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

0 Prolog
↳1 PrologToPiTRSViaGraphTransformerProof (⇒, 7512 ms)
↳2 PiTRS
↳3 DependencyPairsProof (⇔, 1401 ms)
↳4 PiDP
↳5 DependencyGraphProof (⇔, 187 ms)
↳6 AND
    ↳7 PiDP
        ↳8 UsableRulesProof (⇔, 0 ms)
        ↳9 PiDP
        ↳10 PiDPToQDPProof (⇔, 0 ms)
        ↳11 QDP
        ↳12 QDPSizeChangeProof (⇔, 0 ms)
        ↳13 YES
    ↳14 PiDP
        ↳15 UsableRulesProof (⇔, 0 ms)
        ↳16 PiDP
        ↳17 PiDPToQDPProof (⇒, 0 ms)
        ↳18 QDP
        ↳19 QDPSizeChangeProof (⇔, 0 ms)
        ↳20 YES
    ↳21 PiDP
        ↳22 UsableRulesProof (⇔, 0 ms)
        ↳23 PiDP
        ↳24 PiDPToQDPProof (⇒, 0 ms)
        ↳25 QDP
        ↳26 QDPSizeChangeProof (⇔, 0 ms)
        ↳27 YES
    ↳28 PiDP
        ↳29 UsableRulesProof (⇔, 0 ms)
        ↳30 PiDP
        ↳31 PiDPToQDPProof (⇒, 0 ms)
        ↳32 QDP
        ↳33 QDPSizeChangeProof (⇔, 0 ms)
        ↳34 YES
    ↳35 PiDP
        ↳36 UsableRulesProof (⇔, 0 ms)
        ↳37 PiDP
        ↳38 PiDPToQDPProof (⇒, 0 ms)
        ↳39 QDP
        ↳40 QDPSizeChangeProof (⇔, 0 ms)
        ↳41 YES
    ↳42 PiDP
        ↳43 UsableRulesProof (⇔, 0 ms)
        ↳44 PiDP
        ↳45 PiDPToQDPProof (⇒, 0 ms)
        ↳46 QDP
        ↳47 QDPSizeChangeProof (⇔, 0 ms)
        ↳48 YES
    ↳49 PiDP
        ↳50 UsableRulesProof (⇔, 0 ms)
        ↳51 PiDP
        ↳52 PiDPToQDPProof (⇒, 1 ms)
        ↳53 QDP
        ↳54 QDPSizeChangeProof (⇔, 0 ms)
        ↳55 YES
    ↳56 PiDP
        ↳57 UsableRulesProof (⇔, 0 ms)
        ↳58 PiDP
        ↳59 PiDPToQDPProof (⇒, 0 ms)
        ↳60 QDP
        ↳61 QDPSizeChangeProof (⇔, 0 ms)
        ↳62 YES
    ↳63 PiDP
        ↳64 UsableRulesProof (⇔, 0 ms)
        ↳65 PiDP
        ↳66 PiDPToQDPProof (⇒, 94 ms)
        ↳67 QDP
        ↳68 QDPSizeChangeProof (⇔, 0 ms)
        ↳69 YES

(0) Obligation:

Clauses:

transpose(A, B) :- transpose_aux(A, [], B).
transpose_aux([], Y, Z) :- ','(!, eq(Y, Z)).
transpose_aux(R, X1, L) :- ','(head(R, Rh), ','(tail(R, Rt), ','(row2col(Rh, L, Cols, Accm), transpose_aux(Rt, Accm, Cols)))).
row2col([], X, Y, Z) :- ','(!, ','(eq(X, []), ','(eq(Y, []), eq(Z, [])))).
row2col(X, Y, C, A) :- ','(head(X, Xh), ','(head(Y, Yh), ','(head(Yh, Xh), ','(head(A, []), ','(tail(X, Xt), ','(tail(Y, Yt), ','(tail(Yh, Yht), ','(head(C, Yht), ','(tail(C, Ct), ','(tail(A, At), row2col(Xt, Yt, Ct, At))))))))))).
head([], X2).
head(.(H, X3), H).
tail([], []).
tail(.(X4, T), T).
eq(X, X).

Query: transpose(g,a)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

(2) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)

(3) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
The TRS P consists of the following rules:

TRANSPOSEA_IN_GA(.(T34, T35), T20) → U1_GA(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
TRANSPOSEA_IN_GA(.(T34, T35), T20) → PB_IN_GAAAG(T34, T20, X38, X39, T35)
PB_IN_GAAAG(T34, T20, T37, T38, T35) → U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
PB_IN_GAAAG(T34, T20, T37, T38, T35) → ROW2COLJ_IN_GAAA(T34, T20, T37, T38)
ROW2COLJ_IN_GAAA(.(T70, T71), [], [], []) → U40_GAAA(T70, T71, row2colC_in_g(T71))
ROW2COLJ_IN_GAAA(.(T70, T71), [], [], []) → ROW2COLC_IN_G(T71)
ROW2COLC_IN_G(.(T90, T91)) → U2_G(T90, T91, row2colC_in_g(T91))
ROW2COLC_IN_G(.(T90, T91)) → ROW2COLC_IN_G(T91)
ROW2COLC_IN_G(.(T103, T100)) → U3_G(T103, T100, row2colC_in_g(T100))
ROW2COLJ_IN_GAAA(.(T70, T71), [], .([], X759), []) → U41_GAAA(T70, T71, X759, row2colD_in_ga(T71, X759))
ROW2COLJ_IN_GAAA(.(T70, T71), [], .([], X759), []) → ROW2COLD_IN_GA(T71, X759)
ROW2COLD_IN_GA(.(T122, T123), []) → U4_GA(T122, T123, row2colC_in_g(T123))
ROW2COLD_IN_GA(.(T122, T123), []) → ROW2COLC_IN_G(T123)
ROW2COLD_IN_GA(.(T122, T123), .([], X1058)) → U5_GA(T122, T123, X1058, row2colD_in_ga(T123, X1058))
ROW2COLD_IN_GA(.(T122, T123), .([], X1058)) → ROW2COLD_IN_GA(T123, X1058)
ROW2COLD_IN_GA(.(T135, T132), []) → U6_GA(T135, T132, row2colC_in_g(T132))
ROW2COLD_IN_GA(.(T135, T132), .(X1270, X1271)) → U7_GA(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
ROW2COLD_IN_GA(.(T135, T132), .(X1270, X1271)) → ROW2COLD_IN_GA(T132, X1271)
ROW2COLJ_IN_GAAA(.(T140, T141), [], [], .([], X1419)) → U42_GAAA(T140, T141, X1419, row2colE_in_ga(T141, X1419))
ROW2COLJ_IN_GAAA(.(T140, T141), [], [], .([], X1419)) → ROW2COLE_IN_GA(T141, X1419)
ROW2COLE_IN_GA(.(T160, T161), []) → U8_GA(T160, T161, row2colC_in_g(T161))
ROW2COLE_IN_GA(.(T160, T161), []) → ROW2COLC_IN_G(T161)
ROW2COLE_IN_GA(.(T166, T167), .([], X1792)) → U9_GA(T166, T167, X1792, row2colE_in_ga(T167, X1792))
ROW2COLE_IN_GA(.(T166, T167), .([], X1792)) → ROW2COLE_IN_GA(T167, X1792)
ROW2COLE_IN_GA(.(T179, T176), []) → U10_GA(T179, T176, row2colC_in_g(T176))
ROW2COLE_IN_GA(.(T188, T185), .([], X2083)) → U11_GA(T188, T185, X2083, row2colE_in_ga(T185, X2083))
ROW2COLJ_IN_GAAA(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_GAAA(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
ROW2COLJ_IN_GAAA(.(T140, T141), [], .([], X2133), .([], X2152)) → ROW2COLF_IN_GAA(T141, X2133, X2152)
ROW2COLF_IN_GAA(.(T207, T208), [], []) → U12_GAA(T207, T208, row2colC_in_g(T208))
ROW2COLF_IN_GAA(.(T207, T208), [], []) → ROW2COLC_IN_G(T208)
ROW2COLF_IN_GAA(.(T207, T208), .([], X2448), []) → U13_GAA(T207, T208, X2448, row2colD_in_ga(T208, X2448))
ROW2COLF_IN_GAA(.(T207, T208), .([], X2448), []) → ROW2COLD_IN_GA(T208, X2448)
ROW2COLF_IN_GAA(.(T213, T214), [], .([], X2588)) → U14_GAA(T213, T214, X2588, row2colE_in_ga(T214, X2588))
ROW2COLF_IN_GAA(.(T213, T214), [], .([], X2588)) → ROW2COLE_IN_GA(T214, X2588)
ROW2COLF_IN_GAA(.(T213, T214), .([], X2630), .([], X2649)) → U15_GAA(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
ROW2COLF_IN_GAA(.(T213, T214), .([], X2630), .([], X2649)) → ROW2COLF_IN_GAA(T214, X2630, X2649)
ROW2COLF_IN_GAA(.(T226, T223), [], []) → U16_GAA(T226, T223, row2colC_in_g(T223))
ROW2COLF_IN_GAA(.(T226, T223), .(X2845, X2846), []) → U17_GAA(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
ROW2COLF_IN_GAA(.(T226, T223), .(X2845, X2846), []) → ROW2COLD_IN_GA(T223, X2846)
ROW2COLF_IN_GAA(.(T235, T232), [], .([], X2993)) → U18_GAA(T235, T232, X2993, row2colE_in_ga(T232, X2993))
ROW2COLF_IN_GAA(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_GAA(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
ROW2COLF_IN_GAA(.(T235, T232), .(X3037, X3038), .([], X3057)) → ROW2COLF_IN_GAA(T232, X3038, X3057)
ROW2COLJ_IN_GAAA(.(T247, T244), [], [], []) → U44_GAAA(T247, T244, row2colC_in_g(T244))
ROW2COLJ_IN_GAAA(.(T247, T244), [], .(X3257, X3258), []) → U45_GAAA(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
ROW2COLJ_IN_GAAA(.(T247, T244), [], .(X3257, X3258), []) → ROW2COLD_IN_GA(T244, X3258)
ROW2COLJ_IN_GAAA(.(T256, T253), [], [], .([], X3405)) → U46_GAAA(T256, T253, X3405, row2colE_in_ga(T253, X3405))
ROW2COLJ_IN_GAAA(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_GAAA(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
ROW2COLJ_IN_GAAA(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → ROW2COLF_IN_GAA(T253, X3450, X3469)
ROW2COLJ_IN_GAAA(.(T275, T276), .([], T282), [], []) → U48_GAAA(T275, T276, T282, row2colG_in_ga(T276, T282))
ROW2COLJ_IN_GAAA(.(T275, T276), .([], T282), [], []) → ROW2COLG_IN_GA(T276, T282)
ROW2COLG_IN_GA(.(T326, T327), []) → U20_GA(T326, T327, row2colC_in_g(T327))
ROW2COLG_IN_GA(.(T326, T327), []) → ROW2COLC_IN_G(T327)
ROW2COLG_IN_GA(.(T339, T336), []) → U21_GA(T339, T336, row2colC_in_g(T336))
ROW2COLG_IN_GA(.(T358, T359), .([], T365)) → U22_GA(T358, T359, T365, row2colG_in_ga(T359, T365))
ROW2COLG_IN_GA(.(T358, T359), .([], T365)) → ROW2COLG_IN_GA(T359, T365)
ROW2COLG_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → U23_GA(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
ROW2COLG_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → ROW2COLG_IN_GA(T392, T429)
ROW2COLJ_IN_GAAA(.(T275, T276), .([], T282), .([], X4320), []) → U49_GAAA(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
ROW2COLJ_IN_GAAA(.(T275, T276), .([], T282), .([], X4320), []) → ROW2COLH_IN_GAA(T276, T282, X4320)
ROW2COLH_IN_GAA(.(T474, T475), [], []) → U24_GAA(T474, T475, row2colC_in_g(T475))
ROW2COLH_IN_GAA(.(T474, T475), [], []) → ROW2COLC_IN_G(T475)
ROW2COLH_IN_GAA(.(T474, T475), [], .([], X4607)) → U25_GAA(T474, T475, X4607, row2colD_in_ga(T475, X4607))
ROW2COLH_IN_GAA(.(T474, T475), [], .([], X4607)) → ROW2COLD_IN_GA(T475, X4607)
ROW2COLH_IN_GAA(.(T487, T484), [], []) → U26_GAA(T487, T484, row2colC_in_g(T484))
ROW2COLH_IN_GAA(.(T487, T484), [], .(X4819, X4820)) → U27_GAA(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
ROW2COLH_IN_GAA(.(T487, T484), [], .(X4819, X4820)) → ROW2COLD_IN_GA(T484, X4820)
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), []) → U28_GAA(T506, T507, T513, row2colG_in_ga(T507, T513))
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), []) → ROW2COLG_IN_GA(T507, T513)
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), .([], X5019)) → U29_GAA(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), .([], X5019)) → ROW2COLH_IN_GAA(T507, T513, X5019)
ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T583), T584), []) → U30_GAA(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T583), T584), []) → ROW2COLG_IN_GA(T547, T584)
ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_GAA(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → ROW2COLH_IN_GAA(T547, T606, X5208)
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), [], .([], X5351)) → U50_GAAA(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), [], .([], X5351)) → ROW2COLI_IN_GAA(T616, T622, X5351)
ROW2COLI_IN_GAA(.(T665, T666), [], []) → U32_GAA(T665, T666, row2colC_in_g(T666))
ROW2COLI_IN_GAA(.(T665, T666), [], []) → ROW2COLC_IN_G(T666)
ROW2COLI_IN_GAA(.(T671, T672), [], .([], X5712)) → U33_GAA(T671, T672, X5712, row2colE_in_ga(T672, X5712))
ROW2COLI_IN_GAA(.(T671, T672), [], .([], X5712)) → ROW2COLE_IN_GA(T672, X5712)
ROW2COLI_IN_GAA(.(T684, T681), [], []) → U34_GAA(T684, T681, row2colC_in_g(T681))
ROW2COLI_IN_GAA(.(T693, T690), [], .([], X6003)) → U35_GAA(T693, T690, X6003, row2colE_in_ga(T690, X6003))
ROW2COLI_IN_GAA(.(T712, T713), .([], T719), []) → U36_GAA(T712, T713, T719, row2colG_in_ga(T713, T719))
ROW2COLI_IN_GAA(.(T712, T713), .([], T719), []) → ROW2COLG_IN_GA(T713, T719)
ROW2COLI_IN_GAA(.(T737, T738), .([], T744), .([], X6275)) → U37_GAA(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
ROW2COLI_IN_GAA(.(T737, T738), .([], T744), .([], X6275)) → ROW2COLI_IN_GAA(T738, T744, X6275)
ROW2COLI_IN_GAA(.(T793, T770), .(.(T793, T806), T807), []) → U38_GAA(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
ROW2COLI_IN_GAA(.(T793, T770), .(.(T793, T806), T807), []) → ROW2COLG_IN_GA(T770, T807)
ROW2COLI_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_GAA(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
ROW2COLI_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → ROW2COLI_IN_GAA(T820, T857, X6536)
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_GAAA(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → ROW2COLJ_IN_GAAA(T616, T622, X6582, X6601)
ROW2COLJ_IN_GAAA(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_GAAA(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
ROW2COLJ_IN_GAAA(.(T906, T883), .(.(T906, T919), T920), [], []) → ROW2COLG_IN_GA(T883, T920)
ROW2COLJ_IN_GAAA(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_GAAA(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
ROW2COLJ_IN_GAAA(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → ROW2COLH_IN_GAA(T883, T942, X6774)
ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_GAAA(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → ROW2COLI_IN_GAA(T952, T989, X6912)
ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_GAAA(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → ROW2COLJ_IN_GAAA(T952, T1010, X6954, X6973)
U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_GAAAG(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → TRANSPOSE_AUXK_IN_GGA(T35, T38, T37)
TRANSPOSE_AUXK_IN_GGA(.(T1052, T1053), T1036, T1038) → U56_GGA(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
TRANSPOSE_AUXK_IN_GGA(.(T1052, T1053), T1036, T1038) → PB_IN_GAAAG(T1052, T1038, X7010, X7011, T1053)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
TRANSPOSEA_IN_GA(x1, x2)  =  TRANSPOSEA_IN_GA(x1)
U1_GA(x1, x2, x3, x4)  =  U1_GA(x1, x2, x4)
PB_IN_GAAAG(x1, x2, x3, x4, x5)  =  PB_IN_GAAAG(x1, x5)
U57_GAAAG(x1, x2, x3, x4, x5, x6)  =  U57_GAAAG(x1, x5, x6)
ROW2COLJ_IN_GAAA(x1, x2, x3, x4)  =  ROW2COLJ_IN_GAAA(x1)
U40_GAAA(x1, x2, x3)  =  U40_GAAA(x1, x2, x3)
ROW2COLC_IN_G(x1)  =  ROW2COLC_IN_G(x1)
U2_G(x1, x2, x3)  =  U2_G(x1, x2, x3)
U3_G(x1, x2, x3)  =  U3_G(x1, x2, x3)
U41_GAAA(x1, x2, x3, x4)  =  U41_GAAA(x1, x2, x4)
ROW2COLD_IN_GA(x1, x2)  =  ROW2COLD_IN_GA(x1)
U4_GA(x1, x2, x3)  =  U4_GA(x1, x2, x3)
U5_GA(x1, x2, x3, x4)  =  U5_GA(x1, x2, x4)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x2, x3)
U7_GA(x1, x2, x3, x4, x5)  =  U7_GA(x1, x2, x5)
U42_GAAA(x1, x2, x3, x4)  =  U42_GAAA(x1, x2, x4)
ROW2COLE_IN_GA(x1, x2)  =  ROW2COLE_IN_GA(x1)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x2, x3)
U9_GA(x1, x2, x3, x4)  =  U9_GA(x1, x2, x4)
U10_GA(x1, x2, x3)  =  U10_GA(x1, x2, x3)
U11_GA(x1, x2, x3, x4)  =  U11_GA(x1, x2, x4)
U43_GAAA(x1, x2, x3, x4, x5)  =  U43_GAAA(x1, x2, x5)
ROW2COLF_IN_GAA(x1, x2, x3)  =  ROW2COLF_IN_GAA(x1)
U12_GAA(x1, x2, x3)  =  U12_GAA(x1, x2, x3)
U13_GAA(x1, x2, x3, x4)  =  U13_GAA(x1, x2, x4)
U14_GAA(x1, x2, x3, x4)  =  U14_GAA(x1, x2, x4)
U15_GAA(x1, x2, x3, x4, x5)  =  U15_GAA(x1, x2, x5)
U16_GAA(x1, x2, x3)  =  U16_GAA(x1, x2, x3)
U17_GAA(x1, x2, x3, x4, x5)  =  U17_GAA(x1, x2, x5)
U18_GAA(x1, x2, x3, x4)  =  U18_GAA(x1, x2, x4)
U19_GAA(x1, x2, x3, x4, x5, x6)  =  U19_GAA(x1, x2, x6)
U44_GAAA(x1, x2, x3)  =  U44_GAAA(x1, x2, x3)
U45_GAAA(x1, x2, x3, x4, x5)  =  U45_GAAA(x1, x2, x5)
U46_GAAA(x1, x2, x3, x4)  =  U46_GAAA(x1, x2, x4)
U47_GAAA(x1, x2, x3, x4, x5, x6)  =  U47_GAAA(x1, x2, x6)
U48_GAAA(x1, x2, x3, x4)  =  U48_GAAA(x1, x2, x4)
ROW2COLG_IN_GA(x1, x2)  =  ROW2COLG_IN_GA(x1)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x2, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x2, x3)
U22_GA(x1, x2, x3, x4)  =  U22_GA(x1, x2, x4)
U23_GA(x1, x2, x3, x4, x5)  =  U23_GA(x1, x2, x5)
U49_GAAA(x1, x2, x3, x4, x5)  =  U49_GAAA(x1, x2, x5)
ROW2COLH_IN_GAA(x1, x2, x3)  =  ROW2COLH_IN_GAA(x1)
U24_GAA(x1, x2, x3)  =  U24_GAA(x1, x2, x3)
U25_GAA(x1, x2, x3, x4)  =  U25_GAA(x1, x2, x4)
U26_GAA(x1, x2, x3)  =  U26_GAA(x1, x2, x3)
U27_GAA(x1, x2, x3, x4, x5)  =  U27_GAA(x1, x2, x5)
U28_GAA(x1, x2, x3, x4)  =  U28_GAA(x1, x2, x4)
U29_GAA(x1, x2, x3, x4, x5)  =  U29_GAA(x1, x2, x5)
U30_GAA(x1, x2, x3, x4, x5)  =  U30_GAA(x1, x2, x5)
U31_GAA(x1, x2, x3, x4, x5, x6)  =  U31_GAA(x1, x2, x6)
U50_GAAA(x1, x2, x3, x4, x5)  =  U50_GAAA(x1, x2, x5)
ROW2COLI_IN_GAA(x1, x2, x3)  =  ROW2COLI_IN_GAA(x1)
U32_GAA(x1, x2, x3)  =  U32_GAA(x1, x2, x3)
U33_GAA(x1, x2, x3, x4)  =  U33_GAA(x1, x2, x4)
U34_GAA(x1, x2, x3)  =  U34_GAA(x1, x2, x3)
U35_GAA(x1, x2, x3, x4)  =  U35_GAA(x1, x2, x4)
U36_GAA(x1, x2, x3, x4)  =  U36_GAA(x1, x2, x4)
U37_GAA(x1, x2, x3, x4, x5)  =  U37_GAA(x1, x2, x5)
U38_GAA(x1, x2, x3, x4, x5)  =  U38_GAA(x1, x2, x5)
U39_GAA(x1, x2, x3, x4, x5, x6)  =  U39_GAA(x1, x2, x6)
U51_GAAA(x1, x2, x3, x4, x5, x6)  =  U51_GAAA(x1, x2, x6)
U52_GAAA(x1, x2, x3, x4, x5)  =  U52_GAAA(x1, x2, x5)
U53_GAAA(x1, x2, x3, x4, x5, x6)  =  U53_GAAA(x1, x2, x6)
U54_GAAA(x1, x2, x3, x4, x5, x6)  =  U54_GAAA(x1, x2, x6)
U55_GAAA(x1, x2, x3, x4, x5, x6, x7)  =  U55_GAAA(x1, x2, x7)
U58_GAAAG(x1, x2, x3, x4, x5, x6)  =  U58_GAAAG(x1, x4, x5, x6)
TRANSPOSE_AUXK_IN_GGA(x1, x2, x3)  =  TRANSPOSE_AUXK_IN_GGA(x1, x2)
U56_GGA(x1, x2, x3, x4, x5)  =  U56_GGA(x1, x2, x3, x5)

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

(4) Obligation:

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

TRANSPOSEA_IN_GA(.(T34, T35), T20) → U1_GA(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
TRANSPOSEA_IN_GA(.(T34, T35), T20) → PB_IN_GAAAG(T34, T20, X38, X39, T35)
PB_IN_GAAAG(T34, T20, T37, T38, T35) → U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
PB_IN_GAAAG(T34, T20, T37, T38, T35) → ROW2COLJ_IN_GAAA(T34, T20, T37, T38)
ROW2COLJ_IN_GAAA(.(T70, T71), [], [], []) → U40_GAAA(T70, T71, row2colC_in_g(T71))
ROW2COLJ_IN_GAAA(.(T70, T71), [], [], []) → ROW2COLC_IN_G(T71)
ROW2COLC_IN_G(.(T90, T91)) → U2_G(T90, T91, row2colC_in_g(T91))
ROW2COLC_IN_G(.(T90, T91)) → ROW2COLC_IN_G(T91)
ROW2COLC_IN_G(.(T103, T100)) → U3_G(T103, T100, row2colC_in_g(T100))
ROW2COLJ_IN_GAAA(.(T70, T71), [], .([], X759), []) → U41_GAAA(T70, T71, X759, row2colD_in_ga(T71, X759))
ROW2COLJ_IN_GAAA(.(T70, T71), [], .([], X759), []) → ROW2COLD_IN_GA(T71, X759)
ROW2COLD_IN_GA(.(T122, T123), []) → U4_GA(T122, T123, row2colC_in_g(T123))
ROW2COLD_IN_GA(.(T122, T123), []) → ROW2COLC_IN_G(T123)
ROW2COLD_IN_GA(.(T122, T123), .([], X1058)) → U5_GA(T122, T123, X1058, row2colD_in_ga(T123, X1058))
ROW2COLD_IN_GA(.(T122, T123), .([], X1058)) → ROW2COLD_IN_GA(T123, X1058)
ROW2COLD_IN_GA(.(T135, T132), []) → U6_GA(T135, T132, row2colC_in_g(T132))
ROW2COLD_IN_GA(.(T135, T132), .(X1270, X1271)) → U7_GA(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
ROW2COLD_IN_GA(.(T135, T132), .(X1270, X1271)) → ROW2COLD_IN_GA(T132, X1271)
ROW2COLJ_IN_GAAA(.(T140, T141), [], [], .([], X1419)) → U42_GAAA(T140, T141, X1419, row2colE_in_ga(T141, X1419))
ROW2COLJ_IN_GAAA(.(T140, T141), [], [], .([], X1419)) → ROW2COLE_IN_GA(T141, X1419)
ROW2COLE_IN_GA(.(T160, T161), []) → U8_GA(T160, T161, row2colC_in_g(T161))
ROW2COLE_IN_GA(.(T160, T161), []) → ROW2COLC_IN_G(T161)
ROW2COLE_IN_GA(.(T166, T167), .([], X1792)) → U9_GA(T166, T167, X1792, row2colE_in_ga(T167, X1792))
ROW2COLE_IN_GA(.(T166, T167), .([], X1792)) → ROW2COLE_IN_GA(T167, X1792)
ROW2COLE_IN_GA(.(T179, T176), []) → U10_GA(T179, T176, row2colC_in_g(T176))
ROW2COLE_IN_GA(.(T188, T185), .([], X2083)) → U11_GA(T188, T185, X2083, row2colE_in_ga(T185, X2083))
ROW2COLJ_IN_GAAA(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_GAAA(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
ROW2COLJ_IN_GAAA(.(T140, T141), [], .([], X2133), .([], X2152)) → ROW2COLF_IN_GAA(T141, X2133, X2152)
ROW2COLF_IN_GAA(.(T207, T208), [], []) → U12_GAA(T207, T208, row2colC_in_g(T208))
ROW2COLF_IN_GAA(.(T207, T208), [], []) → ROW2COLC_IN_G(T208)
ROW2COLF_IN_GAA(.(T207, T208), .([], X2448), []) → U13_GAA(T207, T208, X2448, row2colD_in_ga(T208, X2448))
ROW2COLF_IN_GAA(.(T207, T208), .([], X2448), []) → ROW2COLD_IN_GA(T208, X2448)
ROW2COLF_IN_GAA(.(T213, T214), [], .([], X2588)) → U14_GAA(T213, T214, X2588, row2colE_in_ga(T214, X2588))
ROW2COLF_IN_GAA(.(T213, T214), [], .([], X2588)) → ROW2COLE_IN_GA(T214, X2588)
ROW2COLF_IN_GAA(.(T213, T214), .([], X2630), .([], X2649)) → U15_GAA(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
ROW2COLF_IN_GAA(.(T213, T214), .([], X2630), .([], X2649)) → ROW2COLF_IN_GAA(T214, X2630, X2649)
ROW2COLF_IN_GAA(.(T226, T223), [], []) → U16_GAA(T226, T223, row2colC_in_g(T223))
ROW2COLF_IN_GAA(.(T226, T223), .(X2845, X2846), []) → U17_GAA(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
ROW2COLF_IN_GAA(.(T226, T223), .(X2845, X2846), []) → ROW2COLD_IN_GA(T223, X2846)
ROW2COLF_IN_GAA(.(T235, T232), [], .([], X2993)) → U18_GAA(T235, T232, X2993, row2colE_in_ga(T232, X2993))
ROW2COLF_IN_GAA(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_GAA(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
ROW2COLF_IN_GAA(.(T235, T232), .(X3037, X3038), .([], X3057)) → ROW2COLF_IN_GAA(T232, X3038, X3057)
ROW2COLJ_IN_GAAA(.(T247, T244), [], [], []) → U44_GAAA(T247, T244, row2colC_in_g(T244))
ROW2COLJ_IN_GAAA(.(T247, T244), [], .(X3257, X3258), []) → U45_GAAA(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
ROW2COLJ_IN_GAAA(.(T247, T244), [], .(X3257, X3258), []) → ROW2COLD_IN_GA(T244, X3258)
ROW2COLJ_IN_GAAA(.(T256, T253), [], [], .([], X3405)) → U46_GAAA(T256, T253, X3405, row2colE_in_ga(T253, X3405))
ROW2COLJ_IN_GAAA(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_GAAA(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
ROW2COLJ_IN_GAAA(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → ROW2COLF_IN_GAA(T253, X3450, X3469)
ROW2COLJ_IN_GAAA(.(T275, T276), .([], T282), [], []) → U48_GAAA(T275, T276, T282, row2colG_in_ga(T276, T282))
ROW2COLJ_IN_GAAA(.(T275, T276), .([], T282), [], []) → ROW2COLG_IN_GA(T276, T282)
ROW2COLG_IN_GA(.(T326, T327), []) → U20_GA(T326, T327, row2colC_in_g(T327))
ROW2COLG_IN_GA(.(T326, T327), []) → ROW2COLC_IN_G(T327)
ROW2COLG_IN_GA(.(T339, T336), []) → U21_GA(T339, T336, row2colC_in_g(T336))
ROW2COLG_IN_GA(.(T358, T359), .([], T365)) → U22_GA(T358, T359, T365, row2colG_in_ga(T359, T365))
ROW2COLG_IN_GA(.(T358, T359), .([], T365)) → ROW2COLG_IN_GA(T359, T365)
ROW2COLG_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → U23_GA(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
ROW2COLG_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → ROW2COLG_IN_GA(T392, T429)
ROW2COLJ_IN_GAAA(.(T275, T276), .([], T282), .([], X4320), []) → U49_GAAA(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
ROW2COLJ_IN_GAAA(.(T275, T276), .([], T282), .([], X4320), []) → ROW2COLH_IN_GAA(T276, T282, X4320)
ROW2COLH_IN_GAA(.(T474, T475), [], []) → U24_GAA(T474, T475, row2colC_in_g(T475))
ROW2COLH_IN_GAA(.(T474, T475), [], []) → ROW2COLC_IN_G(T475)
ROW2COLH_IN_GAA(.(T474, T475), [], .([], X4607)) → U25_GAA(T474, T475, X4607, row2colD_in_ga(T475, X4607))
ROW2COLH_IN_GAA(.(T474, T475), [], .([], X4607)) → ROW2COLD_IN_GA(T475, X4607)
ROW2COLH_IN_GAA(.(T487, T484), [], []) → U26_GAA(T487, T484, row2colC_in_g(T484))
ROW2COLH_IN_GAA(.(T487, T484), [], .(X4819, X4820)) → U27_GAA(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
ROW2COLH_IN_GAA(.(T487, T484), [], .(X4819, X4820)) → ROW2COLD_IN_GA(T484, X4820)
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), []) → U28_GAA(T506, T507, T513, row2colG_in_ga(T507, T513))
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), []) → ROW2COLG_IN_GA(T507, T513)
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), .([], X5019)) → U29_GAA(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), .([], X5019)) → ROW2COLH_IN_GAA(T507, T513, X5019)
ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T583), T584), []) → U30_GAA(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T583), T584), []) → ROW2COLG_IN_GA(T547, T584)
ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_GAA(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → ROW2COLH_IN_GAA(T547, T606, X5208)
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), [], .([], X5351)) → U50_GAAA(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), [], .([], X5351)) → ROW2COLI_IN_GAA(T616, T622, X5351)
ROW2COLI_IN_GAA(.(T665, T666), [], []) → U32_GAA(T665, T666, row2colC_in_g(T666))
ROW2COLI_IN_GAA(.(T665, T666), [], []) → ROW2COLC_IN_G(T666)
ROW2COLI_IN_GAA(.(T671, T672), [], .([], X5712)) → U33_GAA(T671, T672, X5712, row2colE_in_ga(T672, X5712))
ROW2COLI_IN_GAA(.(T671, T672), [], .([], X5712)) → ROW2COLE_IN_GA(T672, X5712)
ROW2COLI_IN_GAA(.(T684, T681), [], []) → U34_GAA(T684, T681, row2colC_in_g(T681))
ROW2COLI_IN_GAA(.(T693, T690), [], .([], X6003)) → U35_GAA(T693, T690, X6003, row2colE_in_ga(T690, X6003))
ROW2COLI_IN_GAA(.(T712, T713), .([], T719), []) → U36_GAA(T712, T713, T719, row2colG_in_ga(T713, T719))
ROW2COLI_IN_GAA(.(T712, T713), .([], T719), []) → ROW2COLG_IN_GA(T713, T719)
ROW2COLI_IN_GAA(.(T737, T738), .([], T744), .([], X6275)) → U37_GAA(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
ROW2COLI_IN_GAA(.(T737, T738), .([], T744), .([], X6275)) → ROW2COLI_IN_GAA(T738, T744, X6275)
ROW2COLI_IN_GAA(.(T793, T770), .(.(T793, T806), T807), []) → U38_GAA(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
ROW2COLI_IN_GAA(.(T793, T770), .(.(T793, T806), T807), []) → ROW2COLG_IN_GA(T770, T807)
ROW2COLI_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_GAA(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
ROW2COLI_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → ROW2COLI_IN_GAA(T820, T857, X6536)
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_GAAA(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → ROW2COLJ_IN_GAAA(T616, T622, X6582, X6601)
ROW2COLJ_IN_GAAA(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_GAAA(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
ROW2COLJ_IN_GAAA(.(T906, T883), .(.(T906, T919), T920), [], []) → ROW2COLG_IN_GA(T883, T920)
ROW2COLJ_IN_GAAA(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_GAAA(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
ROW2COLJ_IN_GAAA(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → ROW2COLH_IN_GAA(T883, T942, X6774)
ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_GAAA(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → ROW2COLI_IN_GAA(T952, T989, X6912)
ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_GAAA(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → ROW2COLJ_IN_GAAA(T952, T1010, X6954, X6973)
U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_GAAAG(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → TRANSPOSE_AUXK_IN_GGA(T35, T38, T37)
TRANSPOSE_AUXK_IN_GGA(.(T1052, T1053), T1036, T1038) → U56_GGA(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
TRANSPOSE_AUXK_IN_GGA(.(T1052, T1053), T1036, T1038) → PB_IN_GAAAG(T1052, T1038, X7010, X7011, T1053)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
TRANSPOSEA_IN_GA(x1, x2)  =  TRANSPOSEA_IN_GA(x1)
U1_GA(x1, x2, x3, x4)  =  U1_GA(x1, x2, x4)
PB_IN_GAAAG(x1, x2, x3, x4, x5)  =  PB_IN_GAAAG(x1, x5)
U57_GAAAG(x1, x2, x3, x4, x5, x6)  =  U57_GAAAG(x1, x5, x6)
ROW2COLJ_IN_GAAA(x1, x2, x3, x4)  =  ROW2COLJ_IN_GAAA(x1)
U40_GAAA(x1, x2, x3)  =  U40_GAAA(x1, x2, x3)
ROW2COLC_IN_G(x1)  =  ROW2COLC_IN_G(x1)
U2_G(x1, x2, x3)  =  U2_G(x1, x2, x3)
U3_G(x1, x2, x3)  =  U3_G(x1, x2, x3)
U41_GAAA(x1, x2, x3, x4)  =  U41_GAAA(x1, x2, x4)
ROW2COLD_IN_GA(x1, x2)  =  ROW2COLD_IN_GA(x1)
U4_GA(x1, x2, x3)  =  U4_GA(x1, x2, x3)
U5_GA(x1, x2, x3, x4)  =  U5_GA(x1, x2, x4)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x2, x3)
U7_GA(x1, x2, x3, x4, x5)  =  U7_GA(x1, x2, x5)
U42_GAAA(x1, x2, x3, x4)  =  U42_GAAA(x1, x2, x4)
ROW2COLE_IN_GA(x1, x2)  =  ROW2COLE_IN_GA(x1)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x2, x3)
U9_GA(x1, x2, x3, x4)  =  U9_GA(x1, x2, x4)
U10_GA(x1, x2, x3)  =  U10_GA(x1, x2, x3)
U11_GA(x1, x2, x3, x4)  =  U11_GA(x1, x2, x4)
U43_GAAA(x1, x2, x3, x4, x5)  =  U43_GAAA(x1, x2, x5)
ROW2COLF_IN_GAA(x1, x2, x3)  =  ROW2COLF_IN_GAA(x1)
U12_GAA(x1, x2, x3)  =  U12_GAA(x1, x2, x3)
U13_GAA(x1, x2, x3, x4)  =  U13_GAA(x1, x2, x4)
U14_GAA(x1, x2, x3, x4)  =  U14_GAA(x1, x2, x4)
U15_GAA(x1, x2, x3, x4, x5)  =  U15_GAA(x1, x2, x5)
U16_GAA(x1, x2, x3)  =  U16_GAA(x1, x2, x3)
U17_GAA(x1, x2, x3, x4, x5)  =  U17_GAA(x1, x2, x5)
U18_GAA(x1, x2, x3, x4)  =  U18_GAA(x1, x2, x4)
U19_GAA(x1, x2, x3, x4, x5, x6)  =  U19_GAA(x1, x2, x6)
U44_GAAA(x1, x2, x3)  =  U44_GAAA(x1, x2, x3)
U45_GAAA(x1, x2, x3, x4, x5)  =  U45_GAAA(x1, x2, x5)
U46_GAAA(x1, x2, x3, x4)  =  U46_GAAA(x1, x2, x4)
U47_GAAA(x1, x2, x3, x4, x5, x6)  =  U47_GAAA(x1, x2, x6)
U48_GAAA(x1, x2, x3, x4)  =  U48_GAAA(x1, x2, x4)
ROW2COLG_IN_GA(x1, x2)  =  ROW2COLG_IN_GA(x1)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x2, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x2, x3)
U22_GA(x1, x2, x3, x4)  =  U22_GA(x1, x2, x4)
U23_GA(x1, x2, x3, x4, x5)  =  U23_GA(x1, x2, x5)
U49_GAAA(x1, x2, x3, x4, x5)  =  U49_GAAA(x1, x2, x5)
ROW2COLH_IN_GAA(x1, x2, x3)  =  ROW2COLH_IN_GAA(x1)
U24_GAA(x1, x2, x3)  =  U24_GAA(x1, x2, x3)
U25_GAA(x1, x2, x3, x4)  =  U25_GAA(x1, x2, x4)
U26_GAA(x1, x2, x3)  =  U26_GAA(x1, x2, x3)
U27_GAA(x1, x2, x3, x4, x5)  =  U27_GAA(x1, x2, x5)
U28_GAA(x1, x2, x3, x4)  =  U28_GAA(x1, x2, x4)
U29_GAA(x1, x2, x3, x4, x5)  =  U29_GAA(x1, x2, x5)
U30_GAA(x1, x2, x3, x4, x5)  =  U30_GAA(x1, x2, x5)
U31_GAA(x1, x2, x3, x4, x5, x6)  =  U31_GAA(x1, x2, x6)
U50_GAAA(x1, x2, x3, x4, x5)  =  U50_GAAA(x1, x2, x5)
ROW2COLI_IN_GAA(x1, x2, x3)  =  ROW2COLI_IN_GAA(x1)
U32_GAA(x1, x2, x3)  =  U32_GAA(x1, x2, x3)
U33_GAA(x1, x2, x3, x4)  =  U33_GAA(x1, x2, x4)
U34_GAA(x1, x2, x3)  =  U34_GAA(x1, x2, x3)
U35_GAA(x1, x2, x3, x4)  =  U35_GAA(x1, x2, x4)
U36_GAA(x1, x2, x3, x4)  =  U36_GAA(x1, x2, x4)
U37_GAA(x1, x2, x3, x4, x5)  =  U37_GAA(x1, x2, x5)
U38_GAA(x1, x2, x3, x4, x5)  =  U38_GAA(x1, x2, x5)
U39_GAA(x1, x2, x3, x4, x5, x6)  =  U39_GAA(x1, x2, x6)
U51_GAAA(x1, x2, x3, x4, x5, x6)  =  U51_GAAA(x1, x2, x6)
U52_GAAA(x1, x2, x3, x4, x5)  =  U52_GAAA(x1, x2, x5)
U53_GAAA(x1, x2, x3, x4, x5, x6)  =  U53_GAAA(x1, x2, x6)
U54_GAAA(x1, x2, x3, x4, x5, x6)  =  U54_GAAA(x1, x2, x6)
U55_GAAA(x1, x2, x3, x4, x5, x6, x7)  =  U55_GAAA(x1, x2, x7)
U58_GAAAG(x1, x2, x3, x4, x5, x6)  =  U58_GAAAG(x1, x4, x5, x6)
TRANSPOSE_AUXK_IN_GGA(x1, x2, x3)  =  TRANSPOSE_AUXK_IN_GGA(x1, x2)
U56_GGA(x1, x2, x3, x4, x5)  =  U56_GGA(x1, x2, x3, x5)

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:

ROW2COLC_IN_G(.(T90, T91)) → ROW2COLC_IN_G(T91)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
ROW2COLC_IN_G(x1)  =  ROW2COLC_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:

ROW2COLC_IN_G(.(T90, T91)) → ROW2COLC_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:

ROW2COLC_IN_G(.(T90, T91)) → ROW2COLC_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:

  • ROW2COLC_IN_G(.(T90, T91)) → ROW2COLC_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:

ROW2COLG_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → ROW2COLG_IN_GA(T392, T429)
ROW2COLG_IN_GA(.(T358, T359), .([], T365)) → ROW2COLG_IN_GA(T359, T365)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
ROW2COLG_IN_GA(x1, x2)  =  ROW2COLG_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:

ROW2COLG_IN_GA(.(T415, T392), .(.(T415, T428), T429)) → ROW2COLG_IN_GA(T392, T429)
ROW2COLG_IN_GA(.(T358, T359), .([], T365)) → ROW2COLG_IN_GA(T359, T365)

R is empty.
The argument filtering Pi contains the following mapping:
[]  =  []
.(x1, x2)  =  .(x1, x2)
ROW2COLG_IN_GA(x1, x2)  =  ROW2COLG_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:

ROW2COLG_IN_GA(.(T415, T392)) → ROW2COLG_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:

  • ROW2COLG_IN_GA(.(T415, T392)) → ROW2COLG_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:

ROW2COLE_IN_GA(.(T166, T167), .([], X1792)) → ROW2COLE_IN_GA(T167, X1792)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
ROW2COLE_IN_GA(x1, x2)  =  ROW2COLE_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:

ROW2COLE_IN_GA(.(T166, T167), .([], X1792)) → ROW2COLE_IN_GA(T167, X1792)

R is empty.
The argument filtering Pi contains the following mapping:
[]  =  []
.(x1, x2)  =  .(x1, x2)
ROW2COLE_IN_GA(x1, x2)  =  ROW2COLE_IN_GA(x1)

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

(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:

ROW2COLE_IN_GA(.(T166, T167)) → ROW2COLE_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:

  • ROW2COLE_IN_GA(.(T166, T167)) → ROW2COLE_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:

ROW2COLI_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → ROW2COLI_IN_GAA(T820, T857, X6536)
ROW2COLI_IN_GAA(.(T737, T738), .([], T744), .([], X6275)) → ROW2COLI_IN_GAA(T738, T744, X6275)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
ROW2COLI_IN_GAA(x1, x2, x3)  =  ROW2COLI_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:

ROW2COLI_IN_GAA(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → ROW2COLI_IN_GAA(T820, T857, X6536)
ROW2COLI_IN_GAA(.(T737, T738), .([], T744), .([], X6275)) → ROW2COLI_IN_GAA(T738, T744, X6275)

R is empty.
The argument filtering Pi contains the following mapping:
[]  =  []
.(x1, x2)  =  .(x1, x2)
ROW2COLI_IN_GAA(x1, x2, x3)  =  ROW2COLI_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:

ROW2COLI_IN_GAA(.(T843, T820)) → ROW2COLI_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:

  • ROW2COLI_IN_GAA(.(T843, T820)) → ROW2COLI_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:

ROW2COLD_IN_GA(.(T135, T132), .(X1270, X1271)) → ROW2COLD_IN_GA(T132, X1271)
ROW2COLD_IN_GA(.(T122, T123), .([], X1058)) → ROW2COLD_IN_GA(T123, X1058)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
ROW2COLD_IN_GA(x1, x2)  =  ROW2COLD_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:

ROW2COLD_IN_GA(.(T135, T132), .(X1270, X1271)) → ROW2COLD_IN_GA(T132, X1271)
ROW2COLD_IN_GA(.(T122, T123), .([], X1058)) → ROW2COLD_IN_GA(T123, X1058)

R is empty.
The argument filtering Pi contains the following mapping:
[]  =  []
.(x1, x2)  =  .(x1, x2)
ROW2COLD_IN_GA(x1, x2)  =  ROW2COLD_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:

ROW2COLD_IN_GA(.(T135, T132)) → ROW2COLD_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:

  • ROW2COLD_IN_GA(.(T135, T132)) → ROW2COLD_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:

ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → ROW2COLH_IN_GAA(T547, T606, X5208)
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), .([], X5019)) → ROW2COLH_IN_GAA(T507, T513, X5019)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
ROW2COLH_IN_GAA(x1, x2, x3)  =  ROW2COLH_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:

ROW2COLH_IN_GAA(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → ROW2COLH_IN_GAA(T547, T606, X5208)
ROW2COLH_IN_GAA(.(T506, T507), .([], T513), .([], X5019)) → ROW2COLH_IN_GAA(T507, T513, X5019)

R is empty.
The argument filtering Pi contains the following mapping:
[]  =  []
.(x1, x2)  =  .(x1, x2)
ROW2COLH_IN_GAA(x1, x2, x3)  =  ROW2COLH_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:

ROW2COLH_IN_GAA(.(T570, T547)) → ROW2COLH_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:

  • ROW2COLH_IN_GAA(.(T570, T547)) → ROW2COLH_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:

ROW2COLF_IN_GAA(.(T235, T232), .(X3037, X3038), .([], X3057)) → ROW2COLF_IN_GAA(T232, X3038, X3057)
ROW2COLF_IN_GAA(.(T213, T214), .([], X2630), .([], X2649)) → ROW2COLF_IN_GAA(T214, X2630, X2649)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
ROW2COLF_IN_GAA(x1, x2, x3)  =  ROW2COLF_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:

ROW2COLF_IN_GAA(.(T235, T232), .(X3037, X3038), .([], X3057)) → ROW2COLF_IN_GAA(T232, X3038, X3057)
ROW2COLF_IN_GAA(.(T213, T214), .([], X2630), .([], X2649)) → ROW2COLF_IN_GAA(T214, X2630, X2649)

R is empty.
The argument filtering Pi contains the following mapping:
[]  =  []
.(x1, x2)  =  .(x1, x2)
ROW2COLF_IN_GAA(x1, x2, x3)  =  ROW2COLF_IN_GAA(x1)

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

(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:

ROW2COLF_IN_GAA(.(T235, T232)) → ROW2COLF_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:

  • ROW2COLF_IN_GAA(.(T235, T232)) → ROW2COLF_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:

ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → ROW2COLJ_IN_GAAA(T952, T1010, X6954, X6973)
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → ROW2COLJ_IN_GAAA(T616, T622, X6582, X6601)

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
ROW2COLJ_IN_GAAA(x1, x2, x3, x4)  =  ROW2COLJ_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:

ROW2COLJ_IN_GAAA(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → ROW2COLJ_IN_GAAA(T952, T1010, X6954, X6973)
ROW2COLJ_IN_GAAA(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → ROW2COLJ_IN_GAAA(T616, T622, X6582, X6601)

R is empty.
The argument filtering Pi contains the following mapping:
[]  =  []
.(x1, x2)  =  .(x1, x2)
ROW2COLJ_IN_GAAA(x1, x2, x3, x4)  =  ROW2COLJ_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:

ROW2COLJ_IN_GAAA(.(T975, T952)) → ROW2COLJ_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:

  • ROW2COLJ_IN_GAAA(.(T975, T952)) → ROW2COLJ_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:

U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → TRANSPOSE_AUXK_IN_GGA(T35, T38, T37)
TRANSPOSE_AUXK_IN_GGA(.(T1052, T1053), T1036, T1038) → PB_IN_GAAAG(T1052, T1038, X7010, X7011, T1053)
PB_IN_GAAAG(T34, T20, T37, T38, T35) → U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))

The TRS R consists of the following rules:

transposeA_in_ga([], []) → transposeA_out_ga([], [])
transposeA_in_ga(.(T34, T35), T20) → U1_ga(T34, T35, T20, pB_in_gaaag(T34, T20, X38, X39, T35))
pB_in_gaaag(T34, T20, T37, T38, T35) → U57_gaaag(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))
row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U57_gaaag(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_in_gga(T35, T38, T37))
transpose_auxK_in_gga([], T1026, T1026) → transpose_auxK_out_gga([], T1026, T1026)
transpose_auxK_in_gga(.(T1052, T1053), T1036, T1038) → U56_gga(T1052, T1053, T1036, T1038, pB_in_gaaag(T1052, T1038, X7010, X7011, T1053))
U56_gga(T1052, T1053, T1036, T1038, pB_out_gaaag(T1052, T1038, X7010, X7011, T1053)) → transpose_auxK_out_gga(.(T1052, T1053), T1036, T1038)
U58_gaaag(T34, T20, T37, T38, T35, transpose_auxK_out_gga(T35, T38, T37)) → pB_out_gaaag(T34, T20, T37, T38, T35)
U1_ga(T34, T35, T20, pB_out_gaaag(T34, T20, X38, X39, T35)) → transposeA_out_ga(.(T34, T35), T20)

The argument filtering Pi contains the following mapping:
transposeA_in_ga(x1, x2)  =  transposeA_in_ga(x1)
[]  =  []
transposeA_out_ga(x1, x2)  =  transposeA_out_ga(x1)
.(x1, x2)  =  .(x1, x2)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x2, x4)
pB_in_gaaag(x1, x2, x3, x4, x5)  =  pB_in_gaaag(x1, x5)
U57_gaaag(x1, x2, x3, x4, x5, x6)  =  U57_gaaag(x1, x5, x6)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
U58_gaaag(x1, x2, x3, x4, x5, x6)  =  U58_gaaag(x1, x4, x5, x6)
transpose_auxK_in_gga(x1, x2, x3)  =  transpose_auxK_in_gga(x1, x2)
transpose_auxK_out_gga(x1, x2, x3)  =  transpose_auxK_out_gga(x1, x2)
U56_gga(x1, x2, x3, x4, x5)  =  U56_gga(x1, x2, x3, x5)
pB_out_gaaag(x1, x2, x3, x4, x5)  =  pB_out_gaaag(x1, x4, x5)
PB_IN_GAAAG(x1, x2, x3, x4, x5)  =  PB_IN_GAAAG(x1, x5)
U57_GAAAG(x1, x2, x3, x4, x5, x6)  =  U57_GAAAG(x1, x5, x6)
TRANSPOSE_AUXK_IN_GGA(x1, x2, x3)  =  TRANSPOSE_AUXK_IN_GGA(x1, x2)

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

(64) UsableRulesProof (EQUIVALENT transformation)

For (infinitary) constructor rewriting [LOPSTR] we can delete all non-usable rules from R.

(65) Obligation:

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

U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_out_gaaa(T34, T20, T37, T38)) → TRANSPOSE_AUXK_IN_GGA(T35, T38, T37)
TRANSPOSE_AUXK_IN_GGA(.(T1052, T1053), T1036, T1038) → PB_IN_GAAAG(T1052, T1038, X7010, X7011, T1053)
PB_IN_GAAAG(T34, T20, T37, T38, T35) → U57_GAAAG(T34, T20, T37, T38, T35, row2colJ_in_gaaa(T34, T20, T37, T38))

The TRS R consists of the following rules:

row2colJ_in_gaaa([], [], [], []) → row2colJ_out_gaaa([], [], [], [])
row2colJ_in_gaaa(.(T70, T71), [], [], []) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colJ_in_gaaa(.(T70, T71), [], .([], X759), []) → U41_gaaa(T70, T71, X759, row2colD_in_ga(T71, X759))
row2colJ_in_gaaa(.(T140, T141), [], [], .([], X1419)) → U42_gaaa(T140, T141, X1419, row2colE_in_ga(T141, X1419))
row2colJ_in_gaaa(.(T140, T141), [], .([], X2133), .([], X2152)) → U43_gaaa(T140, T141, X2133, X2152, row2colF_in_gaa(T141, X2133, X2152))
row2colJ_in_gaaa(.(T247, T244), [], [], []) → U44_gaaa(T247, T244, row2colC_in_g(T244))
row2colJ_in_gaaa(.(T247, T244), [], .(X3257, X3258), []) → U45_gaaa(T247, T244, X3257, X3258, row2colD_in_ga(T244, X3258))
row2colJ_in_gaaa(.(T256, T253), [], [], .([], X3405)) → U46_gaaa(T256, T253, X3405, row2colE_in_ga(T253, X3405))
row2colJ_in_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469)) → U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_in_gaa(T253, X3450, X3469))
row2colJ_in_gaaa(.(T275, T276), .([], T282), [], []) → U48_gaaa(T275, T276, T282, row2colG_in_ga(T276, T282))
row2colJ_in_gaaa(.(T275, T276), .([], T282), .([], X4320), []) → U49_gaaa(T275, T276, T282, X4320, row2colH_in_gaa(T276, T282, X4320))
row2colJ_in_gaaa(.(T615, T616), .([], T622), [], .([], X5351)) → U50_gaaa(T615, T616, T622, X5351, row2colI_in_gaa(T616, T622, X5351))
row2colJ_in_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601)) → U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_in_gaaa(T616, T622, X6582, X6601))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T919), T920), [], []) → U52_gaaa(T906, T883, T919, T920, row2colG_in_ga(T883, T920))
row2colJ_in_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), []) → U53_gaaa(T906, T883, T941, T942, X6774, row2colH_in_gaa(T883, T942, X6774))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912)) → U54_gaaa(T975, T952, T988, T989, X6912, row2colI_in_gaa(T952, T989, X6912))
row2colJ_in_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973)) → U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_in_gaaa(T952, T1010, X6954, X6973))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [], [], [])
U41_gaaa(T70, T71, X759, row2colD_out_ga(T71, X759)) → row2colJ_out_gaaa(.(T70, T71), [], .([], X759), [])
U42_gaaa(T140, T141, X1419, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), [], [], .([], X1419))
U43_gaaa(T140, T141, X2133, X2152, row2colF_out_gaa(T141, X2133, X2152)) → row2colJ_out_gaaa(.(T140, T141), [], .([], X2133), .([], X2152))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [], [], [])
U45_gaaa(T247, T244, X3257, X3258, row2colD_out_ga(T244, X3258)) → row2colJ_out_gaaa(.(T247, T244), [], .(X3257, X3258), [])
U46_gaaa(T256, T253, X3405, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), [], [], .([], X3405))
U47_gaaa(T256, T253, X3449, X3450, X3469, row2colF_out_gaa(T253, X3450, X3469)) → row2colJ_out_gaaa(.(T256, T253), [], .(X3449, X3450), .([], X3469))
U48_gaaa(T275, T276, T282, row2colG_out_ga(T276, T282)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), [], [])
U49_gaaa(T275, T276, T282, X4320, row2colH_out_gaa(T276, T282, X4320)) → row2colJ_out_gaaa(.(T275, T276), .([], T282), .([], X4320), [])
U50_gaaa(T615, T616, T622, X5351, row2colI_out_gaa(T616, T622, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), [], .([], X5351))
U51_gaaa(T615, T616, T622, X6582, X6601, row2colJ_out_gaaa(T616, T622, X6582, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], T622), .([], X6582), .([], X6601))
U52_gaaa(T906, T883, T919, T920, row2colG_out_ga(T883, T920)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T919), T920), [], [])
U53_gaaa(T906, T883, T941, T942, X6774, row2colH_out_gaa(T883, T942, X6774)) → row2colJ_out_gaaa(.(T906, T883), .(.(T906, T941), T942), .(T941, X6774), [])
U54_gaaa(T975, T952, T988, T989, X6912, row2colI_out_gaa(T952, T989, X6912)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T988), T989), [], .([], X6912))
U55_gaaa(T975, T952, T1009, T1010, X6954, X6973, row2colJ_out_gaaa(T952, T1010, X6954, X6973)) → row2colJ_out_gaaa(.(T975, T952), .(.(T975, T1009), T1010), .(T1009, X6954), .([], X6973))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
row2colD_in_ga([], []) → row2colD_out_ga([], [])
row2colD_in_ga(.(T122, T123), []) → U4_ga(T122, T123, row2colC_in_g(T123))
row2colD_in_ga(.(T122, T123), .([], X1058)) → U5_ga(T122, T123, X1058, row2colD_in_ga(T123, X1058))
row2colD_in_ga(.(T135, T132), []) → U6_ga(T135, T132, row2colC_in_g(T132))
row2colD_in_ga(.(T135, T132), .(X1270, X1271)) → U7_ga(T135, T132, X1270, X1271, row2colD_in_ga(T132, X1271))
row2colE_in_ga([], []) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161), []) → U8_ga(T160, T161, row2colC_in_g(T161))
row2colE_in_ga(.(T166, T167), .([], X1792)) → U9_ga(T166, T167, X1792, row2colE_in_ga(T167, X1792))
row2colE_in_ga(.(T179, T176), []) → U10_ga(T179, T176, row2colC_in_g(T176))
row2colE_in_ga(.(T188, T185), .([], X2083)) → U11_ga(T188, T185, X2083, row2colE_in_ga(T185, X2083))
row2colF_in_gaa([], [], []) → row2colF_out_gaa([], [], [])
row2colF_in_gaa(.(T207, T208), [], []) → U12_gaa(T207, T208, row2colC_in_g(T208))
row2colF_in_gaa(.(T207, T208), .([], X2448), []) → U13_gaa(T207, T208, X2448, row2colD_in_ga(T208, X2448))
row2colF_in_gaa(.(T213, T214), [], .([], X2588)) → U14_gaa(T213, T214, X2588, row2colE_in_ga(T214, X2588))
row2colF_in_gaa(.(T213, T214), .([], X2630), .([], X2649)) → U15_gaa(T213, T214, X2630, X2649, row2colF_in_gaa(T214, X2630, X2649))
row2colF_in_gaa(.(T226, T223), [], []) → U16_gaa(T226, T223, row2colC_in_g(T223))
row2colF_in_gaa(.(T226, T223), .(X2845, X2846), []) → U17_gaa(T226, T223, X2845, X2846, row2colD_in_ga(T223, X2846))
row2colF_in_gaa(.(T235, T232), [], .([], X2993)) → U18_gaa(T235, T232, X2993, row2colE_in_ga(T232, X2993))
row2colF_in_gaa(.(T235, T232), .(X3037, X3038), .([], X3057)) → U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_in_gaa(T232, X3038, X3057))
row2colG_in_ga([], []) → row2colG_out_ga([], [])
row2colG_in_ga(.(T326, T327), []) → U20_ga(T326, T327, row2colC_in_g(T327))
row2colG_in_ga(.(T339, T336), []) → U21_ga(T339, T336, row2colC_in_g(T336))
row2colG_in_ga(.(T358, T359), .([], T365)) → U22_ga(T358, T359, T365, row2colG_in_ga(T359, T365))
row2colG_in_ga(.(T415, T392), .(.(T415, T428), T429)) → U23_ga(T415, T392, T428, T429, row2colG_in_ga(T392, T429))
row2colH_in_gaa([], [], []) → row2colH_out_gaa([], [], [])
row2colH_in_gaa(.(T474, T475), [], []) → U24_gaa(T474, T475, row2colC_in_g(T475))
row2colH_in_gaa(.(T474, T475), [], .([], X4607)) → U25_gaa(T474, T475, X4607, row2colD_in_ga(T475, X4607))
row2colH_in_gaa(.(T487, T484), [], []) → U26_gaa(T487, T484, row2colC_in_g(T484))
row2colH_in_gaa(.(T487, T484), [], .(X4819, X4820)) → U27_gaa(T487, T484, X4819, X4820, row2colD_in_ga(T484, X4820))
row2colH_in_gaa(.(T506, T507), .([], T513), []) → U28_gaa(T506, T507, T513, row2colG_in_ga(T507, T513))
row2colH_in_gaa(.(T506, T507), .([], T513), .([], X5019)) → U29_gaa(T506, T507, T513, X5019, row2colH_in_gaa(T507, T513, X5019))
row2colH_in_gaa(.(T570, T547), .(.(T570, T583), T584), []) → U30_gaa(T570, T547, T583, T584, row2colG_in_ga(T547, T584))
row2colH_in_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208)) → U31_gaa(T570, T547, T605, T606, X5208, row2colH_in_gaa(T547, T606, X5208))
row2colI_in_gaa([], [], []) → row2colI_out_gaa([], [], [])
row2colI_in_gaa(.(T665, T666), [], []) → U32_gaa(T665, T666, row2colC_in_g(T666))
row2colI_in_gaa(.(T671, T672), [], .([], X5712)) → U33_gaa(T671, T672, X5712, row2colE_in_ga(T672, X5712))
row2colI_in_gaa(.(T684, T681), [], []) → U34_gaa(T684, T681, row2colC_in_g(T681))
row2colI_in_gaa(.(T693, T690), [], .([], X6003)) → U35_gaa(T693, T690, X6003, row2colE_in_ga(T690, X6003))
row2colI_in_gaa(.(T712, T713), .([], T719), []) → U36_gaa(T712, T713, T719, row2colG_in_ga(T713, T719))
row2colI_in_gaa(.(T737, T738), .([], T744), .([], X6275)) → U37_gaa(T737, T738, T744, X6275, row2colI_in_gaa(T738, T744, X6275))
row2colI_in_gaa(.(T793, T770), .(.(T793, T806), T807), []) → U38_gaa(T793, T770, T806, T807, row2colG_in_ga(T770, T807))
row2colI_in_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536)) → U39_gaa(T843, T820, T856, T857, X6536, row2colI_in_gaa(T820, T857, X6536))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123), [])
U5_ga(T122, T123, X1058, row2colD_out_ga(T123, X1058)) → row2colD_out_ga(.(T122, T123), .([], X1058))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132), [])
U7_ga(T135, T132, X1270, X1271, row2colD_out_ga(T132, X1271)) → row2colD_out_ga(.(T135, T132), .(X1270, X1271))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
U9_ga(T166, T167, X1792, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
U11_ga(T188, T185, X2083, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [], [])
U13_gaa(T207, T208, X2448, row2colD_out_ga(T208, X2448)) → row2colF_out_gaa(.(T207, T208), .([], X2448), [])
U14_gaa(T213, T214, X2588, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), [], .([], X2588))
U15_gaa(T213, T214, X2630, X2649, row2colF_out_gaa(T214, X2630, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2630), .([], X2649))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [], [])
U17_gaa(T226, T223, X2845, X2846, row2colD_out_ga(T223, X2846)) → row2colF_out_gaa(.(T226, T223), .(X2845, X2846), [])
U18_gaa(T235, T232, X2993, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), [], .([], X2993))
U19_gaa(T235, T232, X3037, X3038, X3057, row2colF_out_gaa(T232, X3038, X3057)) → row2colF_out_gaa(.(T235, T232), .(X3037, X3038), .([], X3057))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327), [])
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336), [])
U22_ga(T358, T359, T365, row2colG_out_ga(T359, T365)) → row2colG_out_ga(.(T358, T359), .([], T365))
U23_ga(T415, T392, T428, T429, row2colG_out_ga(T392, T429)) → row2colG_out_ga(.(T415, T392), .(.(T415, T428), T429))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475), [], [])
U25_gaa(T474, T475, X4607, row2colD_out_ga(T475, X4607)) → row2colH_out_gaa(.(T474, T475), [], .([], X4607))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484), [], [])
U27_gaa(T487, T484, X4819, X4820, row2colD_out_ga(T484, X4820)) → row2colH_out_gaa(.(T487, T484), [], .(X4819, X4820))
U28_gaa(T506, T507, T513, row2colG_out_ga(T507, T513)) → row2colH_out_gaa(.(T506, T507), .([], T513), [])
U29_gaa(T506, T507, T513, X5019, row2colH_out_gaa(T507, T513, X5019)) → row2colH_out_gaa(.(T506, T507), .([], T513), .([], X5019))
U30_gaa(T570, T547, T583, T584, row2colG_out_ga(T547, T584)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T583), T584), [])
U31_gaa(T570, T547, T605, T606, X5208, row2colH_out_gaa(T547, T606, X5208)) → row2colH_out_gaa(.(T570, T547), .(.(T570, T605), T606), .(T605, X5208))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [], [])
U33_gaa(T671, T672, X5712, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), [], .([], X5712))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [], [])
U35_gaa(T693, T690, X6003, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), [], .([], X6003))
U36_gaa(T712, T713, T719, row2colG_out_ga(T713, T719)) → row2colI_out_gaa(.(T712, T713), .([], T719), [])
U37_gaa(T737, T738, T744, X6275, row2colI_out_gaa(T738, T744, X6275)) → row2colI_out_gaa(.(T737, T738), .([], T744), .([], X6275))
U38_gaa(T793, T770, T806, T807, row2colG_out_ga(T770, T807)) → row2colI_out_gaa(.(T793, T770), .(.(T793, T806), T807), [])
U39_gaa(T843, T820, T856, T857, X6536, row2colI_out_gaa(T820, T857, X6536)) → row2colI_out_gaa(.(T843, T820), .(.(T843, T856), T857), .([], X6536))

The argument filtering Pi contains the following mapping:
[]  =  []
.(x1, x2)  =  .(x1, x2)
row2colJ_in_gaaa(x1, x2, x3, x4)  =  row2colJ_in_gaaa(x1)
row2colJ_out_gaaa(x1, x2, x3, x4)  =  row2colJ_out_gaaa(x1, x4)
U40_gaaa(x1, x2, x3)  =  U40_gaaa(x1, x2, x3)
row2colC_in_g(x1)  =  row2colC_in_g(x1)
row2colC_out_g(x1)  =  row2colC_out_g(x1)
U2_g(x1, x2, x3)  =  U2_g(x1, x2, x3)
U3_g(x1, x2, x3)  =  U3_g(x1, x2, x3)
U41_gaaa(x1, x2, x3, x4)  =  U41_gaaa(x1, x2, x4)
row2colD_in_ga(x1, x2)  =  row2colD_in_ga(x1)
row2colD_out_ga(x1, x2)  =  row2colD_out_ga(x1)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x2, x3)
U5_ga(x1, x2, x3, x4)  =  U5_ga(x1, x2, x4)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x2, x3)
U7_ga(x1, x2, x3, x4, x5)  =  U7_ga(x1, x2, x5)
U42_gaaa(x1, x2, x3, x4)  =  U42_gaaa(x1, x2, x4)
row2colE_in_ga(x1, x2)  =  row2colE_in_ga(x1)
row2colE_out_ga(x1, x2)  =  row2colE_out_ga(x1, x2)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x2, x3)
U9_ga(x1, x2, x3, x4)  =  U9_ga(x1, x2, x4)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x2, x3)
U11_ga(x1, x2, x3, x4)  =  U11_ga(x1, x2, x4)
U43_gaaa(x1, x2, x3, x4, x5)  =  U43_gaaa(x1, x2, x5)
row2colF_in_gaa(x1, x2, x3)  =  row2colF_in_gaa(x1)
row2colF_out_gaa(x1, x2, x3)  =  row2colF_out_gaa(x1, x3)
U12_gaa(x1, x2, x3)  =  U12_gaa(x1, x2, x3)
U13_gaa(x1, x2, x3, x4)  =  U13_gaa(x1, x2, x4)
U14_gaa(x1, x2, x3, x4)  =  U14_gaa(x1, x2, x4)
U15_gaa(x1, x2, x3, x4, x5)  =  U15_gaa(x1, x2, x5)
U16_gaa(x1, x2, x3)  =  U16_gaa(x1, x2, x3)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x5)
U18_gaa(x1, x2, x3, x4)  =  U18_gaa(x1, x2, x4)
U19_gaa(x1, x2, x3, x4, x5, x6)  =  U19_gaa(x1, x2, x6)
U44_gaaa(x1, x2, x3)  =  U44_gaaa(x1, x2, x3)
U45_gaaa(x1, x2, x3, x4, x5)  =  U45_gaaa(x1, x2, x5)
U46_gaaa(x1, x2, x3, x4)  =  U46_gaaa(x1, x2, x4)
U47_gaaa(x1, x2, x3, x4, x5, x6)  =  U47_gaaa(x1, x2, x6)
U48_gaaa(x1, x2, x3, x4)  =  U48_gaaa(x1, x2, x4)
row2colG_in_ga(x1, x2)  =  row2colG_in_ga(x1)
row2colG_out_ga(x1, x2)  =  row2colG_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x2, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x2, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x2, x4)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
U49_gaaa(x1, x2, x3, x4, x5)  =  U49_gaaa(x1, x2, x5)
row2colH_in_gaa(x1, x2, x3)  =  row2colH_in_gaa(x1)
row2colH_out_gaa(x1, x2, x3)  =  row2colH_out_gaa(x1)
U24_gaa(x1, x2, x3)  =  U24_gaa(x1, x2, x3)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x2, x4)
U26_gaa(x1, x2, x3)  =  U26_gaa(x1, x2, x3)
U27_gaa(x1, x2, x3, x4, x5)  =  U27_gaa(x1, x2, x5)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x2, x4)
U29_gaa(x1, x2, x3, x4, x5)  =  U29_gaa(x1, x2, x5)
U30_gaa(x1, x2, x3, x4, x5)  =  U30_gaa(x1, x2, x5)
U31_gaa(x1, x2, x3, x4, x5, x6)  =  U31_gaa(x1, x2, x6)
U50_gaaa(x1, x2, x3, x4, x5)  =  U50_gaaa(x1, x2, x5)
row2colI_in_gaa(x1, x2, x3)  =  row2colI_in_gaa(x1)
row2colI_out_gaa(x1, x2, x3)  =  row2colI_out_gaa(x1, x3)
U32_gaa(x1, x2, x3)  =  U32_gaa(x1, x2, x3)
U33_gaa(x1, x2, x3, x4)  =  U33_gaa(x1, x2, x4)
U34_gaa(x1, x2, x3)  =  U34_gaa(x1, x2, x3)
U35_gaa(x1, x2, x3, x4)  =  U35_gaa(x1, x2, x4)
U36_gaa(x1, x2, x3, x4)  =  U36_gaa(x1, x2, x4)
U37_gaa(x1, x2, x3, x4, x5)  =  U37_gaa(x1, x2, x5)
U38_gaa(x1, x2, x3, x4, x5)  =  U38_gaa(x1, x2, x5)
U39_gaa(x1, x2, x3, x4, x5, x6)  =  U39_gaa(x1, x2, x6)
U51_gaaa(x1, x2, x3, x4, x5, x6)  =  U51_gaaa(x1, x2, x6)
U52_gaaa(x1, x2, x3, x4, x5)  =  U52_gaaa(x1, x2, x5)
U53_gaaa(x1, x2, x3, x4, x5, x6)  =  U53_gaaa(x1, x2, x6)
U54_gaaa(x1, x2, x3, x4, x5, x6)  =  U54_gaaa(x1, x2, x6)
U55_gaaa(x1, x2, x3, x4, x5, x6, x7)  =  U55_gaaa(x1, x2, x7)
PB_IN_GAAAG(x1, x2, x3, x4, x5)  =  PB_IN_GAAAG(x1, x5)
U57_GAAAG(x1, x2, x3, x4, x5, x6)  =  U57_GAAAG(x1, x5, x6)
TRANSPOSE_AUXK_IN_GGA(x1, x2, x3)  =  TRANSPOSE_AUXK_IN_GGA(x1, x2)

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

(66) PiDPToQDPProof (SOUND transformation)

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

(67) Obligation:

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

U57_GAAAG(T34, T35, row2colJ_out_gaaa(T34, T38)) → TRANSPOSE_AUXK_IN_GGA(T35, T38)
TRANSPOSE_AUXK_IN_GGA(.(T1052, T1053), T1036) → PB_IN_GAAAG(T1052, T1053)
PB_IN_GAAAG(T34, T35) → U57_GAAAG(T34, T35, row2colJ_in_gaaa(T34))

The TRS R consists of the following rules:

row2colJ_in_gaaa([]) → row2colJ_out_gaaa([], [])
row2colJ_in_gaaa(.(T70, T71)) → U40_gaaa(T70, T71, row2colC_in_g(T71))
row2colJ_in_gaaa(.(T70, T71)) → U41_gaaa(T70, T71, row2colD_in_ga(T71))
row2colJ_in_gaaa(.(T140, T141)) → U42_gaaa(T140, T141, row2colE_in_ga(T141))
row2colJ_in_gaaa(.(T140, T141)) → U43_gaaa(T140, T141, row2colF_in_gaa(T141))
row2colJ_in_gaaa(.(T247, T244)) → U44_gaaa(T247, T244, row2colC_in_g(T244))
row2colJ_in_gaaa(.(T247, T244)) → U45_gaaa(T247, T244, row2colD_in_ga(T244))
row2colJ_in_gaaa(.(T256, T253)) → U46_gaaa(T256, T253, row2colE_in_ga(T253))
row2colJ_in_gaaa(.(T256, T253)) → U47_gaaa(T256, T253, row2colF_in_gaa(T253))
row2colJ_in_gaaa(.(T275, T276)) → U48_gaaa(T275, T276, row2colG_in_ga(T276))
row2colJ_in_gaaa(.(T275, T276)) → U49_gaaa(T275, T276, row2colH_in_gaa(T276))
row2colJ_in_gaaa(.(T615, T616)) → U50_gaaa(T615, T616, row2colI_in_gaa(T616))
row2colJ_in_gaaa(.(T615, T616)) → U51_gaaa(T615, T616, row2colJ_in_gaaa(T616))
row2colJ_in_gaaa(.(T906, T883)) → U52_gaaa(T906, T883, row2colG_in_ga(T883))
row2colJ_in_gaaa(.(T906, T883)) → U53_gaaa(T906, T883, row2colH_in_gaa(T883))
row2colJ_in_gaaa(.(T975, T952)) → U54_gaaa(T975, T952, row2colI_in_gaa(T952))
row2colJ_in_gaaa(.(T975, T952)) → U55_gaaa(T975, T952, row2colJ_in_gaaa(T952))
U40_gaaa(T70, T71, row2colC_out_g(T71)) → row2colJ_out_gaaa(.(T70, T71), [])
U41_gaaa(T70, T71, row2colD_out_ga(T71)) → row2colJ_out_gaaa(.(T70, T71), [])
U42_gaaa(T140, T141, row2colE_out_ga(T141, X1419)) → row2colJ_out_gaaa(.(T140, T141), .([], X1419))
U43_gaaa(T140, T141, row2colF_out_gaa(T141, X2152)) → row2colJ_out_gaaa(.(T140, T141), .([], X2152))
U44_gaaa(T247, T244, row2colC_out_g(T244)) → row2colJ_out_gaaa(.(T247, T244), [])
U45_gaaa(T247, T244, row2colD_out_ga(T244)) → row2colJ_out_gaaa(.(T247, T244), [])
U46_gaaa(T256, T253, row2colE_out_ga(T253, X3405)) → row2colJ_out_gaaa(.(T256, T253), .([], X3405))
U47_gaaa(T256, T253, row2colF_out_gaa(T253, X3469)) → row2colJ_out_gaaa(.(T256, T253), .([], X3469))
U48_gaaa(T275, T276, row2colG_out_ga(T276)) → row2colJ_out_gaaa(.(T275, T276), [])
U49_gaaa(T275, T276, row2colH_out_gaa(T276)) → row2colJ_out_gaaa(.(T275, T276), [])
U50_gaaa(T615, T616, row2colI_out_gaa(T616, X5351)) → row2colJ_out_gaaa(.(T615, T616), .([], X5351))
U51_gaaa(T615, T616, row2colJ_out_gaaa(T616, X6601)) → row2colJ_out_gaaa(.(T615, T616), .([], X6601))
U52_gaaa(T906, T883, row2colG_out_ga(T883)) → row2colJ_out_gaaa(.(T906, T883), [])
U53_gaaa(T906, T883, row2colH_out_gaa(T883)) → row2colJ_out_gaaa(.(T906, T883), [])
U54_gaaa(T975, T952, row2colI_out_gaa(T952, X6912)) → row2colJ_out_gaaa(.(T975, T952), .([], X6912))
U55_gaaa(T975, T952, row2colJ_out_gaaa(T952, X6973)) → row2colJ_out_gaaa(.(T975, T952), .([], X6973))
row2colC_in_g([]) → row2colC_out_g([])
row2colC_in_g(.(T90, T91)) → U2_g(T90, T91, row2colC_in_g(T91))
row2colC_in_g(.(T103, T100)) → U3_g(T103, T100, row2colC_in_g(T100))
row2colD_in_ga([]) → row2colD_out_ga([])
row2colD_in_ga(.(T122, T123)) → U4_ga(T122, T123, row2colC_in_g(T123))
row2colD_in_ga(.(T122, T123)) → U5_ga(T122, T123, row2colD_in_ga(T123))
row2colD_in_ga(.(T135, T132)) → U6_ga(T135, T132, row2colC_in_g(T132))
row2colD_in_ga(.(T135, T132)) → U7_ga(T135, T132, row2colD_in_ga(T132))
row2colE_in_ga([]) → row2colE_out_ga([], [])
row2colE_in_ga(.(T160, T161)) → U8_ga(T160, T161, row2colC_in_g(T161))
row2colE_in_ga(.(T166, T167)) → U9_ga(T166, T167, row2colE_in_ga(T167))
row2colE_in_ga(.(T179, T176)) → U10_ga(T179, T176, row2colC_in_g(T176))
row2colE_in_ga(.(T188, T185)) → U11_ga(T188, T185, row2colE_in_ga(T185))
row2colF_in_gaa([]) → row2colF_out_gaa([], [])
row2colF_in_gaa(.(T207, T208)) → U12_gaa(T207, T208, row2colC_in_g(T208))
row2colF_in_gaa(.(T207, T208)) → U13_gaa(T207, T208, row2colD_in_ga(T208))
row2colF_in_gaa(.(T213, T214)) → U14_gaa(T213, T214, row2colE_in_ga(T214))
row2colF_in_gaa(.(T213, T214)) → U15_gaa(T213, T214, row2colF_in_gaa(T214))
row2colF_in_gaa(.(T226, T223)) → U16_gaa(T226, T223, row2colC_in_g(T223))
row2colF_in_gaa(.(T226, T223)) → U17_gaa(T226, T223, row2colD_in_ga(T223))
row2colF_in_gaa(.(T235, T232)) → U18_gaa(T235, T232, row2colE_in_ga(T232))
row2colF_in_gaa(.(T235, T232)) → U19_gaa(T235, T232, row2colF_in_gaa(T232))
row2colG_in_ga([]) → row2colG_out_ga([])
row2colG_in_ga(.(T326, T327)) → U20_ga(T326, T327, row2colC_in_g(T327))
row2colG_in_ga(.(T339, T336)) → U21_ga(T339, T336, row2colC_in_g(T336))
row2colG_in_ga(.(T358, T359)) → U22_ga(T358, T359, row2colG_in_ga(T359))
row2colG_in_ga(.(T415, T392)) → U23_ga(T415, T392, row2colG_in_ga(T392))
row2colH_in_gaa([]) → row2colH_out_gaa([])
row2colH_in_gaa(.(T474, T475)) → U24_gaa(T474, T475, row2colC_in_g(T475))
row2colH_in_gaa(.(T474, T475)) → U25_gaa(T474, T475, row2colD_in_ga(T475))
row2colH_in_gaa(.(T487, T484)) → U26_gaa(T487, T484, row2colC_in_g(T484))
row2colH_in_gaa(.(T487, T484)) → U27_gaa(T487, T484, row2colD_in_ga(T484))
row2colH_in_gaa(.(T506, T507)) → U28_gaa(T506, T507, row2colG_in_ga(T507))
row2colH_in_gaa(.(T506, T507)) → U29_gaa(T506, T507, row2colH_in_gaa(T507))
row2colH_in_gaa(.(T570, T547)) → U30_gaa(T570, T547, row2colG_in_ga(T547))
row2colH_in_gaa(.(T570, T547)) → U31_gaa(T570, T547, row2colH_in_gaa(T547))
row2colI_in_gaa([]) → row2colI_out_gaa([], [])
row2colI_in_gaa(.(T665, T666)) → U32_gaa(T665, T666, row2colC_in_g(T666))
row2colI_in_gaa(.(T671, T672)) → U33_gaa(T671, T672, row2colE_in_ga(T672))
row2colI_in_gaa(.(T684, T681)) → U34_gaa(T684, T681, row2colC_in_g(T681))
row2colI_in_gaa(.(T693, T690)) → U35_gaa(T693, T690, row2colE_in_ga(T690))
row2colI_in_gaa(.(T712, T713)) → U36_gaa(T712, T713, row2colG_in_ga(T713))
row2colI_in_gaa(.(T737, T738)) → U37_gaa(T737, T738, row2colI_in_gaa(T738))
row2colI_in_gaa(.(T793, T770)) → U38_gaa(T793, T770, row2colG_in_ga(T770))
row2colI_in_gaa(.(T843, T820)) → U39_gaa(T843, T820, row2colI_in_gaa(T820))
U2_g(T90, T91, row2colC_out_g(T91)) → row2colC_out_g(.(T90, T91))
U3_g(T103, T100, row2colC_out_g(T100)) → row2colC_out_g(.(T103, T100))
U4_ga(T122, T123, row2colC_out_g(T123)) → row2colD_out_ga(.(T122, T123))
U5_ga(T122, T123, row2colD_out_ga(T123)) → row2colD_out_ga(.(T122, T123))
U6_ga(T135, T132, row2colC_out_g(T132)) → row2colD_out_ga(.(T135, T132))
U7_ga(T135, T132, row2colD_out_ga(T132)) → row2colD_out_ga(.(T135, T132))
U8_ga(T160, T161, row2colC_out_g(T161)) → row2colE_out_ga(.(T160, T161), [])
U9_ga(T166, T167, row2colE_out_ga(T167, X1792)) → row2colE_out_ga(.(T166, T167), .([], X1792))
U10_ga(T179, T176, row2colC_out_g(T176)) → row2colE_out_ga(.(T179, T176), [])
U11_ga(T188, T185, row2colE_out_ga(T185, X2083)) → row2colE_out_ga(.(T188, T185), .([], X2083))
U12_gaa(T207, T208, row2colC_out_g(T208)) → row2colF_out_gaa(.(T207, T208), [])
U13_gaa(T207, T208, row2colD_out_ga(T208)) → row2colF_out_gaa(.(T207, T208), [])
U14_gaa(T213, T214, row2colE_out_ga(T214, X2588)) → row2colF_out_gaa(.(T213, T214), .([], X2588))
U15_gaa(T213, T214, row2colF_out_gaa(T214, X2649)) → row2colF_out_gaa(.(T213, T214), .([], X2649))
U16_gaa(T226, T223, row2colC_out_g(T223)) → row2colF_out_gaa(.(T226, T223), [])
U17_gaa(T226, T223, row2colD_out_ga(T223)) → row2colF_out_gaa(.(T226, T223), [])
U18_gaa(T235, T232, row2colE_out_ga(T232, X2993)) → row2colF_out_gaa(.(T235, T232), .([], X2993))
U19_gaa(T235, T232, row2colF_out_gaa(T232, X3057)) → row2colF_out_gaa(.(T235, T232), .([], X3057))
U20_ga(T326, T327, row2colC_out_g(T327)) → row2colG_out_ga(.(T326, T327))
U21_ga(T339, T336, row2colC_out_g(T336)) → row2colG_out_ga(.(T339, T336))
U22_ga(T358, T359, row2colG_out_ga(T359)) → row2colG_out_ga(.(T358, T359))
U23_ga(T415, T392, row2colG_out_ga(T392)) → row2colG_out_ga(.(T415, T392))
U24_gaa(T474, T475, row2colC_out_g(T475)) → row2colH_out_gaa(.(T474, T475))
U25_gaa(T474, T475, row2colD_out_ga(T475)) → row2colH_out_gaa(.(T474, T475))
U26_gaa(T487, T484, row2colC_out_g(T484)) → row2colH_out_gaa(.(T487, T484))
U27_gaa(T487, T484, row2colD_out_ga(T484)) → row2colH_out_gaa(.(T487, T484))
U28_gaa(T506, T507, row2colG_out_ga(T507)) → row2colH_out_gaa(.(T506, T507))
U29_gaa(T506, T507, row2colH_out_gaa(T507)) → row2colH_out_gaa(.(T506, T507))
U30_gaa(T570, T547, row2colG_out_ga(T547)) → row2colH_out_gaa(.(T570, T547))
U31_gaa(T570, T547, row2colH_out_gaa(T547)) → row2colH_out_gaa(.(T570, T547))
U32_gaa(T665, T666, row2colC_out_g(T666)) → row2colI_out_gaa(.(T665, T666), [])
U33_gaa(T671, T672, row2colE_out_ga(T672, X5712)) → row2colI_out_gaa(.(T671, T672), .([], X5712))
U34_gaa(T684, T681, row2colC_out_g(T681)) → row2colI_out_gaa(.(T684, T681), [])
U35_gaa(T693, T690, row2colE_out_ga(T690, X6003)) → row2colI_out_gaa(.(T693, T690), .([], X6003))
U36_gaa(T712, T713, row2colG_out_ga(T713)) → row2colI_out_gaa(.(T712, T713), [])
U37_gaa(T737, T738, row2colI_out_gaa(T738, X6275)) → row2colI_out_gaa(.(T737, T738), .([], X6275))
U38_gaa(T793, T770, row2colG_out_ga(T770)) → row2colI_out_gaa(.(T793, T770), [])
U39_gaa(T843, T820, row2colI_out_gaa(T820, X6536)) → row2colI_out_gaa(.(T843, T820), .([], X6536))

The set Q consists of the following terms:

row2colJ_in_gaaa(x0)
U40_gaaa(x0, x1, x2)
U41_gaaa(x0, x1, x2)
U42_gaaa(x0, x1, x2)
U43_gaaa(x0, x1, x2)
U44_gaaa(x0, x1, x2)
U45_gaaa(x0, x1, x2)
U46_gaaa(x0, x1, x2)
U47_gaaa(x0, x1, x2)
U48_gaaa(x0, x1, x2)
U49_gaaa(x0, x1, x2)
U50_gaaa(x0, x1, x2)
U51_gaaa(x0, x1, x2)
U52_gaaa(x0, x1, x2)
U53_gaaa(x0, x1, x2)
U54_gaaa(x0, x1, x2)
U55_gaaa(x0, x1, x2)
row2colC_in_g(x0)
row2colD_in_ga(x0)
row2colE_in_ga(x0)
row2colF_in_gaa(x0)
row2colG_in_ga(x0)
row2colH_in_gaa(x0)
row2colI_in_gaa(x0)
U2_g(x0, x1, x2)
U3_g(x0, x1, x2)
U4_ga(x0, x1, x2)
U5_ga(x0, x1, x2)
U6_ga(x0, x1, x2)
U7_ga(x0, x1, x2)
U8_ga(x0, x1, x2)
U9_ga(x0, x1, x2)
U10_ga(x0, x1, x2)
U11_ga(x0, x1, x2)
U12_gaa(x0, x1, x2)
U13_gaa(x0, x1, x2)
U14_gaa(x0, x1, x2)
U15_gaa(x0, x1, x2)
U16_gaa(x0, x1, x2)
U17_gaa(x0, x1, x2)
U18_gaa(x0, x1, x2)
U19_gaa(x0, x1, x2)
U20_ga(x0, x1, x2)
U21_ga(x0, x1, x2)
U22_ga(x0, x1, x2)
U23_ga(x0, x1, x2)
U24_gaa(x0, x1, x2)
U25_gaa(x0, x1, x2)
U26_gaa(x0, x1, x2)
U27_gaa(x0, x1, x2)
U28_gaa(x0, x1, x2)
U29_gaa(x0, x1, x2)
U30_gaa(x0, x1, x2)
U31_gaa(x0, x1, x2)
U32_gaa(x0, x1, x2)
U33_gaa(x0, x1, x2)
U34_gaa(x0, x1, x2)
U35_gaa(x0, x1, x2)
U36_gaa(x0, x1, x2)
U37_gaa(x0, x1, x2)
U38_gaa(x0, x1, x2)
U39_gaa(x0, x1, x2)

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

(68) 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:

  • TRANSPOSE_AUXK_IN_GGA(.(T1052, T1053), T1036) → PB_IN_GAAAG(T1052, T1053)
    The graph contains the following edges 1 > 1, 1 > 2

  • PB_IN_GAAAG(T34, T35) → U57_GAAAG(T34, T35, row2colJ_in_gaaa(T34))
    The graph contains the following edges 1 >= 1, 2 >= 2

  • U57_GAAAG(T34, T35, row2colJ_out_gaaa(T34, T38)) → TRANSPOSE_AUXK_IN_GGA(T35, T38)
    The graph contains the following edges 2 >= 1, 3 > 2

(69) YES