/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern transpose(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToDTProblemTransformerProof [SOUND, 2491 ms] (2) TRIPLES (3) TriplesToPiDPProof [SOUND, 296 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 9 ms] (6) AND (7) PiDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) PiDP (10) PiDPToQDPProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) PiDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) PiDP (17) PiDPToQDPProof [SOUND, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) PiDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) PiDP (24) PiDPToQDPProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES (28) PiDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) PiDP (31) PiDPToQDPProof [SOUND, 0 ms] (32) QDP (33) QDPSizeChangeProof [EQUIVALENT, 0 ms] (34) YES (35) PiDP (36) UsableRulesProof [EQUIVALENT, 0 ms] (37) PiDP (38) PiDPToQDPProof [SOUND, 0 ms] (39) QDP (40) QDPSizeChangeProof [EQUIVALENT, 0 ms] (41) YES (42) PiDP (43) UsableRulesProof [EQUIVALENT, 0 ms] (44) PiDP (45) PiDPToQDPProof [SOUND, 0 ms] (46) QDP (47) QDPSizeChangeProof [EQUIVALENT, 0 ms] (48) YES (49) PiDP (50) UsableRulesProof [EQUIVALENT, 0 ms] (51) PiDP (52) PiDPToQDPProof [SOUND, 0 ms] (53) QDP (54) QDPSizeChangeProof [EQUIVALENT, 0 ms] (55) YES (56) PiDP (57) UsableRulesProof [EQUIVALENT, 0 ms] (58) PiDP (59) PiDPToQDPProof [SOUND, 0 ms] (60) QDP (61) QDPSizeChangeProof [EQUIVALENT, 0 ms] (62) YES (63) PiDP (64) UsableRulesProof [EQUIVALENT, 0 ms] (65) PiDP (66) PiDPToQDPProof [SOUND, 0 ms] (67) QDP (68) QDPSizeChangeProof [EQUIVALENT, 0 ms] (69) YES (70) PiDP (71) UsableRulesProof [EQUIVALENT, 0 ms] (72) PiDP (73) PiDPToQDPProof [SOUND, 0 ms] (74) QDP (75) QDPSizeChangeProof [EQUIVALENT, 0 ms] (76) YES (77) PiDP (78) UsableRulesProof [EQUIVALENT, 0 ms] (79) PiDP (80) PiDPToQDPProof [SOUND, 0 ms] (81) QDP (82) QDPSizeChangeProof [EQUIVALENT, 0 ms] (83) YES (84) PiDP (85) UsableRulesProof [EQUIVALENT, 0 ms] (86) PiDP (87) PiDPToQDPProof [SOUND, 0 ms] (88) QDP (89) QDPSizeChangeProof [EQUIVALENT, 0 ms] (90) YES (91) PiDP (92) UsableRulesProof [EQUIVALENT, 0 ms] (93) PiDP (94) PiDPToQDPProof [SOUND, 0 ms] (95) QDP (96) QDPSizeChangeProof [EQUIVALENT, 0 ms] (97) YES ---------------------------------------- (0) Obligation: Clauses: transpose(A, B) :- transpose_aux(A, [], B). transpose_aux([], Y, Z) :- ','(!, eq(Y, Z)). transpose_aux(R, X1, L) :- ','(head(R, Rh), ','(tail(R, Rt), ','(row2col(Rh, L, Cols, Accm), transpose_aux(Rt, Accm, Cols)))). row2col([], X, Y, Z) :- ','(!, ','(eq(X, []), ','(eq(Y, []), eq(Z, [])))). row2col(X, Y, C, A) :- ','(head(X, Xh), ','(head(Y, Yh), ','(head(Yh, Xh), ','(head(A, []), ','(tail(X, Xt), ','(tail(Y, Yt), ','(tail(Yh, Yht), ','(head(C, Yht), ','(tail(C, Ct), ','(tail(A, At), row2col(Xt, Yt, Ct, At))))))))))). head([], X2). head(.(H, X3), H). tail([], []). tail(.(X4, T), T). eq(X, X). Query: transpose(g,a) ---------------------------------------- (1) PrologToDTProblemTransformerProof (SOUND) Built DT problem from termination graph DT10. { "root": 1, "program": { "directives": [], "clauses": [ [ "(transpose A B)", "(transpose_aux A ([]) B)" ], [ "(transpose_aux ([]) Y Z)", "(',' (!) (eq Y Z))" ], [ "(transpose_aux R X1 L)", "(',' (head R Rh) (',' (tail R Rt) (',' (row2col Rh L Cols Accm) (transpose_aux Rt Accm Cols))))" ], [ "(row2col ([]) X Y Z)", "(',' (!) (',' (eq X ([])) (',' (eq Y ([])) (eq Z ([])))))" ], [ "(row2col X Y C A)", "(',' (head X Xh) (',' (head Y Yh) (',' (head Yh Xh) (',' (head A ([])) (',' (tail X Xt) (',' (tail Y Yt) (',' (tail Yh Yht) (',' (head C Yht) (',' (tail C Ct) (',' (tail A At) (row2col Xt Yt Ct At)))))))))))" ], [ "(head ([]) X2)", null ], [ "(head (. H X3) H)", null ], [ "(tail ([]) ([]))", null ], [ "(tail (. X4 T) T)", null ], [ "(eq X X)", null ] ] }, "graph": { "nodes": { "3881": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (tail (. T222 T60) X140) (',' (tail (. ([]) T223) X141) (',' (tail ([]) X142) (',' (head X145 X142) (',' (tail X145 X143) (',' (tail ([]) X144) (row2col X140 X141 X143 X144)))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T60", "T222" ], "free": [ "X145", "X140", "X141", "X142", "X143", "X144" ], "exprvars": [] } }, "4970": { "goal": [ { "clause": 3, "scope": 172, "term": "(row2col T229 T235 X3411 ([]))" }, { "clause": 4, "scope": 172, "term": "(row2col T229 T235 X3411 ([]))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T229"], "free": ["X3411"], "exprvars": [] } }, "2793": { "goal": [ { "clause": 7, "scope": 97, "term": "(',' (tail (. T175 X1822) X1479) (',' (head ([]) X1479) (',' (tail ([]) X1480) (',' (tail ([]) X1481) (row2col T176 ([]) X1480 X1481)))))" }, { "clause": 8, "scope": 97, "term": "(',' (tail (. T175 X1822) X1479) (',' (head ([]) X1479) (',' (tail ([]) X1480) (',' (tail ([]) X1481) (row2col T176 ([]) X1480 X1481)))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T175", "T176" ], "free": [ "X1479", "X1480", "X1481", "X1822" ], "exprvars": [] } }, "2792": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (tail (. T175 X1822) X1479) (',' (head ([]) X1479) (',' (tail ([]) X1480) (',' (tail ([]) X1481) (row2col T176 ([]) X1480 X1481)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T175", "T176" ], "free": [ "X1479", "X1480", "X1481", "X1822" ], "exprvars": [] } }, "5816": { "goal": [ { "clause": 7, "scope": 232, "term": "(',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 ([]) X4503 X4504)))))" }, { "clause": 8, "scope": 232, "term": "(',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 ([]) X4503 X4504)))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T619"], "free": [ "X4502", "X4503", "X4504" ], "exprvars": [] } }, "1699": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2304": { "goal": [{ "clause": 6, "scope": 80, "term": "(',' (head X1524 T149) (',' (head X1482 ([])) (',' (tail (. T149 T150) X1477) (',' (tail ([]) X1478) (',' (tail X1524 X1479) (',' (head ([]) X1479) (',' (tail ([]) X1480) (',' (tail X1482 X1481) (row2col X1477 X1478 X1480 X1481)))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T149", "T150" ], "free": [ "X1482", "X1477", "X1478", "X1479", "X1480", "X1481", "X1524" ], "exprvars": [] } }, "1698": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2303": { "goal": [{ "clause": 5, "scope": 80, "term": "(',' (head X1524 T149) (',' (head X1482 ([])) (',' (tail (. T149 T150) X1477) (',' (tail ([]) X1478) (',' (tail X1524 X1479) (',' (head ([]) X1479) (',' (tail ([]) X1480) (',' (tail X1482 X1481) (row2col X1477 X1478 X1480 X1481)))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T149", "T150" ], "free": [ "X1482", "X1477", "X1478", "X1479", "X1480", "X1481", "X1524" ], "exprvars": [] } }, "5819": { "goal": [{ "clause": 7, "scope": 232, "term": "(',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 ([]) X4503 X4504)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T619"], "free": [ "X4502", "X4503", "X4504" ], "exprvars": [] } }, "1697": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "1695": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "2542": { "goal": [ { "clause": 5, "scope": 91, "term": "(',' (head ([]) ([])) (',' (tail ([]) X1480) (',' (tail (. ([]) X1693) X1481) (row2col T167 ([]) X1480 X1481))))" }, { "clause": 6, "scope": 91, "term": "(',' (head ([]) ([])) (',' (tail ([]) X1480) (',' (tail (. ([]) X1693) X1481) (row2col T167 ([]) X1480 X1481))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T167"], "free": [ "X1480", "X1481", "X1693" ], "exprvars": [] } }, "1452": { "goal": [ { "clause": 7, "scope": 29, "term": "(',' (tail ([]) X364) (',' (tail ([]) X365) (',' (head ([]) X365) (',' (tail ([]) X366) (',' (tail ([]) X367) (row2col T91 X364 X366 X367))))))" }, { "clause": 8, "scope": 29, "term": "(',' (tail ([]) X364) (',' (tail ([]) X365) (',' (head ([]) X365) (',' (tail ([]) X366) (',' (tail ([]) X367) (row2col T91 X364 X366 X367))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T91"], "free": [ "X364", "X365", "X366", "X367" ], "exprvars": [] } }, "1694": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } }, "4961": { "goal": [{ "clause": 7, "scope": 171, "term": "(',' (tail ([]) X144) (row2col T229 T235 X3411 X144))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T229"], "free": [ "X144", "X3411" ], "exprvars": [] } }, "4962": { "goal": [{ "clause": 8, "scope": 171, "term": "(',' (tail ([]) X144) (row2col T229 T235 X3411 X144))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T229"], "free": [ "X144", "X3411" ], "exprvars": [] } }, "5810": { "goal": [{ "clause": 7, "scope": 231, "term": "(',' (tail ([]) X4501) (',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 X4501 X4503 X4504))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T619"], "free": [ "X4501", "X4502", "X4503", "X4504" ], "exprvars": [] } }, "4722": { "goal": [ { "clause": 7, "scope": 158, "term": "(',' (tail (. ([]) T306) X2750) (',' (tail ([]) X2751) (',' (head ([]) X2751) (',' (tail ([]) X2752) (',' (tail ([]) X2753) (row2col T312 X2750 X2752 X2753))))))" }, { "clause": 8, "scope": 158, "term": "(',' (tail (. ([]) T306) X2750) (',' (tail ([]) X2751) (',' (head ([]) X2751) (',' (tail ([]) X2752) (',' (tail ([]) X2753) (row2col T312 X2750 X2752 X2753))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T312"], "free": [ "X2750", "X2751", "X2752", "X2753" ], "exprvars": [] } }, "5811": { "goal": [{ "clause": 8, "scope": 231, "term": "(',' (tail ([]) X4501) (',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 X4501 X4503 X4504))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T619"], "free": [ "X4501", "X4502", "X4503", "X4504" ], "exprvars": [] } }, "4723": { "goal": [{ "clause": 8, "scope": 158, "term": "(',' (tail (. ([]) T306) X2750) (',' (tail ([]) X2751) (',' (head ([]) X2751) (',' (tail ([]) X2752) (',' (tail ([]) X2753) (row2col T312 X2750 X2752 X2753))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T312"], "free": [ "X2750", "X2751", "X2752", "X2753" ], "exprvars": [] } }, "4965": { "goal": [{ "clause": -1, "scope": -1, "term": "(row2col T229 T235 X3411 ([]))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T229"], "free": ["X3411"], "exprvars": [] } }, "5813": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 ([]) X4503 X4504)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T619"], "free": [ "X4502", "X4503", "X4504" ], "exprvars": [] } }, "1219": { "goal": [{ "clause": 6, "scope": 25, "term": "(',' (head ([]) X362) (',' (head X362 T79) (',' (head ([]) ([])) (',' (tail (. T79 T80) X363) (',' (tail ([]) X364) (',' (tail X362 X365) (',' (head ([]) X365) (',' (tail ([]) X366) (',' (tail ([]) X367) (row2col X363 X364 X366 X367))))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T79", "T80" ], "free": [ "X362", "X363", "X364", "X365", "X366", "X367" ], "exprvars": [] } }, "1218": { "goal": [{ "clause": 5, "scope": 25, "term": "(',' (head ([]) X362) (',' (head X362 T79) (',' (head ([]) ([])) (',' (tail (. T79 T80) X363) (',' (tail ([]) X364) (',' (tail X362 X365) (',' (head ([]) X365) (',' (tail ([]) X366) (',' (tail ([]) X367) (row2col X363 X364 X366 X367))))))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T79", "T80" ], "free": [ "X362", "X363", "X364", "X365", "X366", "X367" ], "exprvars": [] } }, "3891": { "goal": [ { "clause": 7, "scope": 128, "term": "(',' (tail (. T222 T60) X140) (',' (tail (. ([]) T223) X141) (',' (tail ([]) X142) (',' (head X145 X142) (',' (tail X145 X143) (',' (tail ([]) X144) (row2col X140 X141 X143 X144)))))))" }, { "clause": 8, "scope": 128, "term": "(',' (tail (. T222 T60) X140) (',' (tail (. ([]) T223) X141) (',' (tail ([]) X142) (',' (head X145 X142) (',' (tail X145 X143) (',' (tail ([]) X144) (row2col X140 X141 X143 X144)))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [ "T60", "T222" ], "free": [ "X145", "X140", "X141", "X142", "X143", "X144" ], "exprvars": [] } }, "4980": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (eq T400 ([])) (',' (eq X3440 ([])) (eq ([]) ([]))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": ["X3440"], "exprvars": [] } }, "3650": { "goal": [{ "clause": 6, "scope": 121, "term": "(',' (head X145 X2441) (',' (tail X145 X143) (',' (tail (. 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([]) X3392) X143) (',' (tail ([]) X144) (row2col T229 T235 X143 X144)))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T229"], "free": [ "X143", "X144", "X3392" ], "exprvars": [] } }, "4952": { "goal": [{ "clause": 8, "scope": 170, "term": "(',' (tail (. ([]) X3392) X143) (',' (tail ([]) X144) (row2col T229 T235 X143 X144)))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T229"], "free": [ "X143", "X144", "X3392" ], "exprvars": [] } }, "5802": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (tail ([]) X4501) (',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 X4501 X4503 X4504))))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T619"], "free": [ "X4501", "X4502", "X4503", "X4504" ], "exprvars": [] } }, "5804": { "goal": [ { "clause": 7, "scope": 231, "term": "(',' (tail ([]) X4501) (',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 X4501 X4503 X4504))))))" }, { "clause": 8, "scope": 231, "term": "(',' (tail ([]) X4501) (',' (tail ([]) X4502) (',' (head ([]) X4502) (',' (tail ([]) X4503) (',' (tail ([]) X4504) (row2col T619 X4501 X4503 X4504))))))" } ], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": ["T619"], "free": [ "X4501", "X4502", "X4503", "X4504" ], "exprvars": [] } } }, "edges": [ { "from": 1, "to": 5, "label": "CASE" }, { "from": 5, "to": 7, "label": "ONLY EVAL with clause\ntranspose(X7, X8) :- transpose_aux(X7, [], X8).\nand substitutionT1 -> T5,\nX7 -> T5,\nT2 -> T7,\nX8 -> T7,\nT6 -> T7" }, { "from": 7, "to": 8, "label": "CASE" }, { "from": 8, "to": 10, "label": "EVAL with clause\ntranspose_aux([], X13, X14) :- ','(!_2, eq(X13, X14)).\nand substitutionT5 -> [],\nX13 -> [],\nT7 -> T11,\nX14 -> T11,\nT10 -> T11" }, { "from": 8, "to": 11, "label": "EVAL-BACKTRACK" }, { "from": 10, "to": 12, "label": "CUT" }, { "from": 11, "to": 25, "label": "ONLY EVAL with clause\ntranspose_aux(X33, X34, X35) :- ','(head(X33, X36), ','(tail(X33, X37), ','(row2col(X36, X35, X38, X39), transpose_aux(X37, X39, X38)))).\nand substitutionT5 -> T18,\nX33 -> T18,\nX34 -> [],\nT7 -> T20,\nX35 -> T20,\nT19 -> T20" }, { "from": 12, "to": 13, "label": "CASE" }, { "from": 13, "to": 14, "label": "EVAL with clause\neq(X17, X17).\nand substitutionX17 -> [],\nT11 -> []" }, { "from": 13, "to": 16, "label": "EVAL-BACKTRACK" }, { "from": 14, "to": 17, "label": "SUCCESS" }, { "from": 25, "to": 26, "label": "CASE" }, { "from": 26, "to": 27, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (transpose_aux(T18, [], T7), transpose_aux([], X13, X14))" }, { "from": 27, "to": 47, "label": "EVAL with clause\nhead(.(X51, X52), X51).\nand substitutionX51 -> T26,\nX52 -> T27,\nT18 -> .(T26, T27),\nX36 -> T26" }, { "from": 27, "to": 48, "label": "EVAL-BACKTRACK" }, { "from": 47, "to": 49, "label": "CASE" }, { "from": 49, "to": 50, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 50, "to": 82, "label": "ONLY EVAL with clause\ntail(.(X67, X68), X68).\nand substitutionT26 -> T34,\nX67 -> T34,\nT27 -> T35,\nX68 -> T35,\nX37 -> T35" }, { "from": 82, "to": 481, "label": "SPLIT 1" }, { "from": 82, "to": 482, "label": "SPLIT 2\nnew knowledge:\nT34 is ground\nreplacements:X38 -> T37,\nX39 -> T38" }, { "from": 481, "to": 483, "label": "CASE" }, { "from": 482, "to": 6726, "label": "CASE" }, { "from": 483, "to": 486, "label": "EVAL with clause\nrow2col([], X89, X90, X91) :- ','(!_6, ','(eq(X89, []), ','(eq(X90, []), eq(X91, [])))).\nand substitutionT34 -> [],\nT20 -> T43,\nX89 -> T43,\nX38 -> X92,\nX90 -> X92,\nX39 -> X93,\nX91 -> X93,\nT42 -> T43" }, { "from": 483, "to": 487, "label": "EVAL-BACKTRACK" }, { "from": 486, "to": 488, "label": "CUT" }, { "from": 487, "to": 545, "label": "ONLY EVAL with clause\nrow2col(X134, X135, X136, X137) :- ','(head(X134, X138), ','(head(X135, X139), ','(head(X139, X138), ','(head(X137, []), ','(tail(X134, X140), ','(tail(X135, X141), ','(tail(X139, X142), ','(head(X136, X142), ','(tail(X136, X143), ','(tail(X137, X144), row2col(X140, X141, X143, X144))))))))))).\nand substitutionT34 -> T52,\nX134 -> T52,\nT20 -> T54,\nX135 -> T54,\nX38 -> X145,\nX136 -> X145,\nX39 -> X146,\nX137 -> X146,\nT53 -> T54" }, { "from": 488, "to": 489, "label": "CASE" }, { "from": 489, "to": 491, "label": "EVAL with clause\neq(X96, X96).\nand substitutionT43 -> [],\nX96 -> [],\nT46 -> []" }, { "from": 489, "to": 492, "label": "EVAL-BACKTRACK" }, { "from": 491, "to": 493, "label": "CASE" }, { "from": 493, "to": 495, "label": "ONLY EVAL with clause\neq(X101, X101).\nand substitutionX92 -> [],\nX101 -> [],\nX102 -> []" }, { "from": 495, "to": 496, "label": "CASE" }, { "from": 496, "to": 497, "label": "ONLY EVAL with clause\neq(X107, X107).\nand substitutionX93 -> [],\nX107 -> [],\nX108 -> []" }, { "from": 497, "to": 498, "label": "SUCCESS" }, { "from": 545, "to": 623, "label": "CASE" }, { "from": 623, "to": 648, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (row2col(T52, T20, X38, X39), row2col([], X89, X90, X91))" }, { "from": 648, "to": 729, "label": "EVAL with clause\nhead(.(X159, X160), X159).\nand substitutionX159 -> T59,\nX160 -> T60,\nT52 -> .(T59, T60),\nX138 -> T59" }, { "from": 648, "to": 743, "label": "EVAL-BACKTRACK" }, { "from": 729, "to": 833, "label": "CASE" }, { "from": 833, "to": 847, "label": "PARALLEL" }, { "from": 833, "to": 849, "label": "PARALLEL" }, { "from": 847, "to": 859, "label": "EVAL with clause\nhead([], X175).\nand substitutionT54 -> [],\nX139 -> X176,\nX175 -> X176" }, { "from": 847, "to": 860, "label": "EVAL-BACKTRACK" }, { "from": 849, "to": 3829, "label": "EVAL with clause\nhead(.(X2572, X2573), X2572).\nand substitutionX2572 -> T216,\nX2573 -> T217,\nT54 -> .(T216, T217),\nX139 -> T216,\nT214 -> T216,\nT215 -> T217" }, { "from": 849, "to": 3830, "label": "EVAL-BACKTRACK" }, { "from": 859, "to": 865, "label": "CASE" }, { "from": 865, "to": 866, "label": "PARALLEL" }, { "from": 865, "to": 867, "label": "PARALLEL" }, { "from": 866, "to": 868, "label": "ONLY EVAL with clause\nhead([], X199).\nand substitutionX176 -> [],\nT59 -> T65,\nX199 -> T65" }, { "from": 867, "to": 3304, "label": "ONLY EVAL with clause\nhead(.(X2176, X2177), X2176).\nand substitutionX2176 -> T191,\nX2177 -> X2179,\nX176 -> .(T191, X2179),\nT59 -> T191,\nX2178 -> T191" }, { "from": 868, "to": 869, "label": "CASE" }, { "from": 869, "to": 870, "label": "PARALLEL" }, { "from": 869, "to": 871, "label": "PARALLEL" }, { "from": 870, "to": 872, "label": "ONLY EVAL with clause\nhead([], X222).\nand substitutionX146 -> [],\nX222 -> []" }, { "from": 871, "to": 2177, "label": "ONLY EVAL with clause\nhead(.(X1317, X1318), X1317).\nand substitutionX1317 -> [],\nX1318 -> X1320,\nX146 -> .([], X1320),\nX1319 -> []" }, { "from": 872, "to": 878, "label": "CASE" }, { "from": 878, "to": 881, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 881, "to": 891, "label": "ONLY EVAL with clause\ntail(.(X239, X240), X240).\nand substitutionT65 -> T70,\nX239 -> T70,\nT60 -> T71,\nX240 -> T71,\nX140 -> T71" }, { "from": 891, "to": 894, "label": "CASE" }, { "from": 894, "to": 895, "label": "PARALLEL" }, { "from": 894, "to": 896, "label": "PARALLEL" }, { "from": 895, "to": 903, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX141 -> []" }, { "from": 896, "to": 2171, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 903, "to": 915, "label": "CASE" }, { "from": 915, "to": 928, "label": "PARALLEL" }, { "from": 915, "to": 930, "label": "PARALLEL" }, { "from": 928, "to": 945, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX142 -> []" }, { "from": 930, "to": 2170, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 945, "to": 950, "label": "CASE" }, { "from": 950, "to": 953, "label": "PARALLEL" }, { "from": 950, "to": 954, "label": "PARALLEL" }, { "from": 953, "to": 958, "label": "ONLY EVAL with clause\nhead([], X291).\nand substitutionX145 -> [],\nX291 -> []" }, { "from": 954, "to": 1762, "label": "ONLY EVAL with clause\nhead(.(X737, X738), X737).\nand substitutionX737 -> [],\nX738 -> X740,\nX145 -> .([], X740),\nX739 -> []" }, { "from": 958, "to": 961, "label": "CASE" }, { "from": 961, "to": 962, "label": "PARALLEL" }, { "from": 961, "to": 964, "label": "PARALLEL" }, { "from": 962, "to": 965, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX143 -> []" }, { "from": 964, "to": 1700, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 965, "to": 968, "label": "CASE" }, { "from": 968, "to": 969, "label": "PARALLEL" }, { "from": 968, "to": 970, "label": "PARALLEL" }, { "from": 969, "to": 972, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX144 -> []" }, { "from": 970, "to": 1699, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 972, "to": 974, "label": "CASE" }, { "from": 974, "to": 999, "label": "EVAL with clause\nrow2col([], X324, X325, X326) :- ','(!_20, ','(eq(X324, []), ','(eq(X325, []), eq(X326, [])))).\nand substitutionT71 -> [],\nX324 -> [],\nX325 -> [],\nX326 -> []" }, { "from": 974, "to": 1002, "label": "EVAL-BACKTRACK" }, { "from": 999, "to": 1004, "label": "CUT" }, { "from": 1002, "to": 1169, "label": "ONLY EVAL with clause\nrow2col(X357, X358, X359, X360) :- ','(head(X357, X361), ','(head(X358, X362), ','(head(X362, X361), ','(head(X360, []), ','(tail(X357, X363), ','(tail(X358, X364), ','(tail(X362, X365), ','(head(X359, X365), ','(tail(X359, X366), ','(tail(X360, X367), row2col(X363, X364, X366, X367))))))))))).\nand substitutionT71 -> T74,\nX357 -> T74,\nX358 -> [],\nX359 -> [],\nX360 -> []" }, { "from": 1004, "to": 1006, "label": "CASE" }, { "from": 1006, "to": 1020, "label": "ONLY EVAL with clause\neq(X329, X329).\nand substitutionX329 -> []" }, { "from": 1020, "to": 1026, "label": "CASE" }, { "from": 1026, "to": 1042, "label": "ONLY EVAL with clause\neq(X332, X332).\nand substitutionX332 -> []" }, { "from": 1042, "to": 1045, "label": "CASE" }, { "from": 1045, "to": 1059, "label": "ONLY EVAL with clause\neq(X335, X335).\nand substitutionX335 -> []" }, { "from": 1059, "to": 1061, "label": "SUCCESS" }, { "from": 1169, "to": 1182, "label": "CASE" }, { "from": 1182, "to": 1184, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (row2col(T74, [], [], []), row2col([], X324, X325, X326))" }, { "from": 1184, "to": 1187, "label": "EVAL with clause\nhead(.(X380, X381), X380).\nand substitutionX380 -> T79,\nX381 -> T80,\nT74 -> .(T79, T80),\nX361 -> T79" }, { "from": 1184, "to": 1188, "label": "EVAL-BACKTRACK" }, { "from": 1187, "to": 1190, "label": "CASE" }, { "from": 1190, "to": 1218, "label": "PARALLEL" }, { "from": 1190, "to": 1219, "label": "PARALLEL" }, { "from": 1218, "to": 1224, "label": "ONLY EVAL with clause\nhead([], X408).\nand substitutionX362 -> X409,\nX408 -> X409" }, { "from": 1219, "to": 1698, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 1224, "to": 1225, "label": "CASE" }, { "from": 1225, "to": 1229, "label": "PARALLEL" }, { "from": 1225, "to": 1230, "label": "PARALLEL" }, { "from": 1229, "to": 1235, "label": "ONLY EVAL with clause\nhead([], X432).\nand substitutionX409 -> [],\nT79 -> T85,\nX432 -> T85" }, { "from": 1230, "to": 1621, "label": "ONLY EVAL with clause\nhead(.(X577, X578), X577).\nand substitutionX577 -> T94,\nX578 -> X580,\nX409 -> .(T94, X580),\nT79 -> T94,\nX579 -> T94" }, { "from": 1235, "to": 1239, "label": "CASE" }, { "from": 1239, "to": 1371, "label": "PARALLEL" }, { "from": 1239, "to": 1372, "label": "PARALLEL" }, { "from": 1371, "to": 1392, "label": "ONLY EVAL with clause\nhead([], X455).\nand substitutionX455 -> []" }, { "from": 1372, "to": 1609, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 1392, "to": 1395, "label": "CASE" }, { "from": 1395, "to": 1396, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 1396, "to": 1450, "label": "ONLY EVAL with clause\ntail(.(X472, X473), X473).\nand substitutionT85 -> T90,\nX472 -> T90,\nT80 -> T91,\nX473 -> T91,\nX363 -> T91" }, { "from": 1450, "to": 1452, "label": "CASE" }, { "from": 1452, "to": 1539, "label": "PARALLEL" }, { "from": 1452, "to": 1540, "label": "PARALLEL" }, { "from": 1539, "to": 1542, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX364 -> []" }, { "from": 1540, "to": 1607, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1542, "to": 1544, "label": "CASE" }, { "from": 1544, "to": 1547, "label": "PARALLEL" }, { "from": 1544, "to": 1548, "label": "PARALLEL" }, { "from": 1547, "to": 1550, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX365 -> []" }, { "from": 1548, "to": 1605, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1550, "to": 1552, "label": "CASE" }, { "from": 1552, "to": 1571, "label": "PARALLEL" }, { "from": 1552, "to": 1572, "label": "PARALLEL" }, { "from": 1571, "to": 1574, "label": "ONLY EVAL with clause\nhead([], X524).\nand substitutionX524 -> []" }, { "from": 1572, "to": 1603, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 1574, "to": 1578, "label": "CASE" }, { "from": 1578, "to": 1579, "label": "PARALLEL" }, { "from": 1578, "to": 1581, "label": "PARALLEL" }, { "from": 1579, "to": 1584, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX366 -> []" }, { "from": 1581, "to": 1601, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1584, "to": 1586, "label": "CASE" }, { "from": 1586, "to": 1588, "label": "PARALLEL" }, { "from": 1586, "to": 1589, "label": "PARALLEL" }, { "from": 1588, "to": 1593, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX367 -> []" }, { "from": 1589, "to": 1599, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1593, "to": 972, "label": "INSTANCE with matching:\nT71 -> T91" }, { "from": 1621, "to": 1622, "label": "CASE" }, { "from": 1622, "to": 1624, "label": "PARALLEL" }, { "from": 1622, "to": 1625, "label": "PARALLEL" }, { "from": 1624, "to": 1630, "label": "ONLY EVAL with clause\nhead([], X603).\nand substitutionX603 -> []" }, { "from": 1625, "to": 1697, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 1630, "to": 1632, "label": "CASE" }, { "from": 1632, "to": 1633, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 1633, "to": 1642, "label": "ONLY EVAL with clause\ntail(.(X620, X621), X621).\nand substitutionT94 -> T99,\nX620 -> T99,\nT80 -> T100,\nX621 -> T100,\nX363 -> T100" }, { "from": 1642, "to": 1643, "label": "CASE" }, { "from": 1643, "to": 1644, "label": "PARALLEL" }, { "from": 1643, "to": 1645, "label": "PARALLEL" }, { "from": 1644, "to": 1647, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX364 -> []" }, { "from": 1645, "to": 1695, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1647, "to": 1664, "label": "CASE" }, { "from": 1664, "to": 1665, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 1665, "to": 1666, "label": "ONLY EVAL with clause\ntail(.(X654, X655), X655).\nand substitutionT99 -> T103,\nX654 -> T103,\nX580 -> X656,\nX655 -> X656,\nX365 -> X656" }, { "from": 1666, "to": 1680, "label": "CASE" }, { "from": 1680, "to": 1681, "label": "PARALLEL" }, { "from": 1680, "to": 1682, "label": "PARALLEL" }, { "from": 1681, "to": 1683, "label": "ONLY EVAL with clause\nhead([], X680).\nand substitutionX656 -> X681,\nX680 -> X681" }, { "from": 1682, "to": 1694, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 1683, "to": 1684, "label": "CASE" }, { "from": 1684, "to": 1685, "label": "PARALLEL" }, { "from": 1684, "to": 1686, "label": "PARALLEL" }, { "from": 1685, "to": 1687, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX366 -> []" }, { "from": 1686, "to": 1693, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1687, "to": 1688, "label": "CASE" }, { "from": 1688, "to": 1689, "label": "PARALLEL" }, { "from": 1688, "to": 1690, "label": "PARALLEL" }, { "from": 1689, "to": 1691, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX367 -> []" }, { "from": 1690, "to": 1692, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1691, "to": 972, "label": "INSTANCE with matching:\nT71 -> T100" }, { "from": 1762, "to": 1763, "label": "CASE" }, { "from": 1763, "to": 1764, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 1764, "to": 1779, "label": "ONLY EVAL with clause\ntail(.(X757, X758), X758).\nand substitutionX757 -> [],\nX740 -> X759,\nX758 -> X759,\nX143 -> X759" }, { "from": 1779, "to": 1780, "label": "CASE" }, { "from": 1780, "to": 1782, "label": "PARALLEL" }, { "from": 1780, "to": 1783, "label": "PARALLEL" }, { "from": 1782, "to": 1784, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX144 -> []" }, { "from": 1783, "to": 2169, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1784, "to": 1789, "label": "CASE" }, { "from": 1789, "to": 1792, "label": "EVAL with clause\nrow2col([], X785, X786, X787) :- ','(!_43, ','(eq(X785, []), ','(eq(X786, []), eq(X787, [])))).\nand substitutionT71 -> [],\nX785 -> [],\nX759 -> X788,\nX786 -> X788,\nX787 -> []" }, { "from": 1789, "to": 1793, "label": "EVAL-BACKTRACK" }, { "from": 1792, "to": 1794, "label": "CUT" }, { "from": 1793, "to": 1823, "label": "ONLY EVAL with clause\nrow2col(X824, X825, X826, X827) :- ','(head(X824, X828), ','(head(X825, X829), ','(head(X829, X828), ','(head(X827, []), ','(tail(X824, X830), ','(tail(X825, X831), ','(tail(X829, X832), ','(head(X826, X832), ','(tail(X826, X833), ','(tail(X827, X834), row2col(X830, X831, X833, X834))))))))))).\nand substitutionT71 -> T106,\nX824 -> T106,\nX825 -> [],\nX759 -> X835,\nX826 -> X835,\nX827 -> []" }, { "from": 1794, "to": 1795, "label": "CASE" }, { "from": 1795, "to": 1798, "label": "ONLY EVAL with clause\neq(X791, X791).\nand substitutionX791 -> []" }, { "from": 1798, "to": 1799, "label": "CASE" }, { "from": 1799, "to": 1803, "label": "ONLY EVAL with clause\neq(X796, X796).\nand substitutionX788 -> [],\nX796 -> [],\nX797 -> []" }, { "from": 1803, "to": 1805, "label": "CASE" }, { "from": 1805, "to": 1807, "label": "ONLY EVAL with clause\neq(X800, X800).\nand substitutionX800 -> []" }, { "from": 1807, "to": 1808, "label": "SUCCESS" }, { "from": 1823, "to": 1826, "label": "CASE" }, { "from": 1826, "to": 1829, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (row2col(T106, [], X759, []), row2col([], X785, X786, X787))" }, { "from": 1829, "to": 1830, "label": "EVAL with clause\nhead(.(X848, X849), X848).\nand substitutionX848 -> T111,\nX849 -> T112,\nT106 -> .(T111, T112),\nX828 -> T111" }, { "from": 1829, "to": 1831, "label": "EVAL-BACKTRACK" }, { "from": 1830, "to": 1832, "label": "CASE" }, { "from": 1832, "to": 1833, "label": "PARALLEL" }, { "from": 1832, "to": 1834, "label": "PARALLEL" }, { "from": 1833, "to": 1836, "label": "ONLY EVAL with clause\nhead([], X876).\nand substitutionX829 -> X877,\nX876 -> X877" }, { "from": 1834, "to": 2166, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 1836, "to": 1837, "label": "CASE" }, { "from": 1837, "to": 1867, "label": "PARALLEL" }, { "from": 1837, "to": 1870, "label": "PARALLEL" }, { "from": 1867, "to": 1872, "label": "ONLY EVAL with clause\nhead([], X900).\nand substitutionX877 -> [],\nT111 -> T117,\nX900 -> T117" }, { "from": 1870, "to": 2015, "label": "ONLY EVAL with clause\nhead(.(X1098, X1099), X1098).\nand substitutionX1098 -> T126,\nX1099 -> X1101,\nX877 -> .(T126, X1101),\nT111 -> T126,\nX1100 -> T126" }, { "from": 1872, "to": 1873, "label": "CASE" }, { "from": 1873, "to": 1874, "label": "PARALLEL" }, { "from": 1873, "to": 1875, "label": "PARALLEL" }, { "from": 1874, "to": 1878, "label": "ONLY EVAL with clause\nhead([], X923).\nand substitutionX923 -> []" }, { "from": 1875, "to": 2009, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 1878, "to": 1879, "label": "CASE" }, { "from": 1879, "to": 1880, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 1880, "to": 1884, "label": "ONLY EVAL with clause\ntail(.(X940, X941), X941).\nand substitutionT117 -> T122,\nX940 -> T122,\nT112 -> T123,\nX941 -> T123,\nX830 -> T123" }, { "from": 1884, "to": 1887, "label": "CASE" }, { "from": 1887, "to": 1888, "label": "PARALLEL" }, { "from": 1887, "to": 1889, "label": "PARALLEL" }, { "from": 1888, "to": 1891, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX831 -> []" }, { "from": 1889, "to": 2007, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1891, "to": 1898, "label": "CASE" }, { "from": 1898, "to": 1899, "label": "PARALLEL" }, { "from": 1898, "to": 1900, "label": "PARALLEL" }, { "from": 1899, "to": 1901, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX832 -> []" }, { "from": 1900, "to": 2006, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1901, "to": 1903, "label": "CASE" }, { "from": 1903, "to": 1906, "label": "PARALLEL" }, { "from": 1903, "to": 1907, "label": "PARALLEL" }, { "from": 1906, "to": 1910, "label": "ONLY EVAL with clause\nhead([], X992).\nand substitutionX835 -> [],\nX992 -> []" }, { "from": 1907, "to": 1956, "label": "ONLY EVAL with clause\nhead(.(X1036, X1037), X1036).\nand substitutionX1036 -> [],\nX1037 -> X1039,\nX835 -> .([], X1039),\nX1038 -> []" }, { "from": 1910, "to": 1913, "label": "CASE" }, { "from": 1913, "to": 1915, "label": "PARALLEL" }, { "from": 1913, "to": 1916, "label": "PARALLEL" }, { "from": 1915, "to": 1918, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX833 -> []" }, { "from": 1916, "to": 1949, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1918, "to": 1919, "label": "CASE" }, { "from": 1919, "to": 1922, "label": "PARALLEL" }, { "from": 1919, "to": 1923, "label": "PARALLEL" }, { "from": 1922, "to": 1924, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX834 -> []" }, { "from": 1923, "to": 1948, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1924, "to": 972, "label": "INSTANCE with matching:\nT71 -> T123" }, { "from": 1956, "to": 1958, "label": "CASE" }, { "from": 1958, "to": 1959, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 1959, "to": 1962, "label": "ONLY EVAL with clause\ntail(.(X1056, X1057), X1057).\nand substitutionX1056 -> [],\nX1039 -> X1058,\nX1057 -> X1058,\nX833 -> X1058" }, { "from": 1962, "to": 1966, "label": "CASE" }, { "from": 1966, "to": 1967, "label": "PARALLEL" }, { "from": 1966, "to": 1968, "label": "PARALLEL" }, { "from": 1967, "to": 1971, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX834 -> []" }, { "from": 1968, "to": 2003, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 1971, "to": 1784, "label": "INSTANCE with matching:\nT71 -> T123\nX759 -> X1058" }, { "from": 2015, "to": 2016, "label": "CASE" }, { "from": 2016, "to": 2017, "label": "PARALLEL" }, { "from": 2016, "to": 2018, "label": "PARALLEL" }, { "from": 2017, "to": 2019, "label": "ONLY EVAL with clause\nhead([], X1124).\nand substitutionX1124 -> []" }, { "from": 2018, "to": 2165, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 2019, "to": 2020, "label": "CASE" }, { "from": 2020, "to": 2021, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2021, "to": 2022, "label": "ONLY EVAL with clause\ntail(.(X1141, X1142), X1142).\nand substitutionT126 -> T131,\nX1141 -> T131,\nT112 -> T132,\nX1142 -> T132,\nX830 -> T132" }, { "from": 2022, "to": 2023, "label": "CASE" }, { "from": 2023, "to": 2024, "label": "PARALLEL" }, { "from": 2023, "to": 2025, "label": "PARALLEL" }, { "from": 2024, "to": 2026, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX831 -> []" }, { "from": 2025, "to": 2159, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2026, "to": 2029, "label": "CASE" }, { "from": 2029, "to": 2030, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2030, "to": 2032, "label": "ONLY EVAL with clause\ntail(.(X1175, X1176), X1176).\nand substitutionT131 -> T135,\nX1175 -> T135,\nX1101 -> X1177,\nX1176 -> X1177,\nX832 -> X1177" }, { "from": 2032, "to": 2034, "label": "CASE" }, { "from": 2034, "to": 2038, "label": "PARALLEL" }, { "from": 2034, "to": 2039, "label": "PARALLEL" }, { "from": 2038, "to": 2043, "label": "ONLY EVAL with clause\nhead([], X1201).\nand substitutionX835 -> [],\nX1177 -> X1202,\nX1201 -> X1202" }, { "from": 2039, "to": 2097, "label": "ONLY EVAL with clause\nhead(.(X1246, X1247), X1246).\nand substitutionX1246 -> X1248,\nX1247 -> X1249,\nX835 -> .(X1248, X1249),\nX1177 -> X1248" }, { "from": 2043, "to": 2046, "label": "CASE" }, { "from": 2046, "to": 2047, "label": "PARALLEL" }, { "from": 2046, "to": 2048, "label": "PARALLEL" }, { "from": 2047, "to": 2058, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX833 -> []" }, { "from": 2048, "to": 2085, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2058, "to": 2070, "label": "CASE" }, { "from": 2070, "to": 2079, "label": "PARALLEL" }, { "from": 2070, "to": 2080, "label": "PARALLEL" }, { "from": 2079, "to": 2081, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX834 -> []" }, { "from": 2080, "to": 2084, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2081, "to": 972, "label": "INSTANCE with matching:\nT71 -> T132" }, { "from": 2097, "to": 2099, "label": "CASE" }, { "from": 2099, "to": 2100, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2100, "to": 2134, "label": "ONLY EVAL with clause\ntail(.(X1268, X1269), X1269).\nand substitutionX1248 -> X1270,\nX1268 -> X1270,\nX1249 -> X1271,\nX1269 -> X1271,\nX833 -> X1271" }, { "from": 2134, "to": 2138, "label": "CASE" }, { "from": 2138, "to": 2139, "label": "PARALLEL" }, { "from": 2138, "to": 2140, "label": "PARALLEL" }, { "from": 2139, "to": 2141, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX834 -> []" }, { "from": 2140, "to": 2146, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2141, "to": 1784, "label": "INSTANCE with matching:\nT71 -> T132\nX759 -> X1271" }, { "from": 2177, "to": 2181, "label": "CASE" }, { "from": 2181, "to": 2182, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2182, "to": 2185, "label": "ONLY EVAL with clause\ntail(.(X1337, X1338), X1338).\nand substitutionT65 -> T140,\nX1337 -> T140,\nT60 -> T141,\nX1338 -> T141,\nX140 -> T141" }, { "from": 2185, "to": 2187, "label": "CASE" }, { "from": 2187, "to": 2188, "label": "PARALLEL" }, { "from": 2187, "to": 2189, "label": "PARALLEL" }, { "from": 2188, "to": 2191, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX141 -> []" }, { "from": 2189, "to": 3271, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2191, "to": 2193, "label": "CASE" }, { "from": 2193, "to": 2196, "label": "PARALLEL" }, { "from": 2193, "to": 2197, "label": "PARALLEL" }, { "from": 2196, "to": 2202, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX142 -> []" }, { "from": 2197, "to": 3270, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2202, "to": 2205, "label": "CASE" }, { "from": 2205, "to": 2206, "label": "PARALLEL" }, { "from": 2205, "to": 2207, "label": "PARALLEL" }, { "from": 2206, "to": 2229, "label": "ONLY EVAL with clause\nhead([], X1389).\nand substitutionX145 -> [],\nX1389 -> []" }, { "from": 2207, "to": 3230, "label": "ONLY EVAL with clause\nhead(.(X2111, X2112), X2111).\nand substitutionX2111 -> [],\nX2112 -> X2114,\nX145 -> .([], X2114),\nX2113 -> []" }, { "from": 2229, "to": 2230, "label": "CASE" }, { "from": 2230, "to": 2231, "label": "PARALLEL" }, { "from": 2230, "to": 2232, "label": "PARALLEL" }, { "from": 2231, "to": 2233, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX143 -> []" }, { "from": 2232, "to": 3161, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2233, "to": 2234, "label": "CASE" }, { "from": 2234, "to": 2235, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2235, "to": 2240, "label": "ONLY EVAL with clause\ntail(.(X1417, X1418), X1418).\nand substitutionX1417 -> [],\nX1320 -> X1419,\nX1418 -> X1419,\nX144 -> X1419" }, { "from": 2240, "to": 2241, "label": "CASE" }, { "from": 2241, "to": 2244, "label": "EVAL with clause\nrow2col([], X1432, X1433, X1434) :- ','(!_74, ','(eq(X1432, []), ','(eq(X1433, []), eq(X1434, [])))).\nand substitutionT141 -> [],\nX1432 -> [],\nX1433 -> [],\nX1419 -> X1435,\nX1434 -> X1435" }, { "from": 2241, "to": 2245, "label": "EVAL-BACKTRACK" }, { "from": 2244, "to": 2246, "label": "CUT" }, { "from": 2245, "to": 2268, "label": "ONLY EVAL with clause\nrow2col(X1471, X1472, X1473, X1474) :- ','(head(X1471, X1475), ','(head(X1472, X1476), ','(head(X1476, X1475), ','(head(X1474, []), ','(tail(X1471, X1477), ','(tail(X1472, X1478), ','(tail(X1476, X1479), ','(head(X1473, X1479), ','(tail(X1473, X1480), ','(tail(X1474, X1481), row2col(X1477, X1478, X1480, X1481))))))))))).\nand substitutionT141 -> T144,\nX1471 -> T144,\nX1472 -> [],\nX1473 -> [],\nX1419 -> X1482,\nX1474 -> X1482" }, { "from": 2246, "to": 2247, "label": "CASE" }, { "from": 2247, "to": 2249, "label": "ONLY EVAL with clause\neq(X1438, X1438).\nand substitutionX1438 -> []" }, { "from": 2249, "to": 2250, "label": "CASE" }, { "from": 2250, "to": 2251, "label": "ONLY EVAL with clause\neq(X1441, X1441).\nand substitutionX1441 -> []" }, { "from": 2251, "to": 2252, "label": "CASE" }, { "from": 2252, "to": 2255, "label": "ONLY EVAL with clause\neq(X1446, X1446).\nand substitutionX1435 -> [],\nX1446 -> [],\nX1447 -> []" }, { "from": 2255, "to": 2256, "label": "SUCCESS" }, { "from": 2268, "to": 2272, "label": "CASE" }, { "from": 2272, "to": 2274, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (row2col(T144, [], [], X1419), row2col([], X1432, X1433, X1434))" }, { "from": 2274, "to": 2276, "label": "EVAL with clause\nhead(.(X1495, X1496), X1495).\nand substitutionX1495 -> T149,\nX1496 -> T150,\nT144 -> .(T149, T150),\nX1475 -> T149" }, { "from": 2274, "to": 2277, "label": "EVAL-BACKTRACK" }, { "from": 2276, "to": 2283, "label": "CASE" }, { "from": 2283, "to": 2293, "label": "PARALLEL" }, { "from": 2283, "to": 2295, "label": "PARALLEL" }, { "from": 2293, "to": 2297, "label": "ONLY EVAL with clause\nhead([], X1523).\nand substitutionX1476 -> X1524,\nX1523 -> X1524" }, { "from": 2295, "to": 3160, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 2297, "to": 2299, "label": "CASE" }, { "from": 2299, "to": 2303, "label": "PARALLEL" }, { "from": 2299, "to": 2304, "label": "PARALLEL" }, { "from": 2303, "to": 2317, "label": "ONLY EVAL with clause\nhead([], X1547).\nand substitutionX1524 -> [],\nT149 -> T155,\nX1547 -> T155" }, { "from": 2304, "to": 2721, "label": "ONLY EVAL with clause\nhead(.(X1819, X1820), X1819).\nand substitutionX1819 -> T170,\nX1820 -> X1822,\nX1524 -> .(T170, X1822),\nT149 -> T170,\nX1821 -> T170" }, { "from": 2317, "to": 2318, "label": "CASE" }, { "from": 2318, "to": 2321, "label": "PARALLEL" }, { "from": 2318, "to": 2322, "label": "PARALLEL" }, { "from": 2321, "to": 2325, "label": "ONLY EVAL with clause\nhead([], X1570).\nand substitutionX1482 -> [],\nX1570 -> []" }, { "from": 2322, "to": 2498, "label": "ONLY EVAL with clause\nhead(.(X1690, X1691), X1690).\nand substitutionX1690 -> [],\nX1691 -> X1693,\nX1482 -> .([], X1693),\nX1692 -> []" }, { "from": 2325, "to": 2327, "label": "CASE" }, { "from": 2327, "to": 2328, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2328, "to": 2333, "label": "ONLY EVAL with clause\ntail(.(X1587, X1588), X1588).\nand substitutionT155 -> T160,\nX1587 -> T160,\nT150 -> T161,\nX1588 -> T161,\nX1477 -> T161" }, { "from": 2333, "to": 2337, "label": "CASE" }, { "from": 2337, "to": 2339, "label": "PARALLEL" }, { "from": 2337, "to": 2340, "label": "PARALLEL" }, { "from": 2339, "to": 2341, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1478 -> []" }, { "from": 2340, "to": 2420, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2341, "to": 2345, "label": "CASE" }, { "from": 2345, "to": 2371, "label": "PARALLEL" }, { "from": 2345, "to": 2372, "label": "PARALLEL" }, { "from": 2371, "to": 2375, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1479 -> []" }, { "from": 2372, "to": 2418, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2375, "to": 2377, "label": "CASE" }, { "from": 2377, "to": 2381, "label": "PARALLEL" }, { "from": 2377, "to": 2382, "label": "PARALLEL" }, { "from": 2381, "to": 2385, "label": "ONLY EVAL with clause\nhead([], X1639).\nand substitutionX1639 -> []" }, { "from": 2382, "to": 2415, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 2385, "to": 2389, "label": "CASE" }, { "from": 2389, "to": 2390, "label": "PARALLEL" }, { "from": 2389, "to": 2391, "label": "PARALLEL" }, { "from": 2390, "to": 2395, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1480 -> []" }, { "from": 2391, "to": 2414, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2395, "to": 2398, "label": "CASE" }, { "from": 2398, "to": 2403, "label": "PARALLEL" }, { "from": 2398, "to": 2404, "label": "PARALLEL" }, { "from": 2403, "to": 2405, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1481 -> []" }, { "from": 2404, "to": 2408, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2405, "to": 972, "label": "INSTANCE with matching:\nT71 -> T161" }, { "from": 2498, "to": 2504, "label": "CASE" }, { "from": 2504, "to": 2505, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2505, "to": 2510, "label": "ONLY EVAL with clause\ntail(.(X1710, X1711), X1711).\nand substitutionT155 -> T166,\nX1710 -> T166,\nT150 -> T167,\nX1711 -> T167,\nX1477 -> T167" }, { "from": 2510, "to": 2512, "label": "CASE" }, { "from": 2512, "to": 2515, "label": "PARALLEL" }, { "from": 2512, "to": 2516, "label": "PARALLEL" }, { "from": 2515, "to": 2518, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1478 -> []" }, { "from": 2516, "to": 2632, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2518, "to": 2520, "label": "CASE" }, { "from": 2520, "to": 2524, "label": "PARALLEL" }, { "from": 2520, "to": 2525, "label": "PARALLEL" }, { "from": 2524, "to": 2534, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1479 -> []" }, { "from": 2525, "to": 2629, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2534, "to": 2542, "label": "CASE" }, { "from": 2542, "to": 2552, "label": "PARALLEL" }, { "from": 2542, "to": 2553, "label": "PARALLEL" }, { "from": 2552, "to": 2560, "label": "ONLY EVAL with clause\nhead([], X1762).\nand substitutionX1762 -> []" }, { "from": 2553, "to": 2628, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 2560, "to": 2569, "label": "CASE" }, { "from": 2569, "to": 2604, "label": "PARALLEL" }, { "from": 2569, "to": 2605, "label": "PARALLEL" }, { "from": 2604, "to": 2606, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1480 -> []" }, { "from": 2605, "to": 2626, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2606, "to": 2607, "label": "CASE" }, { "from": 2607, "to": 2608, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2608, "to": 2611, "label": "ONLY EVAL with clause\ntail(.(X1790, X1791), X1791).\nand substitutionX1790 -> [],\nX1693 -> X1792,\nX1791 -> X1792,\nX1481 -> X1792" }, { "from": 2611, "to": 2240, "label": "INSTANCE with matching:\nT141 -> T167\nX1419 -> X1792" }, { "from": 2721, "to": 2722, "label": "CASE" }, { "from": 2722, "to": 2732, "label": "PARALLEL" }, { "from": 2722, "to": 2733, "label": "PARALLEL" }, { "from": 2732, "to": 2741, "label": "ONLY EVAL with clause\nhead([], X1845).\nand substitutionX1482 -> [],\nX1845 -> []" }, { "from": 2733, "to": 2985, "label": "ONLY EVAL with clause\nhead(.(X1972, X1973), X1972).\nand substitutionX1972 -> [],\nX1973 -> X1975,\nX1482 -> .([], X1975),\nX1974 -> []" }, { "from": 2741, "to": 2745, "label": "CASE" }, { "from": 2745, "to": 2746, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2746, "to": 2776, "label": "ONLY EVAL with clause\ntail(.(X1862, X1863), X1863).\nand substitutionT170 -> T175,\nX1862 -> T175,\nT150 -> T176,\nX1863 -> T176,\nX1477 -> T176" }, { "from": 2776, "to": 2780, "label": "CASE" }, { "from": 2780, "to": 2781, "label": "PARALLEL" }, { "from": 2780, "to": 2782, "label": "PARALLEL" }, { "from": 2781, "to": 2792, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1478 -> []" }, { "from": 2782, "to": 2975, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2792, "to": 2793, "label": "CASE" }, { "from": 2793, "to": 2794, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2794, "to": 2833, "label": "ONLY EVAL with clause\ntail(.(X1896, X1897), X1897).\nand substitutionT175 -> T179,\nX1896 -> T179,\nX1822 -> X1898,\nX1897 -> X1898,\nX1479 -> X1898" }, { "from": 2833, "to": 2835, "label": "CASE" }, { "from": 2835, "to": 2846, "label": "PARALLEL" }, { "from": 2835, "to": 2847, "label": "PARALLEL" }, { "from": 2846, "to": 2854, "label": "ONLY EVAL with clause\nhead([], X1922).\nand substitutionX1898 -> X1923,\nX1922 -> X1923" }, { "from": 2847, "to": 2974, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 2854, "to": 2899, "label": "CASE" }, { "from": 2899, "to": 2901, "label": "PARALLEL" }, { "from": 2899, "to": 2902, "label": "PARALLEL" }, { "from": 2901, "to": 2911, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1480 -> []" }, { "from": 2902, "to": 2973, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2911, "to": 2914, "label": "CASE" }, { "from": 2914, "to": 2915, "label": "PARALLEL" }, { "from": 2914, "to": 2916, "label": "PARALLEL" }, { "from": 2915, "to": 2917, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1481 -> []" }, { "from": 2916, "to": 2966, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 2917, "to": 972, "label": "INSTANCE with matching:\nT71 -> T176" }, { "from": 2985, "to": 2987, "label": "CASE" }, { "from": 2987, "to": 2988, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 2988, "to": 2998, "label": "ONLY EVAL with clause\ntail(.(X1992, X1993), X1993).\nand substitutionT170 -> T184,\nX1992 -> T184,\nT150 -> T185,\nX1993 -> T185,\nX1477 -> T185" }, { "from": 2998, "to": 3006, "label": "CASE" }, { "from": 3006, "to": 3008, "label": "PARALLEL" }, { "from": 3006, "to": 3009, "label": "PARALLEL" }, { "from": 3008, "to": 3050, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1478 -> []" }, { "from": 3009, "to": 3158, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3050, "to": 3054, "label": "CASE" }, { "from": 3054, "to": 3055, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3055, "to": 3057, "label": "ONLY EVAL with clause\ntail(.(X2026, X2027), X2027).\nand substitutionT184 -> T188,\nX2026 -> T188,\nX1822 -> X2028,\nX2027 -> X2028,\nX1479 -> X2028" }, { "from": 3057, "to": 3059, "label": "CASE" }, { "from": 3059, "to": 3060, "label": "PARALLEL" }, { "from": 3059, "to": 3061, "label": "PARALLEL" }, { "from": 3060, "to": 3102, "label": "ONLY EVAL with clause\nhead([], X2052).\nand substitutionX2028 -> X2053,\nX2052 -> X2053" }, { "from": 3061, "to": 3157, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 3102, "to": 3103, "label": "CASE" }, { "from": 3103, "to": 3104, "label": "PARALLEL" }, { "from": 3103, "to": 3105, "label": "PARALLEL" }, { "from": 3104, "to": 3106, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX1480 -> []" }, { "from": 3105, "to": 3156, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3106, "to": 3108, "label": "CASE" }, { "from": 3108, "to": 3109, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3109, "to": 3153, "label": "ONLY EVAL with clause\ntail(.(X2081, X2082), X2082).\nand substitutionX2081 -> [],\nX1975 -> X2083,\nX2082 -> X2083,\nX1481 -> X2083" }, { "from": 3153, "to": 2240, "label": "INSTANCE with matching:\nT141 -> T185\nX1419 -> X2083" }, { "from": 3230, "to": 3232, "label": "CASE" }, { "from": 3232, "to": 3233, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3233, "to": 3236, "label": "ONLY EVAL with clause\ntail(.(X2131, X2132), X2132).\nand substitutionX2131 -> [],\nX2114 -> X2133,\nX2132 -> X2133,\nX143 -> X2133" }, { "from": 3236, "to": 3238, "label": "CASE" }, { "from": 3238, "to": 3239, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3239, "to": 3269, "label": "ONLY EVAL with clause\ntail(.(X2150, X2151), X2151).\nand substitutionX2150 -> [],\nX1320 -> X2152,\nX2151 -> X2152,\nX144 -> X2152" }, { "from": 3269, "to": 481, "label": "INSTANCE with matching:\nT34 -> T141\nT20 -> []\nX38 -> X2133\nX39 -> X2152" }, { "from": 3304, "to": 3305, "label": "CASE" }, { "from": 3305, "to": 3308, "label": "PARALLEL" }, { "from": 3305, "to": 3309, "label": "PARALLEL" }, { "from": 3308, "to": 3317, "label": "ONLY EVAL with clause\nhead([], X2202).\nand substitutionX146 -> [],\nX2202 -> []" }, { "from": 3309, "to": 3593, "label": "ONLY EVAL with clause\nhead(.(X2385, X2386), X2385).\nand substitutionX2385 -> [],\nX2386 -> X2388,\nX146 -> .([], X2388),\nX2387 -> []" }, { "from": 3317, "to": 3322, "label": "CASE" }, { "from": 3322, "to": 3323, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3323, "to": 3332, "label": "ONLY EVAL with clause\ntail(.(X2219, X2220), X2220).\nand substitutionT191 -> T196,\nX2219 -> T196,\nT60 -> T197,\nX2220 -> T197,\nX140 -> T197" }, { "from": 3332, "to": 3334, "label": "CASE" }, { "from": 3334, "to": 3357, "label": "PARALLEL" }, { "from": 3334, "to": 3358, "label": "PARALLEL" }, { "from": 3357, "to": 3362, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX141 -> []" }, { "from": 3358, "to": 3591, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3362, "to": 3363, "label": "CASE" }, { "from": 3363, "to": 3365, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3365, "to": 3374, "label": "ONLY EVAL with clause\ntail(.(X2253, X2254), X2254).\nand substitutionT196 -> T200,\nX2253 -> T200,\nX2179 -> X2255,\nX2254 -> X2255,\nX142 -> X2255" }, { "from": 3374, "to": 3380, "label": "CASE" }, { "from": 3380, "to": 3384, "label": "PARALLEL" }, { "from": 3380, "to": 3385, "label": "PARALLEL" }, { "from": 3384, "to": 3389, "label": "ONLY EVAL with clause\nhead([], X2279).\nand substitutionX145 -> [],\nX2255 -> X2280,\nX2279 -> X2280" }, { "from": 3385, "to": 3538, "label": "ONLY EVAL with clause\nhead(.(X2324, X2325), X2324).\nand substitutionX2324 -> X2326,\nX2325 -> X2327,\nX145 -> .(X2326, X2327),\nX2255 -> X2326" }, { "from": 3389, "to": 3390, "label": "CASE" }, { "from": 3390, "to": 3392, "label": "PARALLEL" }, { "from": 3390, "to": 3393, "label": "PARALLEL" }, { "from": 3392, "to": 3396, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX143 -> []" }, { "from": 3393, "to": 3452, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3396, "to": 3397, "label": "CASE" }, { "from": 3397, "to": 3399, "label": "PARALLEL" }, { "from": 3397, "to": 3400, "label": "PARALLEL" }, { "from": 3399, "to": 3424, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX144 -> []" }, { "from": 3400, "to": 3436, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3424, "to": 972, "label": "INSTANCE with matching:\nT71 -> T197" }, { "from": 3538, "to": 3551, "label": "CASE" }, { "from": 3551, "to": 3552, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3552, "to": 3565, "label": "ONLY EVAL with clause\ntail(.(X2346, X2347), X2347).\nand substitutionX2326 -> X2348,\nX2346 -> X2348,\nX2327 -> X2349,\nX2347 -> X2349,\nX143 -> X2349" }, { "from": 3565, "to": 3567, "label": "CASE" }, { "from": 3567, "to": 3570, "label": "PARALLEL" }, { "from": 3567, "to": 3571, "label": "PARALLEL" }, { "from": 3570, "to": 3576, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX144 -> []" }, { "from": 3571, "to": 3579, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3576, "to": 1784, "label": "INSTANCE with matching:\nT71 -> T197\nX759 -> X2349" }, { "from": 3593, "to": 3596, "label": "CASE" }, { "from": 3596, "to": 3597, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3597, "to": 3598, "label": "ONLY EVAL with clause\ntail(.(X2405, X2406), X2406).\nand substitutionT191 -> T205,\nX2405 -> T205,\nT60 -> T206,\nX2406 -> T206,\nX140 -> T206" }, { "from": 3598, "to": 3600, "label": "CASE" }, { "from": 3600, "to": 3604, "label": "PARALLEL" }, { "from": 3600, "to": 3605, "label": "PARALLEL" }, { "from": 3604, "to": 3619, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX141 -> []" }, { "from": 3605, "to": 3823, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3619, "to": 3620, "label": "CASE" }, { "from": 3620, "to": 3621, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3621, "to": 3623, "label": "ONLY EVAL with clause\ntail(.(X2439, X2440), X2440).\nand substitutionT205 -> T209,\nX2439 -> T209,\nX2179 -> X2441,\nX2440 -> X2441,\nX142 -> X2441" }, { "from": 3623, "to": 3624, "label": "CASE" }, { "from": 3624, "to": 3649, "label": "PARALLEL" }, { "from": 3624, "to": 3650, "label": "PARALLEL" }, { "from": 3649, "to": 3654, "label": "ONLY EVAL with clause\nhead([], X2465).\nand substitutionX145 -> [],\nX2441 -> X2466,\nX2465 -> X2466" }, { "from": 3650, "to": 3751, "label": "ONLY EVAL with clause\nhead(.(X2516, X2517), X2516).\nand substitutionX2516 -> X2518,\nX2517 -> X2519,\nX145 -> .(X2518, X2519),\nX2441 -> X2518" }, { "from": 3654, "to": 3678, "label": "CASE" }, { "from": 3678, "to": 3679, "label": "PARALLEL" }, { "from": 3678, "to": 3680, "label": "PARALLEL" }, { "from": 3679, "to": 3681, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX143 -> []" }, { "from": 3680, "to": 3727, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3681, "to": 3683, "label": "CASE" }, { "from": 3683, "to": 3684, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3684, "to": 3724, "label": "ONLY EVAL with clause\ntail(.(X2494, X2495), X2495).\nand substitutionX2494 -> [],\nX2388 -> X2496,\nX2495 -> X2496,\nX144 -> X2496" }, { "from": 3724, "to": 2240, "label": "INSTANCE with matching:\nT141 -> T206\nX1419 -> X2496" }, { "from": 3751, "to": 3753, "label": "CASE" }, { "from": 3753, "to": 3754, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3754, "to": 3761, "label": "ONLY EVAL with clause\ntail(.(X2538, X2539), X2539).\nand substitutionX2518 -> X2540,\nX2538 -> X2540,\nX2519 -> X2541,\nX2539 -> X2541,\nX143 -> X2541" }, { "from": 3761, "to": 3762, "label": "CASE" }, { "from": 3762, "to": 3763, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3763, "to": 3787, "label": "ONLY EVAL with clause\ntail(.(X2558, X2559), X2559).\nand substitutionX2558 -> [],\nX2388 -> X2560,\nX2559 -> X2560,\nX144 -> X2560" }, { "from": 3787, "to": 481, "label": "INSTANCE with matching:\nT34 -> T206\nT20 -> []\nX38 -> X2541\nX39 -> X2560" }, { "from": 3829, "to": 3832, "label": "CASE" }, { "from": 3832, "to": 3834, "label": "PARALLEL" }, { "from": 3832, "to": 3835, "label": "PARALLEL" }, { "from": 3834, "to": 3838, "label": "EVAL with clause\nhead([], X2584).\nand substitutionT216 -> [],\nT59 -> T222,\nX2584 -> T222,\nT217 -> T223" }, { "from": 3834, "to": 3839, "label": "EVAL-BACKTRACK" }, { "from": 3835, "to": 6520, "label": "EVAL with clause\nhead(.(X5704, X5705), X5704).\nand substitutionX5704 -> T827,\nX5705 -> T830,\nT216 -> .(T827, T830),\nT59 -> T827,\nT217 -> T829,\nT828 -> T830" }, { "from": 3835, "to": 6521, "label": "EVAL-BACKTRACK" }, { "from": 3838, "to": 3842, "label": "CASE" }, { "from": 3842, "to": 3850, "label": "PARALLEL" }, { "from": 3842, "to": 3851, "label": "PARALLEL" }, { "from": 3850, "to": 3881, "label": "ONLY EVAL with clause\nhead([], X2607).\nand substitutionX146 -> [],\nX2607 -> []" }, { "from": 3851, "to": 5627, "label": "ONLY EVAL with clause\nhead(.(X4339, X4340), X4339).\nand substitutionX4339 -> [],\nX4340 -> X4342,\nX146 -> .([], X4342),\nX4341 -> []" }, { "from": 3881, "to": 3891, "label": "CASE" }, { "from": 3891, "to": 3892, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3892, "to": 3908, "label": "ONLY EVAL with clause\ntail(.(X2624, X2625), X2625).\nand substitutionT222 -> T228,\nX2624 -> T228,\nT60 -> T229,\nX2625 -> T229,\nX140 -> T229" }, { "from": 3908, "to": 3915, "label": "CASE" }, { "from": 3915, "to": 3916, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 3916, "to": 3934, "label": "ONLY EVAL with clause\ntail(.(X2641, X2642), X2642).\nand substitutionX2641 -> [],\nT223 -> T235,\nX2642 -> T235,\nX141 -> T235,\nT234 -> T235" }, { "from": 3934, "to": 3938, "label": "CASE" }, { "from": 3938, "to": 3945, "label": "PARALLEL" }, { "from": 3938, "to": 3946, "label": "PARALLEL" }, { "from": 3945, "to": 3950, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX142 -> []" }, { "from": 3946, "to": 5621, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 3950, "to": 3955, "label": "CASE" }, { "from": 3955, "to": 3961, "label": "PARALLEL" }, { "from": 3955, "to": 3962, "label": "PARALLEL" }, { "from": 3961, "to": 3969, "label": "ONLY EVAL with clause\nhead([], X2677).\nand substitutionX145 -> [],\nX2677 -> []" }, { "from": 3962, "to": 4949, "label": "ONLY EVAL with clause\nhead(.(X3389, X3390), X3389).\nand substitutionX3389 -> [],\nX3390 -> X3392,\nX145 -> .([], X3392),\nX3391 -> []" }, { "from": 3969, "to": 4036, "label": "CASE" }, { "from": 4036, "to": 4084, "label": "PARALLEL" }, { "from": 4036, "to": 4085, "label": "PARALLEL" }, { "from": 4084, "to": 4086, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX143 -> []" }, { "from": 4085, "to": 4947, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4086, "to": 4088, "label": "CASE" }, { "from": 4088, "to": 4091, "label": "PARALLEL" }, { "from": 4088, "to": 4092, "label": "PARALLEL" }, { "from": 4091, "to": 4093, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX144 -> []" }, { "from": 4092, "to": 4946, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4093, "to": 4095, "label": "CASE" }, { "from": 4095, "to": 4098, "label": "EVAL with clause\nrow2col([], X2710, X2711, X2712) :- ','(!_134, ','(eq(X2710, []), ','(eq(X2711, []), eq(X2712, [])))).\nand substitutionT229 -> [],\nT235 -> T252,\nX2710 -> T252,\nX2711 -> [],\nX2712 -> [],\nT251 -> T252" }, { "from": 4095, "to": 4099, "label": "EVAL-BACKTRACK" }, { "from": 4098, "to": 4100, "label": "CUT" }, { "from": 4099, "to": 4141, "label": "ONLY EVAL with clause\nrow2col(X2743, X2744, X2745, X2746) :- ','(head(X2743, X2747), ','(head(X2744, X2748), ','(head(X2748, X2747), ','(head(X2746, []), ','(tail(X2743, X2749), ','(tail(X2744, X2750), ','(tail(X2748, X2751), ','(head(X2745, X2751), ','(tail(X2745, X2752), ','(tail(X2746, X2753), row2col(X2749, X2750, X2752, X2753))))))))))).\nand substitutionT229 -> T261,\nX2743 -> T261,\nT235 -> T263,\nX2744 -> T263,\nX2745 -> [],\nX2746 -> [],\nT262 -> T263" }, { "from": 4100, "to": 4101, "label": "CASE" }, { "from": 4101, "to": 4104, "label": "EVAL with clause\neq(X2715, X2715).\nand substitutionT252 -> [],\nX2715 -> [],\nT255 -> []" }, { "from": 4101, "to": 4105, "label": "EVAL-BACKTRACK" }, { "from": 4104, "to": 4106, "label": "CASE" }, { "from": 4106, "to": 4107, "label": "ONLY EVAL with clause\neq(X2718, X2718).\nand substitutionX2718 -> []" }, { "from": 4107, "to": 4108, "label": "CASE" }, { "from": 4108, "to": 4111, "label": "ONLY EVAL with clause\neq(X2721, X2721).\nand substitutionX2721 -> []" }, { "from": 4111, "to": 4112, "label": "SUCCESS" }, { "from": 4141, "to": 4144, "label": "CASE" }, { "from": 4144, "to": 4145, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (row2col(T261, T235, [], []), row2col([], X2710, X2711, X2712))" }, { "from": 4145, "to": 4151, "label": "EVAL with clause\nhead(.(X2766, X2767), X2766).\nand substitutionX2766 -> T268,\nX2767 -> T269,\nT261 -> .(T268, T269),\nX2747 -> T268" }, { "from": 4145, "to": 4152, "label": "EVAL-BACKTRACK" }, { "from": 4151, "to": 4156, "label": "CASE" }, { "from": 4156, "to": 4157, "label": "PARALLEL" }, { "from": 4156, "to": 4158, "label": "PARALLEL" }, { "from": 4157, "to": 4162, "label": "EVAL with clause\nhead([], X2782).\nand substitutionT263 -> [],\nX2748 -> X2783,\nX2782 -> X2783" }, { "from": 4157, "to": 4163, "label": "EVAL-BACKTRACK" }, { "from": 4158, "to": 4644, "label": "EVAL with clause\nhead(.(X3096, X3097), X3096).\nand substitutionX3096 -> T299,\nX3097 -> T300,\nT263 -> .(T299, T300),\nX2748 -> T299,\nT297 -> T299,\nT298 -> T300" }, { "from": 4158, "to": 4645, "label": "EVAL-BACKTRACK" }, { "from": 4162, "to": 4167, "label": "CASE" }, { "from": 4167, "to": 4171, "label": "PARALLEL" }, { "from": 4167, "to": 4172, "label": "PARALLEL" }, { "from": 4171, "to": 4186, "label": "ONLY EVAL with clause\nhead([], X2806).\nand substitutionX2783 -> [],\nT268 -> T274,\nX2806 -> T274" }, { "from": 4172, "to": 4395, "label": "ONLY EVAL with clause\nhead(.(X2951, X2952), X2951).\nand substitutionX2951 -> T283,\nX2952 -> X2954,\nX2783 -> .(T283, X2954),\nT268 -> T283,\nX2953 -> T283" }, { "from": 4186, "to": 4190, "label": "CASE" }, { "from": 4190, "to": 4195, "label": "PARALLEL" }, { "from": 4190, "to": 4196, "label": "PARALLEL" }, { "from": 4195, "to": 4202, "label": "ONLY EVAL with clause\nhead([], X2829).\nand substitutionX2829 -> []" }, { "from": 4196, "to": 4378, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 4202, "to": 4206, "label": "CASE" }, { "from": 4206, "to": 4207, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4207, "to": 4214, "label": "ONLY EVAL with clause\ntail(.(X2846, X2847), X2847).\nand substitutionT274 -> T279,\nX2846 -> T279,\nT269 -> T280,\nX2847 -> T280,\nX2749 -> T280" }, { "from": 4214, "to": 4227, "label": "CASE" }, { "from": 4227, "to": 4230, "label": "PARALLEL" }, { "from": 4227, "to": 4231, "label": "PARALLEL" }, { "from": 4230, "to": 4233, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2750 -> []" }, { "from": 4231, "to": 4376, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4233, "to": 4243, "label": "CASE" }, { "from": 4243, "to": 4244, "label": "PARALLEL" }, { "from": 4243, "to": 4245, "label": "PARALLEL" }, { "from": 4244, "to": 4247, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2751 -> []" }, { "from": 4245, "to": 4375, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4247, "to": 4252, "label": "CASE" }, { "from": 4252, "to": 4257, "label": "PARALLEL" }, { "from": 4252, "to": 4258, "label": "PARALLEL" }, { "from": 4257, "to": 4263, "label": "ONLY EVAL with clause\nhead([], X2898).\nand substitutionX2898 -> []" }, { "from": 4258, "to": 4374, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 4263, "to": 4264, "label": "CASE" }, { "from": 4264, "to": 4265, "label": "PARALLEL" }, { "from": 4264, "to": 4266, "label": "PARALLEL" }, { "from": 4265, "to": 4279, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2752 -> []" }, { "from": 4266, "to": 4373, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4279, "to": 4319, "label": "CASE" }, { "from": 4319, "to": 4331, "label": "PARALLEL" }, { "from": 4319, "to": 4332, "label": "PARALLEL" }, { "from": 4331, "to": 4342, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2753 -> []" }, { "from": 4332, "to": 4370, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4342, "to": 972, "label": "INSTANCE with matching:\nT71 -> T280" }, { "from": 4395, "to": 4408, "label": "CASE" }, { "from": 4408, "to": 4418, "label": "PARALLEL" }, { "from": 4408, "to": 4421, "label": "PARALLEL" }, { "from": 4418, "to": 4431, "label": "ONLY EVAL with clause\nhead([], X2977).\nand substitutionX2977 -> []" }, { "from": 4421, "to": 4590, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 4431, "to": 4503, "label": "CASE" }, { "from": 4503, "to": 4504, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4504, "to": 4506, "label": "ONLY EVAL with clause\ntail(.(X2994, X2995), X2995).\nand substitutionT283 -> T288,\nX2994 -> T288,\nT269 -> T289,\nX2995 -> T289,\nX2749 -> T289" }, { "from": 4506, "to": 4515, "label": "CASE" }, { "from": 4515, "to": 4520, "label": "PARALLEL" }, { "from": 4515, "to": 4522, "label": "PARALLEL" }, { "from": 4520, "to": 4527, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2750 -> []" }, { "from": 4522, "to": 4584, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4527, "to": 4547, "label": "CASE" }, { "from": 4547, "to": 4548, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4548, "to": 4554, "label": "ONLY EVAL with clause\ntail(.(X3028, X3029), X3029).\nand substitutionT288 -> T292,\nX3028 -> T292,\nX2954 -> X3030,\nX3029 -> X3030,\nX2751 -> X3030" }, { "from": 4554, "to": 4555, "label": "CASE" }, { "from": 4555, "to": 4557, "label": "PARALLEL" }, { "from": 4555, "to": 4558, "label": "PARALLEL" }, { "from": 4557, "to": 4561, "label": "ONLY EVAL with clause\nhead([], X3054).\nand substitutionX3030 -> X3055,\nX3054 -> X3055" }, { "from": 4558, "to": 4583, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 4561, "to": 4563, "label": "CASE" }, { "from": 4563, "to": 4565, "label": "PARALLEL" }, { "from": 4563, "to": 4566, "label": "PARALLEL" }, { "from": 4565, "to": 4571, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2752 -> []" }, { "from": 4566, "to": 4581, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4571, "to": 4572, "label": "CASE" }, { "from": 4572, "to": 4574, "label": "PARALLEL" }, { "from": 4572, "to": 4575, "label": "PARALLEL" }, { "from": 4574, "to": 4576, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2753 -> []" }, { "from": 4575, "to": 4580, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4576, "to": 972, "label": "INSTANCE with matching:\nT71 -> T289" }, { "from": 4644, "to": 4650, "label": "CASE" }, { "from": 4650, "to": 4651, "label": "PARALLEL" }, { "from": 4650, "to": 4652, "label": "PARALLEL" }, { "from": 4651, "to": 4657, "label": "EVAL with clause\nhead([], X3108).\nand substitutionT299 -> [],\nT268 -> T305,\nX3108 -> T305,\nT300 -> T306" }, { "from": 4651, "to": 4658, "label": "EVAL-BACKTRACK" }, { "from": 4652, "to": 4833, "label": "EVAL with clause\nhead(.(X3242, X3243), X3242).\nand substitutionX3242 -> T336,\nX3243 -> T339,\nT299 -> .(T336, T339),\nT268 -> T336,\nT300 -> T338,\nT337 -> T339" }, { "from": 4652, "to": 4834, "label": "EVAL-BACKTRACK" }, { "from": 4657, "to": 4663, "label": "CASE" }, { "from": 4663, "to": 4664, "label": "PARALLEL" }, { "from": 4663, "to": 4665, "label": "PARALLEL" }, { "from": 4664, "to": 4673, "label": "ONLY EVAL with clause\nhead([], X3131).\nand substitutionX3131 -> []" }, { "from": 4665, "to": 4830, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 4673, "to": 4678, "label": "CASE" }, { "from": 4678, "to": 4679, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4679, "to": 4716, "label": "ONLY EVAL with clause\ntail(.(X3148, X3149), X3149).\nand substitutionT305 -> T311,\nX3148 -> T311,\nT269 -> T312,\nX3149 -> T312,\nX2749 -> T312" }, { "from": 4716, "to": 4722, "label": "CASE" }, { "from": 4722, "to": 4723, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4723, "to": 4734, "label": "ONLY EVAL with clause\ntail(.(X3165, X3166), X3166).\nand substitutionX3165 -> [],\nT306 -> T318,\nX3166 -> T318,\nX2750 -> T318,\nT317 -> T318" }, { "from": 4734, "to": 4738, "label": "CASE" }, { "from": 4738, "to": 4745, "label": "PARALLEL" }, { "from": 4738, "to": 4746, "label": "PARALLEL" }, { "from": 4745, "to": 4748, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2751 -> []" }, { "from": 4746, "to": 4829, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4748, "to": 4754, "label": "CASE" }, { "from": 4754, "to": 4757, "label": "PARALLEL" }, { "from": 4754, "to": 4758, "label": "PARALLEL" }, { "from": 4757, "to": 4764, "label": "ONLY EVAL with clause\nhead([], X3201).\nand substitutionX3201 -> []" }, { "from": 4758, "to": 4827, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 4764, "to": 4771, "label": "CASE" }, { "from": 4771, "to": 4772, "label": "PARALLEL" }, { "from": 4771, "to": 4773, "label": "PARALLEL" }, { "from": 4772, "to": 4778, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2752 -> []" }, { "from": 4773, "to": 4826, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4778, "to": 4810, "label": "CASE" }, { "from": 4810, "to": 4813, "label": "PARALLEL" }, { "from": 4810, "to": 4814, "label": "PARALLEL" }, { "from": 4813, "to": 4815, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2753 -> []" }, { "from": 4814, "to": 4821, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4815, "to": 4093, "label": "INSTANCE with matching:\nT229 -> T312\nT235 -> T318" }, { "from": 4833, "to": 4836, "label": "CASE" }, { "from": 4836, "to": 4864, "label": "PARALLEL" }, { "from": 4836, "to": 4865, "label": "PARALLEL" }, { "from": 4864, "to": 4868, "label": "ONLY EVAL with clause\nhead([], X3266).\nand substitutionX3266 -> []" }, { "from": 4865, "to": 4945, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 4868, "to": 4876, "label": "CASE" }, { "from": 4876, "to": 4877, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4877, "to": 4878, "label": "ONLY EVAL with clause\ntail(.(X3283, X3284), X3284).\nand substitutionT336 -> T344,\nX3283 -> T344,\nT269 -> T345,\nX3284 -> T345,\nX2749 -> T345" }, { "from": 4878, "to": 4887, "label": "CASE" }, { "from": 4887, "to": 4888, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4888, "to": 4890, "label": "ONLY EVAL with clause\ntail(.(X3300, X3301), X3301).\nand substitutionT344 -> T355,\nT339 -> T358,\nX3300 -> .(T355, T358),\nT338 -> T359,\nX3301 -> T359,\nX2750 -> T359,\nT356 -> T358,\nT357 -> T359" }, { "from": 4890, "to": 4893, "label": "CASE" }, { "from": 4893, "to": 4894, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4894, "to": 4899, "label": "ONLY EVAL with clause\ntail(.(X3316, X3317), X3317).\nand substitutionT355 -> T368,\nX3316 -> T368,\nT358 -> T370,\nX3317 -> T370,\nX2751 -> T370,\nT369 -> T370,\nT359 -> T371" }, { "from": 4899, "to": 4901, "label": "CASE" }, { "from": 4901, "to": 4903, "label": "PARALLEL" }, { "from": 4901, "to": 4904, "label": "PARALLEL" }, { "from": 4903, "to": 4908, "label": "ONLY EVAL with clause\nhead([], X3337).\nand substitutionT370 -> T381,\nX3337 -> T381,\nT371 -> T382" }, { "from": 4904, "to": 4944, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 4908, "to": 4929, "label": "CASE" }, { "from": 4929, "to": 4930, "label": "PARALLEL" }, { "from": 4929, "to": 4931, "label": "PARALLEL" }, { "from": 4930, "to": 4932, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2752 -> []" }, { "from": 4931, "to": 4943, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4932, "to": 4937, "label": "CASE" }, { "from": 4937, "to": 4938, "label": "PARALLEL" }, { "from": 4937, "to": 4939, "label": "PARALLEL" }, { "from": 4938, "to": 4940, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX2753 -> []" }, { "from": 4939, "to": 4942, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4940, "to": 4093, "label": "INSTANCE with matching:\nT229 -> T345\nT235 -> T382" }, { "from": 4949, "to": 4951, "label": "CASE" }, { "from": 4951, "to": 4952, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 4952, "to": 4958, "label": "ONLY EVAL with clause\ntail(.(X3409, X3410), X3410).\nand substitutionX3409 -> [],\nX3392 -> X3411,\nX3410 -> X3411,\nX143 -> X3411" }, { "from": 4958, "to": 4959, "label": "CASE" }, { "from": 4959, "to": 4961, "label": "PARALLEL" }, { "from": 4959, "to": 4962, "label": "PARALLEL" }, { "from": 4961, "to": 4965, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX144 -> []" }, { "from": 4962, "to": 5619, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 4965, "to": 4970, "label": "CASE" }, { "from": 4970, "to": 4978, "label": "EVAL with clause\nrow2col([], X3437, X3438, X3439) :- ','(!_172, ','(eq(X3437, []), ','(eq(X3438, []), eq(X3439, [])))).\nand substitutionT229 -> [],\nT235 -> T400,\nX3437 -> T400,\nX3411 -> X3440,\nX3438 -> X3440,\nX3439 -> [],\nT399 -> T400" }, { "from": 4970, "to": 4979, "label": "EVAL-BACKTRACK" }, { "from": 4978, "to": 4980, "label": "CUT" }, { "from": 4979, "to": 4995, "label": "ONLY EVAL with clause\nrow2col(X3476, X3477, X3478, X3479) :- ','(head(X3476, X3480), ','(head(X3477, X3481), ','(head(X3481, X3480), ','(head(X3479, []), ','(tail(X3476, X3482), ','(tail(X3477, X3483), ','(tail(X3481, X3484), ','(head(X3478, X3484), ','(tail(X3478, X3485), ','(tail(X3479, X3486), row2col(X3482, X3483, X3485, X3486))))))))))).\nand substitutionT229 -> T409,\nX3476 -> T409,\nT235 -> T411,\nX3477 -> T411,\nX3411 -> X3487,\nX3478 -> X3487,\nX3479 -> [],\nT410 -> T411" }, { "from": 4980, "to": 4981, "label": "CASE" }, { "from": 4981, "to": 4982, "label": "EVAL with clause\neq(X3443, X3443).\nand substitutionT400 -> [],\nX3443 -> [],\nT403 -> []" }, { "from": 4981, "to": 4983, "label": "EVAL-BACKTRACK" }, { "from": 4982, "to": 4984, "label": "CASE" }, { "from": 4984, "to": 4985, "label": "ONLY EVAL with clause\neq(X3448, X3448).\nand substitutionX3440 -> [],\nX3448 -> [],\nX3449 -> []" }, { "from": 4985, "to": 4986, "label": "CASE" }, { "from": 4986, "to": 4987, "label": "ONLY EVAL with clause\neq(X3452, X3452).\nand substitutionX3452 -> []" }, { "from": 4987, "to": 4988, "label": "SUCCESS" }, { "from": 4995, "to": 4996, "label": "CASE" }, { "from": 4996, "to": 4997, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (row2col(T409, T235, X3411, []), row2col([], X3437, X3438, X3439))" }, { "from": 4997, "to": 5005, "label": "EVAL with clause\nhead(.(X3500, X3501), X3500).\nand substitutionX3500 -> T416,\nX3501 -> T417,\nT409 -> .(T416, T417),\nX3480 -> T416" }, { "from": 4997, "to": 5006, "label": "EVAL-BACKTRACK" }, { "from": 5005, "to": 5009, "label": "CASE" }, { "from": 5009, "to": 5010, "label": "PARALLEL" }, { "from": 5009, "to": 5011, "label": "PARALLEL" }, { "from": 5010, "to": 5014, "label": "EVAL with clause\nhead([], X3516).\nand substitutionT411 -> [],\nX3481 -> X3517,\nX3516 -> X3517" }, { "from": 5010, "to": 5015, "label": "EVAL-BACKTRACK" }, { "from": 5011, "to": 5360, "label": "EVAL with clause\nhead(.(X3939, X3940), X3939).\nand substitutionX3939 -> T447,\nX3940 -> T448,\nT411 -> .(T447, T448),\nX3481 -> T447,\nT445 -> T447,\nT446 -> T448" }, { "from": 5011, "to": 5361, "label": "EVAL-BACKTRACK" }, { "from": 5014, "to": 5018, "label": "CASE" }, { "from": 5018, "to": 5021, "label": "PARALLEL" }, { "from": 5018, "to": 5022, "label": "PARALLEL" }, { "from": 5021, "to": 5025, "label": "ONLY EVAL with clause\nhead([], X3540).\nand substitutionX3517 -> [],\nT416 -> T422,\nX3540 -> T422" }, { "from": 5022, "to": 5208, "label": "ONLY EVAL with clause\nhead(.(X3738, X3739), X3738).\nand substitutionX3738 -> T431,\nX3739 -> X3741,\nX3517 -> .(T431, X3741),\nT416 -> T431,\nX3740 -> T431" }, { "from": 5025, "to": 5026, "label": "CASE" }, { "from": 5026, "to": 5030, "label": "PARALLEL" }, { "from": 5026, "to": 5031, "label": "PARALLEL" }, { "from": 5030, "to": 5036, "label": "ONLY EVAL with clause\nhead([], X3563).\nand substitutionX3563 -> []" }, { "from": 5031, "to": 5207, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 5036, "to": 5040, "label": "CASE" }, { "from": 5040, "to": 5041, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5041, "to": 5054, "label": "ONLY EVAL with clause\ntail(.(X3580, X3581), X3581).\nand substitutionT422 -> T427,\nX3580 -> T427,\nT417 -> T428,\nX3581 -> T428,\nX3482 -> T428" }, { "from": 5054, "to": 5059, "label": "CASE" }, { "from": 5059, "to": 5064, "label": "PARALLEL" }, { "from": 5059, "to": 5065, "label": "PARALLEL" }, { "from": 5064, "to": 5069, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3483 -> []" }, { "from": 5065, "to": 5206, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5069, "to": 5071, "label": "CASE" }, { "from": 5071, "to": 5074, "label": "PARALLEL" }, { "from": 5071, "to": 5075, "label": "PARALLEL" }, { "from": 5074, "to": 5076, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3484 -> []" }, { "from": 5075, "to": 5205, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5076, "to": 5079, "label": "CASE" }, { "from": 5079, "to": 5082, "label": "PARALLEL" }, { "from": 5079, "to": 5083, "label": "PARALLEL" }, { "from": 5082, "to": 5100, "label": "ONLY EVAL with clause\nhead([], X3632).\nand substitutionX3487 -> [],\nX3632 -> []" }, { "from": 5083, "to": 5168, "label": "ONLY EVAL with clause\nhead(.(X3676, X3677), X3676).\nand substitutionX3676 -> [],\nX3677 -> X3679,\nX3487 -> .([], X3679),\nX3678 -> []" }, { "from": 5100, "to": 5101, "label": "CASE" }, { "from": 5101, "to": 5102, "label": "PARALLEL" }, { "from": 5101, "to": 5103, "label": "PARALLEL" }, { "from": 5102, "to": 5104, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3485 -> []" }, { "from": 5103, "to": 5110, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5104, "to": 5105, "label": "CASE" }, { "from": 5105, "to": 5106, "label": "PARALLEL" }, { "from": 5105, "to": 5107, "label": "PARALLEL" }, { "from": 5106, "to": 5108, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3486 -> []" }, { "from": 5107, "to": 5109, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5108, "to": 972, "label": "INSTANCE with matching:\nT71 -> T428" }, { "from": 5168, "to": 5169, "label": "CASE" }, { "from": 5169, "to": 5170, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5170, "to": 5171, "label": "ONLY EVAL with clause\ntail(.(X3696, X3697), X3697).\nand substitutionX3696 -> [],\nX3679 -> X3698,\nX3697 -> X3698,\nX3485 -> X3698" }, { "from": 5171, "to": 5173, "label": "CASE" }, { "from": 5173, "to": 5176, "label": "PARALLEL" }, { "from": 5173, "to": 5177, "label": "PARALLEL" }, { "from": 5176, "to": 5179, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3486 -> []" }, { "from": 5177, "to": 5181, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5179, "to": 1784, "label": "INSTANCE with matching:\nT71 -> T428\nX759 -> X3698" }, { "from": 5208, "to": 5209, "label": "CASE" }, { "from": 5209, "to": 5222, "label": "PARALLEL" }, { "from": 5209, "to": 5223, "label": "PARALLEL" }, { "from": 5222, "to": 5224, "label": "ONLY EVAL with clause\nhead([], X3764).\nand substitutionX3764 -> []" }, { "from": 5223, "to": 5334, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 5224, "to": 5225, "label": "CASE" }, { "from": 5225, "to": 5226, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5226, "to": 5227, "label": "ONLY EVAL with clause\ntail(.(X3781, X3782), X3782).\nand substitutionT431 -> T436,\nX3781 -> T436,\nT417 -> T437,\nX3782 -> T437,\nX3482 -> T437" }, { "from": 5227, "to": 5275, "label": "CASE" }, { "from": 5275, "to": 5276, "label": "PARALLEL" }, { "from": 5275, "to": 5277, "label": "PARALLEL" }, { "from": 5276, "to": 5278, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3483 -> []" }, { "from": 5277, "to": 5333, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5278, "to": 5279, "label": "CASE" }, { "from": 5279, "to": 5280, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5280, "to": 5281, "label": "ONLY EVAL with clause\ntail(.(X3815, X3816), X3816).\nand substitutionT436 -> T440,\nX3815 -> T440,\nX3741 -> X3817,\nX3816 -> X3817,\nX3484 -> X3817" }, { "from": 5281, "to": 5282, "label": "CASE" }, { "from": 5282, "to": 5288, "label": "PARALLEL" }, { "from": 5282, "to": 5289, "label": "PARALLEL" }, { "from": 5288, "to": 5290, "label": "ONLY EVAL with clause\nhead([], X3841).\nand substitutionX3487 -> [],\nX3817 -> X3842,\nX3841 -> X3842" }, { "from": 5289, "to": 5310, "label": "ONLY EVAL with clause\nhead(.(X3886, X3887), X3886).\nand substitutionX3886 -> X3888,\nX3887 -> X3889,\nX3487 -> .(X3888, X3889),\nX3817 -> X3888" }, { "from": 5290, "to": 5291, "label": "CASE" }, { "from": 5291, "to": 5294, "label": "PARALLEL" }, { "from": 5291, "to": 5295, "label": "PARALLEL" }, { "from": 5294, "to": 5296, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3485 -> []" }, { "from": 5295, "to": 5304, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5296, "to": 5297, "label": "CASE" }, { "from": 5297, "to": 5298, "label": "PARALLEL" }, { "from": 5297, "to": 5299, "label": "PARALLEL" }, { "from": 5298, "to": 5300, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3486 -> []" }, { "from": 5299, "to": 5303, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5300, "to": 972, "label": "INSTANCE with matching:\nT71 -> T437" }, { "from": 5310, "to": 5313, "label": "CASE" }, { "from": 5313, "to": 5314, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5314, "to": 5327, "label": "ONLY EVAL with clause\ntail(.(X3908, X3909), X3909).\nand substitutionX3888 -> X3910,\nX3908 -> X3910,\nX3889 -> X3911,\nX3909 -> X3911,\nX3485 -> X3911" }, { "from": 5327, "to": 5328, "label": "CASE" }, { "from": 5328, "to": 5329, "label": "PARALLEL" }, { "from": 5328, "to": 5330, "label": "PARALLEL" }, { "from": 5329, "to": 5331, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3486 -> []" }, { "from": 5330, "to": 5332, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5331, "to": 1784, "label": "INSTANCE with matching:\nT71 -> T437\nX759 -> X3911" }, { "from": 5360, "to": 5363, "label": "CASE" }, { "from": 5363, "to": 5364, "label": "PARALLEL" }, { "from": 5363, "to": 5365, "label": "PARALLEL" }, { "from": 5364, "to": 5368, "label": "EVAL with clause\nhead([], X3951).\nand substitutionT447 -> [],\nT416 -> T453,\nX3951 -> T453,\nT448 -> T454" }, { "from": 5364, "to": 5369, "label": "EVAL-BACKTRACK" }, { "from": 5365, "to": 5507, "label": "EVAL with clause\nhead(.(X4138, X4139), X4138).\nand substitutionX4138 -> T491,\nX4139 -> T494,\nT447 -> .(T491, T494),\nT416 -> T491,\nT448 -> T493,\nT492 -> T494" }, { "from": 5365, "to": 5508, "label": "EVAL-BACKTRACK" }, { "from": 5368, "to": 5380, "label": "CASE" }, { "from": 5380, "to": 5381, "label": "PARALLEL" }, { "from": 5380, "to": 5382, "label": "PARALLEL" }, { "from": 5381, "to": 5383, "label": "ONLY EVAL with clause\nhead([], X3974).\nand substitutionX3974 -> []" }, { "from": 5382, "to": 5489, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 5383, "to": 5384, "label": "CASE" }, { "from": 5384, "to": 5385, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5385, "to": 5389, "label": "ONLY EVAL with clause\ntail(.(X3991, X3992), X3992).\nand substitutionT453 -> T459,\nX3991 -> T459,\nT417 -> T460,\nX3992 -> T460,\nX3482 -> T460" }, { "from": 5389, "to": 5391, "label": "CASE" }, { "from": 5391, "to": 5392, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5392, "to": 5397, "label": "ONLY EVAL with clause\ntail(.(X4008, X4009), X4009).\nand substitutionX4008 -> [],\nT454 -> T466,\nX4009 -> T466,\nX3483 -> T466,\nT465 -> T466" }, { "from": 5397, "to": 5400, "label": "CASE" }, { "from": 5400, "to": 5403, "label": "PARALLEL" }, { "from": 5400, "to": 5404, "label": "PARALLEL" }, { "from": 5403, "to": 5405, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3484 -> []" }, { "from": 5404, "to": 5488, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5405, "to": 5426, "label": "CASE" }, { "from": 5426, "to": 5429, "label": "PARALLEL" }, { "from": 5426, "to": 5430, "label": "PARALLEL" }, { "from": 5429, "to": 5434, "label": "ONLY EVAL with clause\nhead([], X4044).\nand substitutionX3487 -> [],\nX4044 -> []" }, { "from": 5430, "to": 5464, "label": "ONLY EVAL with clause\nhead(.(X4088, X4089), X4088).\nand substitutionX4088 -> [],\nX4089 -> X4091,\nX3487 -> .([], X4091),\nX4090 -> []" }, { "from": 5434, "to": 5436, "label": "CASE" }, { "from": 5436, "to": 5438, "label": "PARALLEL" }, { "from": 5436, "to": 5440, "label": "PARALLEL" }, { "from": 5438, "to": 5441, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3485 -> []" }, { "from": 5440, "to": 5463, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5441, "to": 5442, "label": "CASE" }, { "from": 5442, "to": 5444, "label": "PARALLEL" }, { "from": 5442, "to": 5445, "label": "PARALLEL" }, { "from": 5444, "to": 5446, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3486 -> []" }, { "from": 5445, "to": 5462, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5446, "to": 4093, "label": "INSTANCE with matching:\nT229 -> T460\nT235 -> T466" }, { "from": 5464, "to": 5468, "label": "CASE" }, { "from": 5468, "to": 5469, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5469, "to": 5473, "label": "ONLY EVAL with clause\ntail(.(X4108, X4109), X4109).\nand substitutionX4108 -> [],\nX4091 -> X4110,\nX4109 -> X4110,\nX3485 -> X4110" }, { "from": 5473, "to": 5476, "label": "CASE" }, { "from": 5476, "to": 5477, "label": "PARALLEL" }, { "from": 5476, "to": 5478, "label": "PARALLEL" }, { "from": 5477, "to": 5486, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3486 -> []" }, { "from": 5478, "to": 5487, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5486, "to": 4965, "label": "INSTANCE with matching:\nT229 -> T460\nT235 -> T466\nX3411 -> X4110" }, { "from": 5507, "to": 5509, "label": "CASE" }, { "from": 5509, "to": 5510, "label": "PARALLEL" }, { "from": 5509, "to": 5511, "label": "PARALLEL" }, { "from": 5510, "to": 5513, "label": "ONLY EVAL with clause\nhead([], X4162).\nand substitutionX4162 -> []" }, { "from": 5511, "to": 5618, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 5513, "to": 5516, "label": "CASE" }, { "from": 5516, "to": 5517, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5517, "to": 5521, "label": "ONLY EVAL with clause\ntail(.(X4179, X4180), X4180).\nand substitutionT491 -> T499,\nX4179 -> T499,\nT417 -> T500,\nX4180 -> T500,\nX3482 -> T500" }, { "from": 5521, "to": 5523, "label": "CASE" }, { "from": 5523, "to": 5524, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5524, "to": 5525, "label": "ONLY EVAL with clause\ntail(.(X4196, X4197), X4197).\nand substitutionT499 -> T510,\nT494 -> T513,\nX4196 -> .(T510, T513),\nT493 -> T514,\nX4197 -> T514,\nX3483 -> T514,\nT511 -> T513,\nT512 -> T514" }, { "from": 5525, "to": 5526, "label": "CASE" }, { "from": 5526, "to": 5527, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5527, "to": 5528, "label": "ONLY EVAL with clause\ntail(.(X4212, X4213), X4213).\nand substitutionT510 -> T523,\nX4212 -> T523,\nT513 -> T525,\nX4213 -> T525,\nX3484 -> T525,\nT524 -> T525,\nT514 -> T526" }, { "from": 5528, "to": 5540, "label": "CASE" }, { "from": 5540, "to": 5543, "label": "PARALLEL" }, { "from": 5540, "to": 5544, "label": "PARALLEL" }, { "from": 5543, "to": 5559, "label": "ONLY EVAL with clause\nhead([], X4233).\nand substitutionX3487 -> [],\nT525 -> T536,\nX4233 -> T536,\nT526 -> T537" }, { "from": 5544, "to": 5586, "label": "ONLY EVAL with clause\nhead(.(X4277, X4278), X4277).\nand substitutionX4277 -> T551,\nX4278 -> X4280,\nX3487 -> .(T551, X4280),\nT525 -> T551,\nX4279 -> T551,\nT550 -> T551,\nT526 -> T552" }, { "from": 5559, "to": 5560, "label": "CASE" }, { "from": 5560, "to": 5561, "label": "PARALLEL" }, { "from": 5560, "to": 5562, "label": "PARALLEL" }, { "from": 5561, "to": 5563, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3485 -> []" }, { "from": 5562, "to": 5581, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5563, "to": 5564, "label": "CASE" }, { "from": 5564, "to": 5565, "label": "PARALLEL" }, { "from": 5564, "to": 5566, "label": "PARALLEL" }, { "from": 5565, "to": 5568, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3486 -> []" }, { "from": 5566, "to": 5580, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5568, "to": 4093, "label": "INSTANCE with matching:\nT229 -> T500\nT235 -> T537" }, { "from": 5586, "to": 5587, "label": "CASE" }, { "from": 5587, "to": 5588, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5588, "to": 5591, "label": "ONLY EVAL with clause\ntail(.(X4297, X4298), X4298).\nand substitutionT551 -> T558,\nX4297 -> T558,\nX4280 -> X4299,\nX4298 -> X4299,\nX3485 -> X4299,\nT552 -> T559" }, { "from": 5591, "to": 5599, "label": "CASE" }, { "from": 5599, "to": 5603, "label": "PARALLEL" }, { "from": 5599, "to": 5604, "label": "PARALLEL" }, { "from": 5603, "to": 5606, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX3486 -> []" }, { "from": 5604, "to": 5616, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5606, "to": 4965, "label": "INSTANCE with matching:\nT229 -> T500\nT235 -> T559\nX3411 -> X4299" }, { "from": 5627, "to": 5628, "label": "CASE" }, { "from": 5628, "to": 5629, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5629, "to": 5631, "label": "ONLY EVAL with clause\ntail(.(X4359, X4360), X4360).\nand substitutionT222 -> T568,\nX4359 -> T568,\nT60 -> T569,\nX4360 -> T569,\nX140 -> T569" }, { "from": 5631, "to": 5632, "label": "CASE" }, { "from": 5632, "to": 5633, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5633, "to": 5659, "label": "ONLY EVAL with clause\ntail(.(X4376, X4377), X4377).\nand substitutionX4376 -> [],\nT223 -> T575,\nX4377 -> T575,\nX141 -> T575,\nT574 -> T575" }, { "from": 5659, "to": 5661, "label": "CASE" }, { "from": 5661, "to": 5664, "label": "PARALLEL" }, { "from": 5661, "to": 5665, "label": "PARALLEL" }, { "from": 5664, "to": 5684, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX142 -> []" }, { "from": 5665, "to": 6518, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5684, "to": 5685, "label": "CASE" }, { "from": 5685, "to": 5686, "label": "PARALLEL" }, { "from": 5685, "to": 5687, "label": "PARALLEL" }, { "from": 5686, "to": 5697, "label": "ONLY EVAL with clause\nhead([], X4412).\nand substitutionX145 -> [],\nX4412 -> []" }, { "from": 5687, "to": 6494, "label": "ONLY EVAL with clause\nhead(.(X5651, X5652), X5651).\nand substitutionX5651 -> [],\nX5652 -> X5654,\nX145 -> .([], X5654),\nX5653 -> []" }, { "from": 5697, "to": 5698, "label": "CASE" }, { "from": 5698, "to": 5699, "label": "PARALLEL" }, { "from": 5698, "to": 5700, "label": "PARALLEL" }, { "from": 5699, "to": 5702, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX143 -> []" }, { "from": 5700, "to": 6488, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5702, "to": 5705, "label": "CASE" }, { "from": 5705, "to": 5706, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5706, "to": 5708, "label": "ONLY EVAL with clause\ntail(.(X4440, X4441), X4441).\nand substitutionX4440 -> [],\nX4342 -> X4442,\nX4441 -> X4442,\nX144 -> X4442" }, { "from": 5708, "to": 5709, "label": "CASE" }, { "from": 5709, "to": 5710, "label": "EVAL with clause\nrow2col([], X4455, X4456, X4457) :- ','(!_222, ','(eq(X4455, []), ','(eq(X4456, []), eq(X4457, [])))).\nand substitutionT569 -> [],\nT575 -> T591,\nX4455 -> T591,\nX4456 -> [],\nX4442 -> X4458,\nX4457 -> X4458,\nT590 -> T591" }, { "from": 5709, "to": 5711, "label": "EVAL-BACKTRACK" }, { "from": 5710, "to": 5712, "label": "CUT" }, { "from": 5711, "to": 5741, "label": "ONLY EVAL with clause\nrow2col(X4494, X4495, X4496, X4497) :- ','(head(X4494, X4498), ','(head(X4495, X4499), ','(head(X4499, X4498), ','(head(X4497, []), ','(tail(X4494, X4500), ','(tail(X4495, X4501), ','(tail(X4499, X4502), ','(head(X4496, X4502), ','(tail(X4496, X4503), ','(tail(X4497, X4504), row2col(X4500, X4501, X4503, X4504))))))))))).\nand substitutionT569 -> T600,\nX4494 -> T600,\nT575 -> T602,\nX4495 -> T602,\nX4496 -> [],\nX4442 -> X4505,\nX4497 -> X4505,\nT601 -> T602" }, { "from": 5712, "to": 5713, "label": "CASE" }, { "from": 5713, "to": 5721, "label": "EVAL with clause\neq(X4461, X4461).\nand substitutionT591 -> [],\nX4461 -> [],\nT594 -> []" }, { "from": 5713, "to": 5722, "label": "EVAL-BACKTRACK" }, { "from": 5721, "to": 5723, "label": "CASE" }, { "from": 5723, "to": 5725, "label": "ONLY EVAL with clause\neq(X4464, X4464).\nand substitutionX4464 -> []" }, { "from": 5725, "to": 5726, "label": "CASE" }, { "from": 5726, "to": 5729, "label": "ONLY EVAL with clause\neq(X4469, X4469).\nand substitutionX4458 -> [],\nX4469 -> [],\nX4470 -> []" }, { "from": 5729, "to": 5730, "label": "SUCCESS" }, { "from": 5741, "to": 5749, "label": "CASE" }, { "from": 5749, "to": 5750, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (row2col(T600, T575, [], X4442), row2col([], X4455, X4456, X4457))" }, { "from": 5750, "to": 5754, "label": "EVAL with clause\nhead(.(X4518, X4519), X4518).\nand substitutionX4518 -> T607,\nX4519 -> T608,\nT600 -> .(T607, T608),\nX4498 -> T607" }, { "from": 5750, "to": 5755, "label": "EVAL-BACKTRACK" }, { "from": 5754, "to": 5759, "label": "CASE" }, { "from": 5759, "to": 5766, "label": "PARALLEL" }, { "from": 5759, "to": 5767, "label": "PARALLEL" }, { "from": 5766, "to": 5769, "label": "EVAL with clause\nhead([], X4534).\nand substitutionT602 -> [],\nX4499 -> X4535,\nX4534 -> X4535" }, { "from": 5766, "to": 5770, "label": "EVAL-BACKTRACK" }, { "from": 5767, "to": 6103, "label": "EVAL with clause\nhead(.(X5109, X5110), X5109).\nand substitutionX5109 -> T653,\nX5110 -> T654,\nT602 -> .(T653, T654),\nX4499 -> T653,\nT651 -> T653,\nT652 -> T654" }, { "from": 5767, "to": 6104, "label": "EVAL-BACKTRACK" }, { "from": 5769, "to": 5772, "label": "CASE" }, { "from": 5772, "to": 5775, "label": "PARALLEL" }, { "from": 5772, "to": 5776, "label": "PARALLEL" }, { "from": 5775, "to": 5780, "label": "ONLY EVAL with clause\nhead([], X4558).\nand substitutionX4535 -> [],\nT607 -> T613,\nX4558 -> T613" }, { "from": 5776, "to": 5962, "label": "ONLY EVAL with clause\nhead(.(X4830, X4831), X4830).\nand substitutionX4830 -> T628,\nX4831 -> X4833,\nX4535 -> .(T628, X4833),\nT607 -> T628,\nX4832 -> T628" }, { "from": 5780, "to": 5781, "label": "CASE" }, { "from": 5781, "to": 5786, "label": "PARALLEL" }, { "from": 5781, "to": 5787, "label": "PARALLEL" }, { "from": 5786, "to": 5791, "label": "ONLY EVAL with clause\nhead([], X4581).\nand substitutionX4505 -> [],\nX4581 -> []" }, { "from": 5787, "to": 5887, "label": "ONLY EVAL with clause\nhead(.(X4701, X4702), X4701).\nand substitutionX4701 -> [],\nX4702 -> X4704,\nX4505 -> .([], X4704),\nX4703 -> []" }, { "from": 5791, "to": 5797, "label": "CASE" }, { "from": 5797, "to": 5798, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5798, "to": 5802, "label": "ONLY EVAL with clause\ntail(.(X4598, X4599), X4599).\nand substitutionT613 -> T618,\nX4598 -> T618,\nT608 -> T619,\nX4599 -> T619,\nX4500 -> T619" }, { "from": 5802, "to": 5804, "label": "CASE" }, { "from": 5804, "to": 5810, "label": "PARALLEL" }, { "from": 5804, "to": 5811, "label": "PARALLEL" }, { "from": 5810, "to": 5813, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4501 -> []" }, { "from": 5811, "to": 5865, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5813, "to": 5816, "label": "CASE" }, { "from": 5816, "to": 5819, "label": "PARALLEL" }, { "from": 5816, "to": 5820, "label": "PARALLEL" }, { "from": 5819, "to": 5826, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4502 -> []" }, { "from": 5820, "to": 5864, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5826, "to": 5829, "label": "CASE" }, { "from": 5829, "to": 5835, "label": "PARALLEL" }, { "from": 5829, "to": 5836, "label": "PARALLEL" }, { "from": 5835, "to": 5838, "label": "ONLY EVAL with clause\nhead([], X4650).\nand substitutionX4650 -> []" }, { "from": 5836, "to": 5861, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 5838, "to": 5847, "label": "CASE" }, { "from": 5847, "to": 5848, "label": "PARALLEL" }, { "from": 5847, "to": 5849, "label": "PARALLEL" }, { "from": 5848, "to": 5850, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4503 -> []" }, { "from": 5849, "to": 5860, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5850, "to": 5852, "label": "CASE" }, { "from": 5852, "to": 5854, "label": "PARALLEL" }, { "from": 5852, "to": 5855, "label": "PARALLEL" }, { "from": 5854, "to": 5856, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4504 -> []" }, { "from": 5855, "to": 5859, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5856, "to": 972, "label": "INSTANCE with matching:\nT71 -> T619" }, { "from": 5887, "to": 5888, "label": "CASE" }, { "from": 5888, "to": 5889, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5889, "to": 5893, "label": "ONLY EVAL with clause\ntail(.(X4721, X4722), X4722).\nand substitutionT613 -> T624,\nX4721 -> T624,\nT608 -> T625,\nX4722 -> T625,\nX4500 -> T625" }, { "from": 5893, "to": 5894, "label": "CASE" }, { "from": 5894, "to": 5896, "label": "PARALLEL" }, { "from": 5894, "to": 5897, "label": "PARALLEL" }, { "from": 5896, "to": 5899, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4501 -> []" }, { "from": 5897, "to": 5954, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5899, "to": 5904, "label": "CASE" }, { "from": 5904, "to": 5908, "label": "PARALLEL" }, { "from": 5904, "to": 5909, "label": "PARALLEL" }, { "from": 5908, "to": 5910, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4502 -> []" }, { "from": 5909, "to": 5953, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5910, "to": 5914, "label": "CASE" }, { "from": 5914, "to": 5915, "label": "PARALLEL" }, { "from": 5914, "to": 5916, "label": "PARALLEL" }, { "from": 5915, "to": 5918, "label": "ONLY EVAL with clause\nhead([], X4773).\nand substitutionX4773 -> []" }, { "from": 5916, "to": 5952, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 5918, "to": 5921, "label": "CASE" }, { "from": 5921, "to": 5928, "label": "PARALLEL" }, { "from": 5921, "to": 5929, "label": "PARALLEL" }, { "from": 5928, "to": 5930, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4503 -> []" }, { "from": 5929, "to": 5951, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5930, "to": 5931, "label": "CASE" }, { "from": 5931, "to": 5933, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5933, "to": 5939, "label": "ONLY EVAL with clause\ntail(.(X4801, X4802), X4802).\nand substitutionX4801 -> [],\nX4704 -> X4803,\nX4802 -> X4803,\nX4504 -> X4803" }, { "from": 5939, "to": 2240, "label": "INSTANCE with matching:\nT141 -> T625\nX1419 -> X4803" }, { "from": 5962, "to": 5964, "label": "CASE" }, { "from": 5964, "to": 5976, "label": "PARALLEL" }, { "from": 5964, "to": 5977, "label": "PARALLEL" }, { "from": 5976, "to": 5980, "label": "ONLY EVAL with clause\nhead([], X4856).\nand substitutionX4505 -> [],\nX4856 -> []" }, { "from": 5977, "to": 6041, "label": "ONLY EVAL with clause\nhead(.(X4983, X4984), X4983).\nand substitutionX4983 -> [],\nX4984 -> X4986,\nX4505 -> .([], X4986),\nX4985 -> []" }, { "from": 5980, "to": 5981, "label": "CASE" }, { "from": 5981, "to": 5982, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5982, "to": 5983, "label": "ONLY EVAL with clause\ntail(.(X4873, X4874), X4874).\nand substitutionT628 -> T633,\nX4873 -> T633,\nT608 -> T634,\nX4874 -> T634,\nX4500 -> T634" }, { "from": 5983, "to": 5985, "label": "CASE" }, { "from": 5985, "to": 5989, "label": "PARALLEL" }, { "from": 5985, "to": 5990, "label": "PARALLEL" }, { "from": 5989, "to": 5992, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4501 -> []" }, { "from": 5990, "to": 6032, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 5992, "to": 5995, "label": "CASE" }, { "from": 5995, "to": 5996, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 5996, "to": 6002, "label": "ONLY EVAL with clause\ntail(.(X4907, X4908), X4908).\nand substitutionT633 -> T637,\nX4907 -> T637,\nX4833 -> X4909,\nX4908 -> X4909,\nX4502 -> X4909" }, { "from": 6002, "to": 6004, "label": "CASE" }, { "from": 6004, "to": 6005, "label": "PARALLEL" }, { "from": 6004, "to": 6007, "label": "PARALLEL" }, { "from": 6005, "to": 6011, "label": "ONLY EVAL with clause\nhead([], X4933).\nand substitutionX4909 -> X4934,\nX4933 -> X4934" }, { "from": 6007, "to": 6031, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 6011, "to": 6013, "label": "CASE" }, { "from": 6013, "to": 6015, "label": "PARALLEL" }, { "from": 6013, "to": 6016, "label": "PARALLEL" }, { "from": 6015, "to": 6017, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4503 -> []" }, { "from": 6016, "to": 6030, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6017, "to": 6018, "label": "CASE" }, { "from": 6018, "to": 6026, "label": "PARALLEL" }, { "from": 6018, "to": 6027, "label": "PARALLEL" }, { "from": 6026, "to": 6028, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4504 -> []" }, { "from": 6027, "to": 6029, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6028, "to": 972, "label": "INSTANCE with matching:\nT71 -> T634" }, { "from": 6041, "to": 6043, "label": "CASE" }, { "from": 6043, "to": 6044, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6044, "to": 6049, "label": "ONLY EVAL with clause\ntail(.(X5003, X5004), X5004).\nand substitutionT628 -> T642,\nX5003 -> T642,\nT608 -> T643,\nX5004 -> T643,\nX4500 -> T643" }, { "from": 6049, "to": 6052, "label": "CASE" }, { "from": 6052, "to": 6053, "label": "PARALLEL" }, { "from": 6052, "to": 6054, "label": "PARALLEL" }, { "from": 6053, "to": 6056, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4501 -> []" }, { "from": 6054, "to": 6098, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6056, "to": 6057, "label": "CASE" }, { "from": 6057, "to": 6058, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6058, "to": 6066, "label": "ONLY EVAL with clause\ntail(.(X5037, X5038), X5038).\nand substitutionT642 -> T646,\nX5037 -> T646,\nX4833 -> X5039,\nX5038 -> X5039,\nX4502 -> X5039" }, { "from": 6066, "to": 6068, "label": "CASE" }, { "from": 6068, "to": 6070, "label": "PARALLEL" }, { "from": 6068, "to": 6071, "label": "PARALLEL" }, { "from": 6070, "to": 6076, "label": "ONLY EVAL with clause\nhead([], X5063).\nand substitutionX5039 -> X5064,\nX5063 -> X5064" }, { "from": 6071, "to": 6096, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 6076, "to": 6079, "label": "CASE" }, { "from": 6079, "to": 6081, "label": "PARALLEL" }, { "from": 6079, "to": 6082, "label": "PARALLEL" }, { "from": 6081, "to": 6084, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4503 -> []" }, { "from": 6082, "to": 6095, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6084, "to": 6087, "label": "CASE" }, { "from": 6087, "to": 6088, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6088, "to": 6094, "label": "ONLY EVAL with clause\ntail(.(X5092, X5093), X5093).\nand substitutionX5092 -> [],\nX4986 -> X5094,\nX5093 -> X5094,\nX4504 -> X5094" }, { "from": 6094, "to": 2240, "label": "INSTANCE with matching:\nT141 -> T643\nX1419 -> X5094" }, { "from": 6103, "to": 6105, "label": "CASE" }, { "from": 6105, "to": 6106, "label": "PARALLEL" }, { "from": 6105, "to": 6107, "label": "PARALLEL" }, { "from": 6106, "to": 6109, "label": "EVAL with clause\nhead([], X5121).\nand substitutionT653 -> [],\nT607 -> T659,\nX5121 -> T659,\nT654 -> T660" }, { "from": 6106, "to": 6110, "label": "EVAL-BACKTRACK" }, { "from": 6107, "to": 6302, "label": "EVAL with clause\nhead(.(X5381, X5382), X5381).\nand substitutionX5381 -> T714,\nX5382 -> T717,\nT653 -> .(T714, T717),\nT607 -> T714,\nT654 -> T716,\nT715 -> T717" }, { "from": 6107, "to": 6303, "label": "EVAL-BACKTRACK" }, { "from": 6109, "to": 6117, "label": "CASE" }, { "from": 6117, "to": 6122, "label": "PARALLEL" }, { "from": 6117, "to": 6123, "label": "PARALLEL" }, { "from": 6122, "to": 6131, "label": "ONLY EVAL with clause\nhead([], X5144).\nand substitutionX4505 -> [],\nX5144 -> []" }, { "from": 6123, "to": 6228, "label": "ONLY EVAL with clause\nhead(.(X5263, X5264), X5263).\nand substitutionX5263 -> [],\nX5264 -> X5266,\nX4505 -> .([], X5266),\nX5265 -> []" }, { "from": 6131, "to": 6139, "label": "CASE" }, { "from": 6139, "to": 6140, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6140, "to": 6153, "label": "ONLY EVAL with clause\ntail(.(X5161, X5162), X5162).\nand substitutionT659 -> T665,\nX5161 -> T665,\nT608 -> T666,\nX5162 -> T666,\nX4500 -> T666" }, { "from": 6153, "to": 6154, "label": "CASE" }, { "from": 6154, "to": 6155, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6155, "to": 6165, "label": "ONLY EVAL with clause\ntail(.(X5178, X5179), X5179).\nand substitutionX5178 -> [],\nT660 -> T672,\nX5179 -> T672,\nX4501 -> T672,\nT671 -> T672" }, { "from": 6165, "to": 6166, "label": "CASE" }, { "from": 6166, "to": 6178, "label": "PARALLEL" }, { "from": 6166, "to": 6179, "label": "PARALLEL" }, { "from": 6178, "to": 6180, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4502 -> []" }, { "from": 6179, "to": 6221, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6180, "to": 6181, "label": "CASE" }, { "from": 6181, "to": 6187, "label": "PARALLEL" }, { "from": 6181, "to": 6188, "label": "PARALLEL" }, { "from": 6187, "to": 6189, "label": "ONLY EVAL with clause\nhead([], X5214).\nand substitutionX5214 -> []" }, { "from": 6188, "to": 6220, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 6189, "to": 6195, "label": "CASE" }, { "from": 6195, "to": 6197, "label": "PARALLEL" }, { "from": 6195, "to": 6198, "label": "PARALLEL" }, { "from": 6197, "to": 6199, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4503 -> []" }, { "from": 6198, "to": 6217, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6199, "to": 6200, "label": "CASE" }, { "from": 6200, "to": 6213, "label": "PARALLEL" }, { "from": 6200, "to": 6214, "label": "PARALLEL" }, { "from": 6213, "to": 6215, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4504 -> []" }, { "from": 6214, "to": 6216, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6215, "to": 4093, "label": "INSTANCE with matching:\nT229 -> T666\nT235 -> T672" }, { "from": 6228, "to": 6240, "label": "CASE" }, { "from": 6240, "to": 6241, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6241, "to": 6246, "label": "ONLY EVAL with clause\ntail(.(X5283, X5284), X5284).\nand substitutionT659 -> T690,\nX5283 -> T690,\nT608 -> T691,\nX5284 -> T691,\nX4500 -> T691" }, { "from": 6246, "to": 6255, "label": "CASE" }, { "from": 6255, "to": 6256, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6256, "to": 6258, "label": "ONLY EVAL with clause\ntail(.(X5300, X5301), X5301).\nand substitutionX5300 -> [],\nT660 -> T697,\nX5301 -> T697,\nX4501 -> T697,\nT696 -> T697" }, { "from": 6258, "to": 6259, "label": "CASE" }, { "from": 6259, "to": 6261, "label": "PARALLEL" }, { "from": 6259, "to": 6262, "label": "PARALLEL" }, { "from": 6261, "to": 6263, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4502 -> []" }, { "from": 6262, "to": 6301, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6263, "to": 6267, "label": "CASE" }, { "from": 6267, "to": 6268, "label": "PARALLEL" }, { "from": 6267, "to": 6269, "label": "PARALLEL" }, { "from": 6268, "to": 6273, "label": "ONLY EVAL with clause\nhead([], X5336).\nand substitutionX5336 -> []" }, { "from": 6269, "to": 6300, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 6273, "to": 6274, "label": "CASE" }, { "from": 6274, "to": 6281, "label": "PARALLEL" }, { "from": 6274, "to": 6282, "label": "PARALLEL" }, { "from": 6281, "to": 6285, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4503 -> []" }, { "from": 6282, "to": 6299, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6285, "to": 6286, "label": "CASE" }, { "from": 6286, "to": 6287, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6287, "to": 6294, "label": "ONLY EVAL with clause\ntail(.(X5364, X5365), X5365).\nand substitutionX5364 -> [],\nX5266 -> X5366,\nX5365 -> X5366,\nX4504 -> X5366" }, { "from": 6294, "to": 5708, "label": "INSTANCE with matching:\nT569 -> T691\nT575 -> T697\nX4442 -> X5366" }, { "from": 6302, "to": 6314, "label": "CASE" }, { "from": 6314, "to": 6318, "label": "PARALLEL" }, { "from": 6314, "to": 6319, "label": "PARALLEL" }, { "from": 6318, "to": 6325, "label": "ONLY EVAL with clause\nhead([], X5405).\nand substitutionX4505 -> [],\nX5405 -> []" }, { "from": 6319, "to": 6418, "label": "ONLY EVAL with clause\nhead(.(X5523, X5524), X5523).\nand substitutionX5523 -> [],\nX5524 -> X5526,\nX4505 -> .([], X5526),\nX5525 -> []" }, { "from": 6325, "to": 6326, "label": "CASE" }, { "from": 6326, "to": 6327, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6327, "to": 6332, "label": "ONLY EVAL with clause\ntail(.(X5422, X5423), X5423).\nand substitutionT714 -> T722,\nX5422 -> T722,\nT608 -> T723,\nX5423 -> T723,\nX4500 -> T723" }, { "from": 6332, "to": 6334, "label": "CASE" }, { "from": 6334, "to": 6335, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6335, "to": 6345, "label": "ONLY EVAL with clause\ntail(.(X5439, X5440), X5440).\nand substitutionT722 -> T733,\nT717 -> T736,\nX5439 -> .(T733, T736),\nT716 -> T737,\nX5440 -> T737,\nX4501 -> T737,\nT734 -> T736,\nT735 -> T737" }, { "from": 6345, "to": 6348, "label": "CASE" }, { "from": 6348, "to": 6349, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6349, "to": 6358, "label": "ONLY EVAL with clause\ntail(.(X5455, X5456), X5456).\nand substitutionT733 -> T746,\nX5455 -> T746,\nT736 -> T748,\nX5456 -> T748,\nX4502 -> T748,\nT747 -> T748,\nT737 -> T749" }, { "from": 6358, "to": 6359, "label": "CASE" }, { "from": 6359, "to": 6367, "label": "PARALLEL" }, { "from": 6359, "to": 6368, "label": "PARALLEL" }, { "from": 6367, "to": 6372, "label": "ONLY EVAL with clause\nhead([], X5476).\nand substitutionT748 -> T759,\nX5476 -> T759,\nT749 -> T760" }, { "from": 6368, "to": 6407, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 6372, "to": 6379, "label": "CASE" }, { "from": 6379, "to": 6381, "label": "PARALLEL" }, { "from": 6379, "to": 6382, "label": "PARALLEL" }, { "from": 6381, "to": 6384, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4503 -> []" }, { "from": 6382, "to": 6406, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6384, "to": 6387, "label": "CASE" }, { "from": 6387, "to": 6400, "label": "PARALLEL" }, { "from": 6387, "to": 6401, "label": "PARALLEL" }, { "from": 6400, "to": 6403, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4504 -> []" }, { "from": 6401, "to": 6405, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6403, "to": 4093, "label": "INSTANCE with matching:\nT229 -> T723\nT235 -> T760" }, { "from": 6418, "to": 6421, "label": "CASE" }, { "from": 6421, "to": 6422, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6422, "to": 6424, "label": "ONLY EVAL with clause\ntail(.(X5543, X5544), X5544).\nand substitutionT714 -> T772,\nX5543 -> T772,\nT608 -> T773,\nX5544 -> T773,\nX4500 -> T773" }, { "from": 6424, "to": 6425, "label": "CASE" }, { "from": 6425, "to": 6426, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6426, "to": 6432, "label": "ONLY EVAL with clause\ntail(.(X5560, X5561), X5561).\nand substitutionT772 -> T783,\nT717 -> T786,\nX5560 -> .(T783, T786),\nT716 -> T787,\nX5561 -> T787,\nX4501 -> T787,\nT784 -> T786,\nT785 -> T787" }, { "from": 6432, "to": 6436, "label": "CASE" }, { "from": 6436, "to": 6437, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6437, "to": 6438, "label": "ONLY EVAL with clause\ntail(.(X5576, X5577), X5577).\nand substitutionT783 -> T796,\nX5576 -> T796,\nT786 -> T798,\nX5577 -> T798,\nX4502 -> T798,\nT797 -> T798,\nT787 -> T799" }, { "from": 6438, "to": 6447, "label": "CASE" }, { "from": 6447, "to": 6449, "label": "PARALLEL" }, { "from": 6447, "to": 6450, "label": "PARALLEL" }, { "from": 6449, "to": 6461, "label": "ONLY EVAL with clause\nhead([], X5597).\nand substitutionT798 -> T809,\nX5597 -> T809,\nT799 -> T810" }, { "from": 6450, "to": 6483, "label": "BACKTRACK\nfor clause: head(.(H, X3), H)because of non-unification" }, { "from": 6461, "to": 6463, "label": "CASE" }, { "from": 6463, "to": 6464, "label": "PARALLEL" }, { "from": 6463, "to": 6465, "label": "PARALLEL" }, { "from": 6464, "to": 6470, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX4503 -> []" }, { "from": 6465, "to": 6480, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6470, "to": 6473, "label": "CASE" }, { "from": 6473, "to": 6474, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6474, "to": 6478, "label": "ONLY EVAL with clause\ntail(.(X5625, X5626), X5626).\nand substitutionX5625 -> [],\nX5526 -> X5627,\nX5626 -> X5627,\nX4504 -> X5627" }, { "from": 6478, "to": 5708, "label": "INSTANCE with matching:\nT569 -> T773\nT575 -> T810\nX4442 -> X5627" }, { "from": 6494, "to": 6495, "label": "CASE" }, { "from": 6495, "to": 6496, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6496, "to": 6502, "label": "ONLY EVAL with clause\ntail(.(X5671, X5672), X5672).\nand substitutionX5671 -> [],\nX5654 -> X5673,\nX5672 -> X5673,\nX143 -> X5673" }, { "from": 6502, "to": 6503, "label": "CASE" }, { "from": 6503, "to": 6504, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6504, "to": 6511, "label": "ONLY EVAL with clause\ntail(.(X5690, X5691), X5691).\nand substitutionX5690 -> [],\nX4342 -> X5692,\nX5691 -> X5692,\nX144 -> X5692" }, { "from": 6511, "to": 481, "label": "INSTANCE with matching:\nT34 -> T569\nT20 -> T575\nX38 -> X5673\nX39 -> X5692" }, { "from": 6520, "to": 6524, "label": "CASE" }, { "from": 6524, "to": 6527, "label": "PARALLEL" }, { "from": 6524, "to": 6528, "label": "PARALLEL" }, { "from": 6527, "to": 6533, "label": "ONLY EVAL with clause\nhead([], X5728).\nand substitutionX146 -> [],\nX5728 -> []" }, { "from": 6528, "to": 6639, "label": "ONLY EVAL with clause\nhead(.(X5899, X5900), X5899).\nand substitutionX5899 -> [],\nX5900 -> X5902,\nX146 -> .([], X5902),\nX5901 -> []" }, { "from": 6533, "to": 6535, "label": "CASE" }, { "from": 6535, "to": 6536, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6536, "to": 6548, "label": "ONLY EVAL with clause\ntail(.(X5745, X5746), X5746).\nand substitutionT827 -> T835,\nX5745 -> T835,\nT60 -> T836,\nX5746 -> T836,\nX140 -> T836" }, { "from": 6548, "to": 6554, "label": "CASE" }, { "from": 6554, "to": 6555, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6555, "to": 6558, "label": "ONLY EVAL with clause\ntail(.(X5762, X5763), X5763).\nand substitutionT835 -> T846,\nT830 -> T849,\nX5762 -> .(T846, T849),\nT829 -> T850,\nX5763 -> T850,\nX141 -> T850,\nT847 -> T849,\nT848 -> T850" }, { "from": 6558, "to": 6564, "label": "CASE" }, { "from": 6564, "to": 6565, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6565, "to": 6567, "label": "ONLY EVAL with clause\ntail(.(X5778, X5779), X5779).\nand substitutionT846 -> T859,\nX5778 -> T859,\nT849 -> T861,\nX5779 -> T861,\nX142 -> T861,\nT860 -> T861,\nT850 -> T862" }, { "from": 6567, "to": 6569, "label": "CASE" }, { "from": 6569, "to": 6574, "label": "PARALLEL" }, { "from": 6569, "to": 6575, "label": "PARALLEL" }, { "from": 6574, "to": 6576, "label": "ONLY EVAL with clause\nhead([], X5799).\nand substitutionX145 -> [],\nT861 -> T872,\nX5799 -> T872,\nT862 -> T873" }, { "from": 6575, "to": 6609, "label": "ONLY EVAL with clause\nhead(.(X5843, X5844), X5843).\nand substitutionX5843 -> T887,\nX5844 -> X5846,\nX145 -> .(T887, X5846),\nT861 -> T887,\nX5845 -> T887,\nT886 -> T887,\nT862 -> T888" }, { "from": 6576, "to": 6582, "label": "CASE" }, { "from": 6582, "to": 6585, "label": "PARALLEL" }, { "from": 6582, "to": 6586, "label": "PARALLEL" }, { "from": 6585, "to": 6587, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX143 -> []" }, { "from": 6586, "to": 6598, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6587, "to": 6588, "label": "CASE" }, { "from": 6588, "to": 6592, "label": "PARALLEL" }, { "from": 6588, "to": 6593, "label": "PARALLEL" }, { "from": 6592, "to": 6594, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX144 -> []" }, { "from": 6593, "to": 6597, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6594, "to": 4093, "label": "INSTANCE with matching:\nT229 -> T836\nT235 -> T873" }, { "from": 6609, "to": 6612, "label": "CASE" }, { "from": 6612, "to": 6613, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6613, "to": 6619, "label": "ONLY EVAL with clause\ntail(.(X5863, X5864), X5864).\nand substitutionT887 -> T894,\nX5863 -> T894,\nX5846 -> X5865,\nX5864 -> X5865,\nX143 -> X5865,\nT888 -> T895" }, { "from": 6619, "to": 6626, "label": "CASE" }, { "from": 6626, "to": 6628, "label": "PARALLEL" }, { "from": 6626, "to": 6629, "label": "PARALLEL" }, { "from": 6628, "to": 6630, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX144 -> []" }, { "from": 6629, "to": 6634, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6630, "to": 4965, "label": "INSTANCE with matching:\nT229 -> T836\nT235 -> T895\nX3411 -> X5865" }, { "from": 6639, "to": 6645, "label": "CASE" }, { "from": 6645, "to": 6646, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6646, "to": 6647, "label": "ONLY EVAL with clause\ntail(.(X5919, X5920), X5920).\nand substitutionT827 -> T904,\nX5919 -> T904,\nT60 -> T905,\nX5920 -> T905,\nX140 -> T905" }, { "from": 6647, "to": 6651, "label": "CASE" }, { "from": 6651, "to": 6652, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6652, "to": 6657, "label": "ONLY EVAL with clause\ntail(.(X5936, X5937), X5937).\nand substitutionT904 -> T915,\nT830 -> T918,\nX5936 -> .(T915, T918),\nT829 -> T919,\nX5937 -> T919,\nX141 -> T919,\nT916 -> T918,\nT917 -> T919" }, { "from": 6657, "to": 6658, "label": "CASE" }, { "from": 6658, "to": 6659, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6659, "to": 6663, "label": "ONLY EVAL with clause\ntail(.(X5952, X5953), X5953).\nand substitutionT915 -> T928,\nX5952 -> T928,\nT918 -> T930,\nX5953 -> T930,\nX142 -> T930,\nT929 -> T930,\nT919 -> T931" }, { "from": 6663, "to": 6670, "label": "CASE" }, { "from": 6670, "to": 6671, "label": "PARALLEL" }, { "from": 6670, "to": 6672, "label": "PARALLEL" }, { "from": 6671, "to": 6680, "label": "ONLY EVAL with clause\nhead([], X5973).\nand substitutionX145 -> [],\nT930 -> T941,\nX5973 -> T941,\nT931 -> T942" }, { "from": 6672, "to": 6708, "label": "ONLY EVAL with clause\nhead(.(X6023, X6024), X6023).\nand substitutionX6023 -> T955,\nX6024 -> X6026,\nX145 -> .(T955, X6026),\nT930 -> T955,\nX6025 -> T955,\nT954 -> T955,\nT931 -> T956" }, { "from": 6680, "to": 6681, "label": "CASE" }, { "from": 6681, "to": 6686, "label": "PARALLEL" }, { "from": 6681, "to": 6687, "label": "PARALLEL" }, { "from": 6686, "to": 6688, "label": "ONLY EVAL with clause\ntail([], []).\nand substitutionX143 -> []" }, { "from": 6687, "to": 6706, "label": "BACKTRACK\nfor clause: tail(.(X4, T), T)because of non-unification" }, { "from": 6688, "to": 6689, "label": "CASE" }, { "from": 6689, "to": 6690, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6690, "to": 6696, "label": "ONLY EVAL with clause\ntail(.(X6001, X6002), X6002).\nand substitutionX6001 -> [],\nX5902 -> X6003,\nX6002 -> X6003,\nX144 -> X6003" }, { "from": 6696, "to": 5708, "label": "INSTANCE with matching:\nT569 -> T905\nT575 -> T942\nX4442 -> X6003" }, { "from": 6708, "to": 6711, "label": "CASE" }, { "from": 6711, "to": 6712, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6712, "to": 6717, "label": "ONLY EVAL with clause\ntail(.(X6043, X6044), X6044).\nand substitutionT955 -> T962,\nX6043 -> T962,\nX6026 -> X6045,\nX6044 -> X6045,\nX143 -> X6045,\nT956 -> T963" }, { "from": 6717, "to": 6722, "label": "CASE" }, { "from": 6722, "to": 6723, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6723, "to": 6724, "label": "ONLY EVAL with clause\ntail(.(X6062, X6063), X6063).\nand substitutionX6062 -> [],\nX5902 -> X6064,\nX6063 -> X6064,\nX144 -> X6064" }, { "from": 6724, "to": 481, "label": "INSTANCE with matching:\nT34 -> T905\nT20 -> T963\nX38 -> X6045\nX39 -> X6064" }, { "from": 6726, "to": 6728, "label": "EVAL with clause\ntranspose_aux([], X6076, X6077) :- ','(!_301, eq(X6076, X6077)).\nand substitutionT35 -> [],\nT38 -> T975,\nX6076 -> T975,\nT37 -> T976,\nX6077 -> T976,\nT973 -> T975,\nT974 -> T976" }, { "from": 6726, "to": 6729, "label": "EVAL-BACKTRACK" }, { "from": 6728, "to": 6730, "label": "CUT" }, { "from": 6729, "to": 6744, "label": "ONLY EVAL with clause\ntranspose_aux(X6096, X6097, X6098) :- ','(head(X6096, X6099), ','(tail(X6096, X6100), ','(row2col(X6099, X6098, X6101, X6102), transpose_aux(X6100, X6102, X6101)))).\nand substitutionT35 -> T988,\nX6096 -> T988,\nT38 -> T989,\nX6097 -> T989,\nT37 -> T991,\nX6098 -> T991,\nT990 -> T991" }, { "from": 6730, "to": 6731, "label": "CASE" }, { "from": 6731, "to": 6739, "label": "EVAL with clause\neq(X6080, X6080).\nand substitutionT975 -> T979,\nX6080 -> T979,\nT976 -> T979" }, { "from": 6731, "to": 6740, "label": "EVAL-BACKTRACK" }, { "from": 6739, "to": 6742, "label": "SUCCESS" }, { "from": 6744, "to": 6761, "label": "CASE" }, { "from": 6761, "to": 6763, "label": "BACKTRACK\nfor clause: head([], X2)\nwith clash: (transpose_aux(T988, T38, T37), transpose_aux([], X6076, X6077))" }, { "from": 6763, "to": 6767, "label": "EVAL with clause\nhead(.(X6114, X6115), X6114).\nand substitutionX6114 -> T997,\nX6115 -> T998,\nT988 -> .(T997, T998),\nX6099 -> T997" }, { "from": 6763, "to": 6768, "label": "EVAL-BACKTRACK" }, { "from": 6767, "to": 6770, "label": "CASE" }, { "from": 6770, "to": 6771, "label": "BACKTRACK\nfor clause: tail([], [])because of non-unification" }, { "from": 6771, "to": 6781, "label": "ONLY EVAL with clause\ntail(.(X6130, X6131), X6131).\nand substitutionT997 -> T1005,\nX6130 -> T1005,\nT998 -> T1006,\nX6131 -> T1006,\nX6100 -> T1006" }, { "from": 6781, "to": 82, "label": "INSTANCE with matching:\nT34 -> T1005\nT20 -> T991\nX38 -> X6101\nX39 -> X6102\nT35 -> T1006" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Triples: row2colA(.(X1, X2)) :- row2colA(X2). row2colA(.(X1, X2)) :- row2colA(X2). row2colB(.(X1, X2), []) :- row2colA(X2). row2colB(.(X1, X2), .([], X3)) :- row2colB(X2, X3). row2colB(.(X1, X2), []) :- row2colA(X2). row2colB(.(X1, X2), .(X3, X4)) :- row2colB(X2, X4). row2colC(.(X1, X2), []) :- row2colA(X2). row2colC(.(X1, X2), .([], X3)) :- row2colC(X2, X3). row2colC(.(X1, X2), []) :- row2colA(X2). row2colC(.(X1, X2), .([], X3)) :- row2colC(X2, X3). row2colD(.(X1, X2), [], [], []) :- row2colA(X2). row2colD(.(X1, X2), [], .([], X3), []) :- row2colB(X2, X3). row2colD(.(X1, X2), [], [], .([], X3)) :- row2colC(X2, X3). row2colD(.(X1, X2), [], .([], X3), .([], X4)) :- row2colD(X2, [], X3, X4). row2colD(.(X1, X2), [], [], []) :- row2colA(X2). row2colD(.(X1, X2), [], .(X3, X4), []) :- row2colB(X2, X4). row2colD(.(X1, X2), [], [], .([], X3)) :- row2colC(X2, X3). row2colD(.(X1, X2), [], .(X3, X4), .([], X5)) :- row2colD(X2, [], X4, X5). row2colD(.(X1, X2), .([], X3), [], []) :- row2colE(X2, X3). row2colD(.(X1, X2), .([], X3), .([], X4), []) :- row2colF(X2, X3, X4). row2colD(.(X1, X2), .([], X3), [], .([], X4)) :- row2colG(X2, X3, X4). row2colD(.(X1, X2), .([], X3), .([], X4), .([], X5)) :- row2colD(X2, X3, X4, X5). row2colD(.(X1, X2), .(.(X1, X3), X4), [], []) :- row2colE(X2, X4). row2colD(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) :- row2colF(X2, X4, X5). row2colD(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) :- row2colG(X2, X4, X5). row2colD(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) :- row2colD(X2, X4, X5, X6). row2colE(.(X1, X2), []) :- row2colA(X2). row2colE(.(X1, X2), []) :- row2colA(X2). row2colE(.(X1, X2), .([], X3)) :- row2colE(X2, X3). row2colE(.(X1, X2), .(.(X1, X3), X4)) :- row2colE(X2, X4). row2colF(.(X1, X2), [], []) :- row2colA(X2). row2colF(.(X1, X2), [], .([], X3)) :- row2colB(X2, X3). row2colF(.(X1, X2), [], []) :- row2colA(X2). row2colF(.(X1, X2), [], .(X3, X4)) :- row2colB(X2, X4). row2colF(.(X1, X2), .([], X3), []) :- row2colE(X2, X3). row2colF(.(X1, X2), .([], X3), .([], X4)) :- row2colF(X2, X3, X4). row2colF(.(X1, X2), .(.(X1, X3), X4), []) :- row2colE(X2, X4). row2colF(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) :- row2colF(X2, X4, X5). row2colG(.(X1, X2), [], []) :- row2colA(X2). row2colG(.(X1, X2), [], .([], X3)) :- row2colC(X2, X3). row2colG(.(X1, X2), [], []) :- row2colA(X2). row2colG(.(X1, X2), [], .([], X3)) :- row2colC(X2, X3). row2colG(.(X1, X2), .([], X3), []) :- row2colE(X2, X3). row2colG(.(X1, X2), .([], X3), .([], X4)) :- row2colG(X2, X3, X4). row2colG(.(X1, X2), .(.(X1, X3), X4), []) :- row2colE(X2, X4). row2colG(.(X1, X2), .(.(X1, X3), X4), .([], X5)) :- row2colG(X2, X4, X5). pH(X1, X2, X3, X4, X5) :- row2colD(X1, X2, X3, X4). pH(X1, X2, X3, X4, .(X5, X6)) :- ','(row2colcD(X1, X2, X3, X4), pH(X5, X3, X7, X8, X6)). transposeI(.(X1, X2), X3) :- pH(X1, X3, X4, X5, X2). Clauses: row2colcA([]). row2colcA(.(X1, X2)) :- row2colcA(X2). row2colcA(.(X1, X2)) :- row2colcA(X2). row2colcB([], []). row2colcB(.(X1, X2), []) :- row2colcA(X2). row2colcB(.(X1, X2), .([], X3)) :- row2colcB(X2, X3). row2colcB(.(X1, X2), []) :- row2colcA(X2). row2colcB(.(X1, X2), .(X3, X4)) :- row2colcB(X2, X4). row2colcC([], []). row2colcC(.(X1, X2), []) :- row2colcA(X2). row2colcC(.(X1, X2), .([], X3)) :- row2colcC(X2, X3). row2colcC(.(X1, X2), []) :- row2colcA(X2). row2colcC(.(X1, X2), .([], X3)) :- row2colcC(X2, X3). row2colcD([], [], [], []). row2colcD(.(X1, X2), [], [], []) :- row2colcA(X2). row2colcD(.(X1, X2), [], .([], X3), []) :- row2colcB(X2, X3). row2colcD(.(X1, X2), [], [], .([], X3)) :- row2colcC(X2, X3). row2colcD(.(X1, X2), [], .([], X3), .([], X4)) :- row2colcD(X2, [], X3, X4). row2colcD(.(X1, X2), [], [], []) :- row2colcA(X2). row2colcD(.(X1, X2), [], .(X3, X4), []) :- row2colcB(X2, X4). row2colcD(.(X1, X2), [], [], .([], X3)) :- row2colcC(X2, X3). row2colcD(.(X1, X2), [], .(X3, X4), .([], X5)) :- row2colcD(X2, [], X4, X5). row2colcD(.(X1, X2), .([], X3), [], []) :- row2colcE(X2, X3). row2colcD(.(X1, X2), .([], X3), .([], X4), []) :- row2colcF(X2, X3, X4). row2colcD(.(X1, X2), .([], X3), [], .([], X4)) :- row2colcG(X2, X3, X4). row2colcD(.(X1, X2), .([], X3), .([], X4), .([], X5)) :- row2colcD(X2, X3, X4, X5). row2colcD(.(X1, X2), .(.(X1, X3), X4), [], []) :- row2colcE(X2, X4). row2colcD(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) :- row2colcF(X2, X4, X5). row2colcD(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) :- row2colcG(X2, X4, X5). row2colcD(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) :- row2colcD(X2, X4, X5, X6). row2colcE([], []). row2colcE(.(X1, X2), []) :- row2colcA(X2). row2colcE(.(X1, X2), []) :- row2colcA(X2). row2colcE(.(X1, X2), .([], X3)) :- row2colcE(X2, X3). row2colcE(.(X1, X2), .(.(X1, X3), X4)) :- row2colcE(X2, X4). row2colcF([], [], []). row2colcF(.(X1, X2), [], []) :- row2colcA(X2). row2colcF(.(X1, X2), [], .([], X3)) :- row2colcB(X2, X3). row2colcF(.(X1, X2), [], []) :- row2colcA(X2). row2colcF(.(X1, X2), [], .(X3, X4)) :- row2colcB(X2, X4). row2colcF(.(X1, X2), .([], X3), []) :- row2colcE(X2, X3). row2colcF(.(X1, X2), .([], X3), .([], X4)) :- row2colcF(X2, X3, X4). row2colcF(.(X1, X2), .(.(X1, X3), X4), []) :- row2colcE(X2, X4). row2colcF(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) :- row2colcF(X2, X4, X5). row2colcG([], [], []). row2colcG(.(X1, X2), [], []) :- row2colcA(X2). row2colcG(.(X1, X2), [], .([], X3)) :- row2colcC(X2, X3). row2colcG(.(X1, X2), [], []) :- row2colcA(X2). row2colcG(.(X1, X2), [], .([], X3)) :- row2colcC(X2, X3). row2colcG(.(X1, X2), .([], X3), []) :- row2colcE(X2, X3). row2colcG(.(X1, X2), .([], X3), .([], X4)) :- row2colcG(X2, X3, X4). row2colcG(.(X1, X2), .(.(X1, X3), X4), []) :- row2colcE(X2, X4). row2colcG(.(X1, X2), .(.(X1, X3), X4), .([], X5)) :- row2colcG(X2, X4, X5). qcH(X1, X2, X3, X3, []) :- row2colcD(X1, X2, X3, X3). qcH(X1, X2, X3, X4, .(X5, X6)) :- ','(row2colcD(X1, X2, X3, X4), qcH(X5, X3, X7, X8, X6)). Afs: transposeI(x1, x2) = transposeI(x1) ---------------------------------------- (3) TriplesToPiDPProof (SOUND) We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes: transposeI_in_2: (b,f) pH_in_5: (b,f,f,f,b) row2colD_in_4: (b,f,f,f) (b,b,f,f) row2colA_in_1: (b) row2colB_in_2: (b,f) row2colC_in_2: (b,f) row2colE_in_2: (b,b) (b,f) row2colF_in_3: (b,b,f) (b,f,f) row2colG_in_3: (b,b,f) (b,f,f) row2colcD_in_4: (b,f,f,f) (b,b,f,f) row2colcA_in_1: (b) row2colcB_in_2: (b,f) row2colcC_in_2: (b,f) row2colcE_in_2: (b,b) (b,f) row2colcF_in_3: (b,b,f) (b,f,f) row2colcG_in_3: (b,b,f) (b,f,f) Transforming TRIPLES into the following Term Rewriting System: Pi DP problem: The TRS P consists of the following rules: TRANSPOSEI_IN_GA(.(X1, X2), X3) -> U40_GA(X1, X2, X3, pH_in_gaaag(X1, X3, X4, X5, X2)) TRANSPOSEI_IN_GA(.(X1, X2), X3) -> PH_IN_GAAAG(X1, X3, X4, X5, X2) PH_IN_GAAAG(X1, X2, X3, X4, X5) -> U37_GAAAG(X1, X2, X3, X4, X5, row2colD_in_gaaa(X1, X2, X3, X4)) PH_IN_GAAAG(X1, X2, X3, X4, X5) -> ROW2COLD_IN_GAAA(X1, X2, X3, X4) ROW2COLD_IN_GAAA(.(X1, X2), [], [], []) -> U7_GAAA(X1, X2, row2colA_in_g(X2)) ROW2COLD_IN_GAAA(.(X1, X2), [], [], []) -> ROW2COLA_IN_G(X2) ROW2COLA_IN_G(.(X1, X2)) -> U1_G(X1, X2, row2colA_in_g(X2)) ROW2COLA_IN_G(.(X1, X2)) -> ROW2COLA_IN_G(X2) ROW2COLD_IN_GAAA(.(X1, X2), [], .([], X3), []) -> U8_GAAA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLD_IN_GAAA(.(X1, X2), [], .([], X3), []) -> ROW2COLB_IN_GA(X2, X3) ROW2COLB_IN_GA(.(X1, X2), []) -> U2_GA(X1, X2, row2colA_in_g(X2)) ROW2COLB_IN_GA(.(X1, X2), []) -> ROW2COLA_IN_G(X2) ROW2COLB_IN_GA(.(X1, X2), .([], X3)) -> U3_GA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLB_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLB_IN_GA(X2, X3) ROW2COLB_IN_GA(.(X1, X2), .(X3, X4)) -> U4_GA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLB_IN_GA(.(X1, X2), .(X3, X4)) -> ROW2COLB_IN_GA(X2, X4) ROW2COLD_IN_GAAA(.(X1, X2), [], [], .([], X3)) -> U9_GAAA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLD_IN_GAAA(.(X1, X2), [], [], .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLC_IN_GA(.(X1, X2), []) -> U5_GA(X1, X2, row2colA_in_g(X2)) ROW2COLC_IN_GA(.(X1, X2), []) -> ROW2COLA_IN_G(X2) ROW2COLC_IN_GA(.(X1, X2), .([], X3)) -> U6_GA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLC_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLD_IN_GAAA(.(X1, X2), [], .([], X3), .([], X4)) -> U10_GAAA(X1, X2, X3, X4, row2colD_in_ggaa(X2, [], X3, X4)) ROW2COLD_IN_GAAA(.(X1, X2), [], .([], X3), .([], X4)) -> ROW2COLD_IN_GGAA(X2, [], X3, X4) ROW2COLD_IN_GGAA(.(X1, X2), [], [], []) -> U7_GGAA(X1, X2, row2colA_in_g(X2)) ROW2COLD_IN_GGAA(.(X1, X2), [], [], []) -> ROW2COLA_IN_G(X2) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), []) -> U8_GGAA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), []) -> ROW2COLB_IN_GA(X2, X3) ROW2COLD_IN_GGAA(.(X1, X2), [], [], .([], X3)) -> U9_GGAA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLD_IN_GGAA(.(X1, X2), [], [], .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), .([], X4)) -> U10_GGAA(X1, X2, X3, X4, row2colD_in_ggaa(X2, [], X3, X4)) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), .([], X4)) -> ROW2COLD_IN_GGAA(X2, [], X3, X4) ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), []) -> U11_GGAA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), []) -> ROW2COLB_IN_GA(X2, X4) ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> U12_GGAA(X1, X2, X3, X4, X5, row2colD_in_ggaa(X2, [], X4, X5)) ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, [], X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), [], []) -> U13_GGAA(X1, X2, X3, row2colE_in_gg(X2, X3)) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), [], []) -> ROW2COLE_IN_GG(X2, X3) ROW2COLE_IN_GG(.(X1, X2), []) -> U21_GG(X1, X2, row2colA_in_g(X2)) ROW2COLE_IN_GG(.(X1, X2), []) -> ROW2COLA_IN_G(X2) ROW2COLE_IN_GG(.(X1, X2), .([], X3)) -> U22_GG(X1, X2, X3, row2colE_in_gg(X2, X3)) ROW2COLE_IN_GG(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GG(X2, X3) ROW2COLE_IN_GG(.(X1, X2), .(.(X1, X3), X4)) -> U23_GG(X1, X2, X3, X4, row2colE_in_gg(X2, X4)) ROW2COLE_IN_GG(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GG(X2, X4) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), []) -> U14_GGAA(X1, X2, X3, X4, row2colF_in_gga(X2, X3, X4)) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), []) -> ROW2COLF_IN_GGA(X2, X3, X4) ROW2COLF_IN_GGA(.(X1, X2), [], []) -> U24_GGA(X1, X2, row2colA_in_g(X2)) ROW2COLF_IN_GGA(.(X1, X2), [], []) -> ROW2COLA_IN_G(X2) ROW2COLF_IN_GGA(.(X1, X2), [], .([], X3)) -> U25_GGA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLF_IN_GGA(.(X1, X2), [], .([], X3)) -> ROW2COLB_IN_GA(X2, X3) ROW2COLF_IN_GGA(.(X1, X2), [], .(X3, X4)) -> U26_GGA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLF_IN_GGA(.(X1, X2), [], .(X3, X4)) -> ROW2COLB_IN_GA(X2, X4) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), []) -> U27_GGA(X1, X2, X3, row2colE_in_gg(X2, X3)) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), []) -> ROW2COLE_IN_GG(X2, X3) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> U28_GGA(X1, X2, X3, X4, row2colF_in_gga(X2, X3, X4)) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLF_IN_GGA(X2, X3, X4) ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), []) -> U29_GGA(X1, X2, X3, X4, row2colE_in_gg(X2, X4)) ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), []) -> ROW2COLE_IN_GG(X2, X4) ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U30_GGA(X1, X2, X3, X4, X5, row2colF_in_gga(X2, X4, X5)) ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> ROW2COLF_IN_GGA(X2, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), [], .([], X4)) -> U15_GGAA(X1, X2, X3, X4, row2colG_in_gga(X2, X3, X4)) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), [], .([], X4)) -> ROW2COLG_IN_GGA(X2, X3, X4) ROW2COLG_IN_GGA(.(X1, X2), [], []) -> U31_GGA(X1, X2, row2colA_in_g(X2)) ROW2COLG_IN_GGA(.(X1, X2), [], []) -> ROW2COLA_IN_G(X2) ROW2COLG_IN_GGA(.(X1, X2), [], .([], X3)) -> U32_GGA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLG_IN_GGA(.(X1, X2), [], .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), []) -> U33_GGA(X1, X2, X3, row2colE_in_gg(X2, X3)) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), []) -> ROW2COLE_IN_GG(X2, X3) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> U34_GGA(X1, X2, X3, X4, row2colG_in_gga(X2, X3, X4)) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLG_IN_GGA(X2, X3, X4) ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), []) -> U35_GGA(X1, X2, X3, X4, row2colE_in_gg(X2, X4)) ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), []) -> ROW2COLE_IN_GG(X2, X4) ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U36_GGA(X1, X2, X3, X4, X5, row2colG_in_gga(X2, X4, X5)) ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> ROW2COLG_IN_GGA(X2, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U16_GGAA(X1, X2, X3, X4, X5, row2colD_in_ggaa(X2, X3, X4, X5)) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, X3, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), [], []) -> U17_GGAA(X1, X2, X3, X4, row2colE_in_gg(X2, X4)) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), [], []) -> ROW2COLE_IN_GG(X2, X4) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U18_GGAA(X1, X2, X3, X4, X5, row2colF_in_gga(X2, X4, X5)) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> ROW2COLF_IN_GGA(X2, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U19_GGAA(X1, X2, X3, X4, X5, row2colG_in_gga(X2, X4, X5)) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> ROW2COLG_IN_GGA(X2, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U20_GGAA(X1, X2, X3, X4, X5, X6, row2colD_in_ggaa(X2, X4, X5, X6)) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> ROW2COLD_IN_GGAA(X2, X4, X5, X6) ROW2COLD_IN_GAAA(.(X1, X2), [], .(X3, X4), []) -> U11_GAAA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLD_IN_GAAA(.(X1, X2), [], .(X3, X4), []) -> ROW2COLB_IN_GA(X2, X4) ROW2COLD_IN_GAAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> U12_GAAA(X1, X2, X3, X4, X5, row2colD_in_ggaa(X2, [], X4, X5)) ROW2COLD_IN_GAAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, [], X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), [], []) -> U13_GAAA(X1, X2, X3, row2colE_in_ga(X2, X3)) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), [], []) -> ROW2COLE_IN_GA(X2, X3) ROW2COLE_IN_GA(.(X1, X2), []) -> U21_GA(X1, X2, row2colA_in_g(X2)) ROW2COLE_IN_GA(.(X1, X2), []) -> ROW2COLA_IN_G(X2) ROW2COLE_IN_GA(.(X1, X2), .([], X3)) -> U22_GA(X1, X2, X3, row2colE_in_ga(X2, X3)) ROW2COLE_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GA(X2, X3) ROW2COLE_IN_GA(.(X1, X2), .(.(X1, X3), X4)) -> U23_GA(X1, X2, X3, X4, row2colE_in_ga(X2, X4)) ROW2COLE_IN_GA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GA(X2, X4) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), []) -> U14_GAAA(X1, X2, X3, X4, row2colF_in_gaa(X2, X3, X4)) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), []) -> ROW2COLF_IN_GAA(X2, X3, X4) ROW2COLF_IN_GAA(.(X1, X2), [], []) -> U24_GAA(X1, X2, row2colA_in_g(X2)) ROW2COLF_IN_GAA(.(X1, X2), [], []) -> ROW2COLA_IN_G(X2) ROW2COLF_IN_GAA(.(X1, X2), [], .([], X3)) -> U25_GAA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLF_IN_GAA(.(X1, X2), [], .([], X3)) -> ROW2COLB_IN_GA(X2, X3) ROW2COLF_IN_GAA(.(X1, X2), [], .(X3, X4)) -> U26_GAA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLF_IN_GAA(.(X1, X2), [], .(X3, X4)) -> ROW2COLB_IN_GA(X2, X4) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), []) -> U27_GAA(X1, X2, X3, row2colE_in_ga(X2, X3)) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), []) -> ROW2COLE_IN_GA(X2, X3) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> U28_GAA(X1, X2, X3, X4, row2colF_in_gaa(X2, X3, X4)) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLF_IN_GAA(X2, X3, X4) ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), []) -> U29_GAA(X1, X2, X3, X4, row2colE_in_ga(X2, X4)) ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), []) -> ROW2COLE_IN_GA(X2, X4) ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U30_GAA(X1, X2, X3, X4, X5, row2colF_in_gaa(X2, X4, X5)) ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> ROW2COLF_IN_GAA(X2, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), [], .([], X4)) -> U15_GAAA(X1, X2, X3, X4, row2colG_in_gaa(X2, X3, X4)) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), [], .([], X4)) -> ROW2COLG_IN_GAA(X2, X3, X4) ROW2COLG_IN_GAA(.(X1, X2), [], []) -> U31_GAA(X1, X2, row2colA_in_g(X2)) ROW2COLG_IN_GAA(.(X1, X2), [], []) -> ROW2COLA_IN_G(X2) ROW2COLG_IN_GAA(.(X1, X2), [], .([], X3)) -> U32_GAA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLG_IN_GAA(.(X1, X2), [], .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), []) -> U33_GAA(X1, X2, X3, row2colE_in_ga(X2, X3)) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), []) -> ROW2COLE_IN_GA(X2, X3) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> U34_GAA(X1, X2, X3, X4, row2colG_in_gaa(X2, X3, X4)) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLG_IN_GAA(X2, X3, X4) ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), []) -> U35_GAA(X1, X2, X3, X4, row2colE_in_ga(X2, X4)) ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), []) -> ROW2COLE_IN_GA(X2, X4) ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U36_GAA(X1, X2, X3, X4, X5, row2colG_in_gaa(X2, X4, X5)) ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> ROW2COLG_IN_GAA(X2, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U16_GAAA(X1, X2, X3, X4, X5, row2colD_in_gaaa(X2, X3, X4, X5)) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> ROW2COLD_IN_GAAA(X2, X3, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), [], []) -> U17_GAAA(X1, X2, X3, X4, row2colE_in_ga(X2, X4)) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), [], []) -> ROW2COLE_IN_GA(X2, X4) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U18_GAAA(X1, X2, X3, X4, X5, row2colF_in_gaa(X2, X4, X5)) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> ROW2COLF_IN_GAA(X2, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U19_GAAA(X1, X2, X3, X4, X5, row2colG_in_gaa(X2, X4, X5)) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> ROW2COLG_IN_GAA(X2, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U20_GAAA(X1, X2, X3, X4, X5, X6, row2colD_in_gaaa(X2, X4, X5, X6)) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> ROW2COLD_IN_GAAA(X2, X4, X5, X6) PH_IN_GAAAG(X1, X2, X3, X4, .(X5, X6)) -> U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X1, X2, X3, X4)) U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X1, X2, X3, X4)) -> U39_GAAAG(X1, X2, X3, X4, X5, X6, pH_in_gaaag(X5, X3, X7, X8, X6)) U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X1, X2, X3, X4)) -> PH_IN_GAAAG(X5, X3, X7, X8, X6) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) pH_in_gaaag(x1, x2, x3, x4, x5) = pH_in_gaaag(x1, x5) row2colD_in_gaaa(x1, x2, x3, x4) = row2colD_in_gaaa(x1) row2colA_in_g(x1) = row2colA_in_g(x1) row2colB_in_ga(x1, x2) = row2colB_in_ga(x1) row2colC_in_ga(x1, x2) = row2colC_in_ga(x1) row2colD_in_ggaa(x1, x2, x3, x4) = row2colD_in_ggaa(x1, x2) [] = [] row2colE_in_gg(x1, x2) = row2colE_in_gg(x1, x2) row2colF_in_gga(x1, x2, x3) = row2colF_in_gga(x1, x2) row2colG_in_gga(x1, x2, x3) = row2colG_in_gga(x1, x2) row2colE_in_ga(x1, x2) = row2colE_in_ga(x1) row2colF_in_gaa(x1, x2, x3) = row2colF_in_gaa(x1) row2colG_in_gaa(x1, x2, x3) = row2colG_in_gaa(x1) row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) TRANSPOSEI_IN_GA(x1, x2) = TRANSPOSEI_IN_GA(x1) U40_GA(x1, x2, x3, x4) = U40_GA(x1, x2, x4) PH_IN_GAAAG(x1, x2, x3, x4, x5) = PH_IN_GAAAG(x1, x5) U37_GAAAG(x1, x2, x3, x4, x5, x6) = U37_GAAAG(x1, x5, x6) ROW2COLD_IN_GAAA(x1, x2, x3, x4) = ROW2COLD_IN_GAAA(x1) U7_GAAA(x1, x2, x3) = U7_GAAA(x1, x2, x3) ROW2COLA_IN_G(x1) = ROW2COLA_IN_G(x1) U1_G(x1, x2, x3) = U1_G(x1, x2, x3) U8_GAAA(x1, x2, x3, x4) = U8_GAAA(x1, x2, x4) ROW2COLB_IN_GA(x1, x2) = ROW2COLB_IN_GA(x1) U2_GA(x1, x2, x3) = U2_GA(x1, x2, x3) U3_GA(x1, x2, x3, x4) = U3_GA(x1, x2, x4) U4_GA(x1, x2, x3, x4, x5) = U4_GA(x1, x2, x5) U9_GAAA(x1, x2, x3, x4) = U9_GAAA(x1, x2, x4) ROW2COLC_IN_GA(x1, x2) = ROW2COLC_IN_GA(x1) U5_GA(x1, x2, x3) = U5_GA(x1, x2, x3) U6_GA(x1, x2, x3, x4) = U6_GA(x1, x2, x4) U10_GAAA(x1, x2, x3, x4, x5) = U10_GAAA(x1, x2, x5) ROW2COLD_IN_GGAA(x1, x2, x3, x4) = ROW2COLD_IN_GGAA(x1, x2) U7_GGAA(x1, x2, x3) = U7_GGAA(x1, x2, x3) U8_GGAA(x1, x2, x3, x4) = U8_GGAA(x1, x2, x4) U9_GGAA(x1, x2, x3, x4) = U9_GGAA(x1, x2, x4) U10_GGAA(x1, x2, x3, x4, x5) = U10_GGAA(x1, x2, x5) U11_GGAA(x1, x2, x3, x4, x5) = U11_GGAA(x1, x2, x5) U12_GGAA(x1, x2, x3, x4, x5, x6) = U12_GGAA(x1, x2, x6) U13_GGAA(x1, x2, x3, x4) = U13_GGAA(x1, x2, x3, x4) ROW2COLE_IN_GG(x1, x2) = ROW2COLE_IN_GG(x1, x2) U21_GG(x1, x2, x3) = U21_GG(x1, x2, x3) U22_GG(x1, x2, x3, x4) = U22_GG(x1, x2, x3, x4) U23_GG(x1, x2, x3, x4, x5) = U23_GG(x1, x2, x3, x4, x5) U14_GGAA(x1, x2, x3, x4, x5) = U14_GGAA(x1, x2, x3, x5) ROW2COLF_IN_GGA(x1, x2, x3) = ROW2COLF_IN_GGA(x1, x2) U24_GGA(x1, x2, x3) = U24_GGA(x1, x2, x3) U25_GGA(x1, x2, x3, x4) = U25_GGA(x1, x2, x4) U26_GGA(x1, x2, x3, x4, x5) = U26_GGA(x1, x2, x5) U27_GGA(x1, x2, x3, x4) = U27_GGA(x1, x2, x3, x4) U28_GGA(x1, x2, x3, x4, x5) = U28_GGA(x1, x2, x3, x5) U29_GGA(x1, x2, x3, x4, x5) = U29_GGA(x1, x2, x3, x4, x5) U30_GGA(x1, x2, x3, x4, x5, x6) = U30_GGA(x1, x2, x3, x4, x6) U15_GGAA(x1, x2, x3, x4, x5) = U15_GGAA(x1, x2, x3, x5) ROW2COLG_IN_GGA(x1, x2, x3) = ROW2COLG_IN_GGA(x1, x2) U31_GGA(x1, x2, x3) = U31_GGA(x1, x2, x3) U32_GGA(x1, x2, x3, x4) = U32_GGA(x1, x2, x4) U33_GGA(x1, x2, x3, x4) = U33_GGA(x1, x2, x3, x4) U34_GGA(x1, x2, x3, x4, x5) = U34_GGA(x1, x2, x3, x5) U35_GGA(x1, x2, x3, x4, x5) = U35_GGA(x1, x2, x3, x4, x5) U36_GGA(x1, x2, x3, x4, x5, x6) = U36_GGA(x1, x2, x3, x4, x6) U16_GGAA(x1, x2, x3, x4, x5, x6) = U16_GGAA(x1, x2, x3, x6) U17_GGAA(x1, x2, x3, x4, x5) = U17_GGAA(x1, x2, x3, x4, x5) U18_GGAA(x1, x2, x3, x4, x5, x6) = U18_GGAA(x1, x2, x3, x4, x6) U19_GGAA(x1, x2, x3, x4, x5, x6) = U19_GGAA(x1, x2, x3, x4, x6) U20_GGAA(x1, x2, x3, x4, x5, x6, x7) = U20_GGAA(x1, x2, x3, x4, x7) U11_GAAA(x1, x2, x3, x4, x5) = U11_GAAA(x1, x2, x5) U12_GAAA(x1, x2, x3, x4, x5, x6) = U12_GAAA(x1, x2, x6) U13_GAAA(x1, x2, x3, x4) = U13_GAAA(x1, x2, x4) ROW2COLE_IN_GA(x1, x2) = ROW2COLE_IN_GA(x1) U21_GA(x1, x2, x3) = U21_GA(x1, x2, x3) U22_GA(x1, x2, x3, x4) = U22_GA(x1, x2, x4) U23_GA(x1, x2, x3, x4, x5) = U23_GA(x1, x2, x5) U14_GAAA(x1, x2, x3, x4, x5) = U14_GAAA(x1, x2, x5) ROW2COLF_IN_GAA(x1, x2, x3) = ROW2COLF_IN_GAA(x1) U24_GAA(x1, x2, x3) = U24_GAA(x1, x2, x3) U25_GAA(x1, x2, x3, x4) = U25_GAA(x1, x2, x4) U26_GAA(x1, x2, x3, x4, x5) = U26_GAA(x1, x2, x5) U27_GAA(x1, x2, x3, x4) = U27_GAA(x1, x2, x4) U28_GAA(x1, x2, x3, x4, x5) = U28_GAA(x1, x2, x5) U29_GAA(x1, x2, x3, x4, x5) = U29_GAA(x1, x2, x5) U30_GAA(x1, x2, x3, x4, x5, x6) = U30_GAA(x1, x2, x6) U15_GAAA(x1, x2, x3, x4, x5) = U15_GAAA(x1, x2, x5) ROW2COLG_IN_GAA(x1, x2, x3) = ROW2COLG_IN_GAA(x1) U31_GAA(x1, x2, x3) = U31_GAA(x1, x2, x3) U32_GAA(x1, x2, x3, x4) = U32_GAA(x1, x2, x4) U33_GAA(x1, x2, x3, x4) = U33_GAA(x1, x2, x4) U34_GAA(x1, x2, x3, x4, x5) = U34_GAA(x1, x2, x5) U35_GAA(x1, x2, x3, x4, x5) = U35_GAA(x1, x2, x5) U36_GAA(x1, x2, x3, x4, x5, x6) = U36_GAA(x1, x2, x6) U16_GAAA(x1, x2, x3, x4, x5, x6) = U16_GAAA(x1, x2, x6) U17_GAAA(x1, x2, x3, x4, x5) = U17_GAAA(x1, x2, x5) U18_GAAA(x1, x2, x3, x4, x5, x6) = U18_GAAA(x1, x2, x6) U19_GAAA(x1, x2, x3, x4, x5, x6) = U19_GAAA(x1, x2, x6) U20_GAAA(x1, x2, x3, x4, x5, x6, x7) = U20_GAAA(x1, x2, x7) U38_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U38_GAAAG(x1, x5, x6, x7) U39_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U39_GAAAG(x1, x4, x5, x6, x7) We have to consider all (P,R,Pi)-chains Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES ---------------------------------------- (4) Obligation: Pi DP problem: The TRS P consists of the following rules: TRANSPOSEI_IN_GA(.(X1, X2), X3) -> U40_GA(X1, X2, X3, pH_in_gaaag(X1, X3, X4, X5, X2)) TRANSPOSEI_IN_GA(.(X1, X2), X3) -> PH_IN_GAAAG(X1, X3, X4, X5, X2) PH_IN_GAAAG(X1, X2, X3, X4, X5) -> U37_GAAAG(X1, X2, X3, X4, X5, row2colD_in_gaaa(X1, X2, X3, X4)) PH_IN_GAAAG(X1, X2, X3, X4, X5) -> ROW2COLD_IN_GAAA(X1, X2, X3, X4) ROW2COLD_IN_GAAA(.(X1, X2), [], [], []) -> U7_GAAA(X1, X2, row2colA_in_g(X2)) ROW2COLD_IN_GAAA(.(X1, X2), [], [], []) -> ROW2COLA_IN_G(X2) ROW2COLA_IN_G(.(X1, X2)) -> U1_G(X1, X2, row2colA_in_g(X2)) ROW2COLA_IN_G(.(X1, X2)) -> ROW2COLA_IN_G(X2) ROW2COLD_IN_GAAA(.(X1, X2), [], .([], X3), []) -> U8_GAAA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLD_IN_GAAA(.(X1, X2), [], .([], X3), []) -> ROW2COLB_IN_GA(X2, X3) ROW2COLB_IN_GA(.(X1, X2), []) -> U2_GA(X1, X2, row2colA_in_g(X2)) ROW2COLB_IN_GA(.(X1, X2), []) -> ROW2COLA_IN_G(X2) ROW2COLB_IN_GA(.(X1, X2), .([], X3)) -> U3_GA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLB_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLB_IN_GA(X2, X3) ROW2COLB_IN_GA(.(X1, X2), .(X3, X4)) -> U4_GA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLB_IN_GA(.(X1, X2), .(X3, X4)) -> ROW2COLB_IN_GA(X2, X4) ROW2COLD_IN_GAAA(.(X1, X2), [], [], .([], X3)) -> U9_GAAA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLD_IN_GAAA(.(X1, X2), [], [], .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLC_IN_GA(.(X1, X2), []) -> U5_GA(X1, X2, row2colA_in_g(X2)) ROW2COLC_IN_GA(.(X1, X2), []) -> ROW2COLA_IN_G(X2) ROW2COLC_IN_GA(.(X1, X2), .([], X3)) -> U6_GA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLC_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLD_IN_GAAA(.(X1, X2), [], .([], X3), .([], X4)) -> U10_GAAA(X1, X2, X3, X4, row2colD_in_ggaa(X2, [], X3, X4)) ROW2COLD_IN_GAAA(.(X1, X2), [], .([], X3), .([], X4)) -> ROW2COLD_IN_GGAA(X2, [], X3, X4) ROW2COLD_IN_GGAA(.(X1, X2), [], [], []) -> U7_GGAA(X1, X2, row2colA_in_g(X2)) ROW2COLD_IN_GGAA(.(X1, X2), [], [], []) -> ROW2COLA_IN_G(X2) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), []) -> U8_GGAA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), []) -> ROW2COLB_IN_GA(X2, X3) ROW2COLD_IN_GGAA(.(X1, X2), [], [], .([], X3)) -> U9_GGAA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLD_IN_GGAA(.(X1, X2), [], [], .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), .([], X4)) -> U10_GGAA(X1, X2, X3, X4, row2colD_in_ggaa(X2, [], X3, X4)) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), .([], X4)) -> ROW2COLD_IN_GGAA(X2, [], X3, X4) ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), []) -> U11_GGAA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), []) -> ROW2COLB_IN_GA(X2, X4) ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> U12_GGAA(X1, X2, X3, X4, X5, row2colD_in_ggaa(X2, [], X4, X5)) ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, [], X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), [], []) -> U13_GGAA(X1, X2, X3, row2colE_in_gg(X2, X3)) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), [], []) -> ROW2COLE_IN_GG(X2, X3) ROW2COLE_IN_GG(.(X1, X2), []) -> U21_GG(X1, X2, row2colA_in_g(X2)) ROW2COLE_IN_GG(.(X1, X2), []) -> ROW2COLA_IN_G(X2) ROW2COLE_IN_GG(.(X1, X2), .([], X3)) -> U22_GG(X1, X2, X3, row2colE_in_gg(X2, X3)) ROW2COLE_IN_GG(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GG(X2, X3) ROW2COLE_IN_GG(.(X1, X2), .(.(X1, X3), X4)) -> U23_GG(X1, X2, X3, X4, row2colE_in_gg(X2, X4)) ROW2COLE_IN_GG(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GG(X2, X4) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), []) -> U14_GGAA(X1, X2, X3, X4, row2colF_in_gga(X2, X3, X4)) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), []) -> ROW2COLF_IN_GGA(X2, X3, X4) ROW2COLF_IN_GGA(.(X1, X2), [], []) -> U24_GGA(X1, X2, row2colA_in_g(X2)) ROW2COLF_IN_GGA(.(X1, X2), [], []) -> ROW2COLA_IN_G(X2) ROW2COLF_IN_GGA(.(X1, X2), [], .([], X3)) -> U25_GGA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLF_IN_GGA(.(X1, X2), [], .([], X3)) -> ROW2COLB_IN_GA(X2, X3) ROW2COLF_IN_GGA(.(X1, X2), [], .(X3, X4)) -> U26_GGA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLF_IN_GGA(.(X1, X2), [], .(X3, X4)) -> ROW2COLB_IN_GA(X2, X4) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), []) -> U27_GGA(X1, X2, X3, row2colE_in_gg(X2, X3)) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), []) -> ROW2COLE_IN_GG(X2, X3) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> U28_GGA(X1, X2, X3, X4, row2colF_in_gga(X2, X3, X4)) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLF_IN_GGA(X2, X3, X4) ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), []) -> U29_GGA(X1, X2, X3, X4, row2colE_in_gg(X2, X4)) ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), []) -> ROW2COLE_IN_GG(X2, X4) ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U30_GGA(X1, X2, X3, X4, X5, row2colF_in_gga(X2, X4, X5)) ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> ROW2COLF_IN_GGA(X2, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), [], .([], X4)) -> U15_GGAA(X1, X2, X3, X4, row2colG_in_gga(X2, X3, X4)) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), [], .([], X4)) -> ROW2COLG_IN_GGA(X2, X3, X4) ROW2COLG_IN_GGA(.(X1, X2), [], []) -> U31_GGA(X1, X2, row2colA_in_g(X2)) ROW2COLG_IN_GGA(.(X1, X2), [], []) -> ROW2COLA_IN_G(X2) ROW2COLG_IN_GGA(.(X1, X2), [], .([], X3)) -> U32_GGA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLG_IN_GGA(.(X1, X2), [], .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), []) -> U33_GGA(X1, X2, X3, row2colE_in_gg(X2, X3)) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), []) -> ROW2COLE_IN_GG(X2, X3) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> U34_GGA(X1, X2, X3, X4, row2colG_in_gga(X2, X3, X4)) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLG_IN_GGA(X2, X3, X4) ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), []) -> U35_GGA(X1, X2, X3, X4, row2colE_in_gg(X2, X4)) ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), []) -> ROW2COLE_IN_GG(X2, X4) ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U36_GGA(X1, X2, X3, X4, X5, row2colG_in_gga(X2, X4, X5)) ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> ROW2COLG_IN_GGA(X2, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U16_GGAA(X1, X2, X3, X4, X5, row2colD_in_ggaa(X2, X3, X4, X5)) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, X3, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), [], []) -> U17_GGAA(X1, X2, X3, X4, row2colE_in_gg(X2, X4)) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), [], []) -> ROW2COLE_IN_GG(X2, X4) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U18_GGAA(X1, X2, X3, X4, X5, row2colF_in_gga(X2, X4, X5)) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> ROW2COLF_IN_GGA(X2, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U19_GGAA(X1, X2, X3, X4, X5, row2colG_in_gga(X2, X4, X5)) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> ROW2COLG_IN_GGA(X2, X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U20_GGAA(X1, X2, X3, X4, X5, X6, row2colD_in_ggaa(X2, X4, X5, X6)) ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> ROW2COLD_IN_GGAA(X2, X4, X5, X6) ROW2COLD_IN_GAAA(.(X1, X2), [], .(X3, X4), []) -> U11_GAAA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLD_IN_GAAA(.(X1, X2), [], .(X3, X4), []) -> ROW2COLB_IN_GA(X2, X4) ROW2COLD_IN_GAAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> U12_GAAA(X1, X2, X3, X4, X5, row2colD_in_ggaa(X2, [], X4, X5)) ROW2COLD_IN_GAAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, [], X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), [], []) -> U13_GAAA(X1, X2, X3, row2colE_in_ga(X2, X3)) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), [], []) -> ROW2COLE_IN_GA(X2, X3) ROW2COLE_IN_GA(.(X1, X2), []) -> U21_GA(X1, X2, row2colA_in_g(X2)) ROW2COLE_IN_GA(.(X1, X2), []) -> ROW2COLA_IN_G(X2) ROW2COLE_IN_GA(.(X1, X2), .([], X3)) -> U22_GA(X1, X2, X3, row2colE_in_ga(X2, X3)) ROW2COLE_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GA(X2, X3) ROW2COLE_IN_GA(.(X1, X2), .(.(X1, X3), X4)) -> U23_GA(X1, X2, X3, X4, row2colE_in_ga(X2, X4)) ROW2COLE_IN_GA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GA(X2, X4) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), []) -> U14_GAAA(X1, X2, X3, X4, row2colF_in_gaa(X2, X3, X4)) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), []) -> ROW2COLF_IN_GAA(X2, X3, X4) ROW2COLF_IN_GAA(.(X1, X2), [], []) -> U24_GAA(X1, X2, row2colA_in_g(X2)) ROW2COLF_IN_GAA(.(X1, X2), [], []) -> ROW2COLA_IN_G(X2) ROW2COLF_IN_GAA(.(X1, X2), [], .([], X3)) -> U25_GAA(X1, X2, X3, row2colB_in_ga(X2, X3)) ROW2COLF_IN_GAA(.(X1, X2), [], .([], X3)) -> ROW2COLB_IN_GA(X2, X3) ROW2COLF_IN_GAA(.(X1, X2), [], .(X3, X4)) -> U26_GAA(X1, X2, X3, X4, row2colB_in_ga(X2, X4)) ROW2COLF_IN_GAA(.(X1, X2), [], .(X3, X4)) -> ROW2COLB_IN_GA(X2, X4) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), []) -> U27_GAA(X1, X2, X3, row2colE_in_ga(X2, X3)) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), []) -> ROW2COLE_IN_GA(X2, X3) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> U28_GAA(X1, X2, X3, X4, row2colF_in_gaa(X2, X3, X4)) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLF_IN_GAA(X2, X3, X4) ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), []) -> U29_GAA(X1, X2, X3, X4, row2colE_in_ga(X2, X4)) ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), []) -> ROW2COLE_IN_GA(X2, X4) ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U30_GAA(X1, X2, X3, X4, X5, row2colF_in_gaa(X2, X4, X5)) ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> ROW2COLF_IN_GAA(X2, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), [], .([], X4)) -> U15_GAAA(X1, X2, X3, X4, row2colG_in_gaa(X2, X3, X4)) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), [], .([], X4)) -> ROW2COLG_IN_GAA(X2, X3, X4) ROW2COLG_IN_GAA(.(X1, X2), [], []) -> U31_GAA(X1, X2, row2colA_in_g(X2)) ROW2COLG_IN_GAA(.(X1, X2), [], []) -> ROW2COLA_IN_G(X2) ROW2COLG_IN_GAA(.(X1, X2), [], .([], X3)) -> U32_GAA(X1, X2, X3, row2colC_in_ga(X2, X3)) ROW2COLG_IN_GAA(.(X1, X2), [], .([], X3)) -> ROW2COLC_IN_GA(X2, X3) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), []) -> U33_GAA(X1, X2, X3, row2colE_in_ga(X2, X3)) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), []) -> ROW2COLE_IN_GA(X2, X3) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> U34_GAA(X1, X2, X3, X4, row2colG_in_gaa(X2, X3, X4)) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLG_IN_GAA(X2, X3, X4) ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), []) -> U35_GAA(X1, X2, X3, X4, row2colE_in_ga(X2, X4)) ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), []) -> ROW2COLE_IN_GA(X2, X4) ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U36_GAA(X1, X2, X3, X4, X5, row2colG_in_gaa(X2, X4, X5)) ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> ROW2COLG_IN_GAA(X2, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U16_GAAA(X1, X2, X3, X4, X5, row2colD_in_gaaa(X2, X3, X4, X5)) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> ROW2COLD_IN_GAAA(X2, X3, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), [], []) -> U17_GAAA(X1, X2, X3, X4, row2colE_in_ga(X2, X4)) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), [], []) -> ROW2COLE_IN_GA(X2, X4) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U18_GAAA(X1, X2, X3, X4, X5, row2colF_in_gaa(X2, X4, X5)) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> ROW2COLF_IN_GAA(X2, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U19_GAAA(X1, X2, X3, X4, X5, row2colG_in_gaa(X2, X4, X5)) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> ROW2COLG_IN_GAA(X2, X4, X5) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U20_GAAA(X1, X2, X3, X4, X5, X6, row2colD_in_gaaa(X2, X4, X5, X6)) ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> ROW2COLD_IN_GAAA(X2, X4, X5, X6) PH_IN_GAAAG(X1, X2, X3, X4, .(X5, X6)) -> U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X1, X2, X3, X4)) U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X1, X2, X3, X4)) -> U39_GAAAG(X1, X2, X3, X4, X5, X6, pH_in_gaaag(X5, X3, X7, X8, X6)) U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X1, X2, X3, X4)) -> PH_IN_GAAAG(X5, X3, X7, X8, X6) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) pH_in_gaaag(x1, x2, x3, x4, x5) = pH_in_gaaag(x1, x5) row2colD_in_gaaa(x1, x2, x3, x4) = row2colD_in_gaaa(x1) row2colA_in_g(x1) = row2colA_in_g(x1) row2colB_in_ga(x1, x2) = row2colB_in_ga(x1) row2colC_in_ga(x1, x2) = row2colC_in_ga(x1) row2colD_in_ggaa(x1, x2, x3, x4) = row2colD_in_ggaa(x1, x2) [] = [] row2colE_in_gg(x1, x2) = row2colE_in_gg(x1, x2) row2colF_in_gga(x1, x2, x3) = row2colF_in_gga(x1, x2) row2colG_in_gga(x1, x2, x3) = row2colG_in_gga(x1, x2) row2colE_in_ga(x1, x2) = row2colE_in_ga(x1) row2colF_in_gaa(x1, x2, x3) = row2colF_in_gaa(x1) row2colG_in_gaa(x1, x2, x3) = row2colG_in_gaa(x1) row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) TRANSPOSEI_IN_GA(x1, x2) = TRANSPOSEI_IN_GA(x1) U40_GA(x1, x2, x3, x4) = U40_GA(x1, x2, x4) PH_IN_GAAAG(x1, x2, x3, x4, x5) = PH_IN_GAAAG(x1, x5) U37_GAAAG(x1, x2, x3, x4, x5, x6) = U37_GAAAG(x1, x5, x6) ROW2COLD_IN_GAAA(x1, x2, x3, x4) = ROW2COLD_IN_GAAA(x1) U7_GAAA(x1, x2, x3) = U7_GAAA(x1, x2, x3) ROW2COLA_IN_G(x1) = ROW2COLA_IN_G(x1) U1_G(x1, x2, x3) = U1_G(x1, x2, x3) U8_GAAA(x1, x2, x3, x4) = U8_GAAA(x1, x2, x4) ROW2COLB_IN_GA(x1, x2) = ROW2COLB_IN_GA(x1) U2_GA(x1, x2, x3) = U2_GA(x1, x2, x3) U3_GA(x1, x2, x3, x4) = U3_GA(x1, x2, x4) U4_GA(x1, x2, x3, x4, x5) = U4_GA(x1, x2, x5) U9_GAAA(x1, x2, x3, x4) = U9_GAAA(x1, x2, x4) ROW2COLC_IN_GA(x1, x2) = ROW2COLC_IN_GA(x1) U5_GA(x1, x2, x3) = U5_GA(x1, x2, x3) U6_GA(x1, x2, x3, x4) = U6_GA(x1, x2, x4) U10_GAAA(x1, x2, x3, x4, x5) = U10_GAAA(x1, x2, x5) ROW2COLD_IN_GGAA(x1, x2, x3, x4) = ROW2COLD_IN_GGAA(x1, x2) U7_GGAA(x1, x2, x3) = U7_GGAA(x1, x2, x3) U8_GGAA(x1, x2, x3, x4) = U8_GGAA(x1, x2, x4) U9_GGAA(x1, x2, x3, x4) = U9_GGAA(x1, x2, x4) U10_GGAA(x1, x2, x3, x4, x5) = U10_GGAA(x1, x2, x5) U11_GGAA(x1, x2, x3, x4, x5) = U11_GGAA(x1, x2, x5) U12_GGAA(x1, x2, x3, x4, x5, x6) = U12_GGAA(x1, x2, x6) U13_GGAA(x1, x2, x3, x4) = U13_GGAA(x1, x2, x3, x4) ROW2COLE_IN_GG(x1, x2) = ROW2COLE_IN_GG(x1, x2) U21_GG(x1, x2, x3) = U21_GG(x1, x2, x3) U22_GG(x1, x2, x3, x4) = U22_GG(x1, x2, x3, x4) U23_GG(x1, x2, x3, x4, x5) = U23_GG(x1, x2, x3, x4, x5) U14_GGAA(x1, x2, x3, x4, x5) = U14_GGAA(x1, x2, x3, x5) ROW2COLF_IN_GGA(x1, x2, x3) = ROW2COLF_IN_GGA(x1, x2) U24_GGA(x1, x2, x3) = U24_GGA(x1, x2, x3) U25_GGA(x1, x2, x3, x4) = U25_GGA(x1, x2, x4) U26_GGA(x1, x2, x3, x4, x5) = U26_GGA(x1, x2, x5) U27_GGA(x1, x2, x3, x4) = U27_GGA(x1, x2, x3, x4) U28_GGA(x1, x2, x3, x4, x5) = U28_GGA(x1, x2, x3, x5) U29_GGA(x1, x2, x3, x4, x5) = U29_GGA(x1, x2, x3, x4, x5) U30_GGA(x1, x2, x3, x4, x5, x6) = U30_GGA(x1, x2, x3, x4, x6) U15_GGAA(x1, x2, x3, x4, x5) = U15_GGAA(x1, x2, x3, x5) ROW2COLG_IN_GGA(x1, x2, x3) = ROW2COLG_IN_GGA(x1, x2) U31_GGA(x1, x2, x3) = U31_GGA(x1, x2, x3) U32_GGA(x1, x2, x3, x4) = U32_GGA(x1, x2, x4) U33_GGA(x1, x2, x3, x4) = U33_GGA(x1, x2, x3, x4) U34_GGA(x1, x2, x3, x4, x5) = U34_GGA(x1, x2, x3, x5) U35_GGA(x1, x2, x3, x4, x5) = U35_GGA(x1, x2, x3, x4, x5) U36_GGA(x1, x2, x3, x4, x5, x6) = U36_GGA(x1, x2, x3, x4, x6) U16_GGAA(x1, x2, x3, x4, x5, x6) = U16_GGAA(x1, x2, x3, x6) U17_GGAA(x1, x2, x3, x4, x5) = U17_GGAA(x1, x2, x3, x4, x5) U18_GGAA(x1, x2, x3, x4, x5, x6) = U18_GGAA(x1, x2, x3, x4, x6) U19_GGAA(x1, x2, x3, x4, x5, x6) = U19_GGAA(x1, x2, x3, x4, x6) U20_GGAA(x1, x2, x3, x4, x5, x6, x7) = U20_GGAA(x1, x2, x3, x4, x7) U11_GAAA(x1, x2, x3, x4, x5) = U11_GAAA(x1, x2, x5) U12_GAAA(x1, x2, x3, x4, x5, x6) = U12_GAAA(x1, x2, x6) U13_GAAA(x1, x2, x3, x4) = U13_GAAA(x1, x2, x4) ROW2COLE_IN_GA(x1, x2) = ROW2COLE_IN_GA(x1) U21_GA(x1, x2, x3) = U21_GA(x1, x2, x3) U22_GA(x1, x2, x3, x4) = U22_GA(x1, x2, x4) U23_GA(x1, x2, x3, x4, x5) = U23_GA(x1, x2, x5) U14_GAAA(x1, x2, x3, x4, x5) = U14_GAAA(x1, x2, x5) ROW2COLF_IN_GAA(x1, x2, x3) = ROW2COLF_IN_GAA(x1) U24_GAA(x1, x2, x3) = U24_GAA(x1, x2, x3) U25_GAA(x1, x2, x3, x4) = U25_GAA(x1, x2, x4) U26_GAA(x1, x2, x3, x4, x5) = U26_GAA(x1, x2, x5) U27_GAA(x1, x2, x3, x4) = U27_GAA(x1, x2, x4) U28_GAA(x1, x2, x3, x4, x5) = U28_GAA(x1, x2, x5) U29_GAA(x1, x2, x3, x4, x5) = U29_GAA(x1, x2, x5) U30_GAA(x1, x2, x3, x4, x5, x6) = U30_GAA(x1, x2, x6) U15_GAAA(x1, x2, x3, x4, x5) = U15_GAAA(x1, x2, x5) ROW2COLG_IN_GAA(x1, x2, x3) = ROW2COLG_IN_GAA(x1) U31_GAA(x1, x2, x3) = U31_GAA(x1, x2, x3) U32_GAA(x1, x2, x3, x4) = U32_GAA(x1, x2, x4) U33_GAA(x1, x2, x3, x4) = U33_GAA(x1, x2, x4) U34_GAA(x1, x2, x3, x4, x5) = U34_GAA(x1, x2, x5) U35_GAA(x1, x2, x3, x4, x5) = U35_GAA(x1, x2, x5) U36_GAA(x1, x2, x3, x4, x5, x6) = U36_GAA(x1, x2, x6) U16_GAAA(x1, x2, x3, x4, x5, x6) = U16_GAAA(x1, x2, x6) U17_GAAA(x1, x2, x3, x4, x5) = U17_GAAA(x1, x2, x5) U18_GAAA(x1, x2, x3, x4, x5, x6) = U18_GAAA(x1, x2, x6) U19_GAAA(x1, x2, x3, x4, x5, x6) = U19_GAAA(x1, x2, x6) U20_GAAA(x1, x2, x3, x4, x5, x6, x7) = U20_GAAA(x1, x2, x7) U38_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U38_GAAAG(x1, x5, x6, x7) U39_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U39_GAAAG(x1, x4, x5, x6, x7) We have to consider all (P,R,Pi)-chains ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LOPSTR] contains 13 SCCs with 115 less nodes. ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLA_IN_G(.(X1, X2)) -> ROW2COLA_IN_G(X2) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLA_IN_G(x1) = ROW2COLA_IN_G(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (8) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (9) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLA_IN_G(.(X1, X2)) -> ROW2COLA_IN_G(X2) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (10) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLA_IN_G(.(X1, X2)) -> ROW2COLA_IN_G(X2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (12) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLA_IN_G(.(X1, X2)) -> ROW2COLA_IN_G(X2) The graph contains the following edges 1 > 1 ---------------------------------------- (13) YES ---------------------------------------- (14) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLE_IN_GA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GA(X2, X4) ROW2COLE_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GA(X2, X3) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLE_IN_GA(x1, x2) = ROW2COLE_IN_GA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (15) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (16) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLE_IN_GA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GA(X2, X4) ROW2COLE_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GA(X2, X3) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLE_IN_GA(x1, x2) = ROW2COLE_IN_GA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (17) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (18) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLE_IN_GA(.(X1, X2)) -> ROW2COLE_IN_GA(X2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (19) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLE_IN_GA(.(X1, X2)) -> ROW2COLE_IN_GA(X2) The graph contains the following edges 1 > 1 ---------------------------------------- (20) YES ---------------------------------------- (21) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLE_IN_GG(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GG(X2, X4) ROW2COLE_IN_GG(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GG(X2, X3) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLE_IN_GG(x1, x2) = ROW2COLE_IN_GG(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (22) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (23) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLE_IN_GG(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GG(X2, X4) ROW2COLE_IN_GG(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GG(X2, X3) R is empty. Pi is empty. We have to consider all (P,R,Pi)-chains ---------------------------------------- (24) PiDPToQDPProof (EQUIVALENT) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (25) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLE_IN_GG(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GG(X2, X4) ROW2COLE_IN_GG(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GG(X2, X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (26) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLE_IN_GG(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLE_IN_GG(X2, X4) The graph contains the following edges 1 > 1, 2 > 2 *ROW2COLE_IN_GG(.(X1, X2), .([], X3)) -> ROW2COLE_IN_GG(X2, X3) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (27) YES ---------------------------------------- (28) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLC_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLC_IN_GA(X2, X3) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLC_IN_GA(x1, x2) = ROW2COLC_IN_GA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (29) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (30) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLC_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLC_IN_GA(X2, X3) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLC_IN_GA(x1, x2) = ROW2COLC_IN_GA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (31) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (32) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLC_IN_GA(.(X1, X2)) -> ROW2COLC_IN_GA(X2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (33) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLC_IN_GA(.(X1, X2)) -> ROW2COLC_IN_GA(X2) The graph contains the following edges 1 > 1 ---------------------------------------- (34) YES ---------------------------------------- (35) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> ROW2COLG_IN_GAA(X2, X4, X5) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLG_IN_GAA(X2, X3, X4) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLG_IN_GAA(x1, x2, x3) = ROW2COLG_IN_GAA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (36) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (37) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLG_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> ROW2COLG_IN_GAA(X2, X4, X5) ROW2COLG_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLG_IN_GAA(X2, X3, X4) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLG_IN_GAA(x1, x2, x3) = ROW2COLG_IN_GAA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (38) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (39) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLG_IN_GAA(.(X1, X2)) -> ROW2COLG_IN_GAA(X2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (40) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLG_IN_GAA(.(X1, X2)) -> ROW2COLG_IN_GAA(X2) The graph contains the following edges 1 > 1 ---------------------------------------- (41) YES ---------------------------------------- (42) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> ROW2COLG_IN_GGA(X2, X4, X5) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLG_IN_GGA(X2, X3, X4) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLG_IN_GGA(x1, x2, x3) = ROW2COLG_IN_GGA(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (43) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (44) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> ROW2COLG_IN_GGA(X2, X4, X5) ROW2COLG_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLG_IN_GGA(X2, X3, X4) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLG_IN_GGA(x1, x2, x3) = ROW2COLG_IN_GGA(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (45) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (46) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLG_IN_GGA(X2, X4) ROW2COLG_IN_GGA(.(X1, X2), .([], X3)) -> ROW2COLG_IN_GGA(X2, X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (47) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLG_IN_GGA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLG_IN_GGA(X2, X4) The graph contains the following edges 1 > 1, 2 > 2 *ROW2COLG_IN_GGA(.(X1, X2), .([], X3)) -> ROW2COLG_IN_GGA(X2, X3) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (48) YES ---------------------------------------- (49) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLB_IN_GA(.(X1, X2), .(X3, X4)) -> ROW2COLB_IN_GA(X2, X4) ROW2COLB_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLB_IN_GA(X2, X3) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLB_IN_GA(x1, x2) = ROW2COLB_IN_GA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (50) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (51) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLB_IN_GA(.(X1, X2), .(X3, X4)) -> ROW2COLB_IN_GA(X2, X4) ROW2COLB_IN_GA(.(X1, X2), .([], X3)) -> ROW2COLB_IN_GA(X2, X3) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLB_IN_GA(x1, x2) = ROW2COLB_IN_GA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (52) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (53) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLB_IN_GA(.(X1, X2)) -> ROW2COLB_IN_GA(X2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (54) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLB_IN_GA(.(X1, X2)) -> ROW2COLB_IN_GA(X2) The graph contains the following edges 1 > 1 ---------------------------------------- (55) YES ---------------------------------------- (56) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> ROW2COLF_IN_GAA(X2, X4, X5) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLF_IN_GAA(X2, X3, X4) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLF_IN_GAA(x1, x2, x3) = ROW2COLF_IN_GAA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (57) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (58) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLF_IN_GAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> ROW2COLF_IN_GAA(X2, X4, X5) ROW2COLF_IN_GAA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLF_IN_GAA(X2, X3, X4) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLF_IN_GAA(x1, x2, x3) = ROW2COLF_IN_GAA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (59) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (60) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLF_IN_GAA(.(X1, X2)) -> ROW2COLF_IN_GAA(X2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (61) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLF_IN_GAA(.(X1, X2)) -> ROW2COLF_IN_GAA(X2) The graph contains the following edges 1 > 1 ---------------------------------------- (62) YES ---------------------------------------- (63) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> ROW2COLF_IN_GGA(X2, X4, X5) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLF_IN_GGA(X2, X3, X4) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLF_IN_GGA(x1, x2, x3) = ROW2COLF_IN_GGA(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (64) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (65) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> ROW2COLF_IN_GGA(X2, X4, X5) ROW2COLF_IN_GGA(.(X1, X2), .([], X3), .([], X4)) -> ROW2COLF_IN_GGA(X2, X3, X4) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLF_IN_GGA(x1, x2, x3) = ROW2COLF_IN_GGA(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (66) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (67) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLF_IN_GGA(X2, X4) ROW2COLF_IN_GGA(.(X1, X2), .([], X3)) -> ROW2COLF_IN_GGA(X2, X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (68) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLF_IN_GGA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLF_IN_GGA(X2, X4) The graph contains the following edges 1 > 1, 2 > 2 *ROW2COLF_IN_GGA(.(X1, X2), .([], X3)) -> ROW2COLF_IN_GGA(X2, X3) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (69) YES ---------------------------------------- (70) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, [], X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), .([], X4)) -> ROW2COLD_IN_GGAA(X2, [], X3, X4) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLD_IN_GGAA(x1, x2, x3, x4) = ROW2COLD_IN_GGAA(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (71) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (72) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GGAA(.(X1, X2), [], .(X3, X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, [], X4, X5) ROW2COLD_IN_GGAA(.(X1, X2), [], .([], X3), .([], X4)) -> ROW2COLD_IN_GGAA(X2, [], X3, X4) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLD_IN_GGAA(x1, x2, x3, x4) = ROW2COLD_IN_GGAA(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (73) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (74) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GGAA(.(X1, X2), []) -> ROW2COLD_IN_GGAA(X2, []) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (75) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLD_IN_GGAA(.(X1, X2), []) -> ROW2COLD_IN_GGAA(X2, []) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (76) YES ---------------------------------------- (77) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> ROW2COLD_IN_GGAA(X2, X4, X5, X6) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, X3, X4, X5) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLD_IN_GGAA(x1, x2, x3, x4) = ROW2COLD_IN_GGAA(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (78) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (79) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> ROW2COLD_IN_GGAA(X2, X4, X5, X6) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> ROW2COLD_IN_GGAA(X2, X3, X4, X5) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLD_IN_GGAA(x1, x2, x3, x4) = ROW2COLD_IN_GGAA(x1, x2) We have to consider all (P,R,Pi)-chains ---------------------------------------- (80) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (81) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLD_IN_GGAA(X2, X4) ROW2COLD_IN_GGAA(.(X1, X2), .([], X3)) -> ROW2COLD_IN_GGAA(X2, X3) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (82) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLD_IN_GGAA(.(X1, X2), .(.(X1, X3), X4)) -> ROW2COLD_IN_GGAA(X2, X4) The graph contains the following edges 1 > 1, 2 > 2 *ROW2COLD_IN_GGAA(.(X1, X2), .([], X3)) -> ROW2COLD_IN_GGAA(X2, X3) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (83) YES ---------------------------------------- (84) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> ROW2COLD_IN_GAAA(X2, X4, X5, X6) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> ROW2COLD_IN_GAAA(X2, X3, X4, X5) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) ROW2COLD_IN_GAAA(x1, x2, x3, x4) = ROW2COLD_IN_GAAA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (85) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (86) Obligation: Pi DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GAAA(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> ROW2COLD_IN_GAAA(X2, X4, X5, X6) ROW2COLD_IN_GAAA(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> ROW2COLD_IN_GAAA(X2, X3, X4, X5) R is empty. The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] ROW2COLD_IN_GAAA(x1, x2, x3, x4) = ROW2COLD_IN_GAAA(x1) We have to consider all (P,R,Pi)-chains ---------------------------------------- (87) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (88) Obligation: Q DP problem: The TRS P consists of the following rules: ROW2COLD_IN_GAAA(.(X1, X2)) -> ROW2COLD_IN_GAAA(X2) R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (89) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *ROW2COLD_IN_GAAA(.(X1, X2)) -> ROW2COLD_IN_GAAA(X2) The graph contains the following edges 1 > 1 ---------------------------------------- (90) YES ---------------------------------------- (91) Obligation: Pi DP problem: The TRS P consists of the following rules: PH_IN_GAAAG(X1, X2, X3, X4, .(X5, X6)) -> U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X1, X2, X3, X4)) U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X1, X2, X3, X4)) -> PH_IN_GAAAG(X5, X3, X7, X8, X6) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], []) -> U54_ggaa(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg([], []) -> row2colcE_out_gg([], []) row2colcE_in_gg(.(X1, X2), []) -> U62_gg(X1, X2, row2colcA_in_g(X2)) U62_gg(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_gg(.(X1, X2), []) row2colcE_in_gg(.(X1, X2), .([], X3)) -> U63_gg(X1, X2, X3, row2colcE_in_gg(X2, X3)) row2colcE_in_gg(.(X1, X2), .(.(X1, X3), X4)) -> U64_gg(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U64_gg(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcE_out_gg(.(X1, X2), .(.(X1, X3), X4)) U63_gg(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcE_out_gg(.(X1, X2), .([], X3)) U54_ggaa(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], []) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_ggaa(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga([], [], []) -> row2colcF_out_gga([], [], []) row2colcF_in_gga(.(X1, X2), [], []) -> U65_gga(X1, X2, row2colcA_in_g(X2)) U65_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gga(.(X1, X2), [], []) row2colcF_in_gga(.(X1, X2), [], .([], X3)) -> U66_gga(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gga(.(X1, X2), [], .([], X3)) row2colcF_in_gga(.(X1, X2), [], .(X3, X4)) -> U67_gga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gga(.(X1, X2), [], .(X3, X4)) row2colcF_in_gga(.(X1, X2), .([], X3), []) -> U68_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U68_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcF_out_gga(.(X1, X2), .([], X3), []) row2colcF_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U69_gga(X1, X2, X3, X4, row2colcF_in_gga(X2, X3, X4)) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U70_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gga(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U71_gga(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcF_out_gga(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gga(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcF_out_gga(.(X1, X2), .([], X3), .([], X4)) U55_ggaa(X1, X2, X3, X4, row2colcF_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_ggaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_ggaa(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga([], [], []) -> row2colcG_out_gga([], [], []) row2colcG_in_gga(.(X1, X2), [], []) -> U72_gga(X1, X2, row2colcA_in_g(X2)) U72_gga(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gga(.(X1, X2), [], []) row2colcG_in_gga(.(X1, X2), [], .([], X3)) -> U73_gga(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gga(.(X1, X2), [], .([], X3)) row2colcG_in_gga(.(X1, X2), .([], X3), []) -> U74_gga(X1, X2, X3, row2colcE_in_gg(X2, X3)) U74_gga(X1, X2, X3, row2colcE_out_gg(X2, X3)) -> row2colcG_out_gga(.(X1, X2), .([], X3), []) row2colcG_in_gga(.(X1, X2), .([], X3), .([], X4)) -> U75_gga(X1, X2, X3, X4, row2colcG_in_gga(X2, X3, X4)) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gga(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U76_gga(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gga(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U77_gga(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcG_out_gga(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gga(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcG_out_gga(.(X1, X2), .([], X3), .([], X4)) U56_ggaa(X1, X2, X3, X4, row2colcG_out_gga(X2, X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, X3, X4, X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_ggaa(X1, X2, X3, X4, row2colcE_in_gg(X2, X4)) U58_ggaa(X1, X2, X3, X4, row2colcE_out_gg(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_ggaa(X1, X2, X3, X4, X5, row2colcF_in_gga(X2, X4, X5)) U59_ggaa(X1, X2, X3, X4, X5, row2colcF_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_ggaa(X1, X2, X3, X4, X5, row2colcG_in_gga(X2, X4, X5)) U60_ggaa(X1, X2, X3, X4, X5, row2colcG_out_gga(X2, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_in_ggaa(X2, X4, X5, X6)) U61_ggaa(X1, X2, X3, X4, X5, X6, row2colcD_out_ggaa(X2, X4, X5, X6)) -> row2colcD_out_ggaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, X3, X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U54_ggaa(x1, x2, x3, x4) = U54_ggaa(x1, x2, x3, x4) row2colcE_in_gg(x1, x2) = row2colcE_in_gg(x1, x2) row2colcE_out_gg(x1, x2) = row2colcE_out_gg(x1, x2) U62_gg(x1, x2, x3) = U62_gg(x1, x2, x3) U63_gg(x1, x2, x3, x4) = U63_gg(x1, x2, x3, x4) U64_gg(x1, x2, x3, x4, x5) = U64_gg(x1, x2, x3, x4, x5) U55_ggaa(x1, x2, x3, x4, x5) = U55_ggaa(x1, x2, x3, x5) row2colcF_in_gga(x1, x2, x3) = row2colcF_in_gga(x1, x2) row2colcF_out_gga(x1, x2, x3) = row2colcF_out_gga(x1, x2) U65_gga(x1, x2, x3) = U65_gga(x1, x2, x3) U66_gga(x1, x2, x3, x4) = U66_gga(x1, x2, x4) U67_gga(x1, x2, x3, x4, x5) = U67_gga(x1, x2, x5) U68_gga(x1, x2, x3, x4) = U68_gga(x1, x2, x3, x4) U69_gga(x1, x2, x3, x4, x5) = U69_gga(x1, x2, x3, x5) U70_gga(x1, x2, x3, x4, x5) = U70_gga(x1, x2, x3, x4, x5) U71_gga(x1, x2, x3, x4, x5, x6) = U71_gga(x1, x2, x3, x4, x6) U56_ggaa(x1, x2, x3, x4, x5) = U56_ggaa(x1, x2, x3, x5) row2colcG_in_gga(x1, x2, x3) = row2colcG_in_gga(x1, x2) row2colcG_out_gga(x1, x2, x3) = row2colcG_out_gga(x1, x2, x3) U72_gga(x1, x2, x3) = U72_gga(x1, x2, x3) U73_gga(x1, x2, x3, x4) = U73_gga(x1, x2, x4) U74_gga(x1, x2, x3, x4) = U74_gga(x1, x2, x3, x4) U75_gga(x1, x2, x3, x4, x5) = U75_gga(x1, x2, x3, x5) U76_gga(x1, x2, x3, x4, x5) = U76_gga(x1, x2, x3, x4, x5) U77_gga(x1, x2, x3, x4, x5, x6) = U77_gga(x1, x2, x3, x4, x6) U57_ggaa(x1, x2, x3, x4, x5, x6) = U57_ggaa(x1, x2, x3, x6) U58_ggaa(x1, x2, x3, x4, x5) = U58_ggaa(x1, x2, x3, x4, x5) U59_ggaa(x1, x2, x3, x4, x5, x6) = U59_ggaa(x1, x2, x3, x4, x6) U60_ggaa(x1, x2, x3, x4, x5, x6) = U60_ggaa(x1, x2, x3, x4, x6) U61_ggaa(x1, x2, x3, x4, x5, x6, x7) = U61_ggaa(x1, x2, x3, x4, x7) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) PH_IN_GAAAG(x1, x2, x3, x4, x5) = PH_IN_GAAAG(x1, x5) U38_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U38_GAAAG(x1, x5, x6, x7) We have to consider all (P,R,Pi)-chains ---------------------------------------- (92) UsableRulesProof (EQUIVALENT) For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R. ---------------------------------------- (93) Obligation: Pi DP problem: The TRS P consists of the following rules: PH_IN_GAAAG(X1, X2, X3, X4, .(X5, X6)) -> U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X1, X2, X3, X4)) U38_GAAAG(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X1, X2, X3, X4)) -> PH_IN_GAAAG(X5, X3, X7, X8, X6) The TRS R consists of the following rules: row2colcD_in_gaaa([], [], [], []) -> row2colcD_out_gaaa([], [], [], []) row2colcD_in_gaaa(.(X1, X2), [], [], []) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), []) -> U49_gaaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcD_in_gaaa(.(X1, X2), [], [], .([], X3)) -> U50_gaaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcD_in_gaaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_gaaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), []) -> U52_gaaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) row2colcD_in_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_gaaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], []) -> U54_gaaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), []) -> U55_gaaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), [], .([], X4)) -> U56_gaaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcD_in_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) -> U57_gaaa(X1, X2, X3, X4, X5, row2colcD_in_gaaa(X2, X3, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) -> U58_gaaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) -> U59_gaaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) -> U60_gaaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) row2colcD_in_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) -> U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_in_gaaa(X2, X4, X5, X6)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), [], [], []) U49_gaaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), []) U50_gaaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), [], [], .([], X3)) U51_gaaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .([], X3), .([], X4)) U52_gaaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), []) U53_gaaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), [], .(X3, X4), .([], X5)) U54_gaaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], []) U55_gaaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), []) U56_gaaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), [], .([], X4)) U57_gaaa(X1, X2, X3, X4, X5, row2colcD_out_gaaa(X2, X3, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3), .([], X4), .([], X5)) U58_gaaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], []) U59_gaaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), []) U60_gaaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), [], .([], X5)) U61_gaaa(X1, X2, X3, X4, X5, X6, row2colcD_out_gaaa(X2, X4, X5, X6)) -> row2colcD_out_gaaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5), .([], X6)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) row2colcB_in_ga([], []) -> row2colcB_out_ga([], []) row2colcB_in_ga(.(X1, X2), []) -> U43_ga(X1, X2, row2colcA_in_g(X2)) row2colcB_in_ga(.(X1, X2), .([], X3)) -> U44_ga(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcB_in_ga(.(X1, X2), .(X3, X4)) -> U45_ga(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) row2colcC_in_ga([], []) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2), []) -> U46_ga(X1, X2, row2colcA_in_g(X2)) row2colcC_in_ga(.(X1, X2), .([], X3)) -> U47_ga(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcD_in_ggaa([], [], [], []) -> row2colcD_out_ggaa([], [], [], []) row2colcD_in_ggaa(.(X1, X2), [], [], []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), []) -> U49_ggaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcD_in_ggaa(.(X1, X2), [], [], .([], X3)) -> U50_ggaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcD_in_ggaa(.(X1, X2), [], .([], X3), .([], X4)) -> U51_ggaa(X1, X2, X3, X4, row2colcD_in_ggaa(X2, [], X3, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), []) -> U52_ggaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) row2colcD_in_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) -> U53_ggaa(X1, X2, X3, X4, X5, row2colcD_in_ggaa(X2, [], X4, X5)) row2colcE_in_ga([], []) -> row2colcE_out_ga([], []) row2colcE_in_ga(.(X1, X2), []) -> U62_ga(X1, X2, row2colcA_in_g(X2)) row2colcE_in_ga(.(X1, X2), .([], X3)) -> U63_ga(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcE_in_ga(.(X1, X2), .(.(X1, X3), X4)) -> U64_ga(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) row2colcF_in_gaa([], [], []) -> row2colcF_out_gaa([], [], []) row2colcF_in_gaa(.(X1, X2), [], []) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) row2colcF_in_gaa(.(X1, X2), [], .([], X3)) -> U66_gaa(X1, X2, X3, row2colcB_in_ga(X2, X3)) row2colcF_in_gaa(.(X1, X2), [], .(X3, X4)) -> U67_gaa(X1, X2, X3, X4, row2colcB_in_ga(X2, X4)) row2colcF_in_gaa(.(X1, X2), .([], X3), []) -> U68_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcF_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U69_gaa(X1, X2, X3, X4, row2colcF_in_gaa(X2, X3, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U70_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) row2colcF_in_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) -> U71_gaa(X1, X2, X3, X4, X5, row2colcF_in_gaa(X2, X4, X5)) row2colcG_in_gaa([], [], []) -> row2colcG_out_gaa([], [], []) row2colcG_in_gaa(.(X1, X2), [], []) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) row2colcG_in_gaa(.(X1, X2), [], .([], X3)) -> U73_gaa(X1, X2, X3, row2colcC_in_ga(X2, X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), []) -> U74_gaa(X1, X2, X3, row2colcE_in_ga(X2, X3)) row2colcG_in_gaa(.(X1, X2), .([], X3), .([], X4)) -> U75_gaa(X1, X2, X3, X4, row2colcG_in_gaa(X2, X3, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), []) -> U76_gaa(X1, X2, X3, X4, row2colcE_in_ga(X2, X4)) row2colcG_in_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) -> U77_gaa(X1, X2, X3, X4, X5, row2colcG_in_gaa(X2, X4, X5)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2), []) U44_ga(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcB_out_ga(.(X1, X2), .([], X3)) U45_ga(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcB_out_ga(.(X1, X2), .(X3, X4)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) U47_ga(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], [], []) U49_ggaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), []) U50_ggaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], [], .([], X3)) U51_ggaa(X1, X2, X3, X4, row2colcD_out_ggaa(X2, [], X3, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3), .([], X4)) U52_ggaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), []) U53_ggaa(X1, X2, X3, X4, X5, row2colcD_out_ggaa(X2, [], X4, X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .(X3, X4), .([], X5)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2), []) U63_ga(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcE_out_ga(.(X1, X2), .([], X3)) U64_ga(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcE_out_ga(.(X1, X2), .(.(X1, X3), X4)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2), [], []) U66_gaa(X1, X2, X3, row2colcB_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), [], .([], X3)) U67_gaa(X1, X2, X3, X4, row2colcB_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), [], .(X3, X4)) U68_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), []) U69_gaa(X1, X2, X3, X4, row2colcF_out_gaa(X2, X3, X4)) -> row2colcF_out_gaa(.(X1, X2), .([], X3), .([], X4)) U70_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) U71_gaa(X1, X2, X3, X4, X5, row2colcF_out_gaa(X2, X4, X5)) -> row2colcF_out_gaa(.(X1, X2), .(.(X1, X3), X4), .(X3, X5)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), [], []) U73_gaa(X1, X2, X3, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), [], .([], X3)) U74_gaa(X1, X2, X3, row2colcE_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), []) U75_gaa(X1, X2, X3, X4, row2colcG_out_gaa(X2, X3, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X3), .([], X4)) U76_gaa(X1, X2, X3, X4, row2colcE_out_ga(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), []) U77_gaa(X1, X2, X3, X4, X5, row2colcG_out_gaa(X2, X4, X5)) -> row2colcG_out_gaa(.(X1, X2), .(.(X1, X3), X4), .([], X5)) The argument filtering Pi contains the following mapping: .(x1, x2) = .(x1, x2) [] = [] row2colcD_in_gaaa(x1, x2, x3, x4) = row2colcD_in_gaaa(x1) row2colcD_out_gaaa(x1, x2, x3, x4) = row2colcD_out_gaaa(x1, x4) U48_gaaa(x1, x2, x3) = U48_gaaa(x1, x2, x3) row2colcA_in_g(x1) = row2colcA_in_g(x1) row2colcA_out_g(x1) = row2colcA_out_g(x1) U42_g(x1, x2, x3) = U42_g(x1, x2, x3) U49_gaaa(x1, x2, x3, x4) = U49_gaaa(x1, x2, x4) row2colcB_in_ga(x1, x2) = row2colcB_in_ga(x1) row2colcB_out_ga(x1, x2) = row2colcB_out_ga(x1) U43_ga(x1, x2, x3) = U43_ga(x1, x2, x3) U44_ga(x1, x2, x3, x4) = U44_ga(x1, x2, x4) U45_ga(x1, x2, x3, x4, x5) = U45_ga(x1, x2, x5) U50_gaaa(x1, x2, x3, x4) = U50_gaaa(x1, x2, x4) row2colcC_in_ga(x1, x2) = row2colcC_in_ga(x1) row2colcC_out_ga(x1, x2) = row2colcC_out_ga(x1, x2) U46_ga(x1, x2, x3) = U46_ga(x1, x2, x3) U47_ga(x1, x2, x3, x4) = U47_ga(x1, x2, x4) U51_gaaa(x1, x2, x3, x4, x5) = U51_gaaa(x1, x2, x5) row2colcD_in_ggaa(x1, x2, x3, x4) = row2colcD_in_ggaa(x1, x2) row2colcD_out_ggaa(x1, x2, x3, x4) = row2colcD_out_ggaa(x1, x2, x4) U48_ggaa(x1, x2, x3) = U48_ggaa(x1, x2, x3) U49_ggaa(x1, x2, x3, x4) = U49_ggaa(x1, x2, x4) U50_ggaa(x1, x2, x3, x4) = U50_ggaa(x1, x2, x4) U51_ggaa(x1, x2, x3, x4, x5) = U51_ggaa(x1, x2, x5) U52_ggaa(x1, x2, x3, x4, x5) = U52_ggaa(x1, x2, x5) U53_ggaa(x1, x2, x3, x4, x5, x6) = U53_ggaa(x1, x2, x6) U52_gaaa(x1, x2, x3, x4, x5) = U52_gaaa(x1, x2, x5) U53_gaaa(x1, x2, x3, x4, x5, x6) = U53_gaaa(x1, x2, x6) U54_gaaa(x1, x2, x3, x4) = U54_gaaa(x1, x2, x4) row2colcE_in_ga(x1, x2) = row2colcE_in_ga(x1) row2colcE_out_ga(x1, x2) = row2colcE_out_ga(x1) U62_ga(x1, x2, x3) = U62_ga(x1, x2, x3) U63_ga(x1, x2, x3, x4) = U63_ga(x1, x2, x4) U64_ga(x1, x2, x3, x4, x5) = U64_ga(x1, x2, x5) U55_gaaa(x1, x2, x3, x4, x5) = U55_gaaa(x1, x2, x5) row2colcF_in_gaa(x1, x2, x3) = row2colcF_in_gaa(x1) row2colcF_out_gaa(x1, x2, x3) = row2colcF_out_gaa(x1) U65_gaa(x1, x2, x3) = U65_gaa(x1, x2, x3) U66_gaa(x1, x2, x3, x4) = U66_gaa(x1, x2, x4) U67_gaa(x1, x2, x3, x4, x5) = U67_gaa(x1, x2, x5) U68_gaa(x1, x2, x3, x4) = U68_gaa(x1, x2, x4) U69_gaa(x1, x2, x3, x4, x5) = U69_gaa(x1, x2, x5) U70_gaa(x1, x2, x3, x4, x5) = U70_gaa(x1, x2, x5) U71_gaa(x1, x2, x3, x4, x5, x6) = U71_gaa(x1, x2, x6) U56_gaaa(x1, x2, x3, x4, x5) = U56_gaaa(x1, x2, x5) row2colcG_in_gaa(x1, x2, x3) = row2colcG_in_gaa(x1) row2colcG_out_gaa(x1, x2, x3) = row2colcG_out_gaa(x1, x3) U72_gaa(x1, x2, x3) = U72_gaa(x1, x2, x3) U73_gaa(x1, x2, x3, x4) = U73_gaa(x1, x2, x4) U74_gaa(x1, x2, x3, x4) = U74_gaa(x1, x2, x4) U75_gaa(x1, x2, x3, x4, x5) = U75_gaa(x1, x2, x5) U76_gaa(x1, x2, x3, x4, x5) = U76_gaa(x1, x2, x5) U77_gaa(x1, x2, x3, x4, x5, x6) = U77_gaa(x1, x2, x6) U57_gaaa(x1, x2, x3, x4, x5, x6) = U57_gaaa(x1, x2, x6) U58_gaaa(x1, x2, x3, x4, x5) = U58_gaaa(x1, x2, x5) U59_gaaa(x1, x2, x3, x4, x5, x6) = U59_gaaa(x1, x2, x6) U60_gaaa(x1, x2, x3, x4, x5, x6) = U60_gaaa(x1, x2, x6) U61_gaaa(x1, x2, x3, x4, x5, x6, x7) = U61_gaaa(x1, x2, x7) PH_IN_GAAAG(x1, x2, x3, x4, x5) = PH_IN_GAAAG(x1, x5) U38_GAAAG(x1, x2, x3, x4, x5, x6, x7) = U38_GAAAG(x1, x5, x6, x7) We have to consider all (P,R,Pi)-chains ---------------------------------------- (94) PiDPToQDPProof (SOUND) Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi. ---------------------------------------- (95) Obligation: Q DP problem: The TRS P consists of the following rules: PH_IN_GAAAG(X1, .(X5, X6)) -> U38_GAAAG(X1, X5, X6, row2colcD_in_gaaa(X1)) U38_GAAAG(X1, X5, X6, row2colcD_out_gaaa(X1, X4)) -> PH_IN_GAAAG(X5, X6) The TRS R consists of the following rules: row2colcD_in_gaaa([]) -> row2colcD_out_gaaa([], []) row2colcD_in_gaaa(.(X1, X2)) -> U48_gaaa(X1, X2, row2colcA_in_g(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U49_gaaa(X1, X2, row2colcB_in_ga(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U50_gaaa(X1, X2, row2colcC_in_ga(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U51_gaaa(X1, X2, row2colcD_in_ggaa(X2, [])) row2colcD_in_gaaa(.(X1, X2)) -> U52_gaaa(X1, X2, row2colcB_in_ga(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U53_gaaa(X1, X2, row2colcD_in_ggaa(X2, [])) row2colcD_in_gaaa(.(X1, X2)) -> U54_gaaa(X1, X2, row2colcE_in_ga(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U55_gaaa(X1, X2, row2colcF_in_gaa(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U56_gaaa(X1, X2, row2colcG_in_gaa(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U57_gaaa(X1, X2, row2colcD_in_gaaa(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U58_gaaa(X1, X2, row2colcE_in_ga(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U59_gaaa(X1, X2, row2colcF_in_gaa(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U60_gaaa(X1, X2, row2colcG_in_gaa(X2)) row2colcD_in_gaaa(.(X1, X2)) -> U61_gaaa(X1, X2, row2colcD_in_gaaa(X2)) U48_gaaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_gaaa(.(X1, X2), []) U49_gaaa(X1, X2, row2colcB_out_ga(X2)) -> row2colcD_out_gaaa(.(X1, X2), []) U50_gaaa(X1, X2, row2colcC_out_ga(X2, X3)) -> row2colcD_out_gaaa(.(X1, X2), .([], X3)) U51_gaaa(X1, X2, row2colcD_out_ggaa(X2, [], X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X4)) U52_gaaa(X1, X2, row2colcB_out_ga(X2)) -> row2colcD_out_gaaa(.(X1, X2), []) U53_gaaa(X1, X2, row2colcD_out_ggaa(X2, [], X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X5)) U54_gaaa(X1, X2, row2colcE_out_ga(X2)) -> row2colcD_out_gaaa(.(X1, X2), []) U55_gaaa(X1, X2, row2colcF_out_gaa(X2)) -> row2colcD_out_gaaa(.(X1, X2), []) U56_gaaa(X1, X2, row2colcG_out_gaa(X2, X4)) -> row2colcD_out_gaaa(.(X1, X2), .([], X4)) U57_gaaa(X1, X2, row2colcD_out_gaaa(X2, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X5)) U58_gaaa(X1, X2, row2colcE_out_ga(X2)) -> row2colcD_out_gaaa(.(X1, X2), []) U59_gaaa(X1, X2, row2colcF_out_gaa(X2)) -> row2colcD_out_gaaa(.(X1, X2), []) U60_gaaa(X1, X2, row2colcG_out_gaa(X2, X5)) -> row2colcD_out_gaaa(.(X1, X2), .([], X5)) U61_gaaa(X1, X2, row2colcD_out_gaaa(X2, X6)) -> row2colcD_out_gaaa(.(X1, X2), .([], X6)) row2colcA_in_g([]) -> row2colcA_out_g([]) row2colcA_in_g(.(X1, X2)) -> U42_g(X1, X2, row2colcA_in_g(X2)) row2colcB_in_ga([]) -> row2colcB_out_ga([]) row2colcB_in_ga(.(X1, X2)) -> U43_ga(X1, X2, row2colcA_in_g(X2)) row2colcB_in_ga(.(X1, X2)) -> U44_ga(X1, X2, row2colcB_in_ga(X2)) row2colcB_in_ga(.(X1, X2)) -> U45_ga(X1, X2, row2colcB_in_ga(X2)) row2colcC_in_ga([]) -> row2colcC_out_ga([], []) row2colcC_in_ga(.(X1, X2)) -> U46_ga(X1, X2, row2colcA_in_g(X2)) row2colcC_in_ga(.(X1, X2)) -> U47_ga(X1, X2, row2colcC_in_ga(X2)) row2colcD_in_ggaa([], []) -> row2colcD_out_ggaa([], [], []) row2colcD_in_ggaa(.(X1, X2), []) -> U48_ggaa(X1, X2, row2colcA_in_g(X2)) row2colcD_in_ggaa(.(X1, X2), []) -> U49_ggaa(X1, X2, row2colcB_in_ga(X2)) row2colcD_in_ggaa(.(X1, X2), []) -> U50_ggaa(X1, X2, row2colcC_in_ga(X2)) row2colcD_in_ggaa(.(X1, X2), []) -> U51_ggaa(X1, X2, row2colcD_in_ggaa(X2, [])) row2colcD_in_ggaa(.(X1, X2), []) -> U52_ggaa(X1, X2, row2colcB_in_ga(X2)) row2colcD_in_ggaa(.(X1, X2), []) -> U53_ggaa(X1, X2, row2colcD_in_ggaa(X2, [])) row2colcE_in_ga([]) -> row2colcE_out_ga([]) row2colcE_in_ga(.(X1, X2)) -> U62_ga(X1, X2, row2colcA_in_g(X2)) row2colcE_in_ga(.(X1, X2)) -> U63_ga(X1, X2, row2colcE_in_ga(X2)) row2colcE_in_ga(.(X1, X2)) -> U64_ga(X1, X2, row2colcE_in_ga(X2)) row2colcF_in_gaa([]) -> row2colcF_out_gaa([]) row2colcF_in_gaa(.(X1, X2)) -> U65_gaa(X1, X2, row2colcA_in_g(X2)) row2colcF_in_gaa(.(X1, X2)) -> U66_gaa(X1, X2, row2colcB_in_ga(X2)) row2colcF_in_gaa(.(X1, X2)) -> U67_gaa(X1, X2, row2colcB_in_ga(X2)) row2colcF_in_gaa(.(X1, X2)) -> U68_gaa(X1, X2, row2colcE_in_ga(X2)) row2colcF_in_gaa(.(X1, X2)) -> U69_gaa(X1, X2, row2colcF_in_gaa(X2)) row2colcF_in_gaa(.(X1, X2)) -> U70_gaa(X1, X2, row2colcE_in_ga(X2)) row2colcF_in_gaa(.(X1, X2)) -> U71_gaa(X1, X2, row2colcF_in_gaa(X2)) row2colcG_in_gaa([]) -> row2colcG_out_gaa([], []) row2colcG_in_gaa(.(X1, X2)) -> U72_gaa(X1, X2, row2colcA_in_g(X2)) row2colcG_in_gaa(.(X1, X2)) -> U73_gaa(X1, X2, row2colcC_in_ga(X2)) row2colcG_in_gaa(.(X1, X2)) -> U74_gaa(X1, X2, row2colcE_in_ga(X2)) row2colcG_in_gaa(.(X1, X2)) -> U75_gaa(X1, X2, row2colcG_in_gaa(X2)) row2colcG_in_gaa(.(X1, X2)) -> U76_gaa(X1, X2, row2colcE_in_ga(X2)) row2colcG_in_gaa(.(X1, X2)) -> U77_gaa(X1, X2, row2colcG_in_gaa(X2)) U42_g(X1, X2, row2colcA_out_g(X2)) -> row2colcA_out_g(.(X1, X2)) U43_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcB_out_ga(.(X1, X2)) U44_ga(X1, X2, row2colcB_out_ga(X2)) -> row2colcB_out_ga(.(X1, X2)) U45_ga(X1, X2, row2colcB_out_ga(X2)) -> row2colcB_out_ga(.(X1, X2)) U46_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcC_out_ga(.(X1, X2), []) U47_ga(X1, X2, row2colcC_out_ga(X2, X3)) -> row2colcC_out_ga(.(X1, X2), .([], X3)) U48_ggaa(X1, X2, row2colcA_out_g(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], []) U49_ggaa(X1, X2, row2colcB_out_ga(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], []) U50_ggaa(X1, X2, row2colcC_out_ga(X2, X3)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X3)) U51_ggaa(X1, X2, row2colcD_out_ggaa(X2, [], X4)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X4)) U52_ggaa(X1, X2, row2colcB_out_ga(X2)) -> row2colcD_out_ggaa(.(X1, X2), [], []) U53_ggaa(X1, X2, row2colcD_out_ggaa(X2, [], X5)) -> row2colcD_out_ggaa(.(X1, X2), [], .([], X5)) U62_ga(X1, X2, row2colcA_out_g(X2)) -> row2colcE_out_ga(.(X1, X2)) U63_ga(X1, X2, row2colcE_out_ga(X2)) -> row2colcE_out_ga(.(X1, X2)) U64_ga(X1, X2, row2colcE_out_ga(X2)) -> row2colcE_out_ga(.(X1, X2)) U65_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcF_out_gaa(.(X1, X2)) U66_gaa(X1, X2, row2colcB_out_ga(X2)) -> row2colcF_out_gaa(.(X1, X2)) U67_gaa(X1, X2, row2colcB_out_ga(X2)) -> row2colcF_out_gaa(.(X1, X2)) U68_gaa(X1, X2, row2colcE_out_ga(X2)) -> row2colcF_out_gaa(.(X1, X2)) U69_gaa(X1, X2, row2colcF_out_gaa(X2)) -> row2colcF_out_gaa(.(X1, X2)) U70_gaa(X1, X2, row2colcE_out_ga(X2)) -> row2colcF_out_gaa(.(X1, X2)) U71_gaa(X1, X2, row2colcF_out_gaa(X2)) -> row2colcF_out_gaa(.(X1, X2)) U72_gaa(X1, X2, row2colcA_out_g(X2)) -> row2colcG_out_gaa(.(X1, X2), []) U73_gaa(X1, X2, row2colcC_out_ga(X2, X3)) -> row2colcG_out_gaa(.(X1, X2), .([], X3)) U74_gaa(X1, X2, row2colcE_out_ga(X2)) -> row2colcG_out_gaa(.(X1, X2), []) U75_gaa(X1, X2, row2colcG_out_gaa(X2, X4)) -> row2colcG_out_gaa(.(X1, X2), .([], X4)) U76_gaa(X1, X2, row2colcE_out_ga(X2)) -> row2colcG_out_gaa(.(X1, X2), []) U77_gaa(X1, X2, row2colcG_out_gaa(X2, X5)) -> row2colcG_out_gaa(.(X1, X2), .([], X5)) The set Q consists of the following terms: row2colcD_in_gaaa(x0) U48_gaaa(x0, x1, x2) U49_gaaa(x0, x1, x2) U50_gaaa(x0, x1, x2) U51_gaaa(x0, x1, x2) U52_gaaa(x0, x1, x2) U53_gaaa(x0, x1, x2) U54_gaaa(x0, x1, x2) U55_gaaa(x0, x1, x2) U56_gaaa(x0, x1, x2) U57_gaaa(x0, x1, x2) U58_gaaa(x0, x1, x2) U59_gaaa(x0, x1, x2) U60_gaaa(x0, x1, x2) U61_gaaa(x0, x1, x2) row2colcA_in_g(x0) row2colcB_in_ga(x0) row2colcC_in_ga(x0) row2colcD_in_ggaa(x0, x1) row2colcE_in_ga(x0) row2colcF_in_gaa(x0) row2colcG_in_gaa(x0) U42_g(x0, x1, x2) U43_ga(x0, x1, x2) U44_ga(x0, x1, x2) U45_ga(x0, x1, x2) U46_ga(x0, x1, x2) U47_ga(x0, x1, x2) U48_ggaa(x0, x1, x2) U49_ggaa(x0, x1, x2) U50_ggaa(x0, x1, x2) U51_ggaa(x0, x1, x2) U52_ggaa(x0, x1, x2) U53_ggaa(x0, x1, x2) U62_ga(x0, x1, x2) U63_ga(x0, x1, x2) U64_ga(x0, x1, x2) U65_gaa(x0, x1, x2) U66_gaa(x0, x1, x2) U67_gaa(x0, x1, x2) U68_gaa(x0, x1, x2) U69_gaa(x0, x1, x2) U70_gaa(x0, x1, x2) U71_gaa(x0, x1, x2) U72_gaa(x0, x1, x2) U73_gaa(x0, x1, x2) U74_gaa(x0, x1, x2) U75_gaa(x0, x1, x2) U76_gaa(x0, x1, x2) U77_gaa(x0, x1, x2) We have to consider all (P,Q,R)-chains. ---------------------------------------- (96) QDPSizeChangeProof (EQUIVALENT) 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. From the DPs we obtained the following set of size-change graphs: *U38_GAAAG(X1, X5, X6, row2colcD_out_gaaa(X1, X4)) -> PH_IN_GAAAG(X5, X6) The graph contains the following edges 2 >= 1, 3 >= 2 *PH_IN_GAAAG(X1, .(X5, X6)) -> U38_GAAAG(X1, X5, X6, row2colcD_in_gaaa(X1)) The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3 ---------------------------------------- (97) YES