Left Termination of the query pattern transpose_in_2(g, a) w.r.t. the given Prolog program could successfully be proven:

0 Prolog
↳1 PrologToDTProblemTransformerProof (⇐)
↳2 TRIPLES
↳3 TriplesToPiDPProof (⇐)
↳4 PiDP
↳5 DependencyGraphProof (⇔)
↳6 AND
    ↳7 PiDP
        ↳8 UsableRulesProof (⇔)
        ↳9 PiDP
        ↳10 PiDPToQDPProof (⇔)
        ↳11 QDP
        ↳12 QDPSizeChangeProof (⇔)
        ↳13 YES
    ↳14 PiDP
        ↳15 UsableRulesProof (⇔)
        ↳16 PiDP
        ↳17 PiDPToQDPProof (⇐)
        ↳18 QDP
        ↳19 QDPSizeChangeProof (⇔)
        ↳20 YES
    ↳21 PiDP
        ↳22 UsableRulesProof (⇔)
        ↳23 PiDP
        ↳24 PiDPToQDPProof (⇐)
        ↳25 QDP
        ↳26 QDPSizeChangeProof (⇔)
        ↳27 YES
    ↳28 PiDP
        ↳29 UsableRulesProof (⇔)
        ↳30 PiDP
        ↳31 PiDPToQDPProof (⇐)
        ↳32 QDP
        ↳33 QDPSizeChangeProof (⇔)
        ↳34 YES
    ↳35 PiDP
        ↳36 UsableRulesProof (⇔)
        ↳37 PiDP
        ↳38 PiDPToQDPProof (⇐)
        ↳39 QDP
        ↳40 QDPSizeChangeProof (⇔)
        ↳41 YES
    ↳42 PiDP
        ↳43 UsableRulesProof (⇔)
        ↳44 PiDP
        ↳45 PiDPToQDPProof (⇐)
        ↳46 QDP
        ↳47 QDPSizeChangeProof (⇔)
        ↳48 YES
    ↳49 PiDP
        ↳50 UsableRulesProof (⇔)
        ↳51 PiDP
        ↳52 PiDPToQDPProof (⇐)
        ↳53 QDP
        ↳54 QDPSizeChangeProof (⇔)
        ↳55 YES
    ↳56 PiDP
        ↳57 UsableRulesProof (⇔)
        ↳58 PiDP
        ↳59 PiDPToQDPProof (⇐)
        ↳60 QDP
        ↳61 QDPSizeChangeProof (⇔)
        ↳62 YES
    ↳63 PiDP
        ↳64 PiDPToQDPProof (⇐)
        ↳65 QDP
        ↳66 QDPSizeChangeProof (⇔)
        ↳67 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).

Queries:

transpose(g,a).

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

(2) Obligation:

Triples:

row2col74(.(T90, T91)) :- row2col74(T91).
row2col74(.(T103, T100)) :- row2col74(T100).
row2col174(.(T122, T123), []) :- row2col74(T123).
row2col174(.(T122, T123), .([], X1080)) :- row2col174(T123, X1080).
row2col174(.(T135, T132), []) :- row2col74(T132).
row2col174(.(T135, T132), .(X1292, X1293)) :- row2col174(T132, X1293).
row2col306(.(T160, T161), []) :- row2col74(T161).
row2col306(.(T166, T167), .([], X1819)) :- row2col306(T167, X1819).
row2col306(.(T179, T176), []) :- row2col74(T176).
row2col306(.(T188, T185), .([], X2110)) :- row2col306(T185, X2110).
row2col454(.(T207, T208), [], []) :- row2col74(T208).
row2col454(.(T207, T208), .([], X2480), []) :- row2col174(T208, X2480).
row2col454(.(T213, T214), [], .([], X2620)) :- row2col306(T214, X2620).
row2col454(.(T213, T214), .([], X2662), .([], X2681)) :- row2col454(T214, X2662, X2681).
row2col454(.(T226, T223), [], []) :- row2col74(T223).
row2col454(.(T226, T223), .(X2877, X2878), []) :- row2col174(T223, X2878).
row2col454(.(T235, T232), [], .([], X3025)) :- row2col306(T232, X3025).
row2col454(.(T235, T232), .(X3069, X3070), .([], X3089)) :- row2col454(T232, X3070, X3089).
row2col727(.(T326, T327), []) :- row2col74(T327).
row2col727(.(T339, T336), []) :- row2col74(T336).
row2col727(.(T358, T359), .([], T365)) :- row2col727(T359, T365).
row2col727(.(T415, T392), .(.(T415, T428), T429)) :- row2col727(T392, T429).
row2col897(.(T474, T475), [], []) :- row2col74(T475).
row2col897(.(T474, T475), [], .([], X4661)) :- row2col174(T475, X4661).
row2col897(.(T487, T484), [], []) :- row2col74(T484).
row2col897(.(T487, T484), [], .(X4873, X4874)) :- row2col174(T484, X4874).
row2col897(.(T506, T507), .([], T513), []) :- row2col727(T507, T513).
row2col897(.(T506, T507), .([], T513), .([], X5076)) :- row2col897(T507, T513, X5076).
row2col897(.(T570, T547), .(.(T570, T583), T584), []) :- row2col727(T547, T584).
row2col897(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) :- row2col897(T547, T606, X5267).
row2col1113(.(T665, T666), [], []) :- row2col74(T666).
row2col1113(.(T671, T672), [], .([], X5778)) :- row2col306(T672, X5778).
row2col1113(.(T684, T681), [], []) :- row2col74(T681).
row2col1113(.(T693, T690), [], .([], X6069)) :- row2col306(T690, X6069).
row2col1113(.(T712, T713), .([], T719), []) :- row2col727(T713, T719).
row2col1113(.(T737, T738), .([], T744), .([], X6344)) :- row2col1113(T738, T744, X6344).
row2col1113(.(T793, T770), .(.(T793, T806), T807), []) :- row2col727(T770, T807).
row2col1113(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) :- row2col1113(T820, T857, X6607).
row2col20(.(T70, T71), [], [], []) :- row2col74(T71).
row2col20(.(T70, T71), [], .([], X776), []) :- row2col174(T71, X776).
row2col20(.(T140, T141), [], [], .([], X1441)) :- row2col306(T141, X1441).
row2col20(.(T140, T141), [], .([], X2160), .([], X2179)) :- row2col454(T141, X2160, X2179).
row2col20(.(T247, T244), [], [], []) :- row2col74(T244).
row2col20(.(T247, T244), [], .(X3289, X3290), []) :- row2col174(T244, X3290).
row2col20(.(T256, T253), [], [], .([], X3437)) :- row2col306(T253, X3437).
row2col20(.(T256, T253), [], .(X3481, X3482), .([], X3501)) :- row2col454(T253, X3482, X3501).
row2col20(.(T275, T276), .([], T282), [], []) :- row2col727(T276, T282).
row2col20(.(T275, T276), .([], T282), .([], X4367), []) :- row2col897(T276, T282, X4367).
row2col20(.(T615, T616), .([], T622), [], .([], X5410)) :- row2col1113(T616, T622, X5410).
row2col20(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) :- row2col20(T616, T622, X6653, X6672).
row2col20(.(T906, T883), .(.(T906, T919), T920), [], []) :- row2col727(T883, T920).
row2col20(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) :- row2col897(T883, T942, X6847).
row2col20(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) :- row2col1113(T952, T989, X6985).
row2col20(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) :- row2col20(T952, T1010, X7027, X7046).
p19(T34, T20, X41, X42, T35) :- row2col20(T34, T20, X41, X42).
p19(T34, T20, T1038, T1036, .(T1052, T1053)) :- ','(row2colc20(T34, T20, T1038, T1036), p19(T1052, T1038, X7086, X7087, T1053)).
transpose1(.(T34, T35), T20) :- p19(T34, T20, X41, X42, T35).

Clauses:

row2colc74([]).
row2colc74(.(T90, T91)) :- row2colc74(T91).
row2colc74(.(T103, T100)) :- row2colc74(T100).
row2colc174([], []).
row2colc174(.(T122, T123), []) :- row2colc74(T123).
row2colc174(.(T122, T123), .([], X1080)) :- row2colc174(T123, X1080).
row2colc174(.(T135, T132), []) :- row2colc74(T132).
row2colc174(.(T135, T132), .(X1292, X1293)) :- row2colc174(T132, X1293).
row2colc306([], []).
row2colc306(.(T160, T161), []) :- row2colc74(T161).
row2colc306(.(T166, T167), .([], X1819)) :- row2colc306(T167, X1819).
row2colc306(.(T179, T176), []) :- row2colc74(T176).
row2colc306(.(T188, T185), .([], X2110)) :- row2colc306(T185, X2110).
row2colc454([], [], []).
row2colc454(.(T207, T208), [], []) :- row2colc74(T208).
row2colc454(.(T207, T208), .([], X2480), []) :- row2colc174(T208, X2480).
row2colc454(.(T213, T214), [], .([], X2620)) :- row2colc306(T214, X2620).
row2colc454(.(T213, T214), .([], X2662), .([], X2681)) :- row2colc454(T214, X2662, X2681).
row2colc454(.(T226, T223), [], []) :- row2colc74(T223).
row2colc454(.(T226, T223), .(X2877, X2878), []) :- row2colc174(T223, X2878).
row2colc454(.(T235, T232), [], .([], X3025)) :- row2colc306(T232, X3025).
row2colc454(.(T235, T232), .(X3069, X3070), .([], X3089)) :- row2colc454(T232, X3070, X3089).
row2colc727([], []).
row2colc727(.(T326, T327), []) :- row2colc74(T327).
row2colc727(.(T339, T336), []) :- row2colc74(T336).
row2colc727(.(T358, T359), .([], T365)) :- row2colc727(T359, T365).
row2colc727(.(T415, T392), .(.(T415, T428), T429)) :- row2colc727(T392, T429).
row2colc897([], [], []).
row2colc897(.(T474, T475), [], []) :- row2colc74(T475).
row2colc897(.(T474, T475), [], .([], X4661)) :- row2colc174(T475, X4661).
row2colc897(.(T487, T484), [], []) :- row2colc74(T484).
row2colc897(.(T487, T484), [], .(X4873, X4874)) :- row2colc174(T484, X4874).
row2colc897(.(T506, T507), .([], T513), []) :- row2colc727(T507, T513).
row2colc897(.(T506, T507), .([], T513), .([], X5076)) :- row2colc897(T507, T513, X5076).
row2colc897(.(T570, T547), .(.(T570, T583), T584), []) :- row2colc727(T547, T584).
row2colc897(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) :- row2colc897(T547, T606, X5267).
row2colc1113([], [], []).
row2colc1113(.(T665, T666), [], []) :- row2colc74(T666).
row2colc1113(.(T671, T672), [], .([], X5778)) :- row2colc306(T672, X5778).
row2colc1113(.(T684, T681), [], []) :- row2colc74(T681).
row2colc1113(.(T693, T690), [], .([], X6069)) :- row2colc306(T690, X6069).
row2colc1113(.(T712, T713), .([], T719), []) :- row2colc727(T713, T719).
row2colc1113(.(T737, T738), .([], T744), .([], X6344)) :- row2colc1113(T738, T744, X6344).
row2colc1113(.(T793, T770), .(.(T793, T806), T807), []) :- row2colc727(T770, T807).
row2colc1113(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) :- row2colc1113(T820, T857, X6607).
row2colc20([], [], [], []).
row2colc20(.(T70, T71), [], [], []) :- row2colc74(T71).
row2colc20(.(T70, T71), [], .([], X776), []) :- row2colc174(T71, X776).
row2colc20(.(T140, T141), [], [], .([], X1441)) :- row2colc306(T141, X1441).
row2colc20(.(T140, T141), [], .([], X2160), .([], X2179)) :- row2colc454(T141, X2160, X2179).
row2colc20(.(T247, T244), [], [], []) :- row2colc74(T244).
row2colc20(.(T247, T244), [], .(X3289, X3290), []) :- row2colc174(T244, X3290).
row2colc20(.(T256, T253), [], [], .([], X3437)) :- row2colc306(T253, X3437).
row2colc20(.(T256, T253), [], .(X3481, X3482), .([], X3501)) :- row2colc454(T253, X3482, X3501).
row2colc20(.(T275, T276), .([], T282), [], []) :- row2colc727(T276, T282).
row2colc20(.(T275, T276), .([], T282), .([], X4367), []) :- row2colc897(T276, T282, X4367).
row2colc20(.(T615, T616), .([], T622), [], .([], X5410)) :- row2colc1113(T616, T622, X5410).
row2colc20(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) :- row2colc20(T616, T622, X6653, X6672).
row2colc20(.(T906, T883), .(.(T906, T919), T920), [], []) :- row2colc727(T883, T920).
row2colc20(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) :- row2colc897(T883, T942, X6847).
row2colc20(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) :- row2colc1113(T952, T989, X6985).
row2colc20(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) :- row2colc20(T952, T1010, X7027, X7046).
qc19(T34, T20, T1026, T1026, []) :- row2colc20(T34, T20, T1026, T1026).
qc19(T34, T20, T1038, T1036, .(T1052, T1053)) :- ','(row2colc20(T34, T20, T1038, T1036), qc19(T1052, T1038, X7086, X7087, T1053)).

Afs:

transpose1(x1, x2)  =  transpose1(x1)

(3) TriplesToPiDPProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
transpose1_in: (b,f)
p19_in: (b,f,f,f,b)
row2col20_in: (b,f,f,f)
row2col74_in: (b)
row2col174_in: (b,f)
row2col306_in: (b,f)
row2col454_in: (b,f,f)
row2col727_in: (b,f)
row2col897_in: (b,f,f)
row2col1113_in: (b,f,f)
row2colc20_in: (b,f,f,f)
row2colc74_in: (b)
row2colc174_in: (b,f)
row2colc306_in: (b,f)
row2colc454_in: (b,f,f)
row2colc727_in: (b,f)
row2colc897_in: (b,f,f)
row2colc1113_in: (b,f,f)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

TRANSPOSE1_IN_GA(.(T34, T35), T20) → U58_GA(T34, T35, T20, p19_in_gaaag(T34, T20, X41, X42, T35))
TRANSPOSE1_IN_GA(.(T34, T35), T20) → P19_IN_GAAAG(T34, T20, X41, X42, T35)
P19_IN_GAAAG(T34, T20, X41, X42, T35) → U55_GAAAG(T34, T20, X41, X42, T35, row2col20_in_gaaa(T34, T20, X41, X42))
P19_IN_GAAAG(T34, T20, X41, X42, T35) → ROW2COL20_IN_GAAA(T34, T20, X41, X42)
ROW2COL20_IN_GAAA(.(T70, T71), [], [], []) → U39_GAAA(T70, T71, row2col74_in_g(T71))
ROW2COL20_IN_GAAA(.(T70, T71), [], [], []) → ROW2COL74_IN_G(T71)
ROW2COL74_IN_G(.(T90, T91)) → U1_G(T90, T91, row2col74_in_g(T91))
ROW2COL74_IN_G(.(T90, T91)) → ROW2COL74_IN_G(T91)
ROW2COL74_IN_G(.(T103, T100)) → U2_G(T103, T100, row2col74_in_g(T100))
ROW2COL20_IN_GAAA(.(T70, T71), [], .([], X776), []) → U40_GAAA(T70, T71, X776, row2col174_in_ga(T71, X776))
ROW2COL20_IN_GAAA(.(T70, T71), [], .([], X776), []) → ROW2COL174_IN_GA(T71, X776)
ROW2COL174_IN_GA(.(T122, T123), []) → U3_GA(T122, T123, row2col74_in_g(T123))
ROW2COL174_IN_GA(.(T122, T123), []) → ROW2COL74_IN_G(T123)
ROW2COL174_IN_GA(.(T122, T123), .([], X1080)) → U4_GA(T122, T123, X1080, row2col174_in_ga(T123, X1080))
ROW2COL174_IN_GA(.(T122, T123), .([], X1080)) → ROW2COL174_IN_GA(T123, X1080)
ROW2COL174_IN_GA(.(T135, T132), []) → U5_GA(T135, T132, row2col74_in_g(T132))
ROW2COL174_IN_GA(.(T135, T132), .(X1292, X1293)) → U6_GA(T135, T132, X1292, X1293, row2col174_in_ga(T132, X1293))
ROW2COL174_IN_GA(.(T135, T132), .(X1292, X1293)) → ROW2COL174_IN_GA(T132, X1293)
ROW2COL20_IN_GAAA(.(T140, T141), [], [], .([], X1441)) → U41_GAAA(T140, T141, X1441, row2col306_in_ga(T141, X1441))
ROW2COL20_IN_GAAA(.(T140, T141), [], [], .([], X1441)) → ROW2COL306_IN_GA(T141, X1441)
ROW2COL306_IN_GA(.(T160, T161), []) → U7_GA(T160, T161, row2col74_in_g(T161))
ROW2COL306_IN_GA(.(T160, T161), []) → ROW2COL74_IN_G(T161)
ROW2COL306_IN_GA(.(T166, T167), .([], X1819)) → U8_GA(T166, T167, X1819, row2col306_in_ga(T167, X1819))
ROW2COL306_IN_GA(.(T166, T167), .([], X1819)) → ROW2COL306_IN_GA(T167, X1819)
ROW2COL306_IN_GA(.(T179, T176), []) → U9_GA(T179, T176, row2col74_in_g(T176))
ROW2COL306_IN_GA(.(T188, T185), .([], X2110)) → U10_GA(T188, T185, X2110, row2col306_in_ga(T185, X2110))
ROW2COL20_IN_GAAA(.(T140, T141), [], .([], X2160), .([], X2179)) → U42_GAAA(T140, T141, X2160, X2179, row2col454_in_gaa(T141, X2160, X2179))
ROW2COL20_IN_GAAA(.(T140, T141), [], .([], X2160), .([], X2179)) → ROW2COL454_IN_GAA(T141, X2160, X2179)
ROW2COL454_IN_GAA(.(T207, T208), [], []) → U11_GAA(T207, T208, row2col74_in_g(T208))
ROW2COL454_IN_GAA(.(T207, T208), [], []) → ROW2COL74_IN_G(T208)
ROW2COL454_IN_GAA(.(T207, T208), .([], X2480), []) → U12_GAA(T207, T208, X2480, row2col174_in_ga(T208, X2480))
ROW2COL454_IN_GAA(.(T207, T208), .([], X2480), []) → ROW2COL174_IN_GA(T208, X2480)
ROW2COL454_IN_GAA(.(T213, T214), [], .([], X2620)) → U13_GAA(T213, T214, X2620, row2col306_in_ga(T214, X2620))
ROW2COL454_IN_GAA(.(T213, T214), [], .([], X2620)) → ROW2COL306_IN_GA(T214, X2620)
ROW2COL454_IN_GAA(.(T213, T214), .([], X2662), .([], X2681)) → U14_GAA(T213, T214, X2662, X2681, row2col454_in_gaa(T214, X2662, X2681))
ROW2COL454_IN_GAA(.(T213, T214), .([], X2662), .([], X2681)) → ROW2COL454_IN_GAA(T214, X2662, X2681)
ROW2COL454_IN_GAA(.(T226, T223), [], []) → U15_GAA(T226, T223, row2col74_in_g(T223))
ROW2COL454_IN_GAA(.(T226, T223), .(X2877, X2878), []) → U16_GAA(T226, T223, X2877, X2878, row2col174_in_ga(T223, X2878))
ROW2COL454_IN_GAA(.(T226, T223), .(X2877, X2878), []) → ROW2COL174_IN_GA(T223, X2878)
ROW2COL454_IN_GAA(.(T235, T232), [], .([], X3025)) → U17_GAA(T235, T232, X3025, row2col306_in_ga(T232, X3025))
ROW2COL454_IN_GAA(.(T235, T232), .(X3069, X3070), .([], X3089)) → U18_GAA(T235, T232, X3069, X3070, X3089, row2col454_in_gaa(T232, X3070, X3089))
ROW2COL454_IN_GAA(.(T235, T232), .(X3069, X3070), .([], X3089)) → ROW2COL454_IN_GAA(T232, X3070, X3089)
ROW2COL20_IN_GAAA(.(T247, T244), [], [], []) → U43_GAAA(T247, T244, row2col74_in_g(T244))
ROW2COL20_IN_GAAA(.(T247, T244), [], .(X3289, X3290), []) → U44_GAAA(T247, T244, X3289, X3290, row2col174_in_ga(T244, X3290))
ROW2COL20_IN_GAAA(.(T247, T244), [], .(X3289, X3290), []) → ROW2COL174_IN_GA(T244, X3290)
ROW2COL20_IN_GAAA(.(T256, T253), [], [], .([], X3437)) → U45_GAAA(T256, T253, X3437, row2col306_in_ga(T253, X3437))
ROW2COL20_IN_GAAA(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U46_GAAA(T256, T253, X3481, X3482, X3501, row2col454_in_gaa(T253, X3482, X3501))
ROW2COL20_IN_GAAA(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → ROW2COL454_IN_GAA(T253, X3482, X3501)
ROW2COL20_IN_GAAA(.(T275, T276), .([], T282), [], []) → U47_GAAA(T275, T276, T282, row2col727_in_ga(T276, T282))
ROW2COL20_IN_GAAA(.(T275, T276), .([], T282), [], []) → ROW2COL727_IN_GA(T276, T282)
ROW2COL727_IN_GA(.(T326, T327), []) → U19_GA(T326, T327, row2col74_in_g(T327))
ROW2COL727_IN_GA(.(T326, T327), []) → ROW2COL74_IN_G(T327)
ROW2COL727_IN_GA(.(T339, T336), []) → U20_GA(T339, T336, row2col74_in_g(T336))
ROW2COL727_IN_GA(.(T358, T359), .([], T365)) → U21_GA(T358, T359, T365, row2col727_in_ga(T359, T365))
ROW2COL727_IN_GA(.(T358, T359), .([], T365)) → ROW2COL727_IN_GA(T359, T365)
ROW2COL727_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → U22_GA(T415, T392, T428, T429, row2col727_in_ga(T392, T429))
ROW2COL727_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → ROW2COL727_IN_GA(T392, T429)
ROW2COL20_IN_GAAA(.(T275, T276), .([], T282), .([], X4367), []) → U48_GAAA(T275, T276, T282, X4367, row2col897_in_gaa(T276, T282, X4367))
ROW2COL20_IN_GAAA(.(T275, T276), .([], T282), .([], X4367), []) → ROW2COL897_IN_GAA(T276, T282, X4367)
ROW2COL897_IN_GAA(.(T474, T475), [], []) → U23_GAA(T474, T475, row2col74_in_g(T475))
ROW2COL897_IN_GAA(.(T474, T475), [], []) → ROW2COL74_IN_G(T475)
ROW2COL897_IN_GAA(.(T474, T475), [], .([], X4661)) → U24_GAA(T474, T475, X4661, row2col174_in_ga(T475, X4661))
ROW2COL897_IN_GAA(.(T474, T475), [], .([], X4661)) → ROW2COL174_IN_GA(T475, X4661)
ROW2COL897_IN_GAA(.(T487, T484), [], []) → U25_GAA(T487, T484, row2col74_in_g(T484))
ROW2COL897_IN_GAA(.(T487, T484), [], .(X4873, X4874)) → U26_GAA(T487, T484, X4873, X4874, row2col174_in_ga(T484, X4874))
ROW2COL897_IN_GAA(.(T487, T484), [], .(X4873, X4874)) → ROW2COL174_IN_GA(T484, X4874)
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), []) → U27_GAA(T506, T507, T513, row2col727_in_ga(T507, T513))
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), []) → ROW2COL727_IN_GA(T507, T513)
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), .([], X5076)) → U28_GAA(T506, T507, T513, X5076, row2col897_in_gaa(T507, T513, X5076))
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), .([], X5076)) → ROW2COL897_IN_GAA(T507, T513, X5076)
ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T583), T584), []) → U29_GAA(T570, T547, T583, T584, row2col727_in_ga(T547, T584))
ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T583), T584), []) → ROW2COL727_IN_GA(T547, T584)
ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U30_GAA(T570, T547, T605, T606, X5267, row2col897_in_gaa(T547, T606, X5267))
ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → ROW2COL897_IN_GAA(T547, T606, X5267)
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), [], .([], X5410)) → U49_GAAA(T615, T616, T622, X5410, row2col1113_in_gaa(T616, T622, X5410))
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), [], .([], X5410)) → ROW2COL1113_IN_GAA(T616, T622, X5410)
ROW2COL1113_IN_GAA(.(T665, T666), [], []) → U31_GAA(T665, T666, row2col74_in_g(T666))
ROW2COL1113_IN_GAA(.(T665, T666), [], []) → ROW2COL74_IN_G(T666)
ROW2COL1113_IN_GAA(.(T671, T672), [], .([], X5778)) → U32_GAA(T671, T672, X5778, row2col306_in_ga(T672, X5778))
ROW2COL1113_IN_GAA(.(T671, T672), [], .([], X5778)) → ROW2COL306_IN_GA(T672, X5778)
ROW2COL1113_IN_GAA(.(T684, T681), [], []) → U33_GAA(T684, T681, row2col74_in_g(T681))
ROW2COL1113_IN_GAA(.(T693, T690), [], .([], X6069)) → U34_GAA(T693, T690, X6069, row2col306_in_ga(T690, X6069))
ROW2COL1113_IN_GAA(.(T712, T713), .([], T719), []) → U35_GAA(T712, T713, T719, row2col727_in_ga(T713, T719))
ROW2COL1113_IN_GAA(.(T712, T713), .([], T719), []) → ROW2COL727_IN_GA(T713, T719)
ROW2COL1113_IN_GAA(.(T737, T738), .([], T744), .([], X6344)) → U36_GAA(T737, T738, T744, X6344, row2col1113_in_gaa(T738, T744, X6344))
ROW2COL1113_IN_GAA(.(T737, T738), .([], T744), .([], X6344)) → ROW2COL1113_IN_GAA(T738, T744, X6344)
ROW2COL1113_IN_GAA(.(T793, T770), .(.(T793, T806), T807), []) → U37_GAA(T793, T770, T806, T807, row2col727_in_ga(T770, T807))
ROW2COL1113_IN_GAA(.(T793, T770), .(.(T793, T806), T807), []) → ROW2COL727_IN_GA(T770, T807)
ROW2COL1113_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U38_GAA(T843, T820, T856, T857, X6607, row2col1113_in_gaa(T820, T857, X6607))
ROW2COL1113_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → ROW2COL1113_IN_GAA(T820, T857, X6607)
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U50_GAAA(T615, T616, T622, X6653, X6672, row2col20_in_gaaa(T616, T622, X6653, X6672))
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → ROW2COL20_IN_GAAA(T616, T622, X6653, X6672)
ROW2COL20_IN_GAAA(.(T906, T883), .(.(T906, T919), T920), [], []) → U51_GAAA(T906, T883, T919, T920, row2col727_in_ga(T883, T920))
ROW2COL20_IN_GAAA(.(T906, T883), .(.(T906, T919), T920), [], []) → ROW2COL727_IN_GA(T883, T920)
ROW2COL20_IN_GAAA(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U52_GAAA(T906, T883, T941, T942, X6847, row2col897_in_gaa(T883, T942, X6847))
ROW2COL20_IN_GAAA(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → ROW2COL897_IN_GAA(T883, T942, X6847)
ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U53_GAAA(T975, T952, T988, T989, X6985, row2col1113_in_gaa(T952, T989, X6985))
ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → ROW2COL1113_IN_GAA(T952, T989, X6985)
ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U54_GAAA(T975, T952, T1009, T1010, X7027, X7046, row2col20_in_gaaa(T952, T1010, X7027, X7046))
ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → ROW2COL20_IN_GAAA(T952, T1010, X7027, X7046)
P19_IN_GAAAG(T34, T20, T1038, T1036, .(T1052, T1053)) → U56_GAAAG(T34, T20, T1038, T1036, T1052, T1053, row2colc20_in_gaaa(T34, T20, T1038, T1036))
U56_GAAAG(T34, T20, T1038, T1036, T1052, T1053, row2colc20_out_gaaa(T34, T20, T1038, T1036)) → U57_GAAAG(T34, T20, T1038, T1036, T1052, T1053, p19_in_gaaag(T1052, T1038, X7086, X7087, T1053))
U56_GAAAG(T34, T20, T1038, T1036, T1052, T1053, row2colc20_out_gaaa(T34, T20, T1038, T1036)) → P19_IN_GAAAG(T1052, T1038, X7086, X7087, T1053)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
p19_in_gaaag(x1, x2, x3, x4, x5)  =  p19_in_gaaag(x1, x5)
row2col20_in_gaaa(x1, x2, x3, x4)  =  row2col20_in_gaaa(x1)
row2col74_in_g(x1)  =  row2col74_in_g(x1)
row2col174_in_ga(x1, x2)  =  row2col174_in_ga(x1)
row2col306_in_ga(x1, x2)  =  row2col306_in_ga(x1)
row2col454_in_gaa(x1, x2, x3)  =  row2col454_in_gaa(x1)
row2col727_in_ga(x1, x2)  =  row2col727_in_ga(x1)
row2col897_in_gaa(x1, x2, x3)  =  row2col897_in_gaa(x1)
row2col1113_in_gaa(x1, x2, x3)  =  row2col1113_in_gaa(x1)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
TRANSPOSE1_IN_GA(x1, x2)  =  TRANSPOSE1_IN_GA(x1)
U58_GA(x1, x2, x3, x4)  =  U58_GA(x1, x2, x4)
P19_IN_GAAAG(x1, x2, x3, x4, x5)  =  P19_IN_GAAAG(x1, x5)
U55_GAAAG(x1, x2, x3, x4, x5, x6)  =  U55_GAAAG(x1, x5, x6)
ROW2COL20_IN_GAAA(x1, x2, x3, x4)  =  ROW2COL20_IN_GAAA(x1)
U39_GAAA(x1, x2, x3)  =  U39_GAAA(x1, x2, x3)
ROW2COL74_IN_G(x1)  =  ROW2COL74_IN_G(x1)
U1_G(x1, x2, x3)  =  U1_G(x1, x2, x3)
U2_G(x1, x2, x3)  =  U2_G(x1, x2, x3)
U40_GAAA(x1, x2, x3, x4)  =  U40_GAAA(x1, x2, x4)
ROW2COL174_IN_GA(x1, x2)  =  ROW2COL174_IN_GA(x1)
U3_GA(x1, x2, x3)  =  U3_GA(x1, x2, x3)
U4_GA(x1, x2, x3, x4)  =  U4_GA(x1, x2, x4)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x2, x3)
U6_GA(x1, x2, x3, x4, x5)  =  U6_GA(x1, x2, x5)
U41_GAAA(x1, x2, x3, x4)  =  U41_GAAA(x1, x2, x4)
ROW2COL306_IN_GA(x1, x2)  =  ROW2COL306_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x2, x3)
U8_GA(x1, x2, x3, x4)  =  U8_GA(x1, x2, x4)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x2, x3)
U10_GA(x1, x2, x3, x4)  =  U10_GA(x1, x2, x4)
U42_GAAA(x1, x2, x3, x4, x5)  =  U42_GAAA(x1, x2, x5)
ROW2COL454_IN_GAA(x1, x2, x3)  =  ROW2COL454_IN_GAA(x1)
U11_GAA(x1, x2, x3)  =  U11_GAA(x1, x2, x3)
U12_GAA(x1, x2, x3, x4)  =  U12_GAA(x1, x2, x4)
U13_GAA(x1, x2, x3, x4)  =  U13_GAA(x1, x2, x4)
U14_GAA(x1, x2, x3, x4, x5)  =  U14_GAA(x1, x2, x5)
U15_GAA(x1, x2, x3)  =  U15_GAA(x1, x2, x3)
U16_GAA(x1, x2, x3, x4, x5)  =  U16_GAA(x1, x2, x5)
U17_GAA(x1, x2, x3, x4)  =  U17_GAA(x1, x2, x4)
U18_GAA(x1, x2, x3, x4, x5, x6)  =  U18_GAA(x1, x2, x6)
U43_GAAA(x1, x2, x3)  =  U43_GAAA(x1, x2, x3)
U44_GAAA(x1, x2, x3, x4, x5)  =  U44_GAAA(x1, x2, x5)
U45_GAAA(x1, x2, x3, x4)  =  U45_GAAA(x1, x2, x4)
U46_GAAA(x1, x2, x3, x4, x5, x6)  =  U46_GAAA(x1, x2, x6)
U47_GAAA(x1, x2, x3, x4)  =  U47_GAAA(x1, x2, x4)
ROW2COL727_IN_GA(x1, x2)  =  ROW2COL727_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x1, x2, x3)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x2, x3)
U21_GA(x1, x2, x3, x4)  =  U21_GA(x1, x2, x4)
U22_GA(x1, x2, x3, x4, x5)  =  U22_GA(x1, x2, x5)
U48_GAAA(x1, x2, x3, x4, x5)  =  U48_GAAA(x1, x2, x5)
ROW2COL897_IN_GAA(x1, x2, x3)  =  ROW2COL897_IN_GAA(x1)
U23_GAA(x1, x2, x3)  =  U23_GAA(x1, x2, x3)
U24_GAA(x1, x2, x3, x4)  =  U24_GAA(x1, x2, x4)
U25_GAA(x1, x2, x3)  =  U25_GAA(x1, x2, x3)
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)
U49_GAAA(x1, x2, x3, x4, x5)  =  U49_GAAA(x1, x2, x5)
ROW2COL1113_IN_GAA(x1, x2, x3)  =  ROW2COL1113_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)  =  U33_GAA(x1, x2, x3)
U34_GAA(x1, x2, x3, x4)  =  U34_GAA(x1, x2, x4)
U35_GAA(x1, x2, x3, x4)  =  U35_GAA(x1, x2, x4)
U36_GAA(x1, x2, x3, x4, x5)  =  U36_GAA(x1, x2, x5)
U37_GAA(x1, x2, x3, x4, x5)  =  U37_GAA(x1, x2, x5)
U38_GAA(x1, x2, x3, x4, x5, x6)  =  U38_GAA(x1, x2, x6)
U50_GAAA(x1, x2, x3, x4, x5, x6)  =  U50_GAAA(x1, x2, x6)
U51_GAAA(x1, x2, x3, x4, x5)  =  U51_GAAA(x1, x2, x5)
U52_GAAA(x1, x2, x3, x4, x5, x6)  =  U52_GAAA(x1, x2, x6)
U53_GAAA(x1, x2, x3, x4, x5, x6)  =  U53_GAAA(x1, x2, x6)
U54_GAAA(x1, x2, x3, x4, x5, x6, x7)  =  U54_GAAA(x1, x2, x7)
U56_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U56_GAAAG(x1, x5, x6, x7)
U57_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U57_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:

TRANSPOSE1_IN_GA(.(T34, T35), T20) → U58_GA(T34, T35, T20, p19_in_gaaag(T34, T20, X41, X42, T35))
TRANSPOSE1_IN_GA(.(T34, T35), T20) → P19_IN_GAAAG(T34, T20, X41, X42, T35)
P19_IN_GAAAG(T34, T20, X41, X42, T35) → U55_GAAAG(T34, T20, X41, X42, T35, row2col20_in_gaaa(T34, T20, X41, X42))
P19_IN_GAAAG(T34, T20, X41, X42, T35) → ROW2COL20_IN_GAAA(T34, T20, X41, X42)
ROW2COL20_IN_GAAA(.(T70, T71), [], [], []) → U39_GAAA(T70, T71, row2col74_in_g(T71))
ROW2COL20_IN_GAAA(.(T70, T71), [], [], []) → ROW2COL74_IN_G(T71)
ROW2COL74_IN_G(.(T90, T91)) → U1_G(T90, T91, row2col74_in_g(T91))
ROW2COL74_IN_G(.(T90, T91)) → ROW2COL74_IN_G(T91)
ROW2COL74_IN_G(.(T103, T100)) → U2_G(T103, T100, row2col74_in_g(T100))
ROW2COL20_IN_GAAA(.(T70, T71), [], .([], X776), []) → U40_GAAA(T70, T71, X776, row2col174_in_ga(T71, X776))
ROW2COL20_IN_GAAA(.(T70, T71), [], .([], X776), []) → ROW2COL174_IN_GA(T71, X776)
ROW2COL174_IN_GA(.(T122, T123), []) → U3_GA(T122, T123, row2col74_in_g(T123))
ROW2COL174_IN_GA(.(T122, T123), []) → ROW2COL74_IN_G(T123)
ROW2COL174_IN_GA(.(T122, T123), .([], X1080)) → U4_GA(T122, T123, X1080, row2col174_in_ga(T123, X1080))
ROW2COL174_IN_GA(.(T122, T123), .([], X1080)) → ROW2COL174_IN_GA(T123, X1080)
ROW2COL174_IN_GA(.(T135, T132), []) → U5_GA(T135, T132, row2col74_in_g(T132))
ROW2COL174_IN_GA(.(T135, T132), .(X1292, X1293)) → U6_GA(T135, T132, X1292, X1293, row2col174_in_ga(T132, X1293))
ROW2COL174_IN_GA(.(T135, T132), .(X1292, X1293)) → ROW2COL174_IN_GA(T132, X1293)
ROW2COL20_IN_GAAA(.(T140, T141), [], [], .([], X1441)) → U41_GAAA(T140, T141, X1441, row2col306_in_ga(T141, X1441))
ROW2COL20_IN_GAAA(.(T140, T141), [], [], .([], X1441)) → ROW2COL306_IN_GA(T141, X1441)
ROW2COL306_IN_GA(.(T160, T161), []) → U7_GA(T160, T161, row2col74_in_g(T161))
ROW2COL306_IN_GA(.(T160, T161), []) → ROW2COL74_IN_G(T161)
ROW2COL306_IN_GA(.(T166, T167), .([], X1819)) → U8_GA(T166, T167, X1819, row2col306_in_ga(T167, X1819))
ROW2COL306_IN_GA(.(T166, T167), .([], X1819)) → ROW2COL306_IN_GA(T167, X1819)
ROW2COL306_IN_GA(.(T179, T176), []) → U9_GA(T179, T176, row2col74_in_g(T176))
ROW2COL306_IN_GA(.(T188, T185), .([], X2110)) → U10_GA(T188, T185, X2110, row2col306_in_ga(T185, X2110))
ROW2COL20_IN_GAAA(.(T140, T141), [], .([], X2160), .([], X2179)) → U42_GAAA(T140, T141, X2160, X2179, row2col454_in_gaa(T141, X2160, X2179))
ROW2COL20_IN_GAAA(.(T140, T141), [], .([], X2160), .([], X2179)) → ROW2COL454_IN_GAA(T141, X2160, X2179)
ROW2COL454_IN_GAA(.(T207, T208), [], []) → U11_GAA(T207, T208, row2col74_in_g(T208))
ROW2COL454_IN_GAA(.(T207, T208), [], []) → ROW2COL74_IN_G(T208)
ROW2COL454_IN_GAA(.(T207, T208), .([], X2480), []) → U12_GAA(T207, T208, X2480, row2col174_in_ga(T208, X2480))
ROW2COL454_IN_GAA(.(T207, T208), .([], X2480), []) → ROW2COL174_IN_GA(T208, X2480)
ROW2COL454_IN_GAA(.(T213, T214), [], .([], X2620)) → U13_GAA(T213, T214, X2620, row2col306_in_ga(T214, X2620))
ROW2COL454_IN_GAA(.(T213, T214), [], .([], X2620)) → ROW2COL306_IN_GA(T214, X2620)
ROW2COL454_IN_GAA(.(T213, T214), .([], X2662), .([], X2681)) → U14_GAA(T213, T214, X2662, X2681, row2col454_in_gaa(T214, X2662, X2681))
ROW2COL454_IN_GAA(.(T213, T214), .([], X2662), .([], X2681)) → ROW2COL454_IN_GAA(T214, X2662, X2681)
ROW2COL454_IN_GAA(.(T226, T223), [], []) → U15_GAA(T226, T223, row2col74_in_g(T223))
ROW2COL454_IN_GAA(.(T226, T223), .(X2877, X2878), []) → U16_GAA(T226, T223, X2877, X2878, row2col174_in_ga(T223, X2878))
ROW2COL454_IN_GAA(.(T226, T223), .(X2877, X2878), []) → ROW2COL174_IN_GA(T223, X2878)
ROW2COL454_IN_GAA(.(T235, T232), [], .([], X3025)) → U17_GAA(T235, T232, X3025, row2col306_in_ga(T232, X3025))
ROW2COL454_IN_GAA(.(T235, T232), .(X3069, X3070), .([], X3089)) → U18_GAA(T235, T232, X3069, X3070, X3089, row2col454_in_gaa(T232, X3070, X3089))
ROW2COL454_IN_GAA(.(T235, T232), .(X3069, X3070), .([], X3089)) → ROW2COL454_IN_GAA(T232, X3070, X3089)
ROW2COL20_IN_GAAA(.(T247, T244), [], [], []) → U43_GAAA(T247, T244, row2col74_in_g(T244))
ROW2COL20_IN_GAAA(.(T247, T244), [], .(X3289, X3290), []) → U44_GAAA(T247, T244, X3289, X3290, row2col174_in_ga(T244, X3290))
ROW2COL20_IN_GAAA(.(T247, T244), [], .(X3289, X3290), []) → ROW2COL174_IN_GA(T244, X3290)
ROW2COL20_IN_GAAA(.(T256, T253), [], [], .([], X3437)) → U45_GAAA(T256, T253, X3437, row2col306_in_ga(T253, X3437))
ROW2COL20_IN_GAAA(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U46_GAAA(T256, T253, X3481, X3482, X3501, row2col454_in_gaa(T253, X3482, X3501))
ROW2COL20_IN_GAAA(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → ROW2COL454_IN_GAA(T253, X3482, X3501)
ROW2COL20_IN_GAAA(.(T275, T276), .([], T282), [], []) → U47_GAAA(T275, T276, T282, row2col727_in_ga(T276, T282))
ROW2COL20_IN_GAAA(.(T275, T276), .([], T282), [], []) → ROW2COL727_IN_GA(T276, T282)
ROW2COL727_IN_GA(.(T326, T327), []) → U19_GA(T326, T327, row2col74_in_g(T327))
ROW2COL727_IN_GA(.(T326, T327), []) → ROW2COL74_IN_G(T327)
ROW2COL727_IN_GA(.(T339, T336), []) → U20_GA(T339, T336, row2col74_in_g(T336))
ROW2COL727_IN_GA(.(T358, T359), .([], T365)) → U21_GA(T358, T359, T365, row2col727_in_ga(T359, T365))
ROW2COL727_IN_GA(.(T358, T359), .([], T365)) → ROW2COL727_IN_GA(T359, T365)
ROW2COL727_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → U22_GA(T415, T392, T428, T429, row2col727_in_ga(T392, T429))
ROW2COL727_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → ROW2COL727_IN_GA(T392, T429)
ROW2COL20_IN_GAAA(.(T275, T276), .([], T282), .([], X4367), []) → U48_GAAA(T275, T276, T282, X4367, row2col897_in_gaa(T276, T282, X4367))
ROW2COL20_IN_GAAA(.(T275, T276), .([], T282), .([], X4367), []) → ROW2COL897_IN_GAA(T276, T282, X4367)
ROW2COL897_IN_GAA(.(T474, T475), [], []) → U23_GAA(T474, T475, row2col74_in_g(T475))
ROW2COL897_IN_GAA(.(T474, T475), [], []) → ROW2COL74_IN_G(T475)
ROW2COL897_IN_GAA(.(T474, T475), [], .([], X4661)) → U24_GAA(T474, T475, X4661, row2col174_in_ga(T475, X4661))
ROW2COL897_IN_GAA(.(T474, T475), [], .([], X4661)) → ROW2COL174_IN_GA(T475, X4661)
ROW2COL897_IN_GAA(.(T487, T484), [], []) → U25_GAA(T487, T484, row2col74_in_g(T484))
ROW2COL897_IN_GAA(.(T487, T484), [], .(X4873, X4874)) → U26_GAA(T487, T484, X4873, X4874, row2col174_in_ga(T484, X4874))
ROW2COL897_IN_GAA(.(T487, T484), [], .(X4873, X4874)) → ROW2COL174_IN_GA(T484, X4874)
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), []) → U27_GAA(T506, T507, T513, row2col727_in_ga(T507, T513))
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), []) → ROW2COL727_IN_GA(T507, T513)
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), .([], X5076)) → U28_GAA(T506, T507, T513, X5076, row2col897_in_gaa(T507, T513, X5076))
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), .([], X5076)) → ROW2COL897_IN_GAA(T507, T513, X5076)
ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T583), T584), []) → U29_GAA(T570, T547, T583, T584, row2col727_in_ga(T547, T584))
ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T583), T584), []) → ROW2COL727_IN_GA(T547, T584)
ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U30_GAA(T570, T547, T605, T606, X5267, row2col897_in_gaa(T547, T606, X5267))
ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → ROW2COL897_IN_GAA(T547, T606, X5267)
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), [], .([], X5410)) → U49_GAAA(T615, T616, T622, X5410, row2col1113_in_gaa(T616, T622, X5410))
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), [], .([], X5410)) → ROW2COL1113_IN_GAA(T616, T622, X5410)
ROW2COL1113_IN_GAA(.(T665, T666), [], []) → U31_GAA(T665, T666, row2col74_in_g(T666))
ROW2COL1113_IN_GAA(.(T665, T666), [], []) → ROW2COL74_IN_G(T666)
ROW2COL1113_IN_GAA(.(T671, T672), [], .([], X5778)) → U32_GAA(T671, T672, X5778, row2col306_in_ga(T672, X5778))
ROW2COL1113_IN_GAA(.(T671, T672), [], .([], X5778)) → ROW2COL306_IN_GA(T672, X5778)
ROW2COL1113_IN_GAA(.(T684, T681), [], []) → U33_GAA(T684, T681, row2col74_in_g(T681))
ROW2COL1113_IN_GAA(.(T693, T690), [], .([], X6069)) → U34_GAA(T693, T690, X6069, row2col306_in_ga(T690, X6069))
ROW2COL1113_IN_GAA(.(T712, T713), .([], T719), []) → U35_GAA(T712, T713, T719, row2col727_in_ga(T713, T719))
ROW2COL1113_IN_GAA(.(T712, T713), .([], T719), []) → ROW2COL727_IN_GA(T713, T719)
ROW2COL1113_IN_GAA(.(T737, T738), .([], T744), .([], X6344)) → U36_GAA(T737, T738, T744, X6344, row2col1113_in_gaa(T738, T744, X6344))
ROW2COL1113_IN_GAA(.(T737, T738), .([], T744), .([], X6344)) → ROW2COL1113_IN_GAA(T738, T744, X6344)
ROW2COL1113_IN_GAA(.(T793, T770), .(.(T793, T806), T807), []) → U37_GAA(T793, T770, T806, T807, row2col727_in_ga(T770, T807))
ROW2COL1113_IN_GAA(.(T793, T770), .(.(T793, T806), T807), []) → ROW2COL727_IN_GA(T770, T807)
ROW2COL1113_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U38_GAA(T843, T820, T856, T857, X6607, row2col1113_in_gaa(T820, T857, X6607))
ROW2COL1113_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → ROW2COL1113_IN_GAA(T820, T857, X6607)
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U50_GAAA(T615, T616, T622, X6653, X6672, row2col20_in_gaaa(T616, T622, X6653, X6672))
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → ROW2COL20_IN_GAAA(T616, T622, X6653, X6672)
ROW2COL20_IN_GAAA(.(T906, T883), .(.(T906, T919), T920), [], []) → U51_GAAA(T906, T883, T919, T920, row2col727_in_ga(T883, T920))
ROW2COL20_IN_GAAA(.(T906, T883), .(.(T906, T919), T920), [], []) → ROW2COL727_IN_GA(T883, T920)
ROW2COL20_IN_GAAA(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U52_GAAA(T906, T883, T941, T942, X6847, row2col897_in_gaa(T883, T942, X6847))
ROW2COL20_IN_GAAA(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → ROW2COL897_IN_GAA(T883, T942, X6847)
ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U53_GAAA(T975, T952, T988, T989, X6985, row2col1113_in_gaa(T952, T989, X6985))
ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → ROW2COL1113_IN_GAA(T952, T989, X6985)
ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U54_GAAA(T975, T952, T1009, T1010, X7027, X7046, row2col20_in_gaaa(T952, T1010, X7027, X7046))
ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → ROW2COL20_IN_GAAA(T952, T1010, X7027, X7046)
P19_IN_GAAAG(T34, T20, T1038, T1036, .(T1052, T1053)) → U56_GAAAG(T34, T20, T1038, T1036, T1052, T1053, row2colc20_in_gaaa(T34, T20, T1038, T1036))
U56_GAAAG(T34, T20, T1038, T1036, T1052, T1053, row2colc20_out_gaaa(T34, T20, T1038, T1036)) → U57_GAAAG(T34, T20, T1038, T1036, T1052, T1053, p19_in_gaaag(T1052, T1038, X7086, X7087, T1053))
U56_GAAAG(T34, T20, T1038, T1036, T1052, T1053, row2colc20_out_gaaa(T34, T20, T1038, T1036)) → P19_IN_GAAAG(T1052, T1038, X7086, X7087, T1053)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
p19_in_gaaag(x1, x2, x3, x4, x5)  =  p19_in_gaaag(x1, x5)
row2col20_in_gaaa(x1, x2, x3, x4)  =  row2col20_in_gaaa(x1)
row2col74_in_g(x1)  =  row2col74_in_g(x1)
row2col174_in_ga(x1, x2)  =  row2col174_in_ga(x1)
row2col306_in_ga(x1, x2)  =  row2col306_in_ga(x1)
row2col454_in_gaa(x1, x2, x3)  =  row2col454_in_gaa(x1)
row2col727_in_ga(x1, x2)  =  row2col727_in_ga(x1)
row2col897_in_gaa(x1, x2, x3)  =  row2col897_in_gaa(x1)
row2col1113_in_gaa(x1, x2, x3)  =  row2col1113_in_gaa(x1)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
TRANSPOSE1_IN_GA(x1, x2)  =  TRANSPOSE1_IN_GA(x1)
U58_GA(x1, x2, x3, x4)  =  U58_GA(x1, x2, x4)
P19_IN_GAAAG(x1, x2, x3, x4, x5)  =  P19_IN_GAAAG(x1, x5)
U55_GAAAG(x1, x2, x3, x4, x5, x6)  =  U55_GAAAG(x1, x5, x6)
ROW2COL20_IN_GAAA(x1, x2, x3, x4)  =  ROW2COL20_IN_GAAA(x1)
U39_GAAA(x1, x2, x3)  =  U39_GAAA(x1, x2, x3)
ROW2COL74_IN_G(x1)  =  ROW2COL74_IN_G(x1)
U1_G(x1, x2, x3)  =  U1_G(x1, x2, x3)
U2_G(x1, x2, x3)  =  U2_G(x1, x2, x3)
U40_GAAA(x1, x2, x3, x4)  =  U40_GAAA(x1, x2, x4)
ROW2COL174_IN_GA(x1, x2)  =  ROW2COL174_IN_GA(x1)
U3_GA(x1, x2, x3)  =  U3_GA(x1, x2, x3)
U4_GA(x1, x2, x3, x4)  =  U4_GA(x1, x2, x4)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x2, x3)
U6_GA(x1, x2, x3, x4, x5)  =  U6_GA(x1, x2, x5)
U41_GAAA(x1, x2, x3, x4)  =  U41_GAAA(x1, x2, x4)
ROW2COL306_IN_GA(x1, x2)  =  ROW2COL306_IN_GA(x1)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x2, x3)
U8_GA(x1, x2, x3, x4)  =  U8_GA(x1, x2, x4)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x2, x3)
U10_GA(x1, x2, x3, x4)  =  U10_GA(x1, x2, x4)
U42_GAAA(x1, x2, x3, x4, x5)  =  U42_GAAA(x1, x2, x5)
ROW2COL454_IN_GAA(x1, x2, x3)  =  ROW2COL454_IN_GAA(x1)
U11_GAA(x1, x2, x3)  =  U11_GAA(x1, x2, x3)
U12_GAA(x1, x2, x3, x4)  =  U12_GAA(x1, x2, x4)
U13_GAA(x1, x2, x3, x4)  =  U13_GAA(x1, x2, x4)
U14_GAA(x1, x2, x3, x4, x5)  =  U14_GAA(x1, x2, x5)
U15_GAA(x1, x2, x3)  =  U15_GAA(x1, x2, x3)
U16_GAA(x1, x2, x3, x4, x5)  =  U16_GAA(x1, x2, x5)
U17_GAA(x1, x2, x3, x4)  =  U17_GAA(x1, x2, x4)
U18_GAA(x1, x2, x3, x4, x5, x6)  =  U18_GAA(x1, x2, x6)
U43_GAAA(x1, x2, x3)  =  U43_GAAA(x1, x2, x3)
U44_GAAA(x1, x2, x3, x4, x5)  =  U44_GAAA(x1, x2, x5)
U45_GAAA(x1, x2, x3, x4)  =  U45_GAAA(x1, x2, x4)
U46_GAAA(x1, x2, x3, x4, x5, x6)  =  U46_GAAA(x1, x2, x6)
U47_GAAA(x1, x2, x3, x4)  =  U47_GAAA(x1, x2, x4)
ROW2COL727_IN_GA(x1, x2)  =  ROW2COL727_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x1, x2, x3)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x2, x3)
U21_GA(x1, x2, x3, x4)  =  U21_GA(x1, x2, x4)
U22_GA(x1, x2, x3, x4, x5)  =  U22_GA(x1, x2, x5)
U48_GAAA(x1, x2, x3, x4, x5)  =  U48_GAAA(x1, x2, x5)
ROW2COL897_IN_GAA(x1, x2, x3)  =  ROW2COL897_IN_GAA(x1)
U23_GAA(x1, x2, x3)  =  U23_GAA(x1, x2, x3)
U24_GAA(x1, x2, x3, x4)  =  U24_GAA(x1, x2, x4)
U25_GAA(x1, x2, x3)  =  U25_GAA(x1, x2, x3)
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)
U49_GAAA(x1, x2, x3, x4, x5)  =  U49_GAAA(x1, x2, x5)
ROW2COL1113_IN_GAA(x1, x2, x3)  =  ROW2COL1113_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)  =  U33_GAA(x1, x2, x3)
U34_GAA(x1, x2, x3, x4)  =  U34_GAA(x1, x2, x4)
U35_GAA(x1, x2, x3, x4)  =  U35_GAA(x1, x2, x4)
U36_GAA(x1, x2, x3, x4, x5)  =  U36_GAA(x1, x2, x5)
U37_GAA(x1, x2, x3, x4, x5)  =  U37_GAA(x1, x2, x5)
U38_GAA(x1, x2, x3, x4, x5, x6)  =  U38_GAA(x1, x2, x6)
U50_GAAA(x1, x2, x3, x4, x5, x6)  =  U50_GAAA(x1, x2, x6)
U51_GAAA(x1, x2, x3, x4, x5)  =  U51_GAAA(x1, x2, x5)
U52_GAAA(x1, x2, x3, x4, x5, x6)  =  U52_GAAA(x1, x2, x6)
U53_GAAA(x1, x2, x3, x4, x5, x6)  =  U53_GAAA(x1, x2, x6)
U54_GAAA(x1, x2, x3, x4, x5, x6, x7)  =  U54_GAAA(x1, x2, x7)
U56_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U56_GAAAG(x1, x5, x6, x7)
U57_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U57_GAAAG(x1, x4, x5, x6, x7)

We have to consider all (P,R,Pi)-chains

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 9 SCCs with 87 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ROW2COL74_IN_G(.(T90, T91)) → ROW2COL74_IN_G(T91)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
ROW2COL74_IN_G(x1)  =  ROW2COL74_IN_G(x1)

We have to consider all (P,R,Pi)-chains

(8) UsableRulesProof (EQUIVALENT transformation)

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:

ROW2COL74_IN_G(.(T90, T91)) → ROW2COL74_IN_G(T91)

R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains

(10) PiDPToQDPProof (EQUIVALENT transformation)

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:

ROW2COL74_IN_G(.(T90, T91)) → ROW2COL74_IN_G(T91)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(12) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • ROW2COL74_IN_G(.(T90, T91)) → ROW2COL74_IN_G(T91)
    The graph contains the following edges 1 > 1

(13) YES

(14) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ROW2COL727_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → ROW2COL727_IN_GA(T392, T429)
ROW2COL727_IN_GA(.(T358, T359), .([], T365)) → ROW2COL727_IN_GA(T359, T365)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
ROW2COL727_IN_GA(x1, x2)  =  ROW2COL727_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(15) UsableRulesProof (EQUIVALENT transformation)

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:

ROW2COL727_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → ROW2COL727_IN_GA(T392, T429)
ROW2COL727_IN_GA(.(T358, T359), .([], T365)) → ROW2COL727_IN_GA(T359, T365)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
[]  =  []
ROW2COL727_IN_GA(x1, x2)  =  ROW2COL727_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(17) PiDPToQDPProof (SOUND transformation)

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:

ROW2COL727_IN_GA(.(T415, T392)) → ROW2COL727_IN_GA(T392)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(19) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • ROW2COL727_IN_GA(.(T415, T392)) → ROW2COL727_IN_GA(T392)
    The graph contains the following edges 1 > 1

(20) YES

(21) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ROW2COL306_IN_GA(.(T166, T167), .([], X1819)) → ROW2COL306_IN_GA(T167, X1819)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
ROW2COL306_IN_GA(x1, x2)  =  ROW2COL306_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(22) UsableRulesProof (EQUIVALENT transformation)

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:

ROW2COL306_IN_GA(.(T166, T167), .([], X1819)) → ROW2COL306_IN_GA(T167, X1819)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
[]  =  []
ROW2COL306_IN_GA(x1, x2)  =  ROW2COL306_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(24) PiDPToQDPProof (SOUND transformation)

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:

ROW2COL306_IN_GA(.(T166, T167)) → ROW2COL306_IN_GA(T167)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(26) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • ROW2COL306_IN_GA(.(T166, T167)) → ROW2COL306_IN_GA(T167)
    The graph contains the following edges 1 > 1

(27) YES

(28) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ROW2COL1113_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → ROW2COL1113_IN_GAA(T820, T857, X6607)
ROW2COL1113_IN_GAA(.(T737, T738), .([], T744), .([], X6344)) → ROW2COL1113_IN_GAA(T738, T744, X6344)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
ROW2COL1113_IN_GAA(x1, x2, x3)  =  ROW2COL1113_IN_GAA(x1)

We have to consider all (P,R,Pi)-chains

(29) UsableRulesProof (EQUIVALENT transformation)

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:

ROW2COL1113_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → ROW2COL1113_IN_GAA(T820, T857, X6607)
ROW2COL1113_IN_GAA(.(T737, T738), .([], T744), .([], X6344)) → ROW2COL1113_IN_GAA(T738, T744, X6344)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
[]  =  []
ROW2COL1113_IN_GAA(x1, x2, x3)  =  ROW2COL1113_IN_GAA(x1)

We have to consider all (P,R,Pi)-chains

(31) PiDPToQDPProof (SOUND transformation)

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:

ROW2COL1113_IN_GAA(.(T843, T820)) → ROW2COL1113_IN_GAA(T820)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(33) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • ROW2COL1113_IN_GAA(.(T843, T820)) → ROW2COL1113_IN_GAA(T820)
    The graph contains the following edges 1 > 1

(34) YES

(35) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ROW2COL174_IN_GA(.(T135, T132), .(X1292, X1293)) → ROW2COL174_IN_GA(T132, X1293)
ROW2COL174_IN_GA(.(T122, T123), .([], X1080)) → ROW2COL174_IN_GA(T123, X1080)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
ROW2COL174_IN_GA(x1, x2)  =  ROW2COL174_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(36) UsableRulesProof (EQUIVALENT transformation)

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:

ROW2COL174_IN_GA(.(T135, T132), .(X1292, X1293)) → ROW2COL174_IN_GA(T132, X1293)
ROW2COL174_IN_GA(.(T122, T123), .([], X1080)) → ROW2COL174_IN_GA(T123, X1080)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
[]  =  []
ROW2COL174_IN_GA(x1, x2)  =  ROW2COL174_IN_GA(x1)

We have to consider all (P,R,Pi)-chains

(38) PiDPToQDPProof (SOUND transformation)

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:

ROW2COL174_IN_GA(.(T135, T132)) → ROW2COL174_IN_GA(T132)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(40) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • ROW2COL174_IN_GA(.(T135, T132)) → ROW2COL174_IN_GA(T132)
    The graph contains the following edges 1 > 1

(41) YES

(42) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → ROW2COL897_IN_GAA(T547, T606, X5267)
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), .([], X5076)) → ROW2COL897_IN_GAA(T507, T513, X5076)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
ROW2COL897_IN_GAA(x1, x2, x3)  =  ROW2COL897_IN_GAA(x1)

We have to consider all (P,R,Pi)-chains

(43) UsableRulesProof (EQUIVALENT transformation)

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:

ROW2COL897_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → ROW2COL897_IN_GAA(T547, T606, X5267)
ROW2COL897_IN_GAA(.(T506, T507), .([], T513), .([], X5076)) → ROW2COL897_IN_GAA(T507, T513, X5076)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
[]  =  []
ROW2COL897_IN_GAA(x1, x2, x3)  =  ROW2COL897_IN_GAA(x1)

We have to consider all (P,R,Pi)-chains

(45) PiDPToQDPProof (SOUND transformation)

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:

ROW2COL897_IN_GAA(.(T570, T547)) → ROW2COL897_IN_GAA(T547)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(47) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • ROW2COL897_IN_GAA(.(T570, T547)) → ROW2COL897_IN_GAA(T547)
    The graph contains the following edges 1 > 1

(48) YES

(49) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ROW2COL454_IN_GAA(.(T235, T232), .(X3069, X3070), .([], X3089)) → ROW2COL454_IN_GAA(T232, X3070, X3089)
ROW2COL454_IN_GAA(.(T213, T214), .([], X2662), .([], X2681)) → ROW2COL454_IN_GAA(T214, X2662, X2681)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
ROW2COL454_IN_GAA(x1, x2, x3)  =  ROW2COL454_IN_GAA(x1)

We have to consider all (P,R,Pi)-chains

(50) UsableRulesProof (EQUIVALENT transformation)

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:

ROW2COL454_IN_GAA(.(T235, T232), .(X3069, X3070), .([], X3089)) → ROW2COL454_IN_GAA(T232, X3070, X3089)
ROW2COL454_IN_GAA(.(T213, T214), .([], X2662), .([], X2681)) → ROW2COL454_IN_GAA(T214, X2662, X2681)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
[]  =  []
ROW2COL454_IN_GAA(x1, x2, x3)  =  ROW2COL454_IN_GAA(x1)

We have to consider all (P,R,Pi)-chains

(52) PiDPToQDPProof (SOUND transformation)

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:

ROW2COL454_IN_GAA(.(T235, T232)) → ROW2COL454_IN_GAA(T232)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(54) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • ROW2COL454_IN_GAA(.(T235, T232)) → ROW2COL454_IN_GAA(T232)
    The graph contains the following edges 1 > 1

(55) YES

(56) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → ROW2COL20_IN_GAAA(T952, T1010, X7027, X7046)
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → ROW2COL20_IN_GAAA(T616, T622, X6653, X6672)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
ROW2COL20_IN_GAAA(x1, x2, x3, x4)  =  ROW2COL20_IN_GAAA(x1)

We have to consider all (P,R,Pi)-chains

(57) UsableRulesProof (EQUIVALENT transformation)

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:

ROW2COL20_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → ROW2COL20_IN_GAAA(T952, T1010, X7027, X7046)
ROW2COL20_IN_GAAA(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → ROW2COL20_IN_GAAA(T616, T622, X6653, X6672)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
[]  =  []
ROW2COL20_IN_GAAA(x1, x2, x3, x4)  =  ROW2COL20_IN_GAAA(x1)

We have to consider all (P,R,Pi)-chains

(59) PiDPToQDPProof (SOUND transformation)

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:

ROW2COL20_IN_GAAA(.(T975, T952)) → ROW2COL20_IN_GAAA(T952)

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.

(61) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • ROW2COL20_IN_GAAA(.(T975, T952)) → ROW2COL20_IN_GAAA(T952)
    The graph contains the following edges 1 > 1

(62) YES

(63) Obligation:

Pi DP problem:
The TRS P consists of the following rules:

P19_IN_GAAAG(T34, T20, T1038, T1036, .(T1052, T1053)) → U56_GAAAG(T34, T20, T1038, T1036, T1052, T1053, row2colc20_in_gaaa(T34, T20, T1038, T1036))
U56_GAAAG(T34, T20, T1038, T1036, T1052, T1053, row2colc20_out_gaaa(T34, T20, T1038, T1036)) → P19_IN_GAAAG(T1052, T1038, X7086, X7087, T1053)

The TRS R consists of the following rules:

row2colc20_in_gaaa([], [], [], []) → row2colc20_out_gaaa([], [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], [], []) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [], [], [])
row2colc20_in_gaaa(.(T70, T71), [], .([], X776), []) → U99_gaaa(T70, T71, X776, row2colc174_in_ga(T71, X776))
row2colc174_in_ga([], []) → row2colc174_out_ga([], [])
row2colc174_in_ga(.(T122, T123), []) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123), [])
row2colc174_in_ga(.(T122, T123), .([], X1080)) → U63_ga(T122, T123, X1080, row2colc174_in_ga(T123, X1080))
row2colc174_in_ga(.(T135, T132), []) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132), [])
row2colc174_in_ga(.(T135, T132), .(X1292, X1293)) → U65_ga(T135, T132, X1292, X1293, row2colc174_in_ga(T132, X1293))
U65_ga(T135, T132, X1292, X1293, row2colc174_out_ga(T132, X1293)) → row2colc174_out_ga(.(T135, T132), .(X1292, X1293))
U63_ga(T122, T123, X1080, row2colc174_out_ga(T123, X1080)) → row2colc174_out_ga(.(T122, T123), .([], X1080))
U99_gaaa(T70, T71, X776, row2colc174_out_ga(T71, X776)) → row2colc20_out_gaaa(.(T70, T71), [], .([], X776), [])
row2colc20_in_gaaa(.(T140, T141), [], [], .([], X1441)) → U100_gaaa(T140, T141, X1441, row2colc306_in_ga(T141, X1441))
row2colc306_in_ga([], []) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161), []) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167), .([], X1819)) → U67_ga(T166, T167, X1819, row2colc306_in_ga(T167, X1819))
row2colc306_in_ga(.(T179, T176), []) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185), .([], X2110)) → U69_ga(T188, T185, X2110, row2colc306_in_ga(T185, X2110))
U69_ga(T188, T185, X2110, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, X1819, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, X1441, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), [], [], .([], X1441))
row2colc20_in_gaaa(.(T140, T141), [], .([], X2160), .([], X2179)) → U101_gaaa(T140, T141, X2160, X2179, row2colc454_in_gaa(T141, X2160, X2179))
row2colc454_in_gaa([], [], []) → row2colc454_out_gaa([], [], [])
row2colc454_in_gaa(.(T207, T208), [], []) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [], [])
row2colc454_in_gaa(.(T207, T208), .([], X2480), []) → U71_gaa(T207, T208, X2480, row2colc174_in_ga(T208, X2480))
U71_gaa(T207, T208, X2480, row2colc174_out_ga(T208, X2480)) → row2colc454_out_gaa(.(T207, T208), .([], X2480), [])
row2colc454_in_gaa(.(T213, T214), [], .([], X2620)) → U72_gaa(T213, T214, X2620, row2colc306_in_ga(T214, X2620))
U72_gaa(T213, T214, X2620, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), [], .([], X2620))
row2colc454_in_gaa(.(T213, T214), .([], X2662), .([], X2681)) → U73_gaa(T213, T214, X2662, X2681, row2colc454_in_gaa(T214, X2662, X2681))
row2colc454_in_gaa(.(T226, T223), [], []) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [], [])
row2colc454_in_gaa(.(T226, T223), .(X2877, X2878), []) → U75_gaa(T226, T223, X2877, X2878, row2colc174_in_ga(T223, X2878))
U75_gaa(T226, T223, X2877, X2878, row2colc174_out_ga(T223, X2878)) → row2colc454_out_gaa(.(T226, T223), .(X2877, X2878), [])
row2colc454_in_gaa(.(T235, T232), [], .([], X3025)) → U76_gaa(T235, T232, X3025, row2colc306_in_ga(T232, X3025))
U76_gaa(T235, T232, X3025, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), [], .([], X3025))
row2colc454_in_gaa(.(T235, T232), .(X3069, X3070), .([], X3089)) → U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_in_gaa(T232, X3070, X3089))
U77_gaa(T235, T232, X3069, X3070, X3089, row2colc454_out_gaa(T232, X3070, X3089)) → row2colc454_out_gaa(.(T235, T232), .(X3069, X3070), .([], X3089))
U73_gaa(T213, T214, X2662, X2681, row2colc454_out_gaa(T214, X2662, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2662), .([], X2681))
U101_gaaa(T140, T141, X2160, X2179, row2colc454_out_gaa(T141, X2160, X2179)) → row2colc20_out_gaaa(.(T140, T141), [], .([], X2160), .([], X2179))
row2colc20_in_gaaa(.(T247, T244), [], [], []) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [], [], [])
row2colc20_in_gaaa(.(T247, T244), [], .(X3289, X3290), []) → U103_gaaa(T247, T244, X3289, X3290, row2colc174_in_ga(T244, X3290))
U103_gaaa(T247, T244, X3289, X3290, row2colc174_out_ga(T244, X3290)) → row2colc20_out_gaaa(.(T247, T244), [], .(X3289, X3290), [])
row2colc20_in_gaaa(.(T256, T253), [], [], .([], X3437)) → U104_gaaa(T256, T253, X3437, row2colc306_in_ga(T253, X3437))
U104_gaaa(T256, T253, X3437, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), [], [], .([], X3437))
row2colc20_in_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501)) → U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_in_gaa(T253, X3482, X3501))
U105_gaaa(T256, T253, X3481, X3482, X3501, row2colc454_out_gaa(T253, X3482, X3501)) → row2colc20_out_gaaa(.(T256, T253), [], .(X3481, X3482), .([], X3501))
row2colc20_in_gaaa(.(T275, T276), .([], T282), [], []) → U106_gaaa(T275, T276, T282, row2colc727_in_ga(T276, T282))
row2colc727_in_ga([], []) → row2colc727_out_ga([], [])
row2colc727_in_ga(.(T326, T327), []) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327), [])
row2colc727_in_ga(.(T339, T336), []) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336), [])
row2colc727_in_ga(.(T358, T359), .([], T365)) → U80_ga(T358, T359, T365, row2colc727_in_ga(T359, T365))
row2colc727_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U81_ga(T415, T392, T428, T429, row2colc727_in_ga(T392, T429))
U81_ga(T415, T392, T428, T429, row2colc727_out_ga(T392, T429)) → row2colc727_out_ga(.(T415, T392), .(.(T415, T428), T429))
U80_ga(T358, T359, T365, row2colc727_out_ga(T359, T365)) → row2colc727_out_ga(.(T358, T359), .([], T365))
U106_gaaa(T275, T276, T282, row2colc727_out_ga(T276, T282)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colc20_in_gaaa(.(T275, T276), .([], T282), .([], X4367), []) → U107_gaaa(T275, T276, T282, X4367, row2colc897_in_gaa(T276, T282, X4367))
row2colc897_in_gaa([], [], []) → row2colc897_out_gaa([], [], [])
row2colc897_in_gaa(.(T474, T475), [], []) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475), [], [])
row2colc897_in_gaa(.(T474, T475), [], .([], X4661)) → U83_gaa(T474, T475, X4661, row2colc174_in_ga(T475, X4661))
U83_gaa(T474, T475, X4661, row2colc174_out_ga(T475, X4661)) → row2colc897_out_gaa(.(T474, T475), [], .([], X4661))
row2colc897_in_gaa(.(T487, T484), [], []) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484), [], [])
row2colc897_in_gaa(.(T487, T484), [], .(X4873, X4874)) → U85_gaa(T487, T484, X4873, X4874, row2colc174_in_ga(T484, X4874))
U85_gaa(T487, T484, X4873, X4874, row2colc174_out_ga(T484, X4874)) → row2colc897_out_gaa(.(T487, T484), [], .(X4873, X4874))
row2colc897_in_gaa(.(T506, T507), .([], T513), []) → U86_gaa(T506, T507, T513, row2colc727_in_ga(T507, T513))
U86_gaa(T506, T507, T513, row2colc727_out_ga(T507, T513)) → row2colc897_out_gaa(.(T506, T507), .([], T513), [])
row2colc897_in_gaa(.(T506, T507), .([], T513), .([], X5076)) → U87_gaa(T506, T507, T513, X5076, row2colc897_in_gaa(T507, T513, X5076))
row2colc897_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U88_gaa(T570, T547, T583, T584, row2colc727_in_ga(T547, T584))
U88_gaa(T570, T547, T583, T584, row2colc727_out_ga(T547, T584)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colc897_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267)) → U89_gaa(T570, T547, T605, T606, X5267, row2colc897_in_gaa(T547, T606, X5267))
U89_gaa(T570, T547, T605, T606, X5267, row2colc897_out_gaa(T547, T606, X5267)) → row2colc897_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5267))
U87_gaa(T506, T507, T513, X5076, row2colc897_out_gaa(T507, T513, X5076)) → row2colc897_out_gaa(.(T506, T507), .([], T513), .([], X5076))
U107_gaaa(T275, T276, T282, X4367, row2colc897_out_gaa(T276, T282, X4367)) → row2colc20_out_gaaa(.(T275, T276), .([], T282), .([], X4367), [])
row2colc20_in_gaaa(.(T615, T616), .([], T622), [], .([], X5410)) → U108_gaaa(T615, T616, T622, X5410, row2colc1113_in_gaa(T616, T622, X5410))
row2colc1113_in_gaa([], [], []) → row2colc1113_out_gaa([], [], [])
row2colc1113_in_gaa(.(T665, T666), [], []) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [], [])
row2colc1113_in_gaa(.(T671, T672), [], .([], X5778)) → U91_gaa(T671, T672, X5778, row2colc306_in_ga(T672, X5778))
U91_gaa(T671, T672, X5778, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), [], .([], X5778))
row2colc1113_in_gaa(.(T684, T681), [], []) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [], [])
row2colc1113_in_gaa(.(T693, T690), [], .([], X6069)) → U93_gaa(T693, T690, X6069, row2colc306_in_ga(T690, X6069))
U93_gaa(T693, T690, X6069, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), [], .([], X6069))
row2colc1113_in_gaa(.(T712, T713), .([], T719), []) → U94_gaa(T712, T713, T719, row2colc727_in_ga(T713, T719))
U94_gaa(T712, T713, T719, row2colc727_out_ga(T713, T719)) → row2colc1113_out_gaa(.(T712, T713), .([], T719), [])
row2colc1113_in_gaa(.(T737, T738), .([], T744), .([], X6344)) → U95_gaa(T737, T738, T744, X6344, row2colc1113_in_gaa(T738, T744, X6344))
row2colc1113_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U96_gaa(T793, T770, T806, T807, row2colc727_in_ga(T770, T807))
U96_gaa(T793, T770, T806, T807, row2colc727_out_ga(T770, T807)) → row2colc1113_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colc1113_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607)) → U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_in_gaa(T820, T857, X6607))
U97_gaa(T843, T820, T856, T857, X6607, row2colc1113_out_gaa(T820, T857, X6607)) → row2colc1113_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6607))
U95_gaa(T737, T738, T744, X6344, row2colc1113_out_gaa(T738, T744, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], T744), .([], X6344))
U108_gaaa(T615, T616, T622, X5410, row2colc1113_out_gaa(T616, T622, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), [], .([], X5410))
row2colc20_in_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672)) → U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_in_gaaa(T616, T622, X6653, X6672))
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U110_gaaa(T906, T883, T919, T920, row2colc727_in_ga(T883, T920))
U110_gaaa(T906, T883, T919, T920, row2colc727_out_ga(T883, T920)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colc20_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), []) → U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_in_gaa(T883, T942, X6847))
U111_gaaa(T906, T883, T941, T942, X6847, row2colc897_out_gaa(T883, T942, X6847)) → row2colc20_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6847), [])
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985)) → U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_in_gaa(T952, T989, X6985))
U112_gaaa(T975, T952, T988, T989, X6985, row2colc1113_out_gaa(T952, T989, X6985)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6985))
row2colc20_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046)) → U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_in_gaaa(T952, T1010, X7027, X7046))
U113_gaaa(T975, T952, T1009, T1010, X7027, X7046, row2colc20_out_gaaa(T952, T1010, X7027, X7046)) → row2colc20_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X7027), .([], X7046))
U109_gaaa(T615, T616, T622, X6653, X6672, row2colc20_out_gaaa(T616, T622, X6653, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], T622), .([], X6653), .([], X6672))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
row2colc20_in_gaaa(x1, x2, x3, x4)  =  row2colc20_in_gaaa(x1)
[]  =  []
row2colc20_out_gaaa(x1, x2, x3, x4)  =  row2colc20_out_gaaa(x1, x4)
U98_gaaa(x1, x2, x3)  =  U98_gaaa(x1, x2, x3)
row2colc74_in_g(x1)  =  row2colc74_in_g(x1)
row2colc74_out_g(x1)  =  row2colc74_out_g(x1)
U60_g(x1, x2, x3)  =  U60_g(x1, x2, x3)
U61_g(x1, x2, x3)  =  U61_g(x1, x2, x3)
U99_gaaa(x1, x2, x3, x4)  =  U99_gaaa(x1, x2, x4)
row2colc174_in_ga(x1, x2)  =  row2colc174_in_ga(x1)
row2colc174_out_ga(x1, x2)  =  row2colc174_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)  =  U64_ga(x1, x2, x3)
U65_ga(x1, x2, x3, x4, x5)  =  U65_ga(x1, x2, x5)
U100_gaaa(x1, x2, x3, x4)  =  U100_gaaa(x1, x2, x4)
row2colc306_in_ga(x1, x2)  =  row2colc306_in_ga(x1)
row2colc306_out_ga(x1, x2)  =  row2colc306_out_ga(x1, x2)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x2, x3)
U67_ga(x1, x2, x3, x4)  =  U67_ga(x1, x2, x4)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x2, x3)
U69_ga(x1, x2, x3, x4)  =  U69_ga(x1, x2, x4)
U101_gaaa(x1, x2, x3, x4, x5)  =  U101_gaaa(x1, x2, x5)
row2colc454_in_gaa(x1, x2, x3)  =  row2colc454_in_gaa(x1)
row2colc454_out_gaa(x1, x2, x3)  =  row2colc454_out_gaa(x1, x3)
U70_gaa(x1, x2, x3)  =  U70_gaa(x1, x2, x3)
U71_gaa(x1, x2, x3, x4)  =  U71_gaa(x1, x2, x4)
U72_gaa(x1, x2, x3, x4)  =  U72_gaa(x1, x2, x4)
U73_gaa(x1, x2, x3, x4, x5)  =  U73_gaa(x1, x2, x5)
U74_gaa(x1, x2, x3)  =  U74_gaa(x1, x2, x3)
U75_gaa(x1, x2, x3, x4, x5)  =  U75_gaa(x1, x2, x5)
U76_gaa(x1, x2, x3, x4)  =  U76_gaa(x1, x2, x4)
U77_gaa(x1, x2, x3, x4, x5, x6)  =  U77_gaa(x1, x2, x6)
U102_gaaa(x1, x2, x3)  =  U102_gaaa(x1, x2, x3)
U103_gaaa(x1, x2, x3, x4, x5)  =  U103_gaaa(x1, x2, x5)
U104_gaaa(x1, x2, x3, x4)  =  U104_gaaa(x1, x2, x4)
U105_gaaa(x1, x2, x3, x4, x5, x6)  =  U105_gaaa(x1, x2, x6)
U106_gaaa(x1, x2, x3, x4)  =  U106_gaaa(x1, x2, x4)
row2colc727_in_ga(x1, x2)  =  row2colc727_in_ga(x1)
row2colc727_out_ga(x1, x2)  =  row2colc727_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x2, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x2, x3)
U80_ga(x1, x2, x3, x4)  =  U80_ga(x1, x2, x4)
U81_ga(x1, x2, x3, x4, x5)  =  U81_ga(x1, x2, x5)
U107_gaaa(x1, x2, x3, x4, x5)  =  U107_gaaa(x1, x2, x5)
row2colc897_in_gaa(x1, x2, x3)  =  row2colc897_in_gaa(x1)
row2colc897_out_gaa(x1, x2, x3)  =  row2colc897_out_gaa(x1)
U82_gaa(x1, x2, x3)  =  U82_gaa(x1, x2, x3)
U83_gaa(x1, x2, x3, x4)  =  U83_gaa(x1, x2, x4)
U84_gaa(x1, x2, x3)  =  U84_gaa(x1, x2, x3)
U85_gaa(x1, x2, x3, x4, x5)  =  U85_gaa(x1, x2, x5)
U86_gaa(x1, x2, x3, x4)  =  U86_gaa(x1, x2, x4)
U87_gaa(x1, x2, x3, x4, x5)  =  U87_gaa(x1, x2, x5)
U88_gaa(x1, x2, x3, x4, x5)  =  U88_gaa(x1, x2, x5)
U89_gaa(x1, x2, x3, x4, x5, x6)  =  U89_gaa(x1, x2, x6)
U108_gaaa(x1, x2, x3, x4, x5)  =  U108_gaaa(x1, x2, x5)
row2colc1113_in_gaa(x1, x2, x3)  =  row2colc1113_in_gaa(x1)
row2colc1113_out_gaa(x1, x2, x3)  =  row2colc1113_out_gaa(x1, x3)
U90_gaa(x1, x2, x3)  =  U90_gaa(x1, x2, x3)
U91_gaa(x1, x2, x3, x4)  =  U91_gaa(x1, x2, x4)
U92_gaa(x1, x2, x3)  =  U92_gaa(x1, x2, x3)
U93_gaa(x1, x2, x3, x4)  =  U93_gaa(x1, x2, x4)
U94_gaa(x1, x2, x3, x4)  =  U94_gaa(x1, x2, x4)
U95_gaa(x1, x2, x3, x4, x5)  =  U95_gaa(x1, x2, x5)
U96_gaa(x1, x2, x3, x4, x5)  =  U96_gaa(x1, x2, x5)
U97_gaa(x1, x2, x3, x4, x5, x6)  =  U97_gaa(x1, x2, x6)
U109_gaaa(x1, x2, x3, x4, x5, x6)  =  U109_gaaa(x1, x2, x6)
U110_gaaa(x1, x2, x3, x4, x5)  =  U110_gaaa(x1, x2, x5)
U111_gaaa(x1, x2, x3, x4, x5, x6)  =  U111_gaaa(x1, x2, x6)
U112_gaaa(x1, x2, x3, x4, x5, x6)  =  U112_gaaa(x1, x2, x6)
U113_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U113_gaaa(x1, x2, x7)
P19_IN_GAAAG(x1, x2, x3, x4, x5)  =  P19_IN_GAAAG(x1, x5)
U56_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U56_GAAAG(x1, x5, x6, x7)

We have to consider all (P,R,Pi)-chains

(64) PiDPToQDPProof (SOUND transformation)

Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.

(65) Obligation:

Q DP problem:
The TRS P consists of the following rules:

P19_IN_GAAAG(T34, .(T1052, T1053)) → U56_GAAAG(T34, T1052, T1053, row2colc20_in_gaaa(T34))
U56_GAAAG(T34, T1052, T1053, row2colc20_out_gaaa(T34, T1036)) → P19_IN_GAAAG(T1052, T1053)

The TRS R consists of the following rules:

row2colc20_in_gaaa([]) → row2colc20_out_gaaa([], [])
row2colc20_in_gaaa(.(T70, T71)) → U98_gaaa(T70, T71, row2colc74_in_g(T71))
row2colc74_in_g([]) → row2colc74_out_g([])
row2colc74_in_g(.(T90, T91)) → U60_g(T90, T91, row2colc74_in_g(T91))
row2colc74_in_g(.(T103, T100)) → U61_g(T103, T100, row2colc74_in_g(T100))
U61_g(T103, T100, row2colc74_out_g(T100)) → row2colc74_out_g(.(T103, T100))
U60_g(T90, T91, row2colc74_out_g(T91)) → row2colc74_out_g(.(T90, T91))
U98_gaaa(T70, T71, row2colc74_out_g(T71)) → row2colc20_out_gaaa(.(T70, T71), [])
row2colc20_in_gaaa(.(T70, T71)) → U99_gaaa(T70, T71, row2colc174_in_ga(T71))
row2colc174_in_ga([]) → row2colc174_out_ga([])
row2colc174_in_ga(.(T122, T123)) → U62_ga(T122, T123, row2colc74_in_g(T123))
U62_ga(T122, T123, row2colc74_out_g(T123)) → row2colc174_out_ga(.(T122, T123))
row2colc174_in_ga(.(T122, T123)) → U63_ga(T122, T123, row2colc174_in_ga(T123))
row2colc174_in_ga(.(T135, T132)) → U64_ga(T135, T132, row2colc74_in_g(T132))
U64_ga(T135, T132, row2colc74_out_g(T132)) → row2colc174_out_ga(.(T135, T132))
row2colc174_in_ga(.(T135, T132)) → U65_ga(T135, T132, row2colc174_in_ga(T132))
U65_ga(T135, T132, row2colc174_out_ga(T132)) → row2colc174_out_ga(.(T135, T132))
U63_ga(T122, T123, row2colc174_out_ga(T123)) → row2colc174_out_ga(.(T122, T123))
U99_gaaa(T70, T71, row2colc174_out_ga(T71)) → row2colc20_out_gaaa(.(T70, T71), [])
row2colc20_in_gaaa(.(T140, T141)) → U100_gaaa(T140, T141, row2colc306_in_ga(T141))
row2colc306_in_ga([]) → row2colc306_out_ga([], [])
row2colc306_in_ga(.(T160, T161)) → U66_ga(T160, T161, row2colc74_in_g(T161))
U66_ga(T160, T161, row2colc74_out_g(T161)) → row2colc306_out_ga(.(T160, T161), [])
row2colc306_in_ga(.(T166, T167)) → U67_ga(T166, T167, row2colc306_in_ga(T167))
row2colc306_in_ga(.(T179, T176)) → U68_ga(T179, T176, row2colc74_in_g(T176))
U68_ga(T179, T176, row2colc74_out_g(T176)) → row2colc306_out_ga(.(T179, T176), [])
row2colc306_in_ga(.(T188, T185)) → U69_ga(T188, T185, row2colc306_in_ga(T185))
U69_ga(T188, T185, row2colc306_out_ga(T185, X2110)) → row2colc306_out_ga(.(T188, T185), .([], X2110))
U67_ga(T166, T167, row2colc306_out_ga(T167, X1819)) → row2colc306_out_ga(.(T166, T167), .([], X1819))
U100_gaaa(T140, T141, row2colc306_out_ga(T141, X1441)) → row2colc20_out_gaaa(.(T140, T141), .([], X1441))
row2colc20_in_gaaa(.(T140, T141)) → U101_gaaa(T140, T141, row2colc454_in_gaa(T141))
row2colc454_in_gaa([]) → row2colc454_out_gaa([], [])
row2colc454_in_gaa(.(T207, T208)) → U70_gaa(T207, T208, row2colc74_in_g(T208))
U70_gaa(T207, T208, row2colc74_out_g(T208)) → row2colc454_out_gaa(.(T207, T208), [])
row2colc454_in_gaa(.(T207, T208)) → U71_gaa(T207, T208, row2colc174_in_ga(T208))
U71_gaa(T207, T208, row2colc174_out_ga(T208)) → row2colc454_out_gaa(.(T207, T208), [])
row2colc454_in_gaa(.(T213, T214)) → U72_gaa(T213, T214, row2colc306_in_ga(T214))
U72_gaa(T213, T214, row2colc306_out_ga(T214, X2620)) → row2colc454_out_gaa(.(T213, T214), .([], X2620))
row2colc454_in_gaa(.(T213, T214)) → U73_gaa(T213, T214, row2colc454_in_gaa(T214))
row2colc454_in_gaa(.(T226, T223)) → U74_gaa(T226, T223, row2colc74_in_g(T223))
U74_gaa(T226, T223, row2colc74_out_g(T223)) → row2colc454_out_gaa(.(T226, T223), [])
row2colc454_in_gaa(.(T226, T223)) → U75_gaa(T226, T223, row2colc174_in_ga(T223))
U75_gaa(T226, T223, row2colc174_out_ga(T223)) → row2colc454_out_gaa(.(T226, T223), [])
row2colc454_in_gaa(.(T235, T232)) → U76_gaa(T235, T232, row2colc306_in_ga(T232))
U76_gaa(T235, T232, row2colc306_out_ga(T232, X3025)) → row2colc454_out_gaa(.(T235, T232), .([], X3025))
row2colc454_in_gaa(.(T235, T232)) → U77_gaa(T235, T232, row2colc454_in_gaa(T232))
U77_gaa(T235, T232, row2colc454_out_gaa(T232, X3089)) → row2colc454_out_gaa(.(T235, T232), .([], X3089))
U73_gaa(T213, T214, row2colc454_out_gaa(T214, X2681)) → row2colc454_out_gaa(.(T213, T214), .([], X2681))
U101_gaaa(T140, T141, row2colc454_out_gaa(T141, X2179)) → row2colc20_out_gaaa(.(T140, T141), .([], X2179))
row2colc20_in_gaaa(.(T247, T244)) → U102_gaaa(T247, T244, row2colc74_in_g(T244))
U102_gaaa(T247, T244, row2colc74_out_g(T244)) → row2colc20_out_gaaa(.(T247, T244), [])
row2colc20_in_gaaa(.(T247, T244)) → U103_gaaa(T247, T244, row2colc174_in_ga(T244))
U103_gaaa(T247, T244, row2colc174_out_ga(T244)) → row2colc20_out_gaaa(.(T247, T244), [])
row2colc20_in_gaaa(.(T256, T253)) → U104_gaaa(T256, T253, row2colc306_in_ga(T253))
U104_gaaa(T256, T253, row2colc306_out_ga(T253, X3437)) → row2colc20_out_gaaa(.(T256, T253), .([], X3437))
row2colc20_in_gaaa(.(T256, T253)) → U105_gaaa(T256, T253, row2colc454_in_gaa(T253))
U105_gaaa(T256, T253, row2colc454_out_gaa(T253, X3501)) → row2colc20_out_gaaa(.(T256, T253), .([], X3501))
row2colc20_in_gaaa(.(T275, T276)) → U106_gaaa(T275, T276, row2colc727_in_ga(T276))
row2colc727_in_ga([]) → row2colc727_out_ga([])
row2colc727_in_ga(.(T326, T327)) → U78_ga(T326, T327, row2colc74_in_g(T327))
U78_ga(T326, T327, row2colc74_out_g(T327)) → row2colc727_out_ga(.(T326, T327))
row2colc727_in_ga(.(T339, T336)) → U79_ga(T339, T336, row2colc74_in_g(T336))
U79_ga(T339, T336, row2colc74_out_g(T336)) → row2colc727_out_ga(.(T339, T336))
row2colc727_in_ga(.(T358, T359)) → U80_ga(T358, T359, row2colc727_in_ga(T359))
row2colc727_in_ga(.(T415, T392)) → U81_ga(T415, T392, row2colc727_in_ga(T392))
U81_ga(T415, T392, row2colc727_out_ga(T392)) → row2colc727_out_ga(.(T415, T392))
U80_ga(T358, T359, row2colc727_out_ga(T359)) → row2colc727_out_ga(.(T358, T359))
U106_gaaa(T275, T276, row2colc727_out_ga(T276)) → row2colc20_out_gaaa(.(T275, T276), [])
row2colc20_in_gaaa(.(T275, T276)) → U107_gaaa(T275, T276, row2colc897_in_gaa(T276))
row2colc897_in_gaa([]) → row2colc897_out_gaa([])
row2colc897_in_gaa(.(T474, T475)) → U82_gaa(T474, T475, row2colc74_in_g(T475))
U82_gaa(T474, T475, row2colc74_out_g(T475)) → row2colc897_out_gaa(.(T474, T475))
row2colc897_in_gaa(.(T474, T475)) → U83_gaa(T474, T475, row2colc174_in_ga(T475))
U83_gaa(T474, T475, row2colc174_out_ga(T475)) → row2colc897_out_gaa(.(T474, T475))
row2colc897_in_gaa(.(T487, T484)) → U84_gaa(T487, T484, row2colc74_in_g(T484))
U84_gaa(T487, T484, row2colc74_out_g(T484)) → row2colc897_out_gaa(.(T487, T484))
row2colc897_in_gaa(.(T487, T484)) → U85_gaa(T487, T484, row2colc174_in_ga(T484))
U85_gaa(T487, T484, row2colc174_out_ga(T484)) → row2colc897_out_gaa(.(T487, T484))
row2colc897_in_gaa(.(T506, T507)) → U86_gaa(T506, T507, row2colc727_in_ga(T507))
U86_gaa(T506, T507, row2colc727_out_ga(T507)) → row2colc897_out_gaa(.(T506, T507))
row2colc897_in_gaa(.(T506, T507)) → U87_gaa(T506, T507, row2colc897_in_gaa(T507))
row2colc897_in_gaa(.(T570, T547)) → U88_gaa(T570, T547, row2colc727_in_ga(T547))
U88_gaa(T570, T547, row2colc727_out_ga(T547)) → row2colc897_out_gaa(.(T570, T547))
row2colc897_in_gaa(.(T570, T547)) → U89_gaa(T570, T547, row2colc897_in_gaa(T547))
U89_gaa(T570, T547, row2colc897_out_gaa(T547)) → row2colc897_out_gaa(.(T570, T547))
U87_gaa(T506, T507, row2colc897_out_gaa(T507)) → row2colc897_out_gaa(.(T506, T507))
U107_gaaa(T275, T276, row2colc897_out_gaa(T276)) → row2colc20_out_gaaa(.(T275, T276), [])
row2colc20_in_gaaa(.(T615, T616)) → U108_gaaa(T615, T616, row2colc1113_in_gaa(T616))
row2colc1113_in_gaa([]) → row2colc1113_out_gaa([], [])
row2colc1113_in_gaa(.(T665, T666)) → U90_gaa(T665, T666, row2colc74_in_g(T666))
U90_gaa(T665, T666, row2colc74_out_g(T666)) → row2colc1113_out_gaa(.(T665, T666), [])
row2colc1113_in_gaa(.(T671, T672)) → U91_gaa(T671, T672, row2colc306_in_ga(T672))
U91_gaa(T671, T672, row2colc306_out_ga(T672, X5778)) → row2colc1113_out_gaa(.(T671, T672), .([], X5778))
row2colc1113_in_gaa(.(T684, T681)) → U92_gaa(T684, T681, row2colc74_in_g(T681))
U92_gaa(T684, T681, row2colc74_out_g(T681)) → row2colc1113_out_gaa(.(T684, T681), [])
row2colc1113_in_gaa(.(T693, T690)) → U93_gaa(T693, T690, row2colc306_in_ga(T690))
U93_gaa(T693, T690, row2colc306_out_ga(T690, X6069)) → row2colc1113_out_gaa(.(T693, T690), .([], X6069))
row2colc1113_in_gaa(.(T712, T713)) → U94_gaa(T712, T713, row2colc727_in_ga(T713))
U94_gaa(T712, T713, row2colc727_out_ga(T713)) → row2colc1113_out_gaa(.(T712, T713), [])
row2colc1113_in_gaa(.(T737, T738)) → U95_gaa(T737, T738, row2colc1113_in_gaa(T738))
row2colc1113_in_gaa(.(T793, T770)) → U96_gaa(T793, T770, row2colc727_in_ga(T770))
U96_gaa(T793, T770, row2colc727_out_ga(T770)) → row2colc1113_out_gaa(.(T793, T770), [])
row2colc1113_in_gaa(.(T843, T820)) → U97_gaa(T843, T820, row2colc1113_in_gaa(T820))
U97_gaa(T843, T820, row2colc1113_out_gaa(T820, X6607)) → row2colc1113_out_gaa(.(T843, T820), .([], X6607))
U95_gaa(T737, T738, row2colc1113_out_gaa(T738, X6344)) → row2colc1113_out_gaa(.(T737, T738), .([], X6344))
U108_gaaa(T615, T616, row2colc1113_out_gaa(T616, X5410)) → row2colc20_out_gaaa(.(T615, T616), .([], X5410))
row2colc20_in_gaaa(.(T615, T616)) → U109_gaaa(T615, T616, row2colc20_in_gaaa(T616))
row2colc20_in_gaaa(.(T906, T883)) → U110_gaaa(T906, T883, row2colc727_in_ga(T883))
U110_gaaa(T906, T883, row2colc727_out_ga(T883)) → row2colc20_out_gaaa(.(T906, T883), [])
row2colc20_in_gaaa(.(T906, T883)) → U111_gaaa(T906, T883, row2colc897_in_gaa(T883))
U111_gaaa(T906, T883, row2colc897_out_gaa(T883)) → row2colc20_out_gaaa(.(T906, T883), [])
row2colc20_in_gaaa(.(T975, T952)) → U112_gaaa(T975, T952, row2colc1113_in_gaa(T952))
U112_gaaa(T975, T952, row2colc1113_out_gaa(T952, X6985)) → row2colc20_out_gaaa(.(T975, T952), .([], X6985))
row2colc20_in_gaaa(.(T975, T952)) → U113_gaaa(T975, T952, row2colc20_in_gaaa(T952))
U113_gaaa(T975, T952, row2colc20_out_gaaa(T952, X7046)) → row2colc20_out_gaaa(.(T975, T952), .([], X7046))
U109_gaaa(T615, T616, row2colc20_out_gaaa(T616, X6672)) → row2colc20_out_gaaa(.(T615, T616), .([], X6672))

The set Q consists of the following terms:

row2colc20_in_gaaa(x0)
row2colc74_in_g(x0)
U61_g(x0, x1, x2)
U60_g(x0, x1, x2)
U98_gaaa(x0, x1, x2)
row2colc174_in_ga(x0)
U62_ga(x0, x1, x2)
U64_ga(x0, x1, x2)
U65_ga(x0, x1, x2)
U63_ga(x0, x1, x2)
U99_gaaa(x0, x1, x2)
row2colc306_in_ga(x0)
U66_ga(x0, x1, x2)
U68_ga(x0, x1, x2)
U69_ga(x0, x1, x2)
U67_ga(x0, x1, x2)
U100_gaaa(x0, x1, x2)
row2colc454_in_gaa(x0)
U70_gaa(x0, x1, x2)
U71_gaa(x0, x1, x2)
U72_gaa(x0, x1, x2)
U74_gaa(x0, x1, x2)
U75_gaa(x0, x1, x2)
U76_gaa(x0, x1, x2)
U77_gaa(x0, x1, x2)
U73_gaa(x0, x1, x2)
U101_gaaa(x0, x1, x2)
U102_gaaa(x0, x1, x2)
U103_gaaa(x0, x1, x2)
U104_gaaa(x0, x1, x2)
U105_gaaa(x0, x1, x2)
row2colc727_in_ga(x0)
U78_ga(x0, x1, x2)
U79_ga(x0, x1, x2)
U81_ga(x0, x1, x2)
U80_ga(x0, x1, x2)
U106_gaaa(x0, x1, x2)
row2colc897_in_gaa(x0)
U82_gaa(x0, x1, x2)
U83_gaa(x0, x1, x2)
U84_gaa(x0, x1, x2)
U85_gaa(x0, x1, x2)
U86_gaa(x0, x1, x2)
U88_gaa(x0, x1, x2)
U89_gaa(x0, x1, x2)
U87_gaa(x0, x1, x2)
U107_gaaa(x0, x1, x2)
row2colc1113_in_gaa(x0)
U90_gaa(x0, x1, x2)
U91_gaa(x0, x1, x2)
U92_gaa(x0, x1, x2)
U93_gaa(x0, x1, x2)
U94_gaa(x0, x1, x2)
U96_gaa(x0, x1, x2)
U97_gaa(x0, x1, x2)
U95_gaa(x0, x1, x2)
U108_gaaa(x0, x1, x2)
U110_gaaa(x0, x1, x2)
U111_gaaa(x0, x1, x2)
U112_gaaa(x0, x1, x2)
U113_gaaa(x0, x1, x2)
U109_gaaa(x0, x1, x2)

We have to consider all (P,Q,R)-chains.

(66) QDPSizeChangeProof (EQUIVALENT transformation)

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:

  • U56_GAAAG(T34, T1052, T1053, row2colc20_out_gaaa(T34, T1036)) → P19_IN_GAAAG(T1052, T1053)
    The graph contains the following edges 2 >= 1, 3 >= 2

  • P19_IN_GAAAG(T34, .(T1052, T1053)) → U56_GAAAG(T34, T1052, T1053, row2colc20_in_gaaa(T34))
    The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3

(67) YES