20.04/6.10 ], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [ 20.04/6.10 "T57", 20.04/6.10 "T58" 20.04/6.10 ], 20.04/6.10 "free": [ 20.04/6.10 "X71", 20.04/6.10 "X72" 20.04/6.10 ], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "744": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": -1, 20.04/6.10 "scope": -1, 20.04/6.10 "term": "(true)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "80": { 20.04/6.10 "goal": [], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "107": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": 4, 20.04/6.10 "scope": 3, 20.04/6.10 "term": "(split (. T57 T58) X72 X71 T61)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [ 20.04/6.10 "T57", 20.04/6.10 "T58" 20.04/6.10 ], 20.04/6.10 "free": [ 20.04/6.10 "X71", 20.04/6.10 "X72" 20.04/6.10 ], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "503": { 20.04/6.10 "goal": [], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "745": { 20.04/6.10 "goal": [], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "81": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": -1, 20.04/6.10 "scope": -1, 20.04/6.10 "term": "(',' (split (. T31 (. T32 T33)) X38 X39 (. T37 T38)) (',' (mergesort X38 X40 T38) (',' (mergesort X39 X41 T38) (merge X40 X41 T39 (. T37 T38)))))" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [ 20.04/6.10 "T31", 20.04/6.10 "T32", 20.04/6.10 "T33" 20.04/6.10 ], 20.04/6.10 "free": [ 20.04/6.10 "X38", 20.04/6.10 "X39", 20.04/6.10 "X40", 20.04/6.10 "X41" 20.04/6.10 ], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "108": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": -1, 20.04/6.10 "scope": -1, 20.04/6.10 "term": "(split T71 X99 X98 T74)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": ["T71"], 20.04/6.10 "free": [ 20.04/6.10 "X98", 20.04/6.10 "X99" 20.04/6.10 ], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "504": { 20.04/6.10 "goal": [], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "82": { 20.04/6.10 "goal": [], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "109": { 20.04/6.10 "goal": [], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "747": { 20.04/6.10 "goal": [], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "749": { 20.04/6.10 "goal": [{ 20.04/6.10 "clause": -1, 20.04/6.10 "scope": -1, 20.04/6.10 "term": "(true)" 20.04/6.10 }], 20.04/6.10 "kb": { 20.04/6.10 "nonunifying": [], 20.04/6.10 "intvars": {}, 20.04/6.10 "arithmetic": { 20.04/6.10 "type": "PlainIntegerRelationState", 20.04/6.10 "relations": [] 20.04/6.10 }, 20.04/6.10 "ground": [], 20.04/6.10 "free": [], 20.04/6.10 "exprvars": [] 20.04/6.10 } 20.04/6.10 } 20.04/6.10 }, 20.04/6.10 "edges": [ 20.04/6.10 { 20.04/6.10 "from": 2, 20.04/6.10 "to": 14, 20.04/6.10 "label": "CASE" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 14, 20.04/6.10 "to": 15, 20.04/6.10 "label": "PARALLEL" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 14, 20.04/6.10 "to": 16, 20.04/6.10 "label": "PARALLEL" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 15, 20.04/6.10 "to": 73, 20.04/6.10 "label": "EVAL with clause\nmergesort([], [], X5).\nand substitutionT1 -> [],\nT2 -> [],\nT3 -> T8,\nX5 -> T8" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 15, 20.04/6.10 "to": 74, 20.04/6.10 "label": "EVAL-BACKTRACK" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 16, 20.04/6.10 "to": 76, 20.04/6.10 "label": "PARALLEL" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 16, 20.04/6.10 "to": 77, 20.04/6.10 "label": "PARALLEL" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 73, 20.04/6.10 "to": 75, 20.04/6.10 "label": "SUCCESS" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 76, 20.04/6.10 "to": 78, 20.04/6.10 "label": "EVAL with clause\nmergesort(.(X14, []), .(X14, []), X15).\nand substitutionX14 -> T17,\nT1 -> .(T17, []),\nT2 -> .(T17, []),\nT3 -> T18,\nX15 -> T18" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 76, 20.04/6.10 "to": 79, 20.04/6.10 "label": "EVAL-BACKTRACK" 20.04/6.10 }, 20.04/6.10 { 20.04/6.10 "from": 77, 20.04/6.10 "to": 81, 20.04/6.10 "label": "EVAL with clause\nmergesort(.(X32, .(X33, X34)), X35, .(X36, X37)) :- ','(split(.(X32, .(X33, X34)), X38, X39, .(X36, X37)), ','(mergesort(X38, X40, X37), ','(mergesort(X39, X41, X37), merge(X40, X41, X35, .(X36, X37))))).\nand substitutionX32 -> T31,\nX33 -> T32,\nX34 -> T33,\nT1 -> .(T31, .(T32, T33)),\nT2 -> T39,\nX35 -> T39,\nX36 -> T37,\nX37 -> T38,\nT3 -> .(T37, T38),\nT35 -> T37,\nT36 -> T38,\nT34 -> T39" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 77, 20.34/6.11 "to": 82, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 78, 20.34/6.11 "to": 80, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 81, 20.34/6.11 "to": 90, 20.34/6.11 "label": "SPLIT 1" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 81, 20.34/6.11 "to": 92, 20.34/6.11 "label": "SPLIT 2\nnew knowledge:\nT31 is ground\nT32 is ground\nT33 is ground\nT40 is ground\nT41 is ground\nreplacements:X38 -> T40,\nX39 -> T41,\nT38 -> T42,\nT39 -> T43,\nT37 -> T44" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 90, 20.34/6.11 "to": 94, 20.34/6.11 "label": "CASE" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 92, 20.34/6.11 "to": 472, 20.34/6.11 "label": "SPLIT 1" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 92, 20.34/6.11 "to": 473, 20.34/6.11 "label": "SPLIT 2\nnew knowledge:\nT40 is ground\nT99 is ground\nreplacements:X40 -> T99,\nT42 -> T100,\nT43 -> T101,\nT44 -> T102" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 94, 20.34/6.11 "to": 95, 20.34/6.11 "label": "BACKTRACK\nfor clause: split([], [], [], Ls)because of non-unification" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 95, 20.34/6.11 "to": 100, 20.34/6.11 "label": "ONLY EVAL with clause\nsplit(.(X65, X66), .(X65, X67), X68, .(X69, X70)) :- split(X66, X68, X67, X70).\nand substitutionT31 -> T56,\nX65 -> T56,\nT32 -> T57,\nT33 -> T58,\nX66 -> .(T57, T58),\nX67 -> X71,\nX38 -> .(T56, X71),\nX39 -> X72,\nX68 -> X72,\nT37 -> T59,\nX69 -> T59,\nT38 -> T61,\nX70 -> T61,\nT60 -> T61" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 100, 20.34/6.11 "to": 106, 20.34/6.11 "label": "CASE" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 106, 20.34/6.11 "to": 107, 20.34/6.11 "label": "BACKTRACK\nfor clause: split([], [], [], Ls)because of non-unification" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 107, 20.34/6.11 "to": 108, 20.34/6.11 "label": "EVAL with clause\nsplit(.(X92, X93), .(X92, X94), X95, .(X96, X97)) :- split(X93, X95, X94, X97).\nand substitutionT57 -> T70,\nX92 -> T70,\nT58 -> T71,\nX93 -> T71,\nX94 -> X98,\nX72 -> .(T70, X98),\nX71 -> X99,\nX95 -> X99,\nX96 -> T72,\nX97 -> T74,\nT61 -> .(T72, T74),\nT73 -> T74" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 107, 20.34/6.11 "to": 109, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 108, 20.34/6.11 "to": 110, 20.34/6.11 "label": "CASE" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 110, 20.34/6.11 "to": 111, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 110, 20.34/6.11 "to": 112, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 111, 20.34/6.11 "to": 120, 20.34/6.11 "label": "EVAL with clause\nsplit([], [], [], X106).\nand substitutionT71 -> [],\nX99 -> [],\nX98 -> [],\nT74 -> T81,\nX106 -> T81" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 111, 20.34/6.11 "to": 127, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 112, 20.34/6.11 "to": 244, 20.34/6.11 "label": "EVAL with clause\nsplit(.(X123, X124), .(X123, X125), X126, .(X127, X128)) :- split(X124, X126, X125, X128).\nand substitutionX123 -> T90,\nX124 -> T91,\nT71 -> .(T90, T91),\nX125 -> X129,\nX99 -> .(T90, X129),\nX98 -> X130,\nX126 -> X130,\nX127 -> T92,\nX128 -> T94,\nT74 -> .(T92, T94),\nT93 -> T94" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 112, 20.34/6.11 "to": 248, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 120, 20.34/6.11 "to": 131, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 244, 20.34/6.11 "to": 108, 20.34/6.11 "label": "INSTANCE with matching:\nT71 -> T91\nX99 -> X130\nX98 -> X129\nT74 -> T94" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 472, 20.34/6.11 "to": 2, 20.34/6.11 "label": "INSTANCE with matching:\nT1 -> T40\nT2 -> X40\nT3 -> T42" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 473, 20.34/6.11 "to": 476, 20.34/6.11 "label": "SPLIT 1" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 473, 20.34/6.11 "to": 477, 20.34/6.11 "label": "SPLIT 2\nnew knowledge:\nT41 is ground\nT107 is ground\nreplacements:X41 -> T107,\nT101 -> T108,\nT102 -> T109,\nT100 -> T110" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 476, 20.34/6.11 "to": 2, 20.34/6.11 "label": "INSTANCE with matching:\nT1 -> T41\nT2 -> X41\nT3 -> T100" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 477, 20.34/6.11 "to": 483, 20.34/6.11 "label": "CASE" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 483, 20.34/6.11 "to": 489, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 483, 20.34/6.11 "to": 491, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 489, 20.34/6.11 "to": 500, 20.34/6.11 "label": "EVAL with clause\nmerge([], X153, X153, X154).\nand substitutionT99 -> [],\nT107 -> T131,\nX153 -> T131,\nT108 -> T131,\nT109 -> T132,\nT110 -> T133,\nX154 -> .(T132, T133)" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 489, 20.34/6.11 "to": 503, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 491, 20.34/6.11 "to": 510, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 491, 20.34/6.11 "to": 511, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 500, 20.34/6.11 "to": 504, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 510, 20.34/6.11 "to": 520, 20.34/6.11 "label": "EVAL with clause\nmerge(X163, [], X163, X164).\nand substitutionT99 -> T146,\nX163 -> T146,\nT107 -> [],\nT108 -> T146,\nT109 -> T147,\nT110 -> T148,\nX164 -> .(T147, T148)" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 510, 20.34/6.11 "to": 522, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 511, 20.34/6.11 "to": 536, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 511, 20.34/6.11 "to": 537, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 520, 20.34/6.11 "to": 523, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 536, 20.34/6.11 "to": 721, 20.34/6.11 "label": "EVAL with clause\nmerge(.(X193, X194), .(X195, X196), .(X193, X197), .(X198, X199)) :- ','(le(X193, X195), merge(X194, .(X195, X196), X197, X199)).\nand substitutionX193 -> T177,\nX194 -> T178,\nT99 -> .(T177, T178),\nX195 -> T179,\nX196 -> T180,\nT107 -> .(T179, T180),\nX197 -> T184,\nT108 -> .(T177, T184),\nT109 -> T182,\nX198 -> T182,\nT110 -> T185,\nX199 -> T185,\nT181 -> T184,\nT183 -> T185" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 536, 20.34/6.11 "to": 722, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 537, 20.34/6.11 "to": 948, 20.34/6.11 "label": "EVAL with clause\nmerge(.(X396, X397), .(X398, X399), .(X398, X400), .(X401, X402)) :- ','(gt(X396, X398), merge(.(X396, X397), X399, X400, X402)).\nand substitutionX396 -> T395,\nX397 -> T396,\nT99 -> .(T395, T396),\nX398 -> T397,\nX399 -> T398,\nT107 -> .(T397, T398),\nX400 -> T402,\nT108 -> .(T397, T402),\nT109 -> T400,\nX401 -> T400,\nT110 -> T403,\nX402 -> T403,\nT399 -> T402,\nT401 -> T403" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 537, 20.34/6.11 "to": 949, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 721, 20.34/6.11 "to": 723, 20.34/6.11 "label": "SPLIT 1" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 721, 20.34/6.11 "to": 724, 20.34/6.11 "label": "SPLIT 2\nnew knowledge:\nT177 is ground\nT179 is ground" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 723, 20.34/6.11 "to": 725, 20.34/6.11 "label": "CASE" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 724, 20.34/6.11 "to": 760, 20.34/6.11 "label": "CASE" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 725, 20.34/6.11 "to": 733, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 725, 20.34/6.11 "to": 734, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 733, 20.34/6.11 "to": 737, 20.34/6.11 "label": "EVAL with clause\nle(s(X212), s(X213)) :- le(X212, X213).\nand substitutionX212 -> T198,\nT177 -> s(T198),\nX213 -> T199,\nT179 -> s(T199)" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 733, 20.34/6.11 "to": 738, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 734, 20.34/6.11 "to": 740, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 734, 20.34/6.11 "to": 741, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 737, 20.34/6.11 "to": 723, 20.34/6.11 "label": "INSTANCE with matching:\nT177 -> T198\nT179 -> T199" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 740, 20.34/6.11 "to": 744, 20.34/6.11 "label": "EVAL with clause\nle(0, s(0)).\nand substitutionT177 -> 0,\nT179 -> s(0)" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 740, 20.34/6.11 "to": 745, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 741, 20.34/6.11 "to": 749, 20.34/6.11 "label": "EVAL with clause\nle(0, 0).\nand substitutionT177 -> 0,\nT179 -> 0" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 741, 20.34/6.11 "to": 750, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 744, 20.34/6.11 "to": 747, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 749, 20.34/6.11 "to": 751, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 760, 20.34/6.11 "to": 762, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 760, 20.34/6.11 "to": 763, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 762, 20.34/6.11 "to": 766, 20.34/6.11 "label": "EVAL with clause\nmerge([], X228, X228, X229).\nand substitutionT178 -> [],\nT179 -> T220,\nT180 -> T221,\nX228 -> .(T220, T221),\nT184 -> .(T220, T221),\nT185 -> T222,\nX229 -> T222" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 762, 20.34/6.11 "to": 767, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 763, 20.34/6.11 "to": 769, 20.34/6.11 "label": "BACKTRACK\nfor clause: merge(Xs, [], Xs, Ls)because of non-unification" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 766, 20.34/6.11 "to": 768, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 769, 20.34/6.11 "to": 774, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 769, 20.34/6.11 "to": 775, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 774, 20.34/6.11 "to": 780, 20.34/6.11 "label": "EVAL with clause\nmerge(.(X260, X261), .(X262, X263), .(X260, X264), .(X265, X266)) :- ','(le(X260, X262), merge(X261, .(X262, X263), X264, X266)).\nand substitutionX260 -> T252,\nX261 -> T253,\nT178 -> .(T252, T253),\nT179 -> T254,\nX262 -> T254,\nT180 -> T255,\nX263 -> T255,\nX264 -> T259,\nT184 -> .(T252, T259),\nX265 -> T257,\nX266 -> T260,\nT185 -> .(T257, T260),\nT256 -> T259,\nT258 -> T260" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 774, 20.34/6.11 "to": 781, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 775, 20.34/6.11 "to": 808, 20.34/6.11 "label": "EVAL with clause\nmerge(.(X283, X284), .(X285, X286), .(X285, X287), .(X288, X289)) :- ','(gt(X283, X285), merge(.(X283, X284), X286, X287, X289)).\nand substitutionX283 -> T277,\nX284 -> T278,\nT178 -> .(T277, T278),\nT179 -> T279,\nX285 -> T279,\nT180 -> T280,\nX286 -> T280,\nX287 -> T284,\nT184 -> .(T279, T284),\nX288 -> T282,\nX289 -> T285,\nT185 -> .(T282, T285),\nT281 -> T284,\nT283 -> T285" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 775, 20.34/6.11 "to": 810, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 780, 20.34/6.11 "to": 721, 20.34/6.11 "label": "INSTANCE with matching:\nT177 -> T252\nT179 -> T254\nT178 -> T253\nT180 -> T255\nT184 -> T259\nT185 -> T260" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 808, 20.34/6.11 "to": 820, 20.34/6.11 "label": "SPLIT 1" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 808, 20.34/6.11 "to": 822, 20.34/6.11 "label": "SPLIT 2\nnew knowledge:\nT277 is ground\nT279 is ground" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 820, 20.34/6.11 "to": 824, 20.34/6.11 "label": "CASE" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 822, 20.34/6.11 "to": 924, 20.34/6.11 "label": "CASE" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 824, 20.34/6.11 "to": 826, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 824, 20.34/6.11 "to": 827, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 826, 20.34/6.11 "to": 831, 20.34/6.11 "label": "EVAL with clause\ngt(s(X302), s(X303)) :- gt(X302, X303).\nand substitutionX302 -> T298,\nT277 -> s(T298),\nX303 -> T299,\nT279 -> s(T299)" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 826, 20.34/6.11 "to": 916, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 827, 20.34/6.11 "to": 921, 20.34/6.11 "label": "EVAL with clause\ngt(s(0), 0).\nand substitutionT277 -> s(0),\nT279 -> 0" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 827, 20.34/6.11 "to": 922, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 831, 20.34/6.11 "to": 820, 20.34/6.11 "label": "INSTANCE with matching:\nT277 -> T298\nT279 -> T299" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 921, 20.34/6.11 "to": 923, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 924, 20.34/6.11 "to": 927, 20.34/6.11 "label": "BACKTRACK\nfor clause: merge([], Xs, Xs, Ls)because of non-unification" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 927, 20.34/6.11 "to": 928, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 927, 20.34/6.11 "to": 929, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 928, 20.34/6.11 "to": 933, 20.34/6.11 "label": "EVAL with clause\nmerge(X320, [], X320, X321).\nand substitutionT277 -> T314,\nT278 -> T315,\nX320 -> .(T314, T315),\nT280 -> [],\nT284 -> .(T314, T315),\nT285 -> T316,\nX321 -> T316" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 928, 20.34/6.11 "to": 934, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 929, 20.34/6.11 "to": 936, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 929, 20.34/6.11 "to": 937, 20.34/6.11 "label": "PARALLEL" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 933, 20.34/6.11 "to": 935, 20.34/6.11 "label": "SUCCESS" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 936, 20.34/6.11 "to": 944, 20.34/6.11 "label": "EVAL with clause\nmerge(.(X350, X351), .(X352, X353), .(X350, X354), .(X355, X356)) :- ','(le(X350, X352), merge(X351, .(X352, X353), X354, X356)).\nand substitutionT277 -> T345,\nX350 -> T345,\nT278 -> T346,\nX351 -> T346,\nX352 -> T347,\nX353 -> T348,\nT280 -> .(T347, T348),\nX354 -> T352,\nT284 -> .(T345, T352),\nX355 -> T350,\nX356 -> T353,\nT285 -> .(T350, T353),\nT349 -> T352,\nT351 -> T353" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 936, 20.34/6.11 "to": 945, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 937, 20.34/6.11 "to": 946, 20.34/6.11 "label": "EVAL with clause\nmerge(.(X373, X374), .(X375, X376), .(X375, X377), .(X378, X379)) :- ','(gt(X373, X375), merge(.(X373, X374), X376, X377, X379)).\nand substitutionT277 -> T370,\nX373 -> T370,\nT278 -> T371,\nX374 -> T371,\nX375 -> T372,\nX376 -> T373,\nT280 -> .(T372, T373),\nX377 -> T377,\nT284 -> .(T372, T377),\nX378 -> T375,\nX379 -> T378,\nT285 -> .(T375, T378),\nT374 -> T377,\nT376 -> T378" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 937, 20.34/6.11 "to": 947, 20.34/6.11 "label": "EVAL-BACKTRACK" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 944, 20.34/6.11 "to": 721, 20.34/6.11 "label": "INSTANCE with matching:\nT177 -> T345\nT179 -> T347\nT178 -> T346\nT180 -> T348\nT184 -> T352\nT185 -> T353" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 946, 20.34/6.11 "to": 808, 20.34/6.11 "label": "INSTANCE with matching:\nT277 -> T370\nT279 -> T372\nT278 -> T371\nT280 -> T373\nT284 -> T377\nT285 -> T378" 20.34/6.11 }, 20.34/6.11 { 20.34/6.11 "from": 948, 20.34/6.11 "to": 808, 20.34/6.11 "label": "INSTANCE with matching:\nT277 -> T395\nT279 -> T397\nT278 -> T396\nT280 -> T398\nT284 -> T402\nT285 -> T403" 20.34/6.11 } 20.34/6.11 ], 20.34/6.11 "type": "Graph" 20.34/6.11 } 20.34/6.11 } 20.34/6.11 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (2) 20.34/6.11 Obligation: 20.34/6.11 Q restricted rewrite system: 20.34/6.11 The TRS R consists of the following rules: 20.34/6.11 20.34/6.11 f2_in([]) -> f2_out1([]) 20.34/6.11 f2_in(.(T17, [])) -> f2_out1(.(T17, [])) 20.34/6.11 f2_in(.(T31, .(T32, T33))) -> U1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.11 U1(f81_out1(X38, X39, X40, X41, T39), .(T31, .(T32, T33))) -> f2_out1(T39) 20.34/6.11 f108_in([]) -> f108_out1([], []) 20.34/6.11 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.11 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.11 f723_in(s(T198), s(T199)) -> U3(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.11 U3(f723_out1, s(T198), s(T199)) -> f723_out1 20.34/6.11 f723_in(0, s(0)) -> f723_out1 20.34/6.11 f723_in(0, 0) -> f723_out1 20.34/6.11 f820_in(s(T298), s(T299)) -> U4(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.11 U4(f820_out1, s(T298), s(T299)) -> f820_out1 20.34/6.11 f820_in(s(0), 0) -> f820_out1 20.34/6.11 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.11 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.11 f477_in([], T131) -> f477_out1(T131) 20.34/6.11 f477_in(T146, []) -> f477_out1(T146) 20.34/6.11 f477_in(.(T177, T178), .(T179, T180)) -> U6(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.11 U6(f721_out1(T184), .(T177, T178), .(T179, T180)) -> f477_out1(.(T177, T184)) 20.34/6.11 f477_in(.(T395, T396), .(T397, T398)) -> U7(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.11 U7(f808_out1(T402), .(T395, T396), .(T397, T398)) -> f477_out1(.(T397, T402)) 20.34/6.11 f724_in([], T220, T221) -> f724_out1(.(T220, T221)) 20.34/6.11 f724_in(.(T252, T253), T254, T255) -> U8(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.11 U8(f721_out1(T259), .(T252, T253), T254, T255) -> f724_out1(.(T252, T259)) 20.34/6.11 f724_in(.(T277, T278), T279, T280) -> U9(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.11 U9(f808_out1(T284), .(T277, T278), T279, T280) -> f724_out1(.(T279, T284)) 20.34/6.11 f822_in(T314, T315, []) -> f822_out1(.(T314, T315)) 20.34/6.11 f822_in(T345, T346, .(T347, T348)) -> U10(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.11 U10(f721_out1(T352), T345, T346, .(T347, T348)) -> f822_out1(.(T345, T352)) 20.34/6.11 f822_in(T370, T371, .(T372, T373)) -> U11(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.11 U11(f808_out1(T377), T370, T371, .(T372, T373)) -> f822_out1(.(T372, T377)) 20.34/6.11 f81_in(T31, T32, T33) -> U12(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.11 U12(f90_out1(T40, T41), T31, T32, T33) -> U13(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.11 U13(f92_out1(X40, X41, T43), T31, T32, T33, T40, T41) -> f81_out1(T40, T41, X40, X41, T43) 20.34/6.11 f92_in(T40, T41) -> U14(f2_in(T40), T40, T41) 20.34/6.11 U14(f2_out1(T99), T40, T41) -> U15(f473_in(T41, T99), T40, T41, T99) 20.34/6.11 U15(f473_out1(X41, T101), T40, T41, T99) -> f92_out1(T99, X41, T101) 20.34/6.11 f473_in(T41, T99) -> U16(f2_in(T41), T41, T99) 20.34/6.11 U16(f2_out1(T107), T41, T99) -> U17(f477_in(T99, T107), T41, T99, T107) 20.34/6.11 U17(f477_out1(T108), T41, T99, T107) -> f473_out1(T107, T108) 20.34/6.11 f721_in(T177, T179, T178, T180) -> U18(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.11 U18(f723_out1, T177, T179, T178, T180) -> U19(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.11 U19(f724_out1(T184), T177, T179, T178, T180) -> f721_out1(T184) 20.34/6.11 f808_in(T277, T279, T278, T280) -> U20(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.11 U20(f820_out1, T277, T279, T278, T280) -> U21(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.11 U21(f822_out1(T284), T277, T279, T278, T280) -> f808_out1(T284) 20.34/6.11 20.34/6.11 Q is empty. 20.34/6.11 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (3) DependencyPairsProof (EQUIVALENT) 20.34/6.11 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (4) 20.34/6.11 Obligation: 20.34/6.11 Q DP problem: 20.34/6.11 The TRS P consists of the following rules: 20.34/6.11 20.34/6.11 F2_IN(.(T31, .(T32, T33))) -> U1^1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.11 F2_IN(.(T31, .(T32, T33))) -> F81_IN(T31, T32, T33) 20.34/6.11 F108_IN(.(T90, T91)) -> U2^1(f108_in(T91), .(T90, T91)) 20.34/6.11 F108_IN(.(T90, T91)) -> F108_IN(T91) 20.34/6.11 F723_IN(s(T198), s(T199)) -> U3^1(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.11 F723_IN(s(T198), s(T199)) -> F723_IN(T198, T199) 20.34/6.11 F820_IN(s(T298), s(T299)) -> U4^1(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.11 F820_IN(s(T298), s(T299)) -> F820_IN(T298, T299) 20.34/6.11 F90_IN(T56, T70, T71) -> U5^1(f108_in(T71), T56, T70, T71) 20.34/6.11 F90_IN(T56, T70, T71) -> F108_IN(T71) 20.34/6.11 F477_IN(.(T177, T178), .(T179, T180)) -> U6^1(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.11 F477_IN(.(T177, T178), .(T179, T180)) -> F721_IN(T177, T179, T178, T180) 20.34/6.11 F477_IN(.(T395, T396), .(T397, T398)) -> U7^1(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.11 F477_IN(.(T395, T396), .(T397, T398)) -> F808_IN(T395, T397, T396, T398) 20.34/6.11 F724_IN(.(T252, T253), T254, T255) -> U8^1(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.11 F724_IN(.(T252, T253), T254, T255) -> F721_IN(T252, T254, T253, T255) 20.34/6.11 F724_IN(.(T277, T278), T279, T280) -> U9^1(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.11 F724_IN(.(T277, T278), T279, T280) -> F808_IN(T277, T279, T278, T280) 20.34/6.11 F822_IN(T345, T346, .(T347, T348)) -> U10^1(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.11 F822_IN(T345, T346, .(T347, T348)) -> F721_IN(T345, T347, T346, T348) 20.34/6.11 F822_IN(T370, T371, .(T372, T373)) -> U11^1(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.11 F822_IN(T370, T371, .(T372, T373)) -> F808_IN(T370, T372, T371, T373) 20.34/6.11 F81_IN(T31, T32, T33) -> U12^1(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.11 F81_IN(T31, T32, T33) -> F90_IN(T31, T32, T33) 20.34/6.11 U12^1(f90_out1(T40, T41), T31, T32, T33) -> U13^1(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.11 U12^1(f90_out1(T40, T41), T31, T32, T33) -> F92_IN(T40, T41) 20.34/6.11 F92_IN(T40, T41) -> U14^1(f2_in(T40), T40, T41) 20.34/6.11 F92_IN(T40, T41) -> F2_IN(T40) 20.34/6.11 U14^1(f2_out1(T99), T40, T41) -> U15^1(f473_in(T41, T99), T40, T41, T99) 20.34/6.11 U14^1(f2_out1(T99), T40, T41) -> F473_IN(T41, T99) 20.34/6.11 F473_IN(T41, T99) -> U16^1(f2_in(T41), T41, T99) 20.34/6.11 F473_IN(T41, T99) -> F2_IN(T41) 20.34/6.11 U16^1(f2_out1(T107), T41, T99) -> U17^1(f477_in(T99, T107), T41, T99, T107) 20.34/6.11 U16^1(f2_out1(T107), T41, T99) -> F477_IN(T99, T107) 20.34/6.11 F721_IN(T177, T179, T178, T180) -> U18^1(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.11 F721_IN(T177, T179, T178, T180) -> F723_IN(T177, T179) 20.34/6.11 U18^1(f723_out1, T177, T179, T178, T180) -> U19^1(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.11 U18^1(f723_out1, T177, T179, T178, T180) -> F724_IN(T178, T179, T180) 20.34/6.11 F808_IN(T277, T279, T278, T280) -> U20^1(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.11 F808_IN(T277, T279, T278, T280) -> F820_IN(T277, T279) 20.34/6.11 U20^1(f820_out1, T277, T279, T278, T280) -> U21^1(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.11 U20^1(f820_out1, T277, T279, T278, T280) -> F822_IN(T277, T278, T280) 20.34/6.11 20.34/6.11 The TRS R consists of the following rules: 20.34/6.11 20.34/6.11 f2_in([]) -> f2_out1([]) 20.34/6.11 f2_in(.(T17, [])) -> f2_out1(.(T17, [])) 20.34/6.11 f2_in(.(T31, .(T32, T33))) -> U1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.11 U1(f81_out1(X38, X39, X40, X41, T39), .(T31, .(T32, T33))) -> f2_out1(T39) 20.34/6.11 f108_in([]) -> f108_out1([], []) 20.34/6.11 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.11 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.11 f723_in(s(T198), s(T199)) -> U3(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.11 U3(f723_out1, s(T198), s(T199)) -> f723_out1 20.34/6.11 f723_in(0, s(0)) -> f723_out1 20.34/6.11 f723_in(0, 0) -> f723_out1 20.34/6.11 f820_in(s(T298), s(T299)) -> U4(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.11 U4(f820_out1, s(T298), s(T299)) -> f820_out1 20.34/6.11 f820_in(s(0), 0) -> f820_out1 20.34/6.11 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.11 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.11 f477_in([], T131) -> f477_out1(T131) 20.34/6.11 f477_in(T146, []) -> f477_out1(T146) 20.34/6.11 f477_in(.(T177, T178), .(T179, T180)) -> U6(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.11 U6(f721_out1(T184), .(T177, T178), .(T179, T180)) -> f477_out1(.(T177, T184)) 20.34/6.11 f477_in(.(T395, T396), .(T397, T398)) -> U7(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.11 U7(f808_out1(T402), .(T395, T396), .(T397, T398)) -> f477_out1(.(T397, T402)) 20.34/6.11 f724_in([], T220, T221) -> f724_out1(.(T220, T221)) 20.34/6.11 f724_in(.(T252, T253), T254, T255) -> U8(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.11 U8(f721_out1(T259), .(T252, T253), T254, T255) -> f724_out1(.(T252, T259)) 20.34/6.11 f724_in(.(T277, T278), T279, T280) -> U9(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.11 U9(f808_out1(T284), .(T277, T278), T279, T280) -> f724_out1(.(T279, T284)) 20.34/6.11 f822_in(T314, T315, []) -> f822_out1(.(T314, T315)) 20.34/6.11 f822_in(T345, T346, .(T347, T348)) -> U10(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.11 U10(f721_out1(T352), T345, T346, .(T347, T348)) -> f822_out1(.(T345, T352)) 20.34/6.11 f822_in(T370, T371, .(T372, T373)) -> U11(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.11 U11(f808_out1(T377), T370, T371, .(T372, T373)) -> f822_out1(.(T372, T377)) 20.34/6.11 f81_in(T31, T32, T33) -> U12(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.11 U12(f90_out1(T40, T41), T31, T32, T33) -> U13(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.11 U13(f92_out1(X40, X41, T43), T31, T32, T33, T40, T41) -> f81_out1(T40, T41, X40, X41, T43) 20.34/6.11 f92_in(T40, T41) -> U14(f2_in(T40), T40, T41) 20.34/6.11 U14(f2_out1(T99), T40, T41) -> U15(f473_in(T41, T99), T40, T41, T99) 20.34/6.11 U15(f473_out1(X41, T101), T40, T41, T99) -> f92_out1(T99, X41, T101) 20.34/6.11 f473_in(T41, T99) -> U16(f2_in(T41), T41, T99) 20.34/6.11 U16(f2_out1(T107), T41, T99) -> U17(f477_in(T99, T107), T41, T99, T107) 20.34/6.11 U17(f477_out1(T108), T41, T99, T107) -> f473_out1(T107, T108) 20.34/6.11 f721_in(T177, T179, T178, T180) -> U18(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.11 U18(f723_out1, T177, T179, T178, T180) -> U19(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.11 U19(f724_out1(T184), T177, T179, T178, T180) -> f721_out1(T184) 20.34/6.11 f808_in(T277, T279, T278, T280) -> U20(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.11 U20(f820_out1, T277, T279, T278, T280) -> U21(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.11 U21(f822_out1(T284), T277, T279, T278, T280) -> f808_out1(T284) 20.34/6.11 20.34/6.11 Q is empty. 20.34/6.11 We have to consider all minimal (P,Q,R)-chains. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (5) DependencyGraphProof (EQUIVALENT) 20.34/6.11 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 5 SCCs with 24 less nodes. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (6) 20.34/6.11 Complex Obligation (AND) 20.34/6.11 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (7) 20.34/6.11 Obligation: 20.34/6.11 Q DP problem: 20.34/6.11 The TRS P consists of the following rules: 20.34/6.11 20.34/6.11 F820_IN(s(T298), s(T299)) -> F820_IN(T298, T299) 20.34/6.11 20.34/6.11 The TRS R consists of the following rules: 20.34/6.11 20.34/6.11 f2_in([]) -> f2_out1([]) 20.34/6.11 f2_in(.(T17, [])) -> f2_out1(.(T17, [])) 20.34/6.11 f2_in(.(T31, .(T32, T33))) -> U1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.11 U1(f81_out1(X38, X39, X40, X41, T39), .(T31, .(T32, T33))) -> f2_out1(T39) 20.34/6.11 f108_in([]) -> f108_out1([], []) 20.34/6.11 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.11 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.11 f723_in(s(T198), s(T199)) -> U3(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.11 U3(f723_out1, s(T198), s(T199)) -> f723_out1 20.34/6.11 f723_in(0, s(0)) -> f723_out1 20.34/6.11 f723_in(0, 0) -> f723_out1 20.34/6.11 f820_in(s(T298), s(T299)) -> U4(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.11 U4(f820_out1, s(T298), s(T299)) -> f820_out1 20.34/6.11 f820_in(s(0), 0) -> f820_out1 20.34/6.11 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.11 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.11 f477_in([], T131) -> f477_out1(T131) 20.34/6.11 f477_in(T146, []) -> f477_out1(T146) 20.34/6.11 f477_in(.(T177, T178), .(T179, T180)) -> U6(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.11 U6(f721_out1(T184), .(T177, T178), .(T179, T180)) -> f477_out1(.(T177, T184)) 20.34/6.11 f477_in(.(T395, T396), .(T397, T398)) -> U7(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.11 U7(f808_out1(T402), .(T395, T396), .(T397, T398)) -> f477_out1(.(T397, T402)) 20.34/6.11 f724_in([], T220, T221) -> f724_out1(.(T220, T221)) 20.34/6.11 f724_in(.(T252, T253), T254, T255) -> U8(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.11 U8(f721_out1(T259), .(T252, T253), T254, T255) -> f724_out1(.(T252, T259)) 20.34/6.11 f724_in(.(T277, T278), T279, T280) -> U9(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.11 U9(f808_out1(T284), .(T277, T278), T279, T280) -> f724_out1(.(T279, T284)) 20.34/6.11 f822_in(T314, T315, []) -> f822_out1(.(T314, T315)) 20.34/6.11 f822_in(T345, T346, .(T347, T348)) -> U10(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.11 U10(f721_out1(T352), T345, T346, .(T347, T348)) -> f822_out1(.(T345, T352)) 20.34/6.11 f822_in(T370, T371, .(T372, T373)) -> U11(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.11 U11(f808_out1(T377), T370, T371, .(T372, T373)) -> f822_out1(.(T372, T377)) 20.34/6.11 f81_in(T31, T32, T33) -> U12(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.11 U12(f90_out1(T40, T41), T31, T32, T33) -> U13(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.11 U13(f92_out1(X40, X41, T43), T31, T32, T33, T40, T41) -> f81_out1(T40, T41, X40, X41, T43) 20.34/6.11 f92_in(T40, T41) -> U14(f2_in(T40), T40, T41) 20.34/6.11 U14(f2_out1(T99), T40, T41) -> U15(f473_in(T41, T99), T40, T41, T99) 20.34/6.11 U15(f473_out1(X41, T101), T40, T41, T99) -> f92_out1(T99, X41, T101) 20.34/6.11 f473_in(T41, T99) -> U16(f2_in(T41), T41, T99) 20.34/6.11 U16(f2_out1(T107), T41, T99) -> U17(f477_in(T99, T107), T41, T99, T107) 20.34/6.11 U17(f477_out1(T108), T41, T99, T107) -> f473_out1(T107, T108) 20.34/6.11 f721_in(T177, T179, T178, T180) -> U18(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.11 U18(f723_out1, T177, T179, T178, T180) -> U19(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.11 U19(f724_out1(T184), T177, T179, T178, T180) -> f721_out1(T184) 20.34/6.11 f808_in(T277, T279, T278, T280) -> U20(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.11 U20(f820_out1, T277, T279, T278, T280) -> U21(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.11 U21(f822_out1(T284), T277, T279, T278, T280) -> f808_out1(T284) 20.34/6.11 20.34/6.11 Q is empty. 20.34/6.11 We have to consider all minimal (P,Q,R)-chains. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (8) UsableRulesProof (EQUIVALENT) 20.34/6.11 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (9) 20.34/6.11 Obligation: 20.34/6.11 Q DP problem: 20.34/6.11 The TRS P consists of the following rules: 20.34/6.11 20.34/6.11 F820_IN(s(T298), s(T299)) -> F820_IN(T298, T299) 20.34/6.11 20.34/6.11 R is empty. 20.34/6.11 Q is empty. 20.34/6.11 We have to consider all minimal (P,Q,R)-chains. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (10) QDPSizeChangeProof (EQUIVALENT) 20.34/6.11 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 20.34/6.11 20.34/6.11 From the DPs we obtained the following set of size-change graphs: 20.34/6.11 *F820_IN(s(T298), s(T299)) -> F820_IN(T298, T299) 20.34/6.11 The graph contains the following edges 1 > 1, 2 > 2 20.34/6.11 20.34/6.11 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (11) 20.34/6.11 YES 20.34/6.11 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (12) 20.34/6.11 Obligation: 20.34/6.11 Q DP problem: 20.34/6.11 The TRS P consists of the following rules: 20.34/6.11 20.34/6.11 F723_IN(s(T198), s(T199)) -> F723_IN(T198, T199) 20.34/6.11 20.34/6.11 The TRS R consists of the following rules: 20.34/6.11 20.34/6.11 f2_in([]) -> f2_out1([]) 20.34/6.11 f2_in(.(T17, [])) -> f2_out1(.(T17, [])) 20.34/6.11 f2_in(.(T31, .(T32, T33))) -> U1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.11 U1(f81_out1(X38, X39, X40, X41, T39), .(T31, .(T32, T33))) -> f2_out1(T39) 20.34/6.11 f108_in([]) -> f108_out1([], []) 20.34/6.11 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.11 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.11 f723_in(s(T198), s(T199)) -> U3(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.11 U3(f723_out1, s(T198), s(T199)) -> f723_out1 20.34/6.11 f723_in(0, s(0)) -> f723_out1 20.34/6.11 f723_in(0, 0) -> f723_out1 20.34/6.11 f820_in(s(T298), s(T299)) -> U4(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.11 U4(f820_out1, s(T298), s(T299)) -> f820_out1 20.34/6.11 f820_in(s(0), 0) -> f820_out1 20.34/6.11 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.11 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.11 f477_in([], T131) -> f477_out1(T131) 20.34/6.11 f477_in(T146, []) -> f477_out1(T146) 20.34/6.11 f477_in(.(T177, T178), .(T179, T180)) -> U6(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.11 U6(f721_out1(T184), .(T177, T178), .(T179, T180)) -> f477_out1(.(T177, T184)) 20.34/6.11 f477_in(.(T395, T396), .(T397, T398)) -> U7(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.11 U7(f808_out1(T402), .(T395, T396), .(T397, T398)) -> f477_out1(.(T397, T402)) 20.34/6.11 f724_in([], T220, T221) -> f724_out1(.(T220, T221)) 20.34/6.11 f724_in(.(T252, T253), T254, T255) -> U8(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.11 U8(f721_out1(T259), .(T252, T253), T254, T255) -> f724_out1(.(T252, T259)) 20.34/6.11 f724_in(.(T277, T278), T279, T280) -> U9(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.11 U9(f808_out1(T284), .(T277, T278), T279, T280) -> f724_out1(.(T279, T284)) 20.34/6.11 f822_in(T314, T315, []) -> f822_out1(.(T314, T315)) 20.34/6.11 f822_in(T345, T346, .(T347, T348)) -> U10(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.11 U10(f721_out1(T352), T345, T346, .(T347, T348)) -> f822_out1(.(T345, T352)) 20.34/6.11 f822_in(T370, T371, .(T372, T373)) -> U11(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.11 U11(f808_out1(T377), T370, T371, .(T372, T373)) -> f822_out1(.(T372, T377)) 20.34/6.11 f81_in(T31, T32, T33) -> U12(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.11 U12(f90_out1(T40, T41), T31, T32, T33) -> U13(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.11 U13(f92_out1(X40, X41, T43), T31, T32, T33, T40, T41) -> f81_out1(T40, T41, X40, X41, T43) 20.34/6.11 f92_in(T40, T41) -> U14(f2_in(T40), T40, T41) 20.34/6.11 U14(f2_out1(T99), T40, T41) -> U15(f473_in(T41, T99), T40, T41, T99) 20.34/6.11 U15(f473_out1(X41, T101), T40, T41, T99) -> f92_out1(T99, X41, T101) 20.34/6.11 f473_in(T41, T99) -> U16(f2_in(T41), T41, T99) 20.34/6.11 U16(f2_out1(T107), T41, T99) -> U17(f477_in(T99, T107), T41, T99, T107) 20.34/6.11 U17(f477_out1(T108), T41, T99, T107) -> f473_out1(T107, T108) 20.34/6.11 f721_in(T177, T179, T178, T180) -> U18(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.11 U18(f723_out1, T177, T179, T178, T180) -> U19(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.11 U19(f724_out1(T184), T177, T179, T178, T180) -> f721_out1(T184) 20.34/6.11 f808_in(T277, T279, T278, T280) -> U20(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.11 U20(f820_out1, T277, T279, T278, T280) -> U21(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.11 U21(f822_out1(T284), T277, T279, T278, T280) -> f808_out1(T284) 20.34/6.11 20.34/6.11 Q is empty. 20.34/6.11 We have to consider all minimal (P,Q,R)-chains. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (13) UsableRulesProof (EQUIVALENT) 20.34/6.11 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (14) 20.34/6.11 Obligation: 20.34/6.11 Q DP problem: 20.34/6.11 The TRS P consists of the following rules: 20.34/6.11 20.34/6.11 F723_IN(s(T198), s(T199)) -> F723_IN(T198, T199) 20.34/6.11 20.34/6.11 R is empty. 20.34/6.11 Q is empty. 20.34/6.11 We have to consider all minimal (P,Q,R)-chains. 20.34/6.11 ---------------------------------------- 20.34/6.11 20.34/6.11 (15) QDPSizeChangeProof (EQUIVALENT) 20.34/6.11 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 20.34/6.11 20.34/6.11 From the DPs we obtained the following set of size-change graphs: 20.34/6.11 *F723_IN(s(T198), s(T199)) -> F723_IN(T198, T199) 20.34/6.12 The graph contains the following edges 1 > 1, 2 > 2 20.34/6.12 20.34/6.12 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (16) 20.34/6.12 YES 20.34/6.12 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (17) 20.34/6.12 Obligation: 20.34/6.12 Q DP problem: 20.34/6.12 The TRS P consists of the following rules: 20.34/6.12 20.34/6.12 F721_IN(T177, T179, T178, T180) -> U18^1(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.12 U18^1(f723_out1, T177, T179, T178, T180) -> F724_IN(T178, T179, T180) 20.34/6.12 F724_IN(.(T252, T253), T254, T255) -> F721_IN(T252, T254, T253, T255) 20.34/6.12 F724_IN(.(T277, T278), T279, T280) -> F808_IN(T277, T279, T278, T280) 20.34/6.12 F808_IN(T277, T279, T278, T280) -> U20^1(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.12 U20^1(f820_out1, T277, T279, T278, T280) -> F822_IN(T277, T278, T280) 20.34/6.12 F822_IN(T345, T346, .(T347, T348)) -> F721_IN(T345, T347, T346, T348) 20.34/6.12 F822_IN(T370, T371, .(T372, T373)) -> F808_IN(T370, T372, T371, T373) 20.34/6.12 20.34/6.12 The TRS R consists of the following rules: 20.34/6.12 20.34/6.12 f2_in([]) -> f2_out1([]) 20.34/6.12 f2_in(.(T17, [])) -> f2_out1(.(T17, [])) 20.34/6.12 f2_in(.(T31, .(T32, T33))) -> U1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.12 U1(f81_out1(X38, X39, X40, X41, T39), .(T31, .(T32, T33))) -> f2_out1(T39) 20.34/6.12 f108_in([]) -> f108_out1([], []) 20.34/6.12 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.12 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.12 f723_in(s(T198), s(T199)) -> U3(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.12 U3(f723_out1, s(T198), s(T199)) -> f723_out1 20.34/6.12 f723_in(0, s(0)) -> f723_out1 20.34/6.12 f723_in(0, 0) -> f723_out1 20.34/6.12 f820_in(s(T298), s(T299)) -> U4(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.12 U4(f820_out1, s(T298), s(T299)) -> f820_out1 20.34/6.12 f820_in(s(0), 0) -> f820_out1 20.34/6.12 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.12 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.12 f477_in([], T131) -> f477_out1(T131) 20.34/6.12 f477_in(T146, []) -> f477_out1(T146) 20.34/6.12 f477_in(.(T177, T178), .(T179, T180)) -> U6(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.12 U6(f721_out1(T184), .(T177, T178), .(T179, T180)) -> f477_out1(.(T177, T184)) 20.34/6.12 f477_in(.(T395, T396), .(T397, T398)) -> U7(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.12 U7(f808_out1(T402), .(T395, T396), .(T397, T398)) -> f477_out1(.(T397, T402)) 20.34/6.12 f724_in([], T220, T221) -> f724_out1(.(T220, T221)) 20.34/6.12 f724_in(.(T252, T253), T254, T255) -> U8(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.12 U8(f721_out1(T259), .(T252, T253), T254, T255) -> f724_out1(.(T252, T259)) 20.34/6.12 f724_in(.(T277, T278), T279, T280) -> U9(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.12 U9(f808_out1(T284), .(T277, T278), T279, T280) -> f724_out1(.(T279, T284)) 20.34/6.12 f822_in(T314, T315, []) -> f822_out1(.(T314, T315)) 20.34/6.12 f822_in(T345, T346, .(T347, T348)) -> U10(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.12 U10(f721_out1(T352), T345, T346, .(T347, T348)) -> f822_out1(.(T345, T352)) 20.34/6.12 f822_in(T370, T371, .(T372, T373)) -> U11(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.12 U11(f808_out1(T377), T370, T371, .(T372, T373)) -> f822_out1(.(T372, T377)) 20.34/6.12 f81_in(T31, T32, T33) -> U12(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.12 U12(f90_out1(T40, T41), T31, T32, T33) -> U13(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.12 U13(f92_out1(X40, X41, T43), T31, T32, T33, T40, T41) -> f81_out1(T40, T41, X40, X41, T43) 20.34/6.12 f92_in(T40, T41) -> U14(f2_in(T40), T40, T41) 20.34/6.12 U14(f2_out1(T99), T40, T41) -> U15(f473_in(T41, T99), T40, T41, T99) 20.34/6.12 U15(f473_out1(X41, T101), T40, T41, T99) -> f92_out1(T99, X41, T101) 20.34/6.12 f473_in(T41, T99) -> U16(f2_in(T41), T41, T99) 20.34/6.12 U16(f2_out1(T107), T41, T99) -> U17(f477_in(T99, T107), T41, T99, T107) 20.34/6.12 U17(f477_out1(T108), T41, T99, T107) -> f473_out1(T107, T108) 20.34/6.12 f721_in(T177, T179, T178, T180) -> U18(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.12 U18(f723_out1, T177, T179, T178, T180) -> U19(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.12 U19(f724_out1(T184), T177, T179, T178, T180) -> f721_out1(T184) 20.34/6.12 f808_in(T277, T279, T278, T280) -> U20(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.12 U20(f820_out1, T277, T279, T278, T280) -> U21(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.12 U21(f822_out1(T284), T277, T279, T278, T280) -> f808_out1(T284) 20.34/6.12 20.34/6.12 Q is empty. 20.34/6.12 We have to consider all minimal (P,Q,R)-chains. 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (18) QDPSizeChangeProof (EQUIVALENT) 20.34/6.12 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 20.34/6.12 20.34/6.12 From the DPs we obtained the following set of size-change graphs: 20.34/6.12 *U18^1(f723_out1, T177, T179, T178, T180) -> F724_IN(T178, T179, T180) 20.34/6.12 The graph contains the following edges 4 >= 1, 3 >= 2, 5 >= 3 20.34/6.12 20.34/6.12 20.34/6.12 *F724_IN(.(T252, T253), T254, T255) -> F721_IN(T252, T254, T253, T255) 20.34/6.12 The graph contains the following edges 1 > 1, 2 >= 2, 1 > 3, 3 >= 4 20.34/6.12 20.34/6.12 20.34/6.12 *F822_IN(T345, T346, .(T347, T348)) -> F721_IN(T345, T347, T346, T348) 20.34/6.12 The graph contains the following edges 1 >= 1, 3 > 2, 2 >= 3, 3 > 4 20.34/6.12 20.34/6.12 20.34/6.12 *F724_IN(.(T277, T278), T279, T280) -> F808_IN(T277, T279, T278, T280) 20.34/6.12 The graph contains the following edges 1 > 1, 2 >= 2, 1 > 3, 3 >= 4 20.34/6.12 20.34/6.12 20.34/6.12 *F721_IN(T177, T179, T178, T180) -> U18^1(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.12 The graph contains the following edges 1 >= 2, 2 >= 3, 3 >= 4, 4 >= 5 20.34/6.12 20.34/6.12 20.34/6.12 *F808_IN(T277, T279, T278, T280) -> U20^1(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.12 The graph contains the following edges 1 >= 2, 2 >= 3, 3 >= 4, 4 >= 5 20.34/6.12 20.34/6.12 20.34/6.12 *U20^1(f820_out1, T277, T279, T278, T280) -> F822_IN(T277, T278, T280) 20.34/6.12 The graph contains the following edges 2 >= 1, 4 >= 2, 5 >= 3 20.34/6.12 20.34/6.12 20.34/6.12 *F822_IN(T370, T371, .(T372, T373)) -> F808_IN(T370, T372, T371, T373) 20.34/6.12 The graph contains the following edges 1 >= 1, 3 > 2, 2 >= 3, 3 > 4 20.34/6.12 20.34/6.12 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (19) 20.34/6.12 YES 20.34/6.12 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (20) 20.34/6.12 Obligation: 20.34/6.12 Q DP problem: 20.34/6.12 The TRS P consists of the following rules: 20.34/6.12 20.34/6.12 F108_IN(.(T90, T91)) -> F108_IN(T91) 20.34/6.12 20.34/6.12 The TRS R consists of the following rules: 20.34/6.12 20.34/6.12 f2_in([]) -> f2_out1([]) 20.34/6.12 f2_in(.(T17, [])) -> f2_out1(.(T17, [])) 20.34/6.12 f2_in(.(T31, .(T32, T33))) -> U1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.12 U1(f81_out1(X38, X39, X40, X41, T39), .(T31, .(T32, T33))) -> f2_out1(T39) 20.34/6.12 f108_in([]) -> f108_out1([], []) 20.34/6.12 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.12 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.12 f723_in(s(T198), s(T199)) -> U3(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.12 U3(f723_out1, s(T198), s(T199)) -> f723_out1 20.34/6.12 f723_in(0, s(0)) -> f723_out1 20.34/6.12 f723_in(0, 0) -> f723_out1 20.34/6.12 f820_in(s(T298), s(T299)) -> U4(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.12 U4(f820_out1, s(T298), s(T299)) -> f820_out1 20.34/6.12 f820_in(s(0), 0) -> f820_out1 20.34/6.12 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.12 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.12 f477_in([], T131) -> f477_out1(T131) 20.34/6.12 f477_in(T146, []) -> f477_out1(T146) 20.34/6.12 f477_in(.(T177, T178), .(T179, T180)) -> U6(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.12 U6(f721_out1(T184), .(T177, T178), .(T179, T180)) -> f477_out1(.(T177, T184)) 20.34/6.12 f477_in(.(T395, T396), .(T397, T398)) -> U7(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.12 U7(f808_out1(T402), .(T395, T396), .(T397, T398)) -> f477_out1(.(T397, T402)) 20.34/6.12 f724_in([], T220, T221) -> f724_out1(.(T220, T221)) 20.34/6.12 f724_in(.(T252, T253), T254, T255) -> U8(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.12 U8(f721_out1(T259), .(T252, T253), T254, T255) -> f724_out1(.(T252, T259)) 20.34/6.12 f724_in(.(T277, T278), T279, T280) -> U9(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.12 U9(f808_out1(T284), .(T277, T278), T279, T280) -> f724_out1(.(T279, T284)) 20.34/6.12 f822_in(T314, T315, []) -> f822_out1(.(T314, T315)) 20.34/6.12 f822_in(T345, T346, .(T347, T348)) -> U10(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.12 U10(f721_out1(T352), T345, T346, .(T347, T348)) -> f822_out1(.(T345, T352)) 20.34/6.12 f822_in(T370, T371, .(T372, T373)) -> U11(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.12 U11(f808_out1(T377), T370, T371, .(T372, T373)) -> f822_out1(.(T372, T377)) 20.34/6.12 f81_in(T31, T32, T33) -> U12(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.12 U12(f90_out1(T40, T41), T31, T32, T33) -> U13(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.12 U13(f92_out1(X40, X41, T43), T31, T32, T33, T40, T41) -> f81_out1(T40, T41, X40, X41, T43) 20.34/6.12 f92_in(T40, T41) -> U14(f2_in(T40), T40, T41) 20.34/6.12 U14(f2_out1(T99), T40, T41) -> U15(f473_in(T41, T99), T40, T41, T99) 20.34/6.12 U15(f473_out1(X41, T101), T40, T41, T99) -> f92_out1(T99, X41, T101) 20.34/6.12 f473_in(T41, T99) -> U16(f2_in(T41), T41, T99) 20.34/6.12 U16(f2_out1(T107), T41, T99) -> U17(f477_in(T99, T107), T41, T99, T107) 20.34/6.12 U17(f477_out1(T108), T41, T99, T107) -> f473_out1(T107, T108) 20.34/6.12 f721_in(T177, T179, T178, T180) -> U18(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.12 U18(f723_out1, T177, T179, T178, T180) -> U19(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.12 U19(f724_out1(T184), T177, T179, T178, T180) -> f721_out1(T184) 20.34/6.12 f808_in(T277, T279, T278, T280) -> U20(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.12 U20(f820_out1, T277, T279, T278, T280) -> U21(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.12 U21(f822_out1(T284), T277, T279, T278, T280) -> f808_out1(T284) 20.34/6.12 20.34/6.12 Q is empty. 20.34/6.12 We have to consider all minimal (P,Q,R)-chains. 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (21) UsableRulesProof (EQUIVALENT) 20.34/6.12 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (22) 20.34/6.12 Obligation: 20.34/6.12 Q DP problem: 20.34/6.12 The TRS P consists of the following rules: 20.34/6.12 20.34/6.12 F108_IN(.(T90, T91)) -> F108_IN(T91) 20.34/6.12 20.34/6.12 R is empty. 20.34/6.12 Q is empty. 20.34/6.12 We have to consider all minimal (P,Q,R)-chains. 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (23) QDPSizeChangeProof (EQUIVALENT) 20.34/6.12 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 20.34/6.12 20.34/6.12 From the DPs we obtained the following set of size-change graphs: 20.34/6.12 *F108_IN(.(T90, T91)) -> F108_IN(T91) 20.34/6.12 The graph contains the following edges 1 > 1 20.34/6.12 20.34/6.12 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (24) 20.34/6.12 YES 20.34/6.12 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (25) 20.34/6.12 Obligation: 20.34/6.12 Q DP problem: 20.34/6.12 The TRS P consists of the following rules: 20.34/6.12 20.34/6.12 F2_IN(.(T31, .(T32, T33))) -> F81_IN(T31, T32, T33) 20.34/6.12 F81_IN(T31, T32, T33) -> U12^1(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.12 U12^1(f90_out1(T40, T41), T31, T32, T33) -> F92_IN(T40, T41) 20.34/6.12 F92_IN(T40, T41) -> U14^1(f2_in(T40), T40, T41) 20.34/6.12 U14^1(f2_out1(T99), T40, T41) -> F473_IN(T41, T99) 20.34/6.12 F473_IN(T41, T99) -> F2_IN(T41) 20.34/6.12 F92_IN(T40, T41) -> F2_IN(T40) 20.34/6.12 20.34/6.12 The TRS R consists of the following rules: 20.34/6.12 20.34/6.12 f2_in([]) -> f2_out1([]) 20.34/6.12 f2_in(.(T17, [])) -> f2_out1(.(T17, [])) 20.34/6.12 f2_in(.(T31, .(T32, T33))) -> U1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.12 U1(f81_out1(X38, X39, X40, X41, T39), .(T31, .(T32, T33))) -> f2_out1(T39) 20.34/6.12 f108_in([]) -> f108_out1([], []) 20.34/6.12 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.12 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.12 f723_in(s(T198), s(T199)) -> U3(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.12 U3(f723_out1, s(T198), s(T199)) -> f723_out1 20.34/6.12 f723_in(0, s(0)) -> f723_out1 20.34/6.12 f723_in(0, 0) -> f723_out1 20.34/6.12 f820_in(s(T298), s(T299)) -> U4(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.12 U4(f820_out1, s(T298), s(T299)) -> f820_out1 20.34/6.12 f820_in(s(0), 0) -> f820_out1 20.34/6.12 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.12 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.12 f477_in([], T131) -> f477_out1(T131) 20.34/6.12 f477_in(T146, []) -> f477_out1(T146) 20.34/6.12 f477_in(.(T177, T178), .(T179, T180)) -> U6(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.12 U6(f721_out1(T184), .(T177, T178), .(T179, T180)) -> f477_out1(.(T177, T184)) 20.34/6.12 f477_in(.(T395, T396), .(T397, T398)) -> U7(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.12 U7(f808_out1(T402), .(T395, T396), .(T397, T398)) -> f477_out1(.(T397, T402)) 20.34/6.12 f724_in([], T220, T221) -> f724_out1(.(T220, T221)) 20.34/6.12 f724_in(.(T252, T253), T254, T255) -> U8(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.12 U8(f721_out1(T259), .(T252, T253), T254, T255) -> f724_out1(.(T252, T259)) 20.34/6.12 f724_in(.(T277, T278), T279, T280) -> U9(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.12 U9(f808_out1(T284), .(T277, T278), T279, T280) -> f724_out1(.(T279, T284)) 20.34/6.12 f822_in(T314, T315, []) -> f822_out1(.(T314, T315)) 20.34/6.12 f822_in(T345, T346, .(T347, T348)) -> U10(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.12 U10(f721_out1(T352), T345, T346, .(T347, T348)) -> f822_out1(.(T345, T352)) 20.34/6.12 f822_in(T370, T371, .(T372, T373)) -> U11(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.12 U11(f808_out1(T377), T370, T371, .(T372, T373)) -> f822_out1(.(T372, T377)) 20.34/6.12 f81_in(T31, T32, T33) -> U12(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.12 U12(f90_out1(T40, T41), T31, T32, T33) -> U13(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.12 U13(f92_out1(X40, X41, T43), T31, T32, T33, T40, T41) -> f81_out1(T40, T41, X40, X41, T43) 20.34/6.12 f92_in(T40, T41) -> U14(f2_in(T40), T40, T41) 20.34/6.12 U14(f2_out1(T99), T40, T41) -> U15(f473_in(T41, T99), T40, T41, T99) 20.34/6.12 U15(f473_out1(X41, T101), T40, T41, T99) -> f92_out1(T99, X41, T101) 20.34/6.12 f473_in(T41, T99) -> U16(f2_in(T41), T41, T99) 20.34/6.12 U16(f2_out1(T107), T41, T99) -> U17(f477_in(T99, T107), T41, T99, T107) 20.34/6.12 U17(f477_out1(T108), T41, T99, T107) -> f473_out1(T107, T108) 20.34/6.12 f721_in(T177, T179, T178, T180) -> U18(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.12 U18(f723_out1, T177, T179, T178, T180) -> U19(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.12 U19(f724_out1(T184), T177, T179, T178, T180) -> f721_out1(T184) 20.34/6.12 f808_in(T277, T279, T278, T280) -> U20(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.12 U20(f820_out1, T277, T279, T278, T280) -> U21(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.12 U21(f822_out1(T284), T277, T279, T278, T280) -> f808_out1(T284) 20.34/6.12 20.34/6.12 Q is empty. 20.34/6.12 We have to consider all minimal (P,Q,R)-chains. 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (26) QDPOrderProof (EQUIVALENT) 20.34/6.12 We use the reduction pair processor [LPAR04,JAR06]. 20.34/6.12 20.34/6.12 20.34/6.12 The following pairs can be oriented strictly and are deleted. 20.34/6.12 20.34/6.12 F2_IN(.(T31, .(T32, T33))) -> F81_IN(T31, T32, T33) 20.34/6.12 The remaining pairs can at least be oriented weakly. 20.34/6.12 Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: 20.34/6.12 20.34/6.12 POL( U12^1_4(x_1, ..., x_4) ) = x_1 + 2 20.34/6.12 POL( U12_4(x_1, ..., x_4) ) = 2x_4 + 2 20.34/6.12 POL( U14^1_3(x_1, ..., x_3) ) = x_3 20.34/6.12 POL( f90_in_3(x_1, ..., x_3) ) = 2x_3 20.34/6.12 POL( U5_4(x_1, ..., x_4) ) = 2x_1 20.34/6.12 POL( f108_in_1(x_1) ) = x_1 20.34/6.12 POL( f2_in_1(x_1) ) = 0 20.34/6.12 POL( [] ) = 0 20.34/6.12 POL( f2_out1_1(x_1) ) = max{0, 2x_1 - 2} 20.34/6.12 POL( ._2(x_1, x_2) ) = 2x_2 + 1 20.34/6.12 POL( U1_2(x_1, x_2) ) = max{0, -2} 20.34/6.12 POL( f81_in_3(x_1, ..., x_3) ) = 0 20.34/6.12 POL( f81_out1_5(x_1, ..., x_5) ) = x_1 + x_2 + 2x_3 + 2x_5 20.34/6.12 POL( f90_out1_2(x_1, x_2) ) = max{0, x_1 + x_2 - 2} 20.34/6.12 POL( U13_6(x_1, ..., x_6) ) = max{0, x_6 - 2} 20.34/6.12 POL( f92_in_2(x_1, x_2) ) = 0 20.34/6.12 POL( f92_out1_3(x_1, ..., x_3) ) = 2x_1 + 2x_2 + 2x_3 20.34/6.12 POL( U14_3(x_1, ..., x_3) ) = max{0, 2x_3 - 2} 20.34/6.12 POL( U15_4(x_1, ..., x_4) ) = max{0, 2x_2 + x_4 - 2} 20.34/6.12 POL( f473_in_2(x_1, x_2) ) = 0 20.34/6.12 POL( f473_out1_2(x_1, x_2) ) = 2x_1 + x_2 20.34/6.12 POL( U16_3(x_1, ..., x_3) ) = 2x_3 + 2 20.34/6.12 POL( U17_4(x_1, ..., x_4) ) = 2x_4 + 2 20.34/6.12 POL( f477_in_2(x_1, x_2) ) = 0 20.34/6.12 POL( f108_out1_2(x_1, x_2) ) = x_1 + x_2 20.34/6.12 POL( U2_2(x_1, x_2) ) = 2x_1 + 1 20.34/6.12 POL( f477_out1_1(x_1) ) = max{0, -2} 20.34/6.12 POL( U6_3(x_1, ..., x_3) ) = max{0, 2x_1 - 2} 20.34/6.12 POL( f721_in_4(x_1, ..., x_4) ) = 2x_2 + 2x_4 + 2 20.34/6.12 POL( U7_3(x_1, ..., x_3) ) = max{0, -2} 20.34/6.12 POL( f808_in_4(x_1, ..., x_4) ) = 2x_1 + x_3 + 2x_4 20.34/6.12 POL( U18_5(x_1, ..., x_5) ) = max{0, x_4 - 2} 20.34/6.12 POL( f723_in_2(x_1, x_2) ) = 2x_1 + 2 20.34/6.12 POL( f721_out1_1(x_1) ) = 2 20.34/6.12 POL( U20_5(x_1, ..., x_5) ) = max{0, 2x_1 + 2x_4 + 2x_5 - 2} 20.34/6.12 POL( f820_in_2(x_1, x_2) ) = 2x_1 20.34/6.12 POL( f808_out1_1(x_1) ) = 2 20.34/6.12 POL( f723_out1 ) = 0 20.34/6.12 POL( U19_5(x_1, ..., x_5) ) = max{0, x_1 + 2x_4 + 2x_5 - 2} 20.34/6.12 POL( f724_in_3(x_1, ..., x_3) ) = 0 20.34/6.12 POL( f724_out1_1(x_1) ) = x_1 + 1 20.34/6.12 POL( U8_4(x_1, ..., x_4) ) = max{0, 2x_1 + x_2 - 2} 20.34/6.12 POL( s_1(x_1) ) = 0 20.34/6.12 POL( U3_3(x_1, ..., x_3) ) = 0 20.34/6.12 POL( 0 ) = 1 20.34/6.12 POL( U9_4(x_1, ..., x_4) ) = 2x_4 + 2 20.34/6.12 POL( U4_3(x_1, ..., x_3) ) = max{0, -2} 20.34/6.12 POL( f820_out1 ) = 0 20.34/6.12 POL( U21_5(x_1, ..., x_5) ) = max{0, x_3 - 2} 20.34/6.12 POL( f822_in_3(x_1, ..., x_3) ) = x_1 + 2x_2 + 2 20.34/6.12 POL( f822_out1_1(x_1) ) = max{0, -2} 20.34/6.12 POL( U10_4(x_1, ..., x_4) ) = max{0, 2x_1 + 2x_2 - 2} 20.34/6.12 POL( U11_4(x_1, ..., x_4) ) = max{0, 2x_1 + x_3 - 2} 20.34/6.12 POL( F2_IN_1(x_1) ) = x_1 20.34/6.12 POL( F81_IN_3(x_1, ..., x_3) ) = 2x_3 + 2 20.34/6.12 POL( F92_IN_2(x_1, x_2) ) = x_1 + x_2 20.34/6.12 POL( F473_IN_2(x_1, x_2) ) = x_1 20.34/6.12 20.34/6.12 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 20.34/6.12 20.34/6.12 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.12 f108_in([]) -> f108_out1([], []) 20.34/6.12 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.12 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.12 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.12 20.34/6.12 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (27) 20.34/6.12 Obligation: 20.34/6.12 Q DP problem: 20.34/6.12 The TRS P consists of the following rules: 20.34/6.12 20.34/6.12 F81_IN(T31, T32, T33) -> U12^1(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.12 U12^1(f90_out1(T40, T41), T31, T32, T33) -> F92_IN(T40, T41) 20.34/6.12 F92_IN(T40, T41) -> U14^1(f2_in(T40), T40, T41) 20.34/6.12 U14^1(f2_out1(T99), T40, T41) -> F473_IN(T41, T99) 20.34/6.12 F473_IN(T41, T99) -> F2_IN(T41) 20.34/6.12 F92_IN(T40, T41) -> F2_IN(T40) 20.34/6.12 20.34/6.12 The TRS R consists of the following rules: 20.34/6.12 20.34/6.12 f2_in([]) -> f2_out1([]) 20.34/6.12 f2_in(.(T17, [])) -> f2_out1(.(T17, [])) 20.34/6.12 f2_in(.(T31, .(T32, T33))) -> U1(f81_in(T31, T32, T33), .(T31, .(T32, T33))) 20.34/6.12 U1(f81_out1(X38, X39, X40, X41, T39), .(T31, .(T32, T33))) -> f2_out1(T39) 20.34/6.12 f108_in([]) -> f108_out1([], []) 20.34/6.12 f108_in(.(T90, T91)) -> U2(f108_in(T91), .(T90, T91)) 20.34/6.12 U2(f108_out1(X130, X129), .(T90, T91)) -> f108_out1(.(T90, X129), X130) 20.34/6.12 f723_in(s(T198), s(T199)) -> U3(f723_in(T198, T199), s(T198), s(T199)) 20.34/6.12 U3(f723_out1, s(T198), s(T199)) -> f723_out1 20.34/6.12 f723_in(0, s(0)) -> f723_out1 20.34/6.12 f723_in(0, 0) -> f723_out1 20.34/6.12 f820_in(s(T298), s(T299)) -> U4(f820_in(T298, T299), s(T298), s(T299)) 20.34/6.12 U4(f820_out1, s(T298), s(T299)) -> f820_out1 20.34/6.12 f820_in(s(0), 0) -> f820_out1 20.34/6.12 f90_in(T56, T70, T71) -> U5(f108_in(T71), T56, T70, T71) 20.34/6.12 U5(f108_out1(X99, X98), T56, T70, T71) -> f90_out1(.(T56, X99), .(T70, X98)) 20.34/6.12 f477_in([], T131) -> f477_out1(T131) 20.34/6.12 f477_in(T146, []) -> f477_out1(T146) 20.34/6.12 f477_in(.(T177, T178), .(T179, T180)) -> U6(f721_in(T177, T179, T178, T180), .(T177, T178), .(T179, T180)) 20.34/6.12 U6(f721_out1(T184), .(T177, T178), .(T179, T180)) -> f477_out1(.(T177, T184)) 20.34/6.12 f477_in(.(T395, T396), .(T397, T398)) -> U7(f808_in(T395, T397, T396, T398), .(T395, T396), .(T397, T398)) 20.34/6.12 U7(f808_out1(T402), .(T395, T396), .(T397, T398)) -> f477_out1(.(T397, T402)) 20.34/6.12 f724_in([], T220, T221) -> f724_out1(.(T220, T221)) 20.34/6.12 f724_in(.(T252, T253), T254, T255) -> U8(f721_in(T252, T254, T253, T255), .(T252, T253), T254, T255) 20.34/6.12 U8(f721_out1(T259), .(T252, T253), T254, T255) -> f724_out1(.(T252, T259)) 20.34/6.12 f724_in(.(T277, T278), T279, T280) -> U9(f808_in(T277, T279, T278, T280), .(T277, T278), T279, T280) 20.34/6.12 U9(f808_out1(T284), .(T277, T278), T279, T280) -> f724_out1(.(T279, T284)) 20.34/6.12 f822_in(T314, T315, []) -> f822_out1(.(T314, T315)) 20.34/6.12 f822_in(T345, T346, .(T347, T348)) -> U10(f721_in(T345, T347, T346, T348), T345, T346, .(T347, T348)) 20.34/6.12 U10(f721_out1(T352), T345, T346, .(T347, T348)) -> f822_out1(.(T345, T352)) 20.34/6.12 f822_in(T370, T371, .(T372, T373)) -> U11(f808_in(T370, T372, T371, T373), T370, T371, .(T372, T373)) 20.34/6.12 U11(f808_out1(T377), T370, T371, .(T372, T373)) -> f822_out1(.(T372, T377)) 20.34/6.12 f81_in(T31, T32, T33) -> U12(f90_in(T31, T32, T33), T31, T32, T33) 20.34/6.12 U12(f90_out1(T40, T41), T31, T32, T33) -> U13(f92_in(T40, T41), T31, T32, T33, T40, T41) 20.34/6.12 U13(f92_out1(X40, X41, T43), T31, T32, T33, T40, T41) -> f81_out1(T40, T41, X40, X41, T43) 20.34/6.12 f92_in(T40, T41) -> U14(f2_in(T40), T40, T41) 20.34/6.12 U14(f2_out1(T99), T40, T41) -> U15(f473_in(T41, T99), T40, T41, T99) 20.34/6.12 U15(f473_out1(X41, T101), T40, T41, T99) -> f92_out1(T99, X41, T101) 20.34/6.12 f473_in(T41, T99) -> U16(f2_in(T41), T41, T99) 20.34/6.12 U16(f2_out1(T107), T41, T99) -> U17(f477_in(T99, T107), T41, T99, T107) 20.34/6.12 U17(f477_out1(T108), T41, T99, T107) -> f473_out1(T107, T108) 20.34/6.12 f721_in(T177, T179, T178, T180) -> U18(f723_in(T177, T179), T177, T179, T178, T180) 20.34/6.12 U18(f723_out1, T177, T179, T178, T180) -> U19(f724_in(T178, T179, T180), T177, T179, T178, T180) 20.34/6.12 U19(f724_out1(T184), T177, T179, T178, T180) -> f721_out1(T184) 20.34/6.12 f808_in(T277, T279, T278, T280) -> U20(f820_in(T277, T279), T277, T279, T278, T280) 20.34/6.12 U20(f820_out1, T277, T279, T278, T280) -> U21(f822_in(T277, T278, T280), T277, T279, T278, T280) 20.34/6.12 U21(f822_out1(T284), T277, T279, T278, T280) -> f808_out1(T284) 20.34/6.12 20.34/6.12 Q is empty. 20.34/6.12 We have to consider all minimal (P,Q,R)-chains. 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (28) DependencyGraphProof (EQUIVALENT) 20.34/6.12 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 6 less nodes. 20.34/6.12 ---------------------------------------- 20.34/6.12 20.34/6.12 (29) 20.34/6.12 TRUE 20.45/6.21 EOF