(0) Obligation:

Clauses:

ms([], []).
ms(.(X, []), .(X, [])).
ms(.(X, .(Y, Xs)), Ys) :- ','(split(.(X, .(Y, Xs)), X1s, X2s), ','(ms(X1s, Y1s), ','(ms(X2s, Y2s), merge(Y1s, Y2s, Ys)))).
split([], [], []).
split(.(X, Xs), .(X, Ys), Zs) :- split(Xs, Zs, Ys).
merge([], Xs, Xs).
merge(Xs, [], Xs).
merge(.(X, Xs), .(Y, Ys), .(X, Zs)) :- ','(less(X, s(Y)), merge(Xs, .(Y, Ys), Zs)).
merge(.(X, Xs), .(Y, Ys), .(Y, Zs)) :- ','(less(Y, X), merge(.(X, Xs), Ys, Zs)).
less(0, s(X1)).
less(s(X), s(Y)) :- less(X, Y).

Queries:

ms(a,g).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

(2) Obligation:

Clauses:

split16([], [], []).
split16(.(T49, T51), .(T49, X89), X90) :- split16(T51, X90, X89).
split12(T42, T44, .(T42, X71), X72) :- split16(T44, X72, X71).
p34(T72, T73, T74, X123, X124, X125, X126, X127) :- split12(T72, .(T73, T74), X123, X124).
p34(T72, T73, T74, T78, T79, X125, X126, X127) :- ','(split12(T72, .(T73, T74), T78, T79), ms38(T78, X125)).
p34(T72, T73, T74, T78, T84, T83, X126, X127) :- ','(split12(T72, .(T73, T74), T78, T84), ','(ms38(T78, T83), ms38(T84, X126))).
p34(T72, T73, T74, T78, T84, T106, T105, X127) :- ','(split12(T72, .(T73, T74), T78, T84), ','(ms38(T78, T106), ','(ms38(T84, T105), merge54(T106, T105, X127)))).
ms38([], []).
ms38(.(T89, []), .(T89, [])).
ms38(.(T99, .(T100, T101)), X172) :- p34(T99, T100, T101, X168, X169, X170, X171, X172).
merge54([], T113, T113).
merge54(T118, [], T118).
merge54(.(T139, T141), .(T140, T142), .(T139, X226)) :- less70(T139, T140).
merge54(.(T139, T145), .(T146, T147), .(T139, X226)) :- ','(less70(T139, T146), merge54(T145, .(T146, T147), X226)).
merge54(.(T197, T199), .(T196, T198), .(T196, X287)) :- less78(T196, T197).
merge54(.(T202, T203), .(T196, T204), .(T196, X287)) :- ','(less78(T196, T202), merge54(.(T202, T203), T204, X287)).
less78(0, s(T169)).
less78(s(T176), s(T177)) :- less78(T176, T177).
ms25(T62, [], .(T62, [])).
ms25(T72, .(T73, T74), X127) :- p34(T72, T73, T74, X123, X124, X125, X126, X127).
less70(0, T154).
less70(s(T161), T162) :- less78(T161, T162).
merge93([], []).
merge93([], []).
p179(T513, T518, T519, T520, T517) :- less70(T513, T518).
p179(T513, T540, [], T541, .(T540, T541)) :- less70(T513, T540).
p179(T513, T568, .(T563, T569), T570, .(T563, T567)) :- ','(less70(T513, T568), p179(T563, T568, T569, T570, T567)).
p179(T513, T585, .(T588, T590), T589, .(T585, T587)) :- ','(less70(T513, T585), p194(T585, T588, T590, T589, T587)).
p194(T585, T588, T590, T589, T587) :- less78(T585, T588).
p194(T585, T610, T611, [], .(T610, T611)) :- less78(T585, T610).
p194(T585, T632, T638, .(T637, T639), .(T632, T636)) :- ','(less78(T585, T632), p179(T632, T637, T638, T639, T636)).
p194(T585, T657, T659, .(T654, T658), .(T654, T656)) :- ','(less78(T585, T657), p194(T654, T657, T659, T658, T656)).
ms1([], []).
ms1(.(T29, .(T27, T28)), []) :- split12(T27, T28, X42, X41).
ms1(.(T34, .(T27, T28)), []) :- ','(split12(T27, T28, T32, T33), ms25(T34, T33, X13)).
ms1(.(T34, .(T27, T28)), []) :- ','(split12(T27, T28, T55, T33), ','(ms25(T34, T33, T54), ms38(T55, X14))).
ms1(.(T34, .(T27, T28)), []) :- ','(split12(T27, T28, T55, T33), ','(ms25(T34, T33, T212), ','(ms38(T55, T211), merge93(T212, T211)))).
ms1(.(T234, []), .(T234, [])).
ms1(.(T262, .(T260, T261)), .(T242, [])) :- split12(T260, T261, X367, X366).
ms1(.(T267, .(T260, T261)), .(T242, [])) :- ','(split12(T260, T261, T265, T266), ms25(T267, T266, X338)).
ms1(.(T267, .(T260, T261)), .(T242, [])) :- ','(split12(T260, T261, T273, T266), ','(ms25(T267, T266, T272), ms38(T273, X339))).
ms1(.(T267, .(T260, T261)), .(T291, [])) :- ','(split12(T260, T261, T273, T266), ','(ms25(T267, T266, []), ms38(T273, .(T291, [])))).
ms1(.(T267, .(T260, T261)), .(T301, [])) :- ','(split12(T260, T261, T273, T266), ','(ms25(T267, T266, .(T301, [])), ms38(T273, []))).
ms1(.(T267, .(T260, T261)), .(T318, [])) :- ','(split12(T260, T261, T273, T266), ','(ms25(T267, T266, .(T318, T323)), ','(ms38(T273, .(T322, T324)), less70(T318, T322)))).
ms1(.(T267, .(T260, T261)), .(T318, [])) :- ','(split12(T260, T261, T273, T266), ','(ms25(T267, T266, .(T318, T327)), ','(ms38(T273, .(T328, T329)), ','(less70(T318, T328), merge93(T327, .(T328, T329)))))).
ms1(.(T267, .(T260, T261)), .(T356, [])) :- ','(split12(T260, T261, T273, T266), ','(ms25(T267, T266, .(T358, T360)), ','(ms38(T273, .(T356, T359)), less78(T356, T358)))).
ms1(.(T267, .(T260, T261)), .(T356, [])) :- ','(split12(T260, T261, T273, T266), ','(ms25(T267, T266, .(T363, T364)), ','(ms38(T273, .(T356, T365)), ','(less78(T356, T363), merge93(.(T363, T364), T365))))).
ms1(.(T407, .(T405, T406)), T387) :- split12(T405, T406, X523, X522).
ms1(.(T412, .(T405, T406)), T387) :- ','(split12(T405, T406, T410, T411), ms25(T412, T411, X494)).
ms1(.(T412, .(T405, T406)), T387) :- ','(split12(T405, T406, T420, T411), ','(ms25(T412, T411, T419), ms38(T420, X495))).
ms1(.(T412, .(T405, T406)), T435) :- ','(split12(T405, T406, T420, T411), ','(ms25(T412, T411, []), ms38(T420, T435))).
ms1(.(T412, .(T405, T406)), T440) :- ','(split12(T405, T406, T420, T411), ','(ms25(T412, T411, T440), ms38(T420, []))).
ms1(.(T412, .(T405, T406)), .(T461, T465)) :- ','(split12(T405, T406, T420, T411), ','(ms25(T412, T411, .(T461, T467)), ','(ms38(T420, .(T466, T468)), less70(T461, T466)))).
ms1(.(T412, .(T405, T406)), .(T461, .(T490, T491))) :- ','(split12(T405, T406, T420, T411), ','(ms25(T412, T411, .(T461, [])), ','(ms38(T420, .(T490, T491)), less70(T461, T490)))).
ms1(.(T412, .(T405, T406)), .(T461, .(T513, T517))) :- ','(split12(T405, T406, T420, T411), ','(ms25(T412, T411, .(T461, .(T513, T519))), ','(ms38(T420, .(T518, T520)), ','(less70(T461, T518), p179(T513, T518, T519, T520, T517))))).
ms1(.(T412, .(T405, T406)), .(T461, .(T674, T676))) :- ','(split12(T405, T406, T420, T411), ','(ms25(T412, T411, .(T461, .(T677, T679))), ','(ms38(T420, .(T674, T678)), ','(less70(T461, T674), p194(T674, T677, T679, T678, T676))))).
ms1(.(T412, .(T405, T406)), .(T694, T696)) :- ','(split12(T405, T406, T420, T411), ','(ms25(T412, T411, .(T697, T699)), ','(ms38(T420, .(T694, T698)), p194(T694, T697, T699, T698, T696)))).

Queries:

ms1(a,g).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
ms1_in: (f,b)
split12_in: (f,f,f,f)
split16_in: (f,f,f)
ms25_in: (f,f,f) (f,f,b)
p34_in: (f,f,f,f,f,f,f,f) (f,f,f,f,f,f,f,b)
ms38_in: (f,f) (f,b)
merge54_in: (f,f,f) (f,f,b)
less70_in: (f,f) (b,f) (b,b)
less78_in: (f,f) (b,f) (b,b)
p179_in: (b,f,f,f,b)
p194_in: (b,f,f,f,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)

(5) 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:

MS1_IN_AG(.(T29, .(T27, T28)), []) → U35_AG(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
MS1_IN_AG(.(T29, .(T27, T28)), []) → SPLIT12_IN_AAAA(T27, T28, X42, X41)
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → U2_AAAA(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → SPLIT16_IN_AAA(T44, X72, X71)
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → U1_AAA(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U36_AG(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_AG(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
U36_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → MS25_IN_AAA(T34, T33, X13)
MS25_IN_AAA(T72, .(T73, T74), X127) → U21_AAA(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAA(T72, .(T73, T74), X127) → P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → U13_AA(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → MERGE54_IN_AAA(T106, T105, X127)
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAA(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_AA(T139, T140)
LESS70_IN_AA(s(T161), T162) → U22_AA(T161, T162, less78_in_aa(T161, T162))
LESS70_IN_AA(s(T161), T162) → LESS78_IN_AA(T161, T162)
LESS78_IN_AA(s(T176), s(T177)) → U20_AA(T176, T177, less78_in_aa(T176, T177))
LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)
MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_AAA(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAA(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_AA(T196, T197)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_AAA(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U38_AG(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_AG(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → MS25_IN_AAA(T34, T33, T54)
U39_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_AG(T34, T27, T28, ms38_in_aa(T55, X14))
U39_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → MS38_IN_AA(T55, X14)
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_AG(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_AG(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U41_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → MS38_IN_AA(T55, T211)
U42_AG(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_AG(T34, T27, T28, merge93_in_aa(T212, T211))
U42_AG(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → MERGE93_IN_AA(T212, T211)
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → U44_AG(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → SPLIT12_IN_AAAA(T260, T261, X367, X366)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U45_AG(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_AG(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U45_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → MS25_IN_AAA(T267, T266, X338)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U47_AG(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_AG(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U47_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, T272)
U48_AG(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_AG(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U48_AG(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → MS38_IN_AA(T273, X339)
MS1_IN_AG(.(T267, .(T260, T261)), .(T291, [])) → U50_AG(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_AG(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_AG(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
U50_AG(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAG(T267, T266, [])
MS25_IN_AAG(T72, .(T73, T74), X127) → U21_AAG(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAG(T72, .(T73, T74), X127) → P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)
U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → MERGE54_IN_AAG(T106, T105, X127)
MERGE54_IN_AAG(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAG(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
MERGE54_IN_AAG(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_GA(T139, T140)
LESS70_IN_GA(s(T161), T162) → U22_GA(T161, T162, less78_in_ga(T161, T162))
LESS70_IN_GA(s(T161), T162) → LESS78_IN_GA(T161, T162)
LESS78_IN_GA(s(T176), s(T177)) → U20_GA(T176, T177, less78_in_ga(T176, T177))
LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)
MERGE54_IN_AAG(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAG(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_AAG(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → MERGE54_IN_AAG(T145, .(T146, T147), X226)
MERGE54_IN_AAG(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAG(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
MERGE54_IN_AAG(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_GA(T196, T197)
MERGE54_IN_AAG(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAG(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_AAG(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → MERGE54_IN_AAG(.(T202, T203), T204, X287)
U51_AG(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_AG(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
U51_AG(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → MS38_IN_AG(T273, .(T291, []))
MS38_IN_AG(.(T99, .(T100, T101)), X172) → U13_AG(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AG(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAG(T99, T100, T101, X168, X169, X170, X171, X172)
MS1_IN_AG(.(T267, .(T260, T261)), .(T301, [])) → U53_AG(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_AG(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_AG(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U53_AG(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAG(T267, T266, .(T301, []))
U54_AG(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_AG(T267, T260, T261, T301, ms38_in_ag(T273, []))
U54_AG(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → MS38_IN_AG(T273, [])
MS1_IN_AG(.(T267, .(T260, T261)), .(T318, [])) → U56_AG(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_AG(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, .(T318, T323))
U57_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_AG(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U57_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → MS38_IN_AA(T273, .(T322, T324))
U58_AG(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_AG(T267, T260, T261, T318, less70_in_ga(T318, T322))
U58_AG(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → LESS70_IN_GA(T318, T322)
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_AG(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_AG(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U60_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → MS38_IN_AA(T273, .(T328, T329))
U61_AG(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U61_AG(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → LESS70_IN_GA(T318, T328)
U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_AG(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → MERGE93_IN_AA(T327, .(T328, T329))
MS1_IN_AG(.(T267, .(T260, T261)), .(T356, [])) → U64_AG(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_AG(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, .(T358, T360))
U65_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_AG(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U65_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → MS38_IN_AA(T273, .(T356, T359))
U66_AG(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_AG(T267, T260, T261, T356, less78_in_ga(T356, T358))
U66_AG(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → LESS78_IN_GA(T356, T358)
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_AG(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_AG(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U68_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → MS38_IN_AA(T273, .(T356, T365))
U69_AG(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U69_AG(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → LESS78_IN_GA(T356, T363)
U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_AG(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → MERGE93_IN_AA(.(T363, T364), T365)
MS1_IN_AG(.(T407, .(T405, T406)), T387) → U72_AG(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
MS1_IN_AG(.(T407, .(T405, T406)), T387) → SPLIT12_IN_AAAA(T405, T406, X523, X522)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U73_AG(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_AG(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U73_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → MS25_IN_AAA(T412, T411, X494)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U75_AG(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_AG(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U75_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, T419)
U76_AG(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_AG(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U76_AG(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → MS38_IN_AA(T420, X495)
MS1_IN_AG(.(T412, .(T405, T406)), T435) → U78_AG(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_AG(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_AG(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U78_AG(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, [])
U79_AG(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_AG(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U79_AG(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → MS38_IN_AG(T420, T435)
MS1_IN_AG(.(T412, .(T405, T406)), T440) → U81_AG(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_AG(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_AG(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U81_AG(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, T440)
U82_AG(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_AG(T412, T405, T406, T440, ms38_in_ag(T420, []))
U82_AG(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → MS38_IN_AG(T420, [])
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → U84_AG(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → SPLIT12_IN_AAAA(T405, T406, T420, T411)
U84_AG(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_AG(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U84_AG(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, T467))
U85_AG(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_AG(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U85_AG(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → MS38_IN_AA(T420, .(T466, T468))
U86_AG(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_AG(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U86_AG(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → LESS70_IN_GA(T461, T466)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_AG(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → SPLIT12_IN_AAAA(T405, T406, T420, T411)
U88_AG(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U88_AG(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, .(T461, []))
U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_AG(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → MS38_IN_AG(T420, .(T490, T491))
U90_AG(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_AG(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
U90_AG(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → LESS70_IN_GG(T461, T490)
LESS70_IN_GG(s(T161), T162) → U22_GG(T161, T162, less78_in_gg(T161, T162))
LESS70_IN_GG(s(T161), T162) → LESS78_IN_GG(T161, T162)
LESS78_IN_GG(s(T176), s(T177)) → U20_GG(T176, T177, less78_in_gg(T176, T177))
LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_AG(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_AG(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U92_AG(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, .(T513, T519)))
U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → MS38_IN_AA(T420, .(T518, T520))
U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → LESS70_IN_GA(T461, T518)
U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_AG(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → P179_IN_GAAAG(T513, T518, T519, T520, T517)
P179_IN_GAAAG(T513, T518, T519, T520, T517) → U23_GAAAG(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
P179_IN_GAAAG(T513, T518, T519, T520, T517) → LESS70_IN_GA(T513, T518)
P179_IN_GAAAG(T513, T540, [], T541, .(T540, T541)) → U24_GAAAG(T513, T540, T541, less70_in_gg(T513, T540))
P179_IN_GAAAG(T513, T540, [], T541, .(T540, T541)) → LESS70_IN_GG(T513, T540)
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → LESS70_IN_GA(T513, T568)
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_GAAAG(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → LESS70_IN_GG(T513, T585)
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_GAAAG(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T588, T590, T589, T587) → U29_GAAAG(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
P194_IN_GAAAG(T585, T588, T590, T589, T587) → LESS78_IN_GA(T585, T588)
P194_IN_GAAAG(T585, T610, T611, [], .(T610, T611)) → U30_GAAAG(T585, T610, T611, less78_in_gg(T585, T610))
P194_IN_GAAAG(T585, T610, T611, [], .(T610, T611)) → LESS78_IN_GG(T585, T610)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → LESS78_IN_GG(T585, T632)
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_GAAAG(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → LESS78_IN_GA(T585, T657)
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_GAAAG(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_AG(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_AG(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U97_AG(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, .(T677, T679)))
U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → MS38_IN_AA(T420, .(T674, T678))
U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → LESS70_IN_GG(T461, T674)
U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_AG(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → P194_IN_GAAAG(T674, T677, T679, T678, T676)
MS1_IN_AG(.(T412, .(T405, T406)), .(T694, T696)) → U102_AG(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_AG(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_AG(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U102_AG(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T697, T699))
U103_AG(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U103_AG(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → MS38_IN_AA(T420, .(T694, T698))
U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_AG(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → P194_IN_GAAAG(T694, T697, T699, T698, T696)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
MS1_IN_AG(x1, x2)  =  MS1_IN_AG(x2)
U35_AG(x1, x2, x3, x4)  =  U35_AG(x4)
SPLIT12_IN_AAAA(x1, x2, x3, x4)  =  SPLIT12_IN_AAAA
U2_AAAA(x1, x2, x3, x4, x5)  =  U2_AAAA(x5)
SPLIT16_IN_AAA(x1, x2, x3)  =  SPLIT16_IN_AAA
U1_AAA(x1, x2, x3, x4, x5)  =  U1_AAA(x5)
U36_AG(x1, x2, x3, x4)  =  U36_AG(x4)
U37_AG(x1, x2, x3, x4)  =  U37_AG(x4)
MS25_IN_AAA(x1, x2, x3)  =  MS25_IN_AAA
U21_AAA(x1, x2, x3, x4, x5)  =  U21_AAA(x5)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAA
U3_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_AAAAAAAA(x9)
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAA(x9)
U5_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_AAAAAAAA(x9)
MS38_IN_AA(x1, x2)  =  MS38_IN_AA
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAA(x9)
U8_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAA(x9)
U11_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_AAAAAAAA(x9)
U12_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_AAAAAAAA(x9)
MERGE54_IN_AAA(x1, x2, x3)  =  MERGE54_IN_AAA
U14_AAA(x1, x2, x3, x4, x5, x6)  =  U14_AAA(x6)
LESS70_IN_AA(x1, x2)  =  LESS70_IN_AA
U22_AA(x1, x2, x3)  =  U22_AA(x3)
LESS78_IN_AA(x1, x2)  =  LESS78_IN_AA
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U16_AAA(x1, x2, x3, x4, x5, x6)  =  U16_AAA(x6)
U17_AAA(x1, x2, x3, x4, x5, x6)  =  U17_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6)  =  U18_AAA(x6)
U19_AAA(x1, x2, x3, x4, x5, x6)  =  U19_AAA(x6)
U38_AG(x1, x2, x3, x4)  =  U38_AG(x4)
U39_AG(x1, x2, x3, x4, x5)  =  U39_AG(x5)
U40_AG(x1, x2, x3, x4)  =  U40_AG(x4)
U41_AG(x1, x2, x3, x4, x5)  =  U41_AG(x5)
U42_AG(x1, x2, x3, x4, x5)  =  U42_AG(x5)
U43_AG(x1, x2, x3, x4)  =  U43_AG(x4)
MERGE93_IN_AA(x1, x2)  =  MERGE93_IN_AA
U44_AG(x1, x2, x3, x4, x5)  =  U44_AG(x5)
U45_AG(x1, x2, x3, x4, x5)  =  U45_AG(x5)
U46_AG(x1, x2, x3, x4, x5)  =  U46_AG(x5)
U47_AG(x1, x2, x3, x4, x5)  =  U47_AG(x5)
U48_AG(x1, x2, x3, x4, x5, x6)  =  U48_AG(x6)
U49_AG(x1, x2, x3, x4, x5)  =  U49_AG(x5)
U50_AG(x1, x2, x3, x4, x5)  =  U50_AG(x4, x5)
U51_AG(x1, x2, x3, x4, x5, x6)  =  U51_AG(x4, x6)
MS25_IN_AAG(x1, x2, x3)  =  MS25_IN_AAG(x3)
U21_AAG(x1, x2, x3, x4, x5)  =  U21_AAG(x5)
P34_IN_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAG(x8)
U3_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_AAAAAAAG(x9)
U4_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAG(x9)
U5_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_AAAAAAAG(x9)
U6_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAG(x9)
U7_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAG(x9)
U8_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_AAAAAAAG(x9)
U9_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAG(x8, x9)
U10_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAG(x8, x9)
U11_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_AAAAAAAG(x8, x9)
U12_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_AAAAAAAG(x9)
MERGE54_IN_AAG(x1, x2, x3)  =  MERGE54_IN_AAG(x3)
U14_AAG(x1, x2, x3, x4, x5, x6)  =  U14_AAG(x6)
LESS70_IN_GA(x1, x2)  =  LESS70_IN_GA(x1)
U22_GA(x1, x2, x3)  =  U22_GA(x3)
LESS78_IN_GA(x1, x2)  =  LESS78_IN_GA(x1)
U20_GA(x1, x2, x3)  =  U20_GA(x3)
U15_AAG(x1, x2, x3, x4, x5, x6)  =  U15_AAG(x5, x6)
U16_AAG(x1, x2, x3, x4, x5, x6)  =  U16_AAG(x6)
U17_AAG(x1, x2, x3, x4, x5, x6)  =  U17_AAG(x6)
U18_AAG(x1, x2, x3, x4, x5, x6)  =  U18_AAG(x5, x6)
U19_AAG(x1, x2, x3, x4, x5, x6)  =  U19_AAG(x6)
U52_AG(x1, x2, x3, x4, x5)  =  U52_AG(x5)
MS38_IN_AG(x1, x2)  =  MS38_IN_AG(x2)
U13_AG(x1, x2, x3, x4, x5)  =  U13_AG(x5)
U53_AG(x1, x2, x3, x4, x5)  =  U53_AG(x4, x5)
U54_AG(x1, x2, x3, x4, x5, x6)  =  U54_AG(x6)
U55_AG(x1, x2, x3, x4, x5)  =  U55_AG(x5)
U56_AG(x1, x2, x3, x4, x5)  =  U56_AG(x4, x5)
U57_AG(x1, x2, x3, x4, x5, x6)  =  U57_AG(x4, x6)
U58_AG(x1, x2, x3, x4, x5)  =  U58_AG(x4, x5)
U59_AG(x1, x2, x3, x4, x5)  =  U59_AG(x5)
U60_AG(x1, x2, x3, x4, x5, x6)  =  U60_AG(x4, x6)
U61_AG(x1, x2, x3, x4, x5, x6)  =  U61_AG(x4, x6)
U62_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_AG(x8)
U63_AG(x1, x2, x3, x4, x5)  =  U63_AG(x5)
U64_AG(x1, x2, x3, x4, x5)  =  U64_AG(x4, x5)
U65_AG(x1, x2, x3, x4, x5, x6)  =  U65_AG(x4, x6)
U66_AG(x1, x2, x3, x4, x5, x6)  =  U66_AG(x4, x6)
U67_AG(x1, x2, x3, x4, x5)  =  U67_AG(x5)
U68_AG(x1, x2, x3, x4, x5, x6)  =  U68_AG(x4, x6)
U69_AG(x1, x2, x3, x4, x5, x6, x7)  =  U69_AG(x4, x7)
U70_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_AG(x8)
U71_AG(x1, x2, x3, x4, x5)  =  U71_AG(x5)
U72_AG(x1, x2, x3, x4, x5)  =  U72_AG(x5)
U73_AG(x1, x2, x3, x4, x5)  =  U73_AG(x5)
U74_AG(x1, x2, x3, x4, x5)  =  U74_AG(x5)
U75_AG(x1, x2, x3, x4, x5)  =  U75_AG(x5)
U76_AG(x1, x2, x3, x4, x5, x6)  =  U76_AG(x6)
U77_AG(x1, x2, x3, x4, x5)  =  U77_AG(x5)
U78_AG(x1, x2, x3, x4, x5)  =  U78_AG(x4, x5)
U79_AG(x1, x2, x3, x4, x5, x6)  =  U79_AG(x4, x6)
U80_AG(x1, x2, x3, x4, x5)  =  U80_AG(x5)
U81_AG(x1, x2, x3, x4, x5)  =  U81_AG(x4, x5)
U82_AG(x1, x2, x3, x4, x5, x6)  =  U82_AG(x6)
U83_AG(x1, x2, x3, x4, x5)  =  U83_AG(x5)
U84_AG(x1, x2, x3, x4, x5, x6)  =  U84_AG(x4, x6)
U85_AG(x1, x2, x3, x4, x5, x6, x7)  =  U85_AG(x4, x7)
U86_AG(x1, x2, x3, x4, x5, x6)  =  U86_AG(x4, x6)
U87_AG(x1, x2, x3, x4, x5, x6)  =  U87_AG(x6)
U88_AG(x1, x2, x3, x4, x5, x6, x7)  =  U88_AG(x4, x5, x6, x7)
U89_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_AG(x4, x5, x6, x8)
U90_AG(x1, x2, x3, x4, x5, x6, x7)  =  U90_AG(x4, x5, x7)
U91_AG(x1, x2, x3, x4, x5, x6, x7)  =  U91_AG(x7)
LESS70_IN_GG(x1, x2)  =  LESS70_IN_GG(x1, x2)
U22_GG(x1, x2, x3)  =  U22_GG(x3)
LESS78_IN_GG(x1, x2)  =  LESS78_IN_GG(x1, x2)
U20_GG(x1, x2, x3)  =  U20_GG(x3)
U92_AG(x1, x2, x3, x4, x5, x6, x7)  =  U92_AG(x4, x5, x6, x7)
U93_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_AG(x4, x5, x6, x8)
U94_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_AG(x4, x5, x6, x8)
U95_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_AG(x5, x6, x10)
U96_AG(x1, x2, x3, x4, x5, x6, x7)  =  U96_AG(x7)
P179_IN_GAAAG(x1, x2, x3, x4, x5)  =  P179_IN_GAAAG(x1, x5)
U23_GAAAG(x1, x2, x3, x4, x5, x6)  =  U23_GAAAG(x6)
U24_GAAAG(x1, x2, x3, x4)  =  U24_GAAAG(x4)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U25_GAAAG(x3, x6, x7)
U26_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U26_GAAAG(x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U27_GAAAG(x2, x6, x7)
U28_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U28_GAAAG(x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5)  =  P194_IN_GAAAG(x1, x5)
U29_GAAAG(x1, x2, x3, x4, x5, x6)  =  U29_GAAAG(x6)
U30_GAAAG(x1, x2, x3, x4)  =  U30_GAAAG(x4)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U31_GAAAG(x2, x6, x7)
U32_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U32_GAAAG(x7)
U33_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U33_GAAAG(x4, x6, x7)
U34_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U34_GAAAG(x7)
U97_AG(x1, x2, x3, x4, x5, x6, x7)  =  U97_AG(x4, x5, x6, x7)
U98_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_AG(x4, x5, x6, x8)
U99_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_AG(x4, x5, x6, x9)
U100_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_AG(x5, x6, x10)
U101_AG(x1, x2, x3, x4, x5, x6, x7)  =  U101_AG(x7)
U102_AG(x1, x2, x3, x4, x5, x6)  =  U102_AG(x4, x5, x6)
U103_AG(x1, x2, x3, x4, x5, x6, x7)  =  U103_AG(x4, x5, x7)
U104_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_AG(x4, x5, x8)
U105_AG(x1, x2, x3, x4, x5, x6)  =  U105_AG(x6)

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

(6) Obligation:

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

MS1_IN_AG(.(T29, .(T27, T28)), []) → U35_AG(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
MS1_IN_AG(.(T29, .(T27, T28)), []) → SPLIT12_IN_AAAA(T27, T28, X42, X41)
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → U2_AAAA(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → SPLIT16_IN_AAA(T44, X72, X71)
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → U1_AAA(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U36_AG(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_AG(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
U36_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → MS25_IN_AAA(T34, T33, X13)
MS25_IN_AAA(T72, .(T73, T74), X127) → U21_AAA(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAA(T72, .(T73, T74), X127) → P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → U13_AA(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → MERGE54_IN_AAA(T106, T105, X127)
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAA(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_AA(T139, T140)
LESS70_IN_AA(s(T161), T162) → U22_AA(T161, T162, less78_in_aa(T161, T162))
LESS70_IN_AA(s(T161), T162) → LESS78_IN_AA(T161, T162)
LESS78_IN_AA(s(T176), s(T177)) → U20_AA(T176, T177, less78_in_aa(T176, T177))
LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)
MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_AAA(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAA(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_AA(T196, T197)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_AAA(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U38_AG(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_AG(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → MS25_IN_AAA(T34, T33, T54)
U39_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_AG(T34, T27, T28, ms38_in_aa(T55, X14))
U39_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → MS38_IN_AA(T55, X14)
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_AG(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_AG(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U41_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → MS38_IN_AA(T55, T211)
U42_AG(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_AG(T34, T27, T28, merge93_in_aa(T212, T211))
U42_AG(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → MERGE93_IN_AA(T212, T211)
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → U44_AG(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → SPLIT12_IN_AAAA(T260, T261, X367, X366)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U45_AG(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_AG(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U45_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → MS25_IN_AAA(T267, T266, X338)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U47_AG(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_AG(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U47_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, T272)
U48_AG(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_AG(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U48_AG(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → MS38_IN_AA(T273, X339)
MS1_IN_AG(.(T267, .(T260, T261)), .(T291, [])) → U50_AG(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_AG(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_AG(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
U50_AG(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAG(T267, T266, [])
MS25_IN_AAG(T72, .(T73, T74), X127) → U21_AAG(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAG(T72, .(T73, T74), X127) → P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)
U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → MERGE54_IN_AAG(T106, T105, X127)
MERGE54_IN_AAG(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAG(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
MERGE54_IN_AAG(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_GA(T139, T140)
LESS70_IN_GA(s(T161), T162) → U22_GA(T161, T162, less78_in_ga(T161, T162))
LESS70_IN_GA(s(T161), T162) → LESS78_IN_GA(T161, T162)
LESS78_IN_GA(s(T176), s(T177)) → U20_GA(T176, T177, less78_in_ga(T176, T177))
LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)
MERGE54_IN_AAG(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAG(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_AAG(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → MERGE54_IN_AAG(T145, .(T146, T147), X226)
MERGE54_IN_AAG(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAG(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
MERGE54_IN_AAG(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_GA(T196, T197)
MERGE54_IN_AAG(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAG(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_AAG(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → MERGE54_IN_AAG(.(T202, T203), T204, X287)
U51_AG(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_AG(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
U51_AG(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → MS38_IN_AG(T273, .(T291, []))
MS38_IN_AG(.(T99, .(T100, T101)), X172) → U13_AG(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AG(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAG(T99, T100, T101, X168, X169, X170, X171, X172)
MS1_IN_AG(.(T267, .(T260, T261)), .(T301, [])) → U53_AG(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_AG(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_AG(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U53_AG(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAG(T267, T266, .(T301, []))
U54_AG(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_AG(T267, T260, T261, T301, ms38_in_ag(T273, []))
U54_AG(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → MS38_IN_AG(T273, [])
MS1_IN_AG(.(T267, .(T260, T261)), .(T318, [])) → U56_AG(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_AG(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, .(T318, T323))
U57_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_AG(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U57_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → MS38_IN_AA(T273, .(T322, T324))
U58_AG(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_AG(T267, T260, T261, T318, less70_in_ga(T318, T322))
U58_AG(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → LESS70_IN_GA(T318, T322)
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_AG(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_AG(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U60_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → MS38_IN_AA(T273, .(T328, T329))
U61_AG(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U61_AG(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → LESS70_IN_GA(T318, T328)
U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_AG(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → MERGE93_IN_AA(T327, .(T328, T329))
MS1_IN_AG(.(T267, .(T260, T261)), .(T356, [])) → U64_AG(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_AG(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, .(T358, T360))
U65_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_AG(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U65_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → MS38_IN_AA(T273, .(T356, T359))
U66_AG(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_AG(T267, T260, T261, T356, less78_in_ga(T356, T358))
U66_AG(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → LESS78_IN_GA(T356, T358)
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_AG(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_AG(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U68_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → MS38_IN_AA(T273, .(T356, T365))
U69_AG(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U69_AG(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → LESS78_IN_GA(T356, T363)
U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_AG(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → MERGE93_IN_AA(.(T363, T364), T365)
MS1_IN_AG(.(T407, .(T405, T406)), T387) → U72_AG(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
MS1_IN_AG(.(T407, .(T405, T406)), T387) → SPLIT12_IN_AAAA(T405, T406, X523, X522)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U73_AG(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_AG(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U73_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → MS25_IN_AAA(T412, T411, X494)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U75_AG(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_AG(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U75_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, T419)
U76_AG(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_AG(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U76_AG(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → MS38_IN_AA(T420, X495)
MS1_IN_AG(.(T412, .(T405, T406)), T435) → U78_AG(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_AG(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_AG(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U78_AG(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, [])
U79_AG(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_AG(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U79_AG(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → MS38_IN_AG(T420, T435)
MS1_IN_AG(.(T412, .(T405, T406)), T440) → U81_AG(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_AG(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_AG(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U81_AG(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, T440)
U82_AG(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_AG(T412, T405, T406, T440, ms38_in_ag(T420, []))
U82_AG(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → MS38_IN_AG(T420, [])
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → U84_AG(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → SPLIT12_IN_AAAA(T405, T406, T420, T411)
U84_AG(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_AG(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U84_AG(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, T467))
U85_AG(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_AG(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U85_AG(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → MS38_IN_AA(T420, .(T466, T468))
U86_AG(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_AG(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U86_AG(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → LESS70_IN_GA(T461, T466)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_AG(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → SPLIT12_IN_AAAA(T405, T406, T420, T411)
U88_AG(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U88_AG(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, .(T461, []))
U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_AG(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → MS38_IN_AG(T420, .(T490, T491))
U90_AG(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_AG(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
U90_AG(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → LESS70_IN_GG(T461, T490)
LESS70_IN_GG(s(T161), T162) → U22_GG(T161, T162, less78_in_gg(T161, T162))
LESS70_IN_GG(s(T161), T162) → LESS78_IN_GG(T161, T162)
LESS78_IN_GG(s(T176), s(T177)) → U20_GG(T176, T177, less78_in_gg(T176, T177))
LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_AG(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_AG(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U92_AG(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, .(T513, T519)))
U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → MS38_IN_AA(T420, .(T518, T520))
U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → LESS70_IN_GA(T461, T518)
U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_AG(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → P179_IN_GAAAG(T513, T518, T519, T520, T517)
P179_IN_GAAAG(T513, T518, T519, T520, T517) → U23_GAAAG(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
P179_IN_GAAAG(T513, T518, T519, T520, T517) → LESS70_IN_GA(T513, T518)
P179_IN_GAAAG(T513, T540, [], T541, .(T540, T541)) → U24_GAAAG(T513, T540, T541, less70_in_gg(T513, T540))
P179_IN_GAAAG(T513, T540, [], T541, .(T540, T541)) → LESS70_IN_GG(T513, T540)
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → LESS70_IN_GA(T513, T568)
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_GAAAG(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → LESS70_IN_GG(T513, T585)
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_GAAAG(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T588, T590, T589, T587) → U29_GAAAG(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
P194_IN_GAAAG(T585, T588, T590, T589, T587) → LESS78_IN_GA(T585, T588)
P194_IN_GAAAG(T585, T610, T611, [], .(T610, T611)) → U30_GAAAG(T585, T610, T611, less78_in_gg(T585, T610))
P194_IN_GAAAG(T585, T610, T611, [], .(T610, T611)) → LESS78_IN_GG(T585, T610)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → LESS78_IN_GG(T585, T632)
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_GAAAG(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → LESS78_IN_GA(T585, T657)
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_GAAAG(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_AG(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_AG(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U97_AG(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, .(T677, T679)))
U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → MS38_IN_AA(T420, .(T674, T678))
U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → LESS70_IN_GG(T461, T674)
U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_AG(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → P194_IN_GAAAG(T674, T677, T679, T678, T676)
MS1_IN_AG(.(T412, .(T405, T406)), .(T694, T696)) → U102_AG(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_AG(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_AG(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U102_AG(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T697, T699))
U103_AG(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U103_AG(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → MS38_IN_AA(T420, .(T694, T698))
U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_AG(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → P194_IN_GAAAG(T694, T697, T699, T698, T696)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
MS1_IN_AG(x1, x2)  =  MS1_IN_AG'(x2)
U35_AG(x1, x2, x3, x4)  =  U35_AG(x4)
SPLIT12_IN_AAAA(x1, x2, x3, x4)  =  SPLIT12_IN_AAAA
U2_AAAA(x1, x2, x3, x4, x5)  =  U2_AAAA(x5)
SPLIT16_IN_AAA(x1, x2, x3)  =  SPLIT16_IN_AAA
U1_AAA(x1, x2, x3, x4, x5)  =  U1_AAA(x5)
U36_AG(x1, x2, x3, x4)  =  U36_AG(x4)
U37_AG(x1, x2, x3, x4)  =  U37_AG(x4)
MS25_IN_AAA(x1, x2, x3)  =  MS25_IN_AAA
U21_AAA(x1, x2, x3, x4, x5)  =  U21_AAA(x5)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAA
U3_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_AAAAAAAA(x9)
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAA(x9)
U5_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_AAAAAAAA(x9)
MS38_IN_AA(x1, x2)  =  MS38_IN_AA
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAA(x9)
U8_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAA(x9)
U11_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_AAAAAAAA(x9)
U12_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_AAAAAAAA(x9)
MERGE54_IN_AAA(x1, x2, x3)  =  MERGE54_IN_AAA
U14_AAA(x1, x2, x3, x4, x5, x6)  =  U14_AAA(x6)
LESS70_IN_AA(x1, x2)  =  LESS70_IN_AA
U22_AA(x1, x2, x3)  =  U22_AA(x3)
LESS78_IN_AA(x1, x2)  =  LESS78_IN_AA
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U16_AAA(x1, x2, x3, x4, x5, x6)  =  U16_AAA(x6)
U17_AAA(x1, x2, x3, x4, x5, x6)  =  U17_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6)  =  U18_AAA(x6)
U19_AAA(x1, x2, x3, x4, x5, x6)  =  U19_AAA(x6)
U38_AG(x1, x2, x3, x4)  =  U38_AG(x4)
U39_AG(x1, x2, x3, x4, x5)  =  U39_AG(x5)
U40_AG(x1, x2, x3, x4)  =  U40_AG(x4)
U41_AG(x1, x2, x3, x4, x5)  =  U41_AG(x5)
U42_AG(x1, x2, x3, x4, x5)  =  U42_AG(x5)
U43_AG(x1, x2, x3, x4)  =  U43_AG(x4)
MERGE93_IN_AA(x1, x2)  =  MERGE93_IN_AA
U44_AG(x1, x2, x3, x4, x5)  =  U44_AG(x5)
U45_AG(x1, x2, x3, x4, x5)  =  U45_AG(x5)
U46_AG(x1, x2, x3, x4, x5)  =  U46_AG(x5)
U47_AG(x1, x2, x3, x4, x5)  =  U47_AG(x5)
U48_AG(x1, x2, x3, x4, x5, x6)  =  U48_AG(x6)
U49_AG(x1, x2, x3, x4, x5)  =  U49_AG(x5)
U50_AG(x1, x2, x3, x4, x5)  =  U50_AG(x4, x5)
U51_AG(x1, x2, x3, x4, x5, x6)  =  U51_AG(x4, x6)
MS25_IN_AAG(x1, x2, x3)  =  MS25_IN_AAG(x3)
U21_AAG(x1, x2, x3, x4, x5)  =  U21_AAG(x5)
P34_IN_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAG(x8)
U3_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_AAAAAAAG(x9)
U4_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAG(x9)
U5_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_AAAAAAAG(x9)
U6_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAG(x9)
U7_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAG(x9)
U8_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_AAAAAAAG(x9)
U9_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAG(x8, x9)
U10_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAG(x8, x9)
U11_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_AAAAAAAG(x8, x9)
U12_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_AAAAAAAG(x9)
MERGE54_IN_AAG(x1, x2, x3)  =  MERGE54_IN_AAG(x3)
U14_AAG(x1, x2, x3, x4, x5, x6)  =  U14_AAG(x6)
LESS70_IN_GA(x1, x2)  =  LESS70_IN_GA(x1)
U22_GA(x1, x2, x3)  =  U22_GA(x3)
LESS78_IN_GA(x1, x2)  =  LESS78_IN_GA(x1)
U20_GA(x1, x2, x3)  =  U20_GA(x3)
U15_AAG(x1, x2, x3, x4, x5, x6)  =  U15_AAG(x5, x6)
U16_AAG(x1, x2, x3, x4, x5, x6)  =  U16_AAG(x6)
U17_AAG(x1, x2, x3, x4, x5, x6)  =  U17_AAG(x6)
U18_AAG(x1, x2, x3, x4, x5, x6)  =  U18_AAG(x5, x6)
U19_AAG(x1, x2, x3, x4, x5, x6)  =  U19_AAG(x6)
U52_AG(x1, x2, x3, x4, x5)  =  U52_AG(x5)
MS38_IN_AG(x1, x2)  =  MS38_IN_AG(x2)
U13_AG(x1, x2, x3, x4, x5)  =  U13_AG(x5)
U53_AG(x1, x2, x3, x4, x5)  =  U53_AG(x4, x5)
U54_AG(x1, x2, x3, x4, x5, x6)  =  U54_AG(x6)
U55_AG(x1, x2, x3, x4, x5)  =  U55_AG(x5)
U56_AG(x1, x2, x3, x4, x5)  =  U56_AG(x4, x5)
U57_AG(x1, x2, x3, x4, x5, x6)  =  U57_AG(x4, x6)
U58_AG(x1, x2, x3, x4, x5)  =  U58_AG(x4, x5)
U59_AG(x1, x2, x3, x4, x5)  =  U59_AG(x5)
U60_AG(x1, x2, x3, x4, x5, x6)  =  U60_AG(x4, x6)
U61_AG(x1, x2, x3, x4, x5, x6)  =  U61_AG(x4, x6)
U62_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_AG(x8)
U63_AG(x1, x2, x3, x4, x5)  =  U63_AG(x5)
U64_AG(x1, x2, x3, x4, x5)  =  U64_AG(x4, x5)
U65_AG(x1, x2, x3, x4, x5, x6)  =  U65_AG(x4, x6)
U66_AG(x1, x2, x3, x4, x5, x6)  =  U66_AG(x4, x6)
U67_AG(x1, x2, x3, x4, x5)  =  U67_AG(x5)
U68_AG(x1, x2, x3, x4, x5, x6)  =  U68_AG(x4, x6)
U69_AG(x1, x2, x3, x4, x5, x6, x7)  =  U69_AG(x4, x7)
U70_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_AG(x8)
U71_AG(x1, x2, x3, x4, x5)  =  U71_AG(x5)
U72_AG(x1, x2, x3, x4, x5)  =  U72_AG(x5)
U73_AG(x1, x2, x3, x4, x5)  =  U73_AG(x5)
U74_AG(x1, x2, x3, x4, x5)  =  U74_AG(x5)
U75_AG(x1, x2, x3, x4, x5)  =  U75_AG(x5)
U76_AG(x1, x2, x3, x4, x5, x6)  =  U76_AG(x6)
U77_AG(x1, x2, x3, x4, x5)  =  U77_AG(x5)
U78_AG(x1, x2, x3, x4, x5)  =  U78_AG(x4, x5)
U79_AG(x1, x2, x3, x4, x5, x6)  =  U79_AG(x4, x6)
U80_AG(x1, x2, x3, x4, x5)  =  U80_AG(x5)
U81_AG(x1, x2, x3, x4, x5)  =  U81_AG(x4, x5)
U82_AG(x1, x2, x3, x4, x5, x6)  =  U82_AG(x6)
U83_AG(x1, x2, x3, x4, x5)  =  U83_AG(x5)
U84_AG(x1, x2, x3, x4, x5, x6)  =  U84_AG(x4, x6)
U85_AG(x1, x2, x3, x4, x5, x6, x7)  =  U85_AG(x4, x7)
U86_AG(x1, x2, x3, x4, x5, x6)  =  U86_AG(x4, x6)
U87_AG(x1, x2, x3, x4, x5, x6)  =  U87_AG(x6)
U88_AG(x1, x2, x3, x4, x5, x6, x7)  =  U88_AG(x4, x5, x6, x7)
U89_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_AG(x4, x5, x6, x8)
U90_AG(x1, x2, x3, x4, x5, x6, x7)  =  U90_AG(x4, x5, x7)
U91_AG(x1, x2, x3, x4, x5, x6, x7)  =  U91_AG(x7)
LESS70_IN_GG(x1, x2)  =  LESS70_IN_GG(x1, x2)
U22_GG(x1, x2, x3)  =  U22_GG(x3)
LESS78_IN_GG(x1, x2)  =  LESS78_IN_GG(x1, x2)
U20_GG(x1, x2, x3)  =  U20_GG(x3)
U92_AG(x1, x2, x3, x4, x5, x6, x7)  =  U92_AG(x4, x5, x6, x7)
U93_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_AG(x4, x5, x6, x8)
U94_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_AG(x4, x5, x6, x8)
U95_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_AG(x5, x6, x10)
U96_AG(x1, x2, x3, x4, x5, x6, x7)  =  U96_AG(x7)
P179_IN_GAAAG(x1, x2, x3, x4, x5)  =  P179_IN_GAAAG(x1, x5)
U23_GAAAG(x1, x2, x3, x4, x5, x6)  =  U23_GAAAG(x6)
U24_GAAAG(x1, x2, x3, x4)  =  U24_GAAAG(x4)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U25_GAAAG(x3, x6, x7)
U26_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U26_GAAAG(x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U27_GAAAG(x2, x6, x7)
U28_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U28_GAAAG(x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5)  =  P194_IN_GAAAG(x1, x5)
U29_GAAAG(x1, x2, x3, x4, x5, x6)  =  U29_GAAAG(x6)
U30_GAAAG(x1, x2, x3, x4)  =  U30_GAAAG(x4)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U31_GAAAG(x2, x6, x7)
U32_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U32_GAAAG(x7)
U33_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U33_GAAAG(x4, x6, x7)
U34_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U34_GAAAG(x7)
U97_AG(x1, x2, x3, x4, x5, x6, x7)  =  U97_AG(x4, x5, x6, x7)
U98_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_AG(x4, x5, x6, x8)
U99_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_AG(x4, x5, x6, x9)
U100_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_AG(x5, x6, x10)
U101_AG(x1, x2, x3, x4, x5, x6, x7)  =  U101_AG(x7)
U102_AG(x1, x2, x3, x4, x5, x6)  =  U102_AG(x4, x5, x6)
U103_AG(x1, x2, x3, x4, x5, x6, x7)  =  U103_AG(x4, x5, x7)
U104_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_AG(x4, x5, x8)
U105_AG(x1, x2, x3, x4, x5, x6)  =  U105_AG(x6)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 195 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
LESS78_IN_GG(x1, x2)  =  LESS78_IN_GG(x1, x2)

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

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)

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

(12) PiDPToQDPProof (EQUIVALENT transformation)

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

(13) Obligation:

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

LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)

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

(14) 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:

  • LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)
    The graph contains the following edges 1 > 1, 2 > 2

(15) YES

(16) Obligation:

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

LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
LESS78_IN_GA(x1, x2)  =  LESS78_IN_GA(x1)

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

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LESS78_IN_GA(x1, x2)  =  LESS78_IN_GA(x1)

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

LESS78_IN_GA(s(T176)) → LESS78_IN_GA(T176)

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

(21) 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:

  • LESS78_IN_GA(s(T176)) → LESS78_IN_GA(T176)
    The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
P179_IN_GAAAG(x1, x2, x3, x4, x5)  =  P179_IN_GAAAG(x1, x5)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U25_GAAAG(x3, x6, x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U27_GAAAG(x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5)  =  P194_IN_GAAAG(x1, x5)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U31_GAAAG(x2, x6, x7)
U33_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U33_GAAAG(x4, x6, x7)

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

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)

The TRS R consists of the following rules:

less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
P179_IN_GAAAG(x1, x2, x3, x4, x5)  =  P179_IN_GAAAG(x1, x5)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U25_GAAAG(x3, x6, x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U27_GAAAG(x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5)  =  P194_IN_GAAAG(x1, x5)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U31_GAAAG(x2, x6, x7)
U33_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U33_GAAAG(x4, x6, x7)

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

(26) PiDPToQDPProof (SOUND transformation)

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

(27) Obligation:

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

P179_IN_GAAAG(T513, .(T563, T567)) → U25_GAAAG(T563, T567, less70_in_ga(T513))
U25_GAAAG(T563, T567, less70_out_ga) → P179_IN_GAAAG(T563, T567)
P179_IN_GAAAG(T513, .(T585, T587)) → U27_GAAAG(T585, T587, less70_in_gg(T513, T585))
U27_GAAAG(T585, T587, less70_out_gg) → P194_IN_GAAAG(T585, T587)
P194_IN_GAAAG(T585, .(T632, T636)) → U31_GAAAG(T632, T636, less78_in_gg(T585, T632))
U31_GAAAG(T632, T636, less78_out_gg) → P179_IN_GAAAG(T632, T636)
P194_IN_GAAAG(T585, .(T654, T656)) → U33_GAAAG(T654, T656, less78_in_ga(T585))
U33_GAAAG(T654, T656, less78_out_ga) → P194_IN_GAAAG(T654, T656)

The TRS R consists of the following rules:

less70_in_ga(0) → less70_out_ga
less70_in_ga(s(T161)) → U22_ga(less78_in_ga(T161))
less70_in_gg(0, T154) → less70_out_gg
less70_in_gg(s(T161), T162) → U22_gg(less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg
less78_in_gg(s(T176), s(T177)) → U20_gg(less78_in_gg(T176, T177))
less78_in_ga(0) → less78_out_ga
less78_in_ga(s(T176)) → U20_ga(less78_in_ga(T176))
U22_ga(less78_out_ga) → less70_out_ga
U22_gg(less78_out_gg) → less70_out_gg
U20_gg(less78_out_gg) → less78_out_gg
U20_ga(less78_out_ga) → less78_out_ga

The set Q consists of the following terms:

less70_in_ga(x0)
less70_in_gg(x0, x1)
less78_in_gg(x0, x1)
less78_in_ga(x0)
U22_ga(x0)
U22_gg(x0)
U20_gg(x0)
U20_ga(x0)

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

(28) 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:

  • U25_GAAAG(T563, T567, less70_out_ga) → P179_IN_GAAAG(T563, T567)
    The graph contains the following edges 1 >= 1, 2 >= 2

  • U31_GAAAG(T632, T636, less78_out_gg) → P179_IN_GAAAG(T632, T636)
    The graph contains the following edges 1 >= 1, 2 >= 2

  • P179_IN_GAAAG(T513, .(T563, T567)) → U25_GAAAG(T563, T567, less70_in_ga(T513))
    The graph contains the following edges 2 > 1, 2 > 2

  • P179_IN_GAAAG(T513, .(T585, T587)) → U27_GAAAG(T585, T587, less70_in_gg(T513, T585))
    The graph contains the following edges 2 > 1, 2 > 2

  • U27_GAAAG(T585, T587, less70_out_gg) → P194_IN_GAAAG(T585, T587)
    The graph contains the following edges 1 >= 1, 2 >= 2

  • U33_GAAAG(T654, T656, less78_out_ga) → P194_IN_GAAAG(T654, T656)
    The graph contains the following edges 1 >= 1, 2 >= 2

  • P194_IN_GAAAG(T585, .(T632, T636)) → U31_GAAAG(T632, T636, less78_in_gg(T585, T632))
    The graph contains the following edges 2 > 1, 2 > 2

  • P194_IN_GAAAG(T585, .(T654, T656)) → U33_GAAAG(T654, T656, less78_in_ga(T585))
    The graph contains the following edges 2 > 1, 2 > 2

(29) YES

(30) Obligation:

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

MERGE54_IN_AAG(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAG(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → MERGE54_IN_AAG(T145, .(T146, T147), X226)
MERGE54_IN_AAG(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAG(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → MERGE54_IN_AAG(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
MERGE54_IN_AAG(x1, x2, x3)  =  MERGE54_IN_AAG(x3)
U15_AAG(x1, x2, x3, x4, x5, x6)  =  U15_AAG(x5, x6)
U18_AAG(x1, x2, x3, x4, x5, x6)  =  U18_AAG(x5, x6)

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

(31) UsableRulesProof (EQUIVALENT transformation)

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

(32) Obligation:

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

MERGE54_IN_AAG(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAG(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → MERGE54_IN_AAG(T145, .(T146, T147), X226)
MERGE54_IN_AAG(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAG(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → MERGE54_IN_AAG(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
MERGE54_IN_AAG(x1, x2, x3)  =  MERGE54_IN_AAG(x3)
U15_AAG(x1, x2, x3, x4, x5, x6)  =  U15_AAG(x5, x6)
U18_AAG(x1, x2, x3, x4, x5, x6)  =  U18_AAG(x5, x6)

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

(33) PiDPToQDPProof (SOUND transformation)

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

(34) Obligation:

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

MERGE54_IN_AAG(.(T139, X226)) → U15_AAG(X226, less70_in_ga(T139))
U15_AAG(X226, less70_out_ga) → MERGE54_IN_AAG(X226)
MERGE54_IN_AAG(.(T196, X287)) → U18_AAG(X287, less78_in_ga(T196))
U18_AAG(X287, less78_out_ga) → MERGE54_IN_AAG(X287)

The TRS R consists of the following rules:

less70_in_ga(0) → less70_out_ga
less70_in_ga(s(T161)) → U22_ga(less78_in_ga(T161))
less78_in_ga(0) → less78_out_ga
less78_in_ga(s(T176)) → U20_ga(less78_in_ga(T176))
U22_ga(less78_out_ga) → less70_out_ga
U20_ga(less78_out_ga) → less78_out_ga

The set Q consists of the following terms:

less70_in_ga(x0)
less78_in_ga(x0)
U22_ga(x0)
U20_ga(x0)

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

(35) 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:

  • U15_AAG(X226, less70_out_ga) → MERGE54_IN_AAG(X226)
    The graph contains the following edges 1 >= 1

  • U18_AAG(X287, less78_out_ga) → MERGE54_IN_AAG(X287)
    The graph contains the following edges 1 >= 1

  • MERGE54_IN_AAG(.(T139, X226)) → U15_AAG(X226, less70_in_ga(T139))
    The graph contains the following edges 1 > 1

  • MERGE54_IN_AAG(.(T196, X287)) → U18_AAG(X287, less78_in_ga(T196))
    The graph contains the following edges 1 > 1

(36) YES

(37) Obligation:

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

LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
LESS78_IN_AA(x1, x2)  =  LESS78_IN_AA

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

(38) UsableRulesProof (EQUIVALENT transformation)

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

(39) Obligation:

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

LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LESS78_IN_AA(x1, x2)  =  LESS78_IN_AA

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

(40) PiDPToQDPProof (SOUND transformation)

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

(41) Obligation:

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

LESS78_IN_AALESS78_IN_AA

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

(42) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = LESS78_IN_AA evaluates to t =LESS78_IN_AA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Semiunifier: [ ]
  • Matcher: [ ]




Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from LESS78_IN_AA to LESS78_IN_AA.



(43) NO

(44) Obligation:

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

MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
MERGE54_IN_AAA(x1, x2, x3)  =  MERGE54_IN_AAA
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6)  =  U18_AAA(x6)

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

(45) UsableRulesProof (EQUIVALENT transformation)

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

(46) Obligation:

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

MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
.(x1, x2)  =  .(x1, x2)
0  =  0
s(x1)  =  s(x1)
MERGE54_IN_AAA(x1, x2, x3)  =  MERGE54_IN_AAA
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6)  =  U18_AAA(x6)

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

(47) PiDPToQDPProof (SOUND transformation)

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

(48) Obligation:

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

MERGE54_IN_AAAU15_AAA(less70_in_aa)
U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAAU18_AAA(less78_in_aa)
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA

The TRS R consists of the following rules:

less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less70_in_aa
less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(49) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule MERGE54_IN_AAAU15_AAA(less70_in_aa) at position [0] we obtained the following new rules [LPAR04]:

MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))

(50) Obligation:

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

U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAAU18_AAA(less78_in_aa)
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))

The TRS R consists of the following rules:

less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less70_in_aa
less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(51) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(52) Obligation:

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

U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAAU18_AAA(less78_in_aa)
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))

The TRS R consists of the following rules:

less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less70_in_aa
less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(53) QReductionProof (EQUIVALENT transformation)

We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].

less70_in_aa

(54) Obligation:

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

U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAAU18_AAA(less78_in_aa)
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))

The TRS R consists of the following rules:

less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(55) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule MERGE54_IN_AAAU18_AAA(less78_in_aa) at position [0] we obtained the following new rules [LPAR04]:

MERGE54_IN_AAAU18_AAA(less78_out_aa(0))
MERGE54_IN_AAAU18_AAA(U20_aa(less78_in_aa))

(56) Obligation:

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

U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))
MERGE54_IN_AAAU18_AAA(less78_out_aa(0))
MERGE54_IN_AAAU18_AAA(U20_aa(less78_in_aa))

The TRS R consists of the following rules:

less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(57) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by narrowing to the left:

s = MERGE54_IN_AAA evaluates to t =MERGE54_IN_AAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Semiunifier: [ ]
  • Matcher: [ ]




Rewriting sequence

MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
with rule MERGE54_IN_AAAU15_AAA(less70_out_aa(0)) at position [] and matcher [ ]

U15_AAA(less70_out_aa(0))MERGE54_IN_AAA
with rule U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA

Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence


All these steps are and every following step will be a correct step w.r.t to Q.



(58) NO

(59) Obligation:

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

SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
SPLIT16_IN_AAA(x1, x2, x3)  =  SPLIT16_IN_AAA

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

(60) UsableRulesProof (EQUIVALENT transformation)

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

(61) Obligation:

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

SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
SPLIT16_IN_AAA(x1, x2, x3)  =  SPLIT16_IN_AAA

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

(62) PiDPToQDPProof (SOUND transformation)

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

(63) Obligation:

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

SPLIT16_IN_AAASPLIT16_IN_AAA

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

(64) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = SPLIT16_IN_AAA evaluates to t =SPLIT16_IN_AAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Semiunifier: [ ]
  • Matcher: [ ]




Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from SPLIT16_IN_AAA to SPLIT16_IN_AAA.



(65) NO

(66) Obligation:

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

P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg
U22_gg(x1, x2, x3)  =  U22_gg(x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg
U20_gg(x1, x2, x3)  =  U20_gg(x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x6)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAA
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAA(x9)
MS38_IN_AA(x1, x2)  =  MS38_IN_AA
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAA(x9)

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

(67) UsableRulesProof (EQUIVALENT transformation)

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

(68) Obligation:

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

P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)

The TRS R consists of the following rules:

split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
[]  =  []
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
.(x1, x2)  =  .(x1, x2)
0  =  0
s(x1)  =  s(x1)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAA
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAA(x9)
MS38_IN_AA(x1, x2)  =  MS38_IN_AA
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAA(x9)

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

(69) PiDPToQDPProof (SOUND transformation)

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

(70) Obligation:

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

P34_IN_AAAAAAAAU4_AAAAAAAA(split12_in_aaaa)
U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
P34_IN_AAAAAAAAU6_AAAAAAAA(split12_in_aaaa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_in_aa)
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(71) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P34_IN_AAAAAAAAU4_AAAAAAAA(split12_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))

(72) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
P34_IN_AAAAAAAAU6_AAAAAAAA(split12_in_aaaa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_in_aa)
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(73) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P34_IN_AAAAAAAAU6_AAAAAAAA(split12_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))

(74) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_in_aa)
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(75) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_in_aa) at position [0] we obtained the following new rules [LPAR04]:

U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_out_aa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))

(76) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_out_aa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(77) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

P34_IN_AAAAAAAAU9_AAAAAAAA(U2_aaaa(split16_in_aaa))

(78) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_out_aa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))
P34_IN_AAAAAAAAU9_AAAAAAAA(U2_aaaa(split16_in_aaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(79) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa) at position [0] we obtained the following new rules [LPAR04]:

U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_out_aa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))

(80) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_out_aa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))
P34_IN_AAAAAAAAU9_AAAAAAAA(U2_aaaa(split16_in_aaa))
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_out_aa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(81) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by narrowing to the left:

s = U4_AAAAAAAA(U2_aaaa(split16_in_aaa)) evaluates to t =U4_AAAAAAAA(U2_aaaa(split16_in_aaa))

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Semiunifier: [ ]
  • Matcher: [ ]




Rewriting sequence

U4_AAAAAAAA(U2_aaaa(split16_in_aaa))U4_AAAAAAAA(U2_aaaa(split16_out_aaa))
with rule split16_in_aaasplit16_out_aaa at position [0,0] and matcher [ ]

U4_AAAAAAAA(U2_aaaa(split16_out_aaa))U4_AAAAAAAA(split12_out_aaaa)
with rule U2_aaaa(split16_out_aaa) → split12_out_aaaa at position [0] and matcher [ ]

U4_AAAAAAAA(split12_out_aaaa)MS38_IN_AA
with rule U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA at position [] and matcher [ ]

MS38_IN_AAP34_IN_AAAAAAAA
with rule MS38_IN_AAP34_IN_AAAAAAAA at position [] and matcher [ ]

P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
with rule P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))

Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence


All these steps are and every following step will be a correct step w.r.t to Q.



(82) NO

(83) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
ms1_in: (f,b)
split12_in: (f,f,f,f)
split16_in: (f,f,f)
ms25_in: (f,f,f) (f,f,b)
p34_in: (f,f,f,f,f,f,f,f) (f,f,f,f,f,f,f,b)
ms38_in: (f,f) (f,b)
merge54_in: (f,f,f) (f,f,b)
less70_in: (f,f) (b,f) (b,b)
less78_in: (f,f) (b,f) (b,b)
p179_in: (b,f,f,f,b)
p194_in: (b,f,f,f,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(84) Obligation:

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

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)

(85) 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:

MS1_IN_AG(.(T29, .(T27, T28)), []) → U35_AG(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
MS1_IN_AG(.(T29, .(T27, T28)), []) → SPLIT12_IN_AAAA(T27, T28, X42, X41)
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → U2_AAAA(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → SPLIT16_IN_AAA(T44, X72, X71)
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → U1_AAA(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U36_AG(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_AG(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
U36_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → MS25_IN_AAA(T34, T33, X13)
MS25_IN_AAA(T72, .(T73, T74), X127) → U21_AAA(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAA(T72, .(T73, T74), X127) → P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → U13_AA(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → MERGE54_IN_AAA(T106, T105, X127)
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAA(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_AA(T139, T140)
LESS70_IN_AA(s(T161), T162) → U22_AA(T161, T162, less78_in_aa(T161, T162))
LESS70_IN_AA(s(T161), T162) → LESS78_IN_AA(T161, T162)
LESS78_IN_AA(s(T176), s(T177)) → U20_AA(T176, T177, less78_in_aa(T176, T177))
LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)
MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_AAA(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAA(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_AA(T196, T197)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_AAA(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U38_AG(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_AG(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → MS25_IN_AAA(T34, T33, T54)
U39_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_AG(T34, T27, T28, ms38_in_aa(T55, X14))
U39_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → MS38_IN_AA(T55, X14)
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_AG(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_AG(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U41_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → MS38_IN_AA(T55, T211)
U42_AG(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_AG(T34, T27, T28, merge93_in_aa(T212, T211))
U42_AG(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → MERGE93_IN_AA(T212, T211)
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → U44_AG(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → SPLIT12_IN_AAAA(T260, T261, X367, X366)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U45_AG(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_AG(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U45_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → MS25_IN_AAA(T267, T266, X338)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U47_AG(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_AG(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U47_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, T272)
U48_AG(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_AG(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U48_AG(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → MS38_IN_AA(T273, X339)
MS1_IN_AG(.(T267, .(T260, T261)), .(T291, [])) → U50_AG(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_AG(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_AG(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
U50_AG(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAG(T267, T266, [])
MS25_IN_AAG(T72, .(T73, T74), X127) → U21_AAG(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAG(T72, .(T73, T74), X127) → P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)
U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → MERGE54_IN_AAG(T106, T105, X127)
MERGE54_IN_AAG(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAG(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
MERGE54_IN_AAG(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_GA(T139, T140)
LESS70_IN_GA(s(T161), T162) → U22_GA(T161, T162, less78_in_ga(T161, T162))
LESS70_IN_GA(s(T161), T162) → LESS78_IN_GA(T161, T162)
LESS78_IN_GA(s(T176), s(T177)) → U20_GA(T176, T177, less78_in_ga(T176, T177))
LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)
MERGE54_IN_AAG(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAG(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_AAG(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → MERGE54_IN_AAG(T145, .(T146, T147), X226)
MERGE54_IN_AAG(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAG(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
MERGE54_IN_AAG(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_GA(T196, T197)
MERGE54_IN_AAG(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAG(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_AAG(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → MERGE54_IN_AAG(.(T202, T203), T204, X287)
U51_AG(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_AG(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
U51_AG(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → MS38_IN_AG(T273, .(T291, []))
MS38_IN_AG(.(T99, .(T100, T101)), X172) → U13_AG(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AG(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAG(T99, T100, T101, X168, X169, X170, X171, X172)
MS1_IN_AG(.(T267, .(T260, T261)), .(T301, [])) → U53_AG(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_AG(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_AG(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U53_AG(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAG(T267, T266, .(T301, []))
U54_AG(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_AG(T267, T260, T261, T301, ms38_in_ag(T273, []))
U54_AG(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → MS38_IN_AG(T273, [])
MS1_IN_AG(.(T267, .(T260, T261)), .(T318, [])) → U56_AG(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_AG(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, .(T318, T323))
U57_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_AG(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U57_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → MS38_IN_AA(T273, .(T322, T324))
U58_AG(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_AG(T267, T260, T261, T318, less70_in_ga(T318, T322))
U58_AG(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → LESS70_IN_GA(T318, T322)
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_AG(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_AG(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U60_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → MS38_IN_AA(T273, .(T328, T329))
U61_AG(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U61_AG(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → LESS70_IN_GA(T318, T328)
U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_AG(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → MERGE93_IN_AA(T327, .(T328, T329))
MS1_IN_AG(.(T267, .(T260, T261)), .(T356, [])) → U64_AG(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_AG(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, .(T358, T360))
U65_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_AG(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U65_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → MS38_IN_AA(T273, .(T356, T359))
U66_AG(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_AG(T267, T260, T261, T356, less78_in_ga(T356, T358))
U66_AG(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → LESS78_IN_GA(T356, T358)
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_AG(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_AG(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U68_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → MS38_IN_AA(T273, .(T356, T365))
U69_AG(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U69_AG(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → LESS78_IN_GA(T356, T363)
U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_AG(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → MERGE93_IN_AA(.(T363, T364), T365)
MS1_IN_AG(.(T407, .(T405, T406)), T387) → U72_AG(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
MS1_IN_AG(.(T407, .(T405, T406)), T387) → SPLIT12_IN_AAAA(T405, T406, X523, X522)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U73_AG(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_AG(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U73_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → MS25_IN_AAA(T412, T411, X494)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U75_AG(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_AG(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U75_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, T419)
U76_AG(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_AG(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U76_AG(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → MS38_IN_AA(T420, X495)
MS1_IN_AG(.(T412, .(T405, T406)), T435) → U78_AG(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_AG(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_AG(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U78_AG(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, [])
U79_AG(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_AG(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U79_AG(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → MS38_IN_AG(T420, T435)
MS1_IN_AG(.(T412, .(T405, T406)), T440) → U81_AG(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_AG(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_AG(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U81_AG(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, T440)
U82_AG(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_AG(T412, T405, T406, T440, ms38_in_ag(T420, []))
U82_AG(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → MS38_IN_AG(T420, [])
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → U84_AG(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → SPLIT12_IN_AAAA(T405, T406, T420, T411)
U84_AG(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_AG(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U84_AG(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, T467))
U85_AG(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_AG(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U85_AG(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → MS38_IN_AA(T420, .(T466, T468))
U86_AG(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_AG(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U86_AG(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → LESS70_IN_GA(T461, T466)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_AG(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → SPLIT12_IN_AAAA(T405, T406, T420, T411)
U88_AG(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U88_AG(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, .(T461, []))
U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_AG(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → MS38_IN_AG(T420, .(T490, T491))
U90_AG(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_AG(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
U90_AG(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → LESS70_IN_GG(T461, T490)
LESS70_IN_GG(s(T161), T162) → U22_GG(T161, T162, less78_in_gg(T161, T162))
LESS70_IN_GG(s(T161), T162) → LESS78_IN_GG(T161, T162)
LESS78_IN_GG(s(T176), s(T177)) → U20_GG(T176, T177, less78_in_gg(T176, T177))
LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_AG(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_AG(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U92_AG(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, .(T513, T519)))
U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → MS38_IN_AA(T420, .(T518, T520))
U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → LESS70_IN_GA(T461, T518)
U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_AG(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → P179_IN_GAAAG(T513, T518, T519, T520, T517)
P179_IN_GAAAG(T513, T518, T519, T520, T517) → U23_GAAAG(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
P179_IN_GAAAG(T513, T518, T519, T520, T517) → LESS70_IN_GA(T513, T518)
P179_IN_GAAAG(T513, T540, [], T541, .(T540, T541)) → U24_GAAAG(T513, T540, T541, less70_in_gg(T513, T540))
P179_IN_GAAAG(T513, T540, [], T541, .(T540, T541)) → LESS70_IN_GG(T513, T540)
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → LESS70_IN_GA(T513, T568)
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_GAAAG(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → LESS70_IN_GG(T513, T585)
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_GAAAG(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T588, T590, T589, T587) → U29_GAAAG(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
P194_IN_GAAAG(T585, T588, T590, T589, T587) → LESS78_IN_GA(T585, T588)
P194_IN_GAAAG(T585, T610, T611, [], .(T610, T611)) → U30_GAAAG(T585, T610, T611, less78_in_gg(T585, T610))
P194_IN_GAAAG(T585, T610, T611, [], .(T610, T611)) → LESS78_IN_GG(T585, T610)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → LESS78_IN_GG(T585, T632)
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_GAAAG(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → LESS78_IN_GA(T585, T657)
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_GAAAG(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_AG(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_AG(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U97_AG(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, .(T677, T679)))
U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → MS38_IN_AA(T420, .(T674, T678))
U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → LESS70_IN_GG(T461, T674)
U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_AG(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → P194_IN_GAAAG(T674, T677, T679, T678, T676)
MS1_IN_AG(.(T412, .(T405, T406)), .(T694, T696)) → U102_AG(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_AG(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_AG(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U102_AG(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T697, T699))
U103_AG(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U103_AG(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → MS38_IN_AA(T420, .(T694, T698))
U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_AG(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → P194_IN_GAAAG(T694, T697, T699, T698, T696)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
MS1_IN_AG(x1, x2)  =  MS1_IN_AG(x2)
U35_AG(x1, x2, x3, x4)  =  U35_AG(x4)
SPLIT12_IN_AAAA(x1, x2, x3, x4)  =  SPLIT12_IN_AAAA
U2_AAAA(x1, x2, x3, x4, x5)  =  U2_AAAA(x5)
SPLIT16_IN_AAA(x1, x2, x3)  =  SPLIT16_IN_AAA
U1_AAA(x1, x2, x3, x4, x5)  =  U1_AAA(x5)
U36_AG(x1, x2, x3, x4)  =  U36_AG(x4)
U37_AG(x1, x2, x3, x4)  =  U37_AG(x4)
MS25_IN_AAA(x1, x2, x3)  =  MS25_IN_AAA
U21_AAA(x1, x2, x3, x4, x5)  =  U21_AAA(x5)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAA
U3_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_AAAAAAAA(x9)
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAA(x9)
U5_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_AAAAAAAA(x9)
MS38_IN_AA(x1, x2)  =  MS38_IN_AA
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAA(x9)
U8_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAA(x9)
U11_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_AAAAAAAA(x9)
U12_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_AAAAAAAA(x9)
MERGE54_IN_AAA(x1, x2, x3)  =  MERGE54_IN_AAA
U14_AAA(x1, x2, x3, x4, x5, x6)  =  U14_AAA(x6)
LESS70_IN_AA(x1, x2)  =  LESS70_IN_AA
U22_AA(x1, x2, x3)  =  U22_AA(x3)
LESS78_IN_AA(x1, x2)  =  LESS78_IN_AA
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U16_AAA(x1, x2, x3, x4, x5, x6)  =  U16_AAA(x6)
U17_AAA(x1, x2, x3, x4, x5, x6)  =  U17_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6)  =  U18_AAA(x6)
U19_AAA(x1, x2, x3, x4, x5, x6)  =  U19_AAA(x6)
U38_AG(x1, x2, x3, x4)  =  U38_AG(x4)
U39_AG(x1, x2, x3, x4, x5)  =  U39_AG(x5)
U40_AG(x1, x2, x3, x4)  =  U40_AG(x4)
U41_AG(x1, x2, x3, x4, x5)  =  U41_AG(x5)
U42_AG(x1, x2, x3, x4, x5)  =  U42_AG(x5)
U43_AG(x1, x2, x3, x4)  =  U43_AG(x4)
MERGE93_IN_AA(x1, x2)  =  MERGE93_IN_AA
U44_AG(x1, x2, x3, x4, x5)  =  U44_AG(x4, x5)
U45_AG(x1, x2, x3, x4, x5)  =  U45_AG(x4, x5)
U46_AG(x1, x2, x3, x4, x5)  =  U46_AG(x4, x5)
U47_AG(x1, x2, x3, x4, x5)  =  U47_AG(x4, x5)
U48_AG(x1, x2, x3, x4, x5, x6)  =  U48_AG(x4, x6)
U49_AG(x1, x2, x3, x4, x5)  =  U49_AG(x4, x5)
U50_AG(x1, x2, x3, x4, x5)  =  U50_AG(x4, x5)
U51_AG(x1, x2, x3, x4, x5, x6)  =  U51_AG(x4, x6)
MS25_IN_AAG(x1, x2, x3)  =  MS25_IN_AAG(x3)
U21_AAG(x1, x2, x3, x4, x5)  =  U21_AAG(x4, x5)
P34_IN_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAG(x8)
U3_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_AAAAAAAG(x8, x9)
U4_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAG(x8, x9)
U5_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_AAAAAAAG(x8, x9)
U6_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAG(x8, x9)
U7_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAG(x8, x9)
U8_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_AAAAAAAG(x8, x9)
U9_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAG(x8, x9)
U10_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAG(x8, x9)
U11_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_AAAAAAAG(x8, x9)
U12_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_AAAAAAAG(x8, x9)
MERGE54_IN_AAG(x1, x2, x3)  =  MERGE54_IN_AAG(x3)
U14_AAG(x1, x2, x3, x4, x5, x6)  =  U14_AAG(x1, x5, x6)
LESS70_IN_GA(x1, x2)  =  LESS70_IN_GA(x1)
U22_GA(x1, x2, x3)  =  U22_GA(x1, x3)
LESS78_IN_GA(x1, x2)  =  LESS78_IN_GA(x1)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U15_AAG(x1, x2, x3, x4, x5, x6)  =  U15_AAG(x1, x5, x6)
U16_AAG(x1, x2, x3, x4, x5, x6)  =  U16_AAG(x1, x5, x6)
U17_AAG(x1, x2, x3, x4, x5, x6)  =  U17_AAG(x3, x5, x6)
U18_AAG(x1, x2, x3, x4, x5, x6)  =  U18_AAG(x3, x5, x6)
U19_AAG(x1, x2, x3, x4, x5, x6)  =  U19_AAG(x3, x5, x6)
U52_AG(x1, x2, x3, x4, x5)  =  U52_AG(x4, x5)
MS38_IN_AG(x1, x2)  =  MS38_IN_AG(x2)
U13_AG(x1, x2, x3, x4, x5)  =  U13_AG(x4, x5)
U53_AG(x1, x2, x3, x4, x5)  =  U53_AG(x4, x5)
U54_AG(x1, x2, x3, x4, x5, x6)  =  U54_AG(x4, x6)
U55_AG(x1, x2, x3, x4, x5)  =  U55_AG(x4, x5)
U56_AG(x1, x2, x3, x4, x5)  =  U56_AG(x4, x5)
U57_AG(x1, x2, x3, x4, x5, x6)  =  U57_AG(x4, x6)
U58_AG(x1, x2, x3, x4, x5)  =  U58_AG(x4, x5)
U59_AG(x1, x2, x3, x4, x5)  =  U59_AG(x4, x5)
U60_AG(x1, x2, x3, x4, x5, x6)  =  U60_AG(x4, x6)
U61_AG(x1, x2, x3, x4, x5, x6)  =  U61_AG(x4, x6)
U62_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_AG(x4, x8)
U63_AG(x1, x2, x3, x4, x5)  =  U63_AG(x4, x5)
U64_AG(x1, x2, x3, x4, x5)  =  U64_AG(x4, x5)
U65_AG(x1, x2, x3, x4, x5, x6)  =  U65_AG(x4, x6)
U66_AG(x1, x2, x3, x4, x5, x6)  =  U66_AG(x4, x6)
U67_AG(x1, x2, x3, x4, x5)  =  U67_AG(x4, x5)
U68_AG(x1, x2, x3, x4, x5, x6)  =  U68_AG(x4, x6)
U69_AG(x1, x2, x3, x4, x5, x6, x7)  =  U69_AG(x4, x7)
U70_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_AG(x4, x8)
U71_AG(x1, x2, x3, x4, x5)  =  U71_AG(x4, x5)
U72_AG(x1, x2, x3, x4, x5)  =  U72_AG(x4, x5)
U73_AG(x1, x2, x3, x4, x5)  =  U73_AG(x4, x5)
U74_AG(x1, x2, x3, x4, x5)  =  U74_AG(x4, x5)
U75_AG(x1, x2, x3, x4, x5)  =  U75_AG(x4, x5)
U76_AG(x1, x2, x3, x4, x5, x6)  =  U76_AG(x4, x6)
U77_AG(x1, x2, x3, x4, x5)  =  U77_AG(x4, x5)
U78_AG(x1, x2, x3, x4, x5)  =  U78_AG(x4, x5)
U79_AG(x1, x2, x3, x4, x5, x6)  =  U79_AG(x4, x6)
U80_AG(x1, x2, x3, x4, x5)  =  U80_AG(x4, x5)
U81_AG(x1, x2, x3, x4, x5)  =  U81_AG(x4, x5)
U82_AG(x1, x2, x3, x4, x5, x6)  =  U82_AG(x4, x6)
U83_AG(x1, x2, x3, x4, x5)  =  U83_AG(x4, x5)
U84_AG(x1, x2, x3, x4, x5, x6)  =  U84_AG(x4, x5, x6)
U85_AG(x1, x2, x3, x4, x5, x6, x7)  =  U85_AG(x4, x5, x7)
U86_AG(x1, x2, x3, x4, x5, x6)  =  U86_AG(x4, x5, x6)
U87_AG(x1, x2, x3, x4, x5, x6)  =  U87_AG(x4, x5, x6)
U88_AG(x1, x2, x3, x4, x5, x6, x7)  =  U88_AG(x4, x5, x6, x7)
U89_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_AG(x4, x5, x6, x8)
U90_AG(x1, x2, x3, x4, x5, x6, x7)  =  U90_AG(x4, x5, x6, x7)
U91_AG(x1, x2, x3, x4, x5, x6, x7)  =  U91_AG(x4, x5, x6, x7)
LESS70_IN_GG(x1, x2)  =  LESS70_IN_GG(x1, x2)
U22_GG(x1, x2, x3)  =  U22_GG(x1, x2, x3)
LESS78_IN_GG(x1, x2)  =  LESS78_IN_GG(x1, x2)
U20_GG(x1, x2, x3)  =  U20_GG(x1, x2, x3)
U92_AG(x1, x2, x3, x4, x5, x6, x7)  =  U92_AG(x4, x5, x6, x7)
U93_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_AG(x4, x5, x6, x8)
U94_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_AG(x4, x5, x6, x8)
U95_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_AG(x4, x5, x6, x10)
U96_AG(x1, x2, x3, x4, x5, x6, x7)  =  U96_AG(x4, x5, x6, x7)
P179_IN_GAAAG(x1, x2, x3, x4, x5)  =  P179_IN_GAAAG(x1, x5)
U23_GAAAG(x1, x2, x3, x4, x5, x6)  =  U23_GAAAG(x1, x5, x6)
U24_GAAAG(x1, x2, x3, x4)  =  U24_GAAAG(x1, x2, x3, x4)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U25_GAAAG(x1, x3, x6, x7)
U26_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U26_GAAAG(x1, x3, x6, x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U27_GAAAG(x1, x2, x6, x7)
U28_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U28_GAAAG(x1, x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5)  =  P194_IN_GAAAG(x1, x5)
U29_GAAAG(x1, x2, x3, x4, x5, x6)  =  U29_GAAAG(x1, x5, x6)
U30_GAAAG(x1, x2, x3, x4)  =  U30_GAAAG(x1, x2, x3, x4)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U31_GAAAG(x1, x2, x6, x7)
U32_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U32_GAAAG(x1, x2, x6, x7)
U33_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U33_GAAAG(x1, x4, x6, x7)
U34_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U34_GAAAG(x1, x4, x6, x7)
U97_AG(x1, x2, x3, x4, x5, x6, x7)  =  U97_AG(x4, x5, x6, x7)
U98_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_AG(x4, x5, x6, x8)
U99_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_AG(x4, x5, x6, x9)
U100_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_AG(x4, x5, x6, x10)
U101_AG(x1, x2, x3, x4, x5, x6, x7)  =  U101_AG(x4, x5, x6, x7)
U102_AG(x1, x2, x3, x4, x5, x6)  =  U102_AG(x4, x5, x6)
U103_AG(x1, x2, x3, x4, x5, x6, x7)  =  U103_AG(x4, x5, x7)
U104_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_AG(x4, x5, x8)
U105_AG(x1, x2, x3, x4, x5, x6)  =  U105_AG(x4, x5, x6)

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

(86) Obligation:

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

MS1_IN_AG(.(T29, .(T27, T28)), []) → U35_AG(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
MS1_IN_AG(.(T29, .(T27, T28)), []) → SPLIT12_IN_AAAA(T27, T28, X42, X41)
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → U2_AAAA(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
SPLIT12_IN_AAAA(T42, T44, .(T42, X71), X72) → SPLIT16_IN_AAA(T44, X72, X71)
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → U1_AAA(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U36_AG(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_AG(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
U36_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → MS25_IN_AAA(T34, T33, X13)
MS25_IN_AAA(T72, .(T73, T74), X127) → U21_AAA(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAA(T72, .(T73, T74), X127) → P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAA(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → U13_AA(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
U11_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → MERGE54_IN_AAA(T106, T105, X127)
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAA(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
MERGE54_IN_AAA(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_AA(T139, T140)
LESS70_IN_AA(s(T161), T162) → U22_AA(T161, T162, less78_in_aa(T161, T162))
LESS70_IN_AA(s(T161), T162) → LESS78_IN_AA(T161, T162)
LESS78_IN_AA(s(T176), s(T177)) → U20_AA(T176, T177, less78_in_aa(T176, T177))
LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)
MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_AAA(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAA(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
MERGE54_IN_AAA(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_AA(T196, T197)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_AAA(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)
MS1_IN_AG(.(T34, .(T27, T28)), []) → U38_AG(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_AG(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → MS25_IN_AAA(T34, T33, T54)
U39_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_AG(T34, T27, T28, ms38_in_aa(T55, X14))
U39_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → MS38_IN_AA(T55, X14)
U38_AG(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_AG(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_AG(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U41_AG(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → MS38_IN_AA(T55, T211)
U42_AG(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_AG(T34, T27, T28, merge93_in_aa(T212, T211))
U42_AG(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → MERGE93_IN_AA(T212, T211)
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → U44_AG(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
MS1_IN_AG(.(T262, .(T260, T261)), .(T242, [])) → SPLIT12_IN_AAAA(T260, T261, X367, X366)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U45_AG(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_AG(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U45_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → MS25_IN_AAA(T267, T266, X338)
MS1_IN_AG(.(T267, .(T260, T261)), .(T242, [])) → U47_AG(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_AG(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U47_AG(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, T272)
U48_AG(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_AG(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U48_AG(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → MS38_IN_AA(T273, X339)
MS1_IN_AG(.(T267, .(T260, T261)), .(T291, [])) → U50_AG(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_AG(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_AG(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
U50_AG(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAG(T267, T266, [])
MS25_IN_AAG(T72, .(T73, T74), X127) → U21_AAG(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
MS25_IN_AAG(T72, .(T73, T74), X127) → P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127)
P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127) → U3_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
P34_IN_AAAAAAAG(T72, T73, T74, X123, X124, X125, X126, X127) → SPLIT12_IN_AAAA(T72, .(T73, T74), X123, X124)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U4_AAAAAAAG(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U6_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U7_AAAAAAAG(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
P34_IN_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U9_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)
U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U10_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
U11_AAAAAAAG(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → MERGE54_IN_AAG(T106, T105, X127)
MERGE54_IN_AAG(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_AAG(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
MERGE54_IN_AAG(.(T139, T141), .(T140, T142), .(T139, X226)) → LESS70_IN_GA(T139, T140)
LESS70_IN_GA(s(T161), T162) → U22_GA(T161, T162, less78_in_ga(T161, T162))
LESS70_IN_GA(s(T161), T162) → LESS78_IN_GA(T161, T162)
LESS78_IN_GA(s(T176), s(T177)) → U20_GA(T176, T177, less78_in_ga(T176, T177))
LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)
MERGE54_IN_AAG(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAG(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_AAG(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → MERGE54_IN_AAG(T145, .(T146, T147), X226)
MERGE54_IN_AAG(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_AAG(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
MERGE54_IN_AAG(.(T197, T199), .(T196, T198), .(T196, X287)) → LESS78_IN_GA(T196, T197)
MERGE54_IN_AAG(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAG(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_AAG(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → MERGE54_IN_AAG(.(T202, T203), T204, X287)
U51_AG(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_AG(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
U51_AG(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → MS38_IN_AG(T273, .(T291, []))
MS38_IN_AG(.(T99, .(T100, T101)), X172) → U13_AG(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
MS38_IN_AG(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAG(T99, T100, T101, X168, X169, X170, X171, X172)
MS1_IN_AG(.(T267, .(T260, T261)), .(T301, [])) → U53_AG(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_AG(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_AG(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U53_AG(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAG(T267, T266, .(T301, []))
U54_AG(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_AG(T267, T260, T261, T301, ms38_in_ag(T273, []))
U54_AG(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → MS38_IN_AG(T273, [])
MS1_IN_AG(.(T267, .(T260, T261)), .(T318, [])) → U56_AG(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_AG(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, .(T318, T323))
U57_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_AG(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U57_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → MS38_IN_AA(T273, .(T322, T324))
U58_AG(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_AG(T267, T260, T261, T318, less70_in_ga(T318, T322))
U58_AG(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → LESS70_IN_GA(T318, T322)
U56_AG(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_AG(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_AG(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U60_AG(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → MS38_IN_AA(T273, .(T328, T329))
U61_AG(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U61_AG(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → LESS70_IN_GA(T318, T328)
U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_AG(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U62_AG(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → MERGE93_IN_AA(T327, .(T328, T329))
MS1_IN_AG(.(T267, .(T260, T261)), .(T356, [])) → U64_AG(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_AG(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → MS25_IN_AAA(T267, T266, .(T358, T360))
U65_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_AG(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U65_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → MS38_IN_AA(T273, .(T356, T359))
U66_AG(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_AG(T267, T260, T261, T356, less78_in_ga(T356, T358))
U66_AG(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → LESS78_IN_GA(T356, T358)
U64_AG(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_AG(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_AG(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U68_AG(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → MS38_IN_AA(T273, .(T356, T365))
U69_AG(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U69_AG(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → LESS78_IN_GA(T356, T363)
U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_AG(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U70_AG(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → MERGE93_IN_AA(.(T363, T364), T365)
MS1_IN_AG(.(T407, .(T405, T406)), T387) → U72_AG(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
MS1_IN_AG(.(T407, .(T405, T406)), T387) → SPLIT12_IN_AAAA(T405, T406, X523, X522)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U73_AG(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_AG(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U73_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → MS25_IN_AAA(T412, T411, X494)
MS1_IN_AG(.(T412, .(T405, T406)), T387) → U75_AG(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_AG(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U75_AG(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, T419)
U76_AG(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_AG(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U76_AG(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → MS38_IN_AA(T420, X495)
MS1_IN_AG(.(T412, .(T405, T406)), T435) → U78_AG(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_AG(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_AG(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U78_AG(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, [])
U79_AG(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_AG(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U79_AG(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → MS38_IN_AG(T420, T435)
MS1_IN_AG(.(T412, .(T405, T406)), T440) → U81_AG(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_AG(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_AG(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U81_AG(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, T440)
U82_AG(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_AG(T412, T405, T406, T440, ms38_in_ag(T420, []))
U82_AG(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → MS38_IN_AG(T420, [])
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → U84_AG(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, T465)) → SPLIT12_IN_AAAA(T405, T406, T420, T411)
U84_AG(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_AG(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U84_AG(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, T467))
U85_AG(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_AG(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U85_AG(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → MS38_IN_AA(T420, .(T466, T468))
U86_AG(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_AG(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U86_AG(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → LESS70_IN_GA(T461, T466)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_AG(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → SPLIT12_IN_AAAA(T405, T406, T420, T411)
U88_AG(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U88_AG(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAG(T412, T411, .(T461, []))
U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_AG(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U89_AG(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → MS38_IN_AG(T420, .(T490, T491))
U90_AG(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_AG(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
U90_AG(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → LESS70_IN_GG(T461, T490)
LESS70_IN_GG(s(T161), T162) → U22_GG(T161, T162, less78_in_gg(T161, T162))
LESS70_IN_GG(s(T161), T162) → LESS78_IN_GG(T161, T162)
LESS78_IN_GG(s(T176), s(T177)) → U20_GG(T176, T177, less78_in_gg(T176, T177))
LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_AG(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_AG(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U92_AG(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, .(T513, T519)))
U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U93_AG(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → MS38_IN_AA(T420, .(T518, T520))
U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U94_AG(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → LESS70_IN_GA(T461, T518)
U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_AG(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
U95_AG(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → P179_IN_GAAAG(T513, T518, T519, T520, T517)
P179_IN_GAAAG(T513, T518, T519, T520, T517) → U23_GAAAG(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
P179_IN_GAAAG(T513, T518, T519, T520, T517) → LESS70_IN_GA(T513, T518)
P179_IN_GAAAG(T513, T540, [], T541, .(T540, T541)) → U24_GAAAG(T513, T540, T541, less70_in_gg(T513, T540))
P179_IN_GAAAG(T513, T540, [], T541, .(T540, T541)) → LESS70_IN_GG(T513, T540)
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → LESS70_IN_GA(T513, T568)
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_GAAAG(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → LESS70_IN_GG(T513, T585)
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_GAAAG(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T588, T590, T589, T587) → U29_GAAAG(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
P194_IN_GAAAG(T585, T588, T590, T589, T587) → LESS78_IN_GA(T585, T588)
P194_IN_GAAAG(T585, T610, T611, [], .(T610, T611)) → U30_GAAAG(T585, T610, T611, less78_in_gg(T585, T610))
P194_IN_GAAAG(T585, T610, T611, [], .(T610, T611)) → LESS78_IN_GG(T585, T610)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → LESS78_IN_GG(T585, T632)
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_GAAAG(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → LESS78_IN_GA(T585, T657)
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_GAAAG(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)
MS1_IN_AG(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_AG(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_AG(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U97_AG(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T461, .(T677, T679)))
U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U98_AG(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → MS38_IN_AA(T420, .(T674, T678))
U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U99_AG(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → LESS70_IN_GG(T461, T674)
U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_AG(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U100_AG(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → P194_IN_GAAAG(T674, T677, T679, T678, T676)
MS1_IN_AG(.(T412, .(T405, T406)), .(T694, T696)) → U102_AG(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_AG(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_AG(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U102_AG(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → MS25_IN_AAA(T412, T411, .(T697, T699))
U103_AG(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U103_AG(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → MS38_IN_AA(T420, .(T694, T698))
U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_AG(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U104_AG(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → P194_IN_GAAAG(T694, T697, T699, T698, T696)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
MS1_IN_AG(x1, x2)  =  MS1_IN_AG(x2)
U35_AG(x1, x2, x3, x4)  =  U35_AG(x4)
SPLIT12_IN_AAAA(x1, x2, x3, x4)  =  SPLIT12_IN_AAAA
U2_AAAA(x1, x2, x3, x4, x5)  =  U2_AAAA(x5)
SPLIT16_IN_AAA(x1, x2, x3)  =  SPLIT16_IN_AAA
U1_AAA(x1, x2, x3, x4, x5)  =  U1_AAA(x5)
U36_AG(x1, x2, x3, x4)  =  U36_AG(x4)
U37_AG(x1, x2, x3, x4)  =  U37_AG(x4)
MS25_IN_AAA(x1, x2, x3)  =  MS25_IN_AAA
U21_AAA(x1, x2, x3, x4, x5)  =  U21_AAA(x5)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAA
U3_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_AAAAAAAA(x9)
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAA(x9)
U5_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_AAAAAAAA(x9)
MS38_IN_AA(x1, x2)  =  MS38_IN_AA
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAA(x9)
U8_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAA(x9)
U11_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_AAAAAAAA(x9)
U12_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_AAAAAAAA(x9)
MERGE54_IN_AAA(x1, x2, x3)  =  MERGE54_IN_AAA
U14_AAA(x1, x2, x3, x4, x5, x6)  =  U14_AAA(x6)
LESS70_IN_AA(x1, x2)  =  LESS70_IN_AA
U22_AA(x1, x2, x3)  =  U22_AA(x3)
LESS78_IN_AA(x1, x2)  =  LESS78_IN_AA
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U16_AAA(x1, x2, x3, x4, x5, x6)  =  U16_AAA(x6)
U17_AAA(x1, x2, x3, x4, x5, x6)  =  U17_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6)  =  U18_AAA(x6)
U19_AAA(x1, x2, x3, x4, x5, x6)  =  U19_AAA(x6)
U38_AG(x1, x2, x3, x4)  =  U38_AG(x4)
U39_AG(x1, x2, x3, x4, x5)  =  U39_AG(x5)
U40_AG(x1, x2, x3, x4)  =  U40_AG(x4)
U41_AG(x1, x2, x3, x4, x5)  =  U41_AG(x5)
U42_AG(x1, x2, x3, x4, x5)  =  U42_AG(x5)
U43_AG(x1, x2, x3, x4)  =  U43_AG(x4)
MERGE93_IN_AA(x1, x2)  =  MERGE93_IN_AA
U44_AG(x1, x2, x3, x4, x5)  =  U44_AG(x4, x5)
U45_AG(x1, x2, x3, x4, x5)  =  U45_AG(x4, x5)
U46_AG(x1, x2, x3, x4, x5)  =  U46_AG(x4, x5)
U47_AG(x1, x2, x3, x4, x5)  =  U47_AG(x4, x5)
U48_AG(x1, x2, x3, x4, x5, x6)  =  U48_AG(x4, x6)
U49_AG(x1, x2, x3, x4, x5)  =  U49_AG(x4, x5)
U50_AG(x1, x2, x3, x4, x5)  =  U50_AG(x4, x5)
U51_AG(x1, x2, x3, x4, x5, x6)  =  U51_AG(x4, x6)
MS25_IN_AAG(x1, x2, x3)  =  MS25_IN_AAG(x3)
U21_AAG(x1, x2, x3, x4, x5)  =  U21_AAG(x4, x5)
P34_IN_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAG(x8)
U3_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_AAAAAAAG(x8, x9)
U4_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAG(x8, x9)
U5_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_AAAAAAAG(x8, x9)
U6_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAG(x8, x9)
U7_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAG(x8, x9)
U8_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_AAAAAAAG(x8, x9)
U9_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAG(x8, x9)
U10_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAG(x8, x9)
U11_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_AAAAAAAG(x8, x9)
U12_AAAAAAAG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_AAAAAAAG(x8, x9)
MERGE54_IN_AAG(x1, x2, x3)  =  MERGE54_IN_AAG(x3)
U14_AAG(x1, x2, x3, x4, x5, x6)  =  U14_AAG(x1, x5, x6)
LESS70_IN_GA(x1, x2)  =  LESS70_IN_GA(x1)
U22_GA(x1, x2, x3)  =  U22_GA(x1, x3)
LESS78_IN_GA(x1, x2)  =  LESS78_IN_GA(x1)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U15_AAG(x1, x2, x3, x4, x5, x6)  =  U15_AAG(x1, x5, x6)
U16_AAG(x1, x2, x3, x4, x5, x6)  =  U16_AAG(x1, x5, x6)
U17_AAG(x1, x2, x3, x4, x5, x6)  =  U17_AAG(x3, x5, x6)
U18_AAG(x1, x2, x3, x4, x5, x6)  =  U18_AAG(x3, x5, x6)
U19_AAG(x1, x2, x3, x4, x5, x6)  =  U19_AAG(x3, x5, x6)
U52_AG(x1, x2, x3, x4, x5)  =  U52_AG(x4, x5)
MS38_IN_AG(x1, x2)  =  MS38_IN_AG(x2)
U13_AG(x1, x2, x3, x4, x5)  =  U13_AG(x4, x5)
U53_AG(x1, x2, x3, x4, x5)  =  U53_AG(x4, x5)
U54_AG(x1, x2, x3, x4, x5, x6)  =  U54_AG(x4, x6)
U55_AG(x1, x2, x3, x4, x5)  =  U55_AG(x4, x5)
U56_AG(x1, x2, x3, x4, x5)  =  U56_AG(x4, x5)
U57_AG(x1, x2, x3, x4, x5, x6)  =  U57_AG(x4, x6)
U58_AG(x1, x2, x3, x4, x5)  =  U58_AG(x4, x5)
U59_AG(x1, x2, x3, x4, x5)  =  U59_AG(x4, x5)
U60_AG(x1, x2, x3, x4, x5, x6)  =  U60_AG(x4, x6)
U61_AG(x1, x2, x3, x4, x5, x6)  =  U61_AG(x4, x6)
U62_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_AG(x4, x8)
U63_AG(x1, x2, x3, x4, x5)  =  U63_AG(x4, x5)
U64_AG(x1, x2, x3, x4, x5)  =  U64_AG(x4, x5)
U65_AG(x1, x2, x3, x4, x5, x6)  =  U65_AG(x4, x6)
U66_AG(x1, x2, x3, x4, x5, x6)  =  U66_AG(x4, x6)
U67_AG(x1, x2, x3, x4, x5)  =  U67_AG(x4, x5)
U68_AG(x1, x2, x3, x4, x5, x6)  =  U68_AG(x4, x6)
U69_AG(x1, x2, x3, x4, x5, x6, x7)  =  U69_AG(x4, x7)
U70_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_AG(x4, x8)
U71_AG(x1, x2, x3, x4, x5)  =  U71_AG(x4, x5)
U72_AG(x1, x2, x3, x4, x5)  =  U72_AG(x4, x5)
U73_AG(x1, x2, x3, x4, x5)  =  U73_AG(x4, x5)
U74_AG(x1, x2, x3, x4, x5)  =  U74_AG(x4, x5)
U75_AG(x1, x2, x3, x4, x5)  =  U75_AG(x4, x5)
U76_AG(x1, x2, x3, x4, x5, x6)  =  U76_AG(x4, x6)
U77_AG(x1, x2, x3, x4, x5)  =  U77_AG(x4, x5)
U78_AG(x1, x2, x3, x4, x5)  =  U78_AG(x4, x5)
U79_AG(x1, x2, x3, x4, x5, x6)  =  U79_AG(x4, x6)
U80_AG(x1, x2, x3, x4, x5)  =  U80_AG(x4, x5)
U81_AG(x1, x2, x3, x4, x5)  =  U81_AG(x4, x5)
U82_AG(x1, x2, x3, x4, x5, x6)  =  U82_AG(x4, x6)
U83_AG(x1, x2, x3, x4, x5)  =  U83_AG(x4, x5)
U84_AG(x1, x2, x3, x4, x5, x6)  =  U84_AG(x4, x5, x6)
U85_AG(x1, x2, x3, x4, x5, x6, x7)  =  U85_AG(x4, x5, x7)
U86_AG(x1, x2, x3, x4, x5, x6)  =  U86_AG(x4, x5, x6)
U87_AG(x1, x2, x3, x4, x5, x6)  =  U87_AG(x4, x5, x6)
U88_AG(x1, x2, x3, x4, x5, x6, x7)  =  U88_AG(x4, x5, x6, x7)
U89_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_AG(x4, x5, x6, x8)
U90_AG(x1, x2, x3, x4, x5, x6, x7)  =  U90_AG(x4, x5, x6, x7)
U91_AG(x1, x2, x3, x4, x5, x6, x7)  =  U91_AG(x4, x5, x6, x7)
LESS70_IN_GG(x1, x2)  =  LESS70_IN_GG(x1, x2)
U22_GG(x1, x2, x3)  =  U22_GG(x1, x2, x3)
LESS78_IN_GG(x1, x2)  =  LESS78_IN_GG(x1, x2)
U20_GG(x1, x2, x3)  =  U20_GG(x1, x2, x3)
U92_AG(x1, x2, x3, x4, x5, x6, x7)  =  U92_AG(x4, x5, x6, x7)
U93_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_AG(x4, x5, x6, x8)
U94_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_AG(x4, x5, x6, x8)
U95_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_AG(x4, x5, x6, x10)
U96_AG(x1, x2, x3, x4, x5, x6, x7)  =  U96_AG(x4, x5, x6, x7)
P179_IN_GAAAG(x1, x2, x3, x4, x5)  =  P179_IN_GAAAG(x1, x5)
U23_GAAAG(x1, x2, x3, x4, x5, x6)  =  U23_GAAAG(x1, x5, x6)
U24_GAAAG(x1, x2, x3, x4)  =  U24_GAAAG(x1, x2, x3, x4)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U25_GAAAG(x1, x3, x6, x7)
U26_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U26_GAAAG(x1, x3, x6, x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U27_GAAAG(x1, x2, x6, x7)
U28_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U28_GAAAG(x1, x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5)  =  P194_IN_GAAAG(x1, x5)
U29_GAAAG(x1, x2, x3, x4, x5, x6)  =  U29_GAAAG(x1, x5, x6)
U30_GAAAG(x1, x2, x3, x4)  =  U30_GAAAG(x1, x2, x3, x4)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U31_GAAAG(x1, x2, x6, x7)
U32_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U32_GAAAG(x1, x2, x6, x7)
U33_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U33_GAAAG(x1, x4, x6, x7)
U34_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U34_GAAAG(x1, x4, x6, x7)
U97_AG(x1, x2, x3, x4, x5, x6, x7)  =  U97_AG(x4, x5, x6, x7)
U98_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_AG(x4, x5, x6, x8)
U99_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_AG(x4, x5, x6, x9)
U100_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_AG(x4, x5, x6, x10)
U101_AG(x1, x2, x3, x4, x5, x6, x7)  =  U101_AG(x4, x5, x6, x7)
U102_AG(x1, x2, x3, x4, x5, x6)  =  U102_AG(x4, x5, x6)
U103_AG(x1, x2, x3, x4, x5, x6, x7)  =  U103_AG(x4, x5, x7)
U104_AG(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_AG(x4, x5, x8)
U105_AG(x1, x2, x3, x4, x5, x6)  =  U105_AG(x4, x5, x6)

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

(87) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 195 less nodes.

(88) Complex Obligation (AND)

(89) Obligation:

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

LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
LESS78_IN_GG(x1, x2)  =  LESS78_IN_GG(x1, x2)

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

(90) UsableRulesProof (EQUIVALENT transformation)

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

(91) Obligation:

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

LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)

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

(92) PiDPToQDPProof (EQUIVALENT transformation)

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

(93) Obligation:

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

LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)

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

(94) 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:

  • LESS78_IN_GG(s(T176), s(T177)) → LESS78_IN_GG(T176, T177)
    The graph contains the following edges 1 > 1, 2 > 2

(95) YES

(96) Obligation:

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

LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
LESS78_IN_GA(x1, x2)  =  LESS78_IN_GA(x1)

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

(97) UsableRulesProof (EQUIVALENT transformation)

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

(98) Obligation:

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

LESS78_IN_GA(s(T176), s(T177)) → LESS78_IN_GA(T176, T177)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LESS78_IN_GA(x1, x2)  =  LESS78_IN_GA(x1)

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

(99) PiDPToQDPProof (SOUND transformation)

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

(100) Obligation:

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

LESS78_IN_GA(s(T176)) → LESS78_IN_GA(T176)

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

(101) 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:

  • LESS78_IN_GA(s(T176)) → LESS78_IN_GA(T176)
    The graph contains the following edges 1 > 1

(102) YES

(103) Obligation:

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

P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
P179_IN_GAAAG(x1, x2, x3, x4, x5)  =  P179_IN_GAAAG(x1, x5)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U25_GAAAG(x1, x3, x6, x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U27_GAAAG(x1, x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5)  =  P194_IN_GAAAG(x1, x5)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U31_GAAAG(x1, x2, x6, x7)
U33_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U33_GAAAG(x1, x4, x6, x7)

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

(104) UsableRulesProof (EQUIVALENT transformation)

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

(105) Obligation:

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

P179_IN_GAAAG(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_GAAAG(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → P179_IN_GAAAG(T563, T568, T569, T570, T567)
P179_IN_GAAAG(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_GAAAG(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T588, T590, T589, T587)
P194_IN_GAAAG(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_GAAAG(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T637, T638, T639, T636)
P194_IN_GAAAG(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_GAAAG(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → P194_IN_GAAAG(T654, T657, T659, T658, T656)

The TRS R consists of the following rules:

less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
P179_IN_GAAAG(x1, x2, x3, x4, x5)  =  P179_IN_GAAAG(x1, x5)
U25_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U25_GAAAG(x1, x3, x6, x7)
U27_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U27_GAAAG(x1, x2, x6, x7)
P194_IN_GAAAG(x1, x2, x3, x4, x5)  =  P194_IN_GAAAG(x1, x5)
U31_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U31_GAAAG(x1, x2, x6, x7)
U33_GAAAG(x1, x2, x3, x4, x5, x6, x7)  =  U33_GAAAG(x1, x4, x6, x7)

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

(106) PiDPToQDPProof (SOUND transformation)

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

(107) Obligation:

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

P179_IN_GAAAG(T513, .(T563, T567)) → U25_GAAAG(T513, T563, T567, less70_in_ga(T513))
U25_GAAAG(T513, T563, T567, less70_out_ga(T513)) → P179_IN_GAAAG(T563, T567)
P179_IN_GAAAG(T513, .(T585, T587)) → U27_GAAAG(T513, T585, T587, less70_in_gg(T513, T585))
U27_GAAAG(T513, T585, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T587)
P194_IN_GAAAG(T585, .(T632, T636)) → U31_GAAAG(T585, T632, T636, less78_in_gg(T585, T632))
U31_GAAAG(T585, T632, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T636)
P194_IN_GAAAG(T585, .(T654, T656)) → U33_GAAAG(T585, T654, T656, less78_in_ga(T585))
U33_GAAAG(T585, T654, T656, less78_out_ga(T585)) → P194_IN_GAAAG(T654, T656)

The TRS R consists of the following rules:

less70_in_ga(0) → less70_out_ga(0)
less70_in_ga(s(T161)) → U22_ga(T161, less78_in_ga(T161))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
less78_in_ga(0) → less78_out_ga(0)
less78_in_ga(s(T176)) → U20_ga(T176, less78_in_ga(T176))
U22_ga(T161, less78_out_ga(T161)) → less70_out_ga(s(T161))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U20_ga(T176, less78_out_ga(T176)) → less78_out_ga(s(T176))

The set Q consists of the following terms:

less70_in_ga(x0)
less70_in_gg(x0, x1)
less78_in_gg(x0, x1)
less78_in_ga(x0)
U22_ga(x0, x1)
U22_gg(x0, x1, x2)
U20_gg(x0, x1, x2)
U20_ga(x0, x1)

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

(108) 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:

  • U25_GAAAG(T513, T563, T567, less70_out_ga(T513)) → P179_IN_GAAAG(T563, T567)
    The graph contains the following edges 2 >= 1, 3 >= 2

  • U31_GAAAG(T585, T632, T636, less78_out_gg(T585, T632)) → P179_IN_GAAAG(T632, T636)
    The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2

  • P179_IN_GAAAG(T513, .(T563, T567)) → U25_GAAAG(T513, T563, T567, less70_in_ga(T513))
    The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3

  • P179_IN_GAAAG(T513, .(T585, T587)) → U27_GAAAG(T513, T585, T587, less70_in_gg(T513, T585))
    The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3

  • U27_GAAAG(T513, T585, T587, less70_out_gg(T513, T585)) → P194_IN_GAAAG(T585, T587)
    The graph contains the following edges 2 >= 1, 4 > 1, 3 >= 2

  • U33_GAAAG(T585, T654, T656, less78_out_ga(T585)) → P194_IN_GAAAG(T654, T656)
    The graph contains the following edges 2 >= 1, 3 >= 2

  • P194_IN_GAAAG(T585, .(T632, T636)) → U31_GAAAG(T585, T632, T636, less78_in_gg(T585, T632))
    The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3

  • P194_IN_GAAAG(T585, .(T654, T656)) → U33_GAAAG(T585, T654, T656, less78_in_ga(T585))
    The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3

(109) YES

(110) Obligation:

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

MERGE54_IN_AAG(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAG(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → MERGE54_IN_AAG(T145, .(T146, T147), X226)
MERGE54_IN_AAG(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAG(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → MERGE54_IN_AAG(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
MERGE54_IN_AAG(x1, x2, x3)  =  MERGE54_IN_AAG(x3)
U15_AAG(x1, x2, x3, x4, x5, x6)  =  U15_AAG(x1, x5, x6)
U18_AAG(x1, x2, x3, x4, x5, x6)  =  U18_AAG(x3, x5, x6)

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

(111) UsableRulesProof (EQUIVALENT transformation)

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

(112) Obligation:

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

MERGE54_IN_AAG(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAG(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_AAG(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → MERGE54_IN_AAG(T145, .(T146, T147), X226)
MERGE54_IN_AAG(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAG(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_AAG(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → MERGE54_IN_AAG(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
MERGE54_IN_AAG(x1, x2, x3)  =  MERGE54_IN_AAG(x3)
U15_AAG(x1, x2, x3, x4, x5, x6)  =  U15_AAG(x1, x5, x6)
U18_AAG(x1, x2, x3, x4, x5, x6)  =  U18_AAG(x3, x5, x6)

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

(113) PiDPToQDPProof (SOUND transformation)

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

(114) Obligation:

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

MERGE54_IN_AAG(.(T139, X226)) → U15_AAG(T139, X226, less70_in_ga(T139))
U15_AAG(T139, X226, less70_out_ga(T139)) → MERGE54_IN_AAG(X226)
MERGE54_IN_AAG(.(T196, X287)) → U18_AAG(T196, X287, less78_in_ga(T196))
U18_AAG(T196, X287, less78_out_ga(T196)) → MERGE54_IN_AAG(X287)

The TRS R consists of the following rules:

less70_in_ga(0) → less70_out_ga(0)
less70_in_ga(s(T161)) → U22_ga(T161, less78_in_ga(T161))
less78_in_ga(0) → less78_out_ga(0)
less78_in_ga(s(T176)) → U20_ga(T176, less78_in_ga(T176))
U22_ga(T161, less78_out_ga(T161)) → less70_out_ga(s(T161))
U20_ga(T176, less78_out_ga(T176)) → less78_out_ga(s(T176))

The set Q consists of the following terms:

less70_in_ga(x0)
less78_in_ga(x0)
U22_ga(x0, x1)
U20_ga(x0, x1)

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

(115) 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:

  • U15_AAG(T139, X226, less70_out_ga(T139)) → MERGE54_IN_AAG(X226)
    The graph contains the following edges 2 >= 1

  • U18_AAG(T196, X287, less78_out_ga(T196)) → MERGE54_IN_AAG(X287)
    The graph contains the following edges 2 >= 1

  • MERGE54_IN_AAG(.(T139, X226)) → U15_AAG(T139, X226, less70_in_ga(T139))
    The graph contains the following edges 1 > 1, 1 > 2

  • MERGE54_IN_AAG(.(T196, X287)) → U18_AAG(T196, X287, less78_in_ga(T196))
    The graph contains the following edges 1 > 1, 1 > 2

(116) YES

(117) Obligation:

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

LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
LESS78_IN_AA(x1, x2)  =  LESS78_IN_AA

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

(118) UsableRulesProof (EQUIVALENT transformation)

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

(119) Obligation:

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

LESS78_IN_AA(s(T176), s(T177)) → LESS78_IN_AA(T176, T177)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LESS78_IN_AA(x1, x2)  =  LESS78_IN_AA

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

(120) PiDPToQDPProof (SOUND transformation)

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

(121) Obligation:

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

LESS78_IN_AALESS78_IN_AA

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

(122) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = LESS78_IN_AA evaluates to t =LESS78_IN_AA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Matcher: [ ]
  • Semiunifier: [ ]




Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from LESS78_IN_AA to LESS78_IN_AA.



(123) NO

(124) Obligation:

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

MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
MERGE54_IN_AAA(x1, x2, x3)  =  MERGE54_IN_AAA
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6)  =  U18_AAA(x6)

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

(125) UsableRulesProof (EQUIVALENT transformation)

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

(126) Obligation:

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

MERGE54_IN_AAA(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_AAA(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_AAA(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → MERGE54_IN_AAA(T145, .(T146, T147), X226)
MERGE54_IN_AAA(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_AAA(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_AAA(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → MERGE54_IN_AAA(.(T202, T203), T204, X287)

The TRS R consists of the following rules:

less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
.(x1, x2)  =  .(x1, x2)
0  =  0
s(x1)  =  s(x1)
MERGE54_IN_AAA(x1, x2, x3)  =  MERGE54_IN_AAA
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U18_AAA(x1, x2, x3, x4, x5, x6)  =  U18_AAA(x6)

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

(127) PiDPToQDPProof (SOUND transformation)

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

(128) Obligation:

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

MERGE54_IN_AAAU15_AAA(less70_in_aa)
U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAAU18_AAA(less78_in_aa)
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA

The TRS R consists of the following rules:

less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less70_in_aa
less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(129) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule MERGE54_IN_AAAU15_AAA(less70_in_aa) at position [0] we obtained the following new rules [LPAR04]:

MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))

(130) Obligation:

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

U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAAU18_AAA(less78_in_aa)
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))

The TRS R consists of the following rules:

less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less70_in_aa
less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(131) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(132) Obligation:

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

U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAAU18_AAA(less78_in_aa)
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))

The TRS R consists of the following rules:

less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less70_in_aa
less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(133) QReductionProof (EQUIVALENT transformation)

We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].

less70_in_aa

(134) Obligation:

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

U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
MERGE54_IN_AAAU18_AAA(less78_in_aa)
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))

The TRS R consists of the following rules:

less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(135) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule MERGE54_IN_AAAU18_AAA(less78_in_aa) at position [0] we obtained the following new rules [LPAR04]:

MERGE54_IN_AAAU18_AAA(less78_out_aa(0))
MERGE54_IN_AAAU18_AAA(U20_aa(less78_in_aa))

(136) Obligation:

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

U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA
U18_AAA(less78_out_aa(T196)) → MERGE54_IN_AAA
MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
MERGE54_IN_AAAU15_AAA(U22_aa(less78_in_aa))
MERGE54_IN_AAAU18_AAA(less78_out_aa(0))
MERGE54_IN_AAAU18_AAA(U20_aa(less78_in_aa))

The TRS R consists of the following rules:

less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

less78_in_aa
U22_aa(x0)
U20_aa(x0)

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

(137) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by narrowing to the left:

s = MERGE54_IN_AAA evaluates to t =MERGE54_IN_AAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Semiunifier: [ ]
  • Matcher: [ ]




Rewriting sequence

MERGE54_IN_AAAU15_AAA(less70_out_aa(0))
with rule MERGE54_IN_AAAU15_AAA(less70_out_aa(0)) at position [] and matcher [ ]

U15_AAA(less70_out_aa(0))MERGE54_IN_AAA
with rule U15_AAA(less70_out_aa(T139)) → MERGE54_IN_AAA

Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence


All these steps are and every following step will be a correct step w.r.t to Q.



(138) NO

(139) Obligation:

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

SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
SPLIT16_IN_AAA(x1, x2, x3)  =  SPLIT16_IN_AAA

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

(140) UsableRulesProof (EQUIVALENT transformation)

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

(141) Obligation:

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

SPLIT16_IN_AAA(.(T49, T51), .(T49, X89), X90) → SPLIT16_IN_AAA(T51, X90, X89)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
SPLIT16_IN_AAA(x1, x2, x3)  =  SPLIT16_IN_AAA

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

(142) PiDPToQDPProof (SOUND transformation)

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

(143) Obligation:

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

SPLIT16_IN_AAASPLIT16_IN_AAA

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

(144) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by semiunifying a rule from P directly.

s = SPLIT16_IN_AAA evaluates to t =SPLIT16_IN_AAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Matcher: [ ]
  • Semiunifier: [ ]




Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from SPLIT16_IN_AAA to SPLIT16_IN_AAA.



(145) NO

(146) Obligation:

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

P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)

The TRS R consists of the following rules:

ms1_in_ag([], []) → ms1_out_ag([], [])
ms1_in_ag(.(T29, .(T27, T28)), []) → U35_ag(T29, T27, T28, split12_in_aaaa(T27, T28, X42, X41))
split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U35_ag(T29, T27, T28, split12_out_aaaa(T27, T28, X42, X41)) → ms1_out_ag(.(T29, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U36_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T32, T33))
U36_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T32, T33)) → U37_ag(T34, T27, T28, ms25_in_aaa(T34, T33, X13))
ms25_in_aaa(T62, [], .(T62, [])) → ms25_out_aaa(T62, [], .(T62, []))
ms25_in_aaa(T72, .(T73, T74), X127) → U21_aaa(T72, T73, T74, X127, p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U21_aaa(T72, T73, T74, X127, p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aaa(T72, .(T73, T74), X127)
U37_ag(T34, T27, T28, ms25_out_aaa(T34, T33, X13)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T34, .(T27, T28)), []) → U38_ag(T34, T27, T28, split12_in_aaaa(T27, T28, T55, T33))
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U39_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T54))
U39_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T54)) → U40_ag(T34, T27, T28, ms38_in_aa(T55, X14))
U40_ag(T34, T27, T28, ms38_out_aa(T55, X14)) → ms1_out_ag(.(T34, .(T27, T28)), [])
U38_ag(T34, T27, T28, split12_out_aaaa(T27, T28, T55, T33)) → U41_ag(T34, T27, T28, T55, ms25_in_aaa(T34, T33, T212))
U41_ag(T34, T27, T28, T55, ms25_out_aaa(T34, T33, T212)) → U42_ag(T34, T27, T28, T212, ms38_in_aa(T55, T211))
U42_ag(T34, T27, T28, T212, ms38_out_aa(T55, T211)) → U43_ag(T34, T27, T28, merge93_in_aa(T212, T211))
merge93_in_aa([], []) → merge93_out_aa([], [])
U43_ag(T34, T27, T28, merge93_out_aa(T212, T211)) → ms1_out_ag(.(T34, .(T27, T28)), [])
ms1_in_ag(.(T234, []), .(T234, [])) → ms1_out_ag(.(T234, []), .(T234, []))
ms1_in_ag(.(T262, .(T260, T261)), .(T242, [])) → U44_ag(T262, T260, T261, T242, split12_in_aaaa(T260, T261, X367, X366))
U44_ag(T262, T260, T261, T242, split12_out_aaaa(T260, T261, X367, X366)) → ms1_out_ag(.(T262, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U45_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T265, T266))
U45_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T265, T266)) → U46_ag(T267, T260, T261, T242, ms25_in_aaa(T267, T266, X338))
U46_ag(T267, T260, T261, T242, ms25_out_aaa(T267, T266, X338)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T242, [])) → U47_ag(T267, T260, T261, T242, split12_in_aaaa(T260, T261, T273, T266))
U47_ag(T267, T260, T261, T242, split12_out_aaaa(T260, T261, T273, T266)) → U48_ag(T267, T260, T261, T242, T273, ms25_in_aaa(T267, T266, T272))
U48_ag(T267, T260, T261, T242, T273, ms25_out_aaa(T267, T266, T272)) → U49_ag(T267, T260, T261, T242, ms38_in_aa(T273, X339))
U49_ag(T267, T260, T261, T242, ms38_out_aa(T273, X339)) → ms1_out_ag(.(T267, .(T260, T261)), .(T242, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T291, [])) → U50_ag(T267, T260, T261, T291, split12_in_aaaa(T260, T261, T273, T266))
U50_ag(T267, T260, T261, T291, split12_out_aaaa(T260, T261, T273, T266)) → U51_ag(T267, T260, T261, T291, T273, ms25_in_aag(T267, T266, []))
ms25_in_aag(T62, [], .(T62, [])) → ms25_out_aag(T62, [], .(T62, []))
ms25_in_aag(T72, .(T73, T74), X127) → U21_aag(T72, T73, T74, X127, p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127))
p34_in_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
U3_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U5_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaag(T72, T73, T74, T78, T79, X125, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U8_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T83, X126, X127)
p34_in_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U11_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aag(T106, T105, X127))
merge54_in_aag([], T113, T113) → merge54_out_aag([], T113, T113)
merge54_in_aag(T118, [], T118) → merge54_out_aag(T118, [], T118)
merge54_in_aag(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aag(T139, T141, T140, T142, X226, less70_in_ga(T139, T140))
less70_in_ga(0, T154) → less70_out_ga(0, T154)
less70_in_ga(s(T161), T162) → U22_ga(T161, T162, less78_in_ga(T161, T162))
less78_in_ga(0, s(T169)) → less78_out_ga(0, s(T169))
less78_in_ga(s(T176), s(T177)) → U20_ga(T176, T177, less78_in_ga(T176, T177))
U20_ga(T176, T177, less78_out_ga(T176, T177)) → less78_out_ga(s(T176), s(T177))
U22_ga(T161, T162, less78_out_ga(T161, T162)) → less70_out_ga(s(T161), T162)
U14_aag(T139, T141, T140, T142, X226, less70_out_ga(T139, T140)) → merge54_out_aag(.(T139, T141), .(T140, T142), .(T139, X226))
merge54_in_aag(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aag(T139, T145, T146, T147, X226, less70_in_ga(T139, T146))
U15_aag(T139, T145, T146, T147, X226, less70_out_ga(T139, T146)) → U16_aag(T139, T145, T146, T147, X226, merge54_in_aag(T145, .(T146, T147), X226))
merge54_in_aag(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aag(T197, T199, T196, T198, X287, less78_in_ga(T196, T197))
U17_aag(T197, T199, T196, T198, X287, less78_out_ga(T196, T197)) → merge54_out_aag(.(T197, T199), .(T196, T198), .(T196, X287))
merge54_in_aag(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aag(T202, T203, T196, T204, X287, less78_in_ga(T196, T202))
U18_aag(T202, T203, T196, T204, X287, less78_out_ga(T196, T202)) → U19_aag(T202, T203, T196, T204, X287, merge54_in_aag(.(T202, T203), T204, X287))
U19_aag(T202, T203, T196, T204, X287, merge54_out_aag(.(T202, T203), T204, X287)) → merge54_out_aag(.(T202, T203), .(T196, T204), .(T196, X287))
U16_aag(T139, T145, T146, T147, X226, merge54_out_aag(T145, .(T146, T147), X226)) → merge54_out_aag(.(T139, T145), .(T146, T147), .(T139, X226))
U12_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aag(T106, T105, X127)) → p34_out_aaaaaaag(T72, T73, T74, T78, T84, T106, T105, X127)
U21_aag(T72, T73, T74, X127, p34_out_aaaaaaag(T72, T73, T74, X123, X124, X125, X126, X127)) → ms25_out_aag(T72, .(T73, T74), X127)
U51_ag(T267, T260, T261, T291, T273, ms25_out_aag(T267, T266, [])) → U52_ag(T267, T260, T261, T291, ms38_in_ag(T273, .(T291, [])))
ms38_in_ag([], []) → ms38_out_ag([], [])
ms38_in_ag(.(T89, []), .(T89, [])) → ms38_out_ag(.(T89, []), .(T89, []))
ms38_in_ag(.(T99, .(T100, T101)), X172) → U13_ag(T99, T100, T101, X172, p34_in_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172))
U13_ag(T99, T100, T101, X172, p34_out_aaaaaaag(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_ag(.(T99, .(T100, T101)), X172)
U52_ag(T267, T260, T261, T291, ms38_out_ag(T273, .(T291, []))) → ms1_out_ag(.(T267, .(T260, T261)), .(T291, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T301, [])) → U53_ag(T267, T260, T261, T301, split12_in_aaaa(T260, T261, T273, T266))
U53_ag(T267, T260, T261, T301, split12_out_aaaa(T260, T261, T273, T266)) → U54_ag(T267, T260, T261, T301, T273, ms25_in_aag(T267, T266, .(T301, [])))
U54_ag(T267, T260, T261, T301, T273, ms25_out_aag(T267, T266, .(T301, []))) → U55_ag(T267, T260, T261, T301, ms38_in_ag(T273, []))
U55_ag(T267, T260, T261, T301, ms38_out_ag(T273, [])) → ms1_out_ag(.(T267, .(T260, T261)), .(T301, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T318, [])) → U56_ag(T267, T260, T261, T318, split12_in_aaaa(T260, T261, T273, T266))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U57_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T323)))
U57_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T323))) → U58_ag(T267, T260, T261, T318, ms38_in_aa(T273, .(T322, T324)))
U58_ag(T267, T260, T261, T318, ms38_out_aa(T273, .(T322, T324))) → U59_ag(T267, T260, T261, T318, less70_in_ga(T318, T322))
U59_ag(T267, T260, T261, T318, less70_out_ga(T318, T322)) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
U56_ag(T267, T260, T261, T318, split12_out_aaaa(T260, T261, T273, T266)) → U60_ag(T267, T260, T261, T318, T273, ms25_in_aaa(T267, T266, .(T318, T327)))
U60_ag(T267, T260, T261, T318, T273, ms25_out_aaa(T267, T266, .(T318, T327))) → U61_ag(T267, T260, T261, T318, T327, ms38_in_aa(T273, .(T328, T329)))
U61_ag(T267, T260, T261, T318, T327, ms38_out_aa(T273, .(T328, T329))) → U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_in_ga(T318, T328))
U62_ag(T267, T260, T261, T318, T327, T328, T329, less70_out_ga(T318, T328)) → U63_ag(T267, T260, T261, T318, merge93_in_aa(T327, .(T328, T329)))
U63_ag(T267, T260, T261, T318, merge93_out_aa(T327, .(T328, T329))) → ms1_out_ag(.(T267, .(T260, T261)), .(T318, []))
ms1_in_ag(.(T267, .(T260, T261)), .(T356, [])) → U64_ag(T267, T260, T261, T356, split12_in_aaaa(T260, T261, T273, T266))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U65_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T358, T360)))
U65_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T358, T360))) → U66_ag(T267, T260, T261, T356, T358, ms38_in_aa(T273, .(T356, T359)))
U66_ag(T267, T260, T261, T356, T358, ms38_out_aa(T273, .(T356, T359))) → U67_ag(T267, T260, T261, T356, less78_in_ga(T356, T358))
U67_ag(T267, T260, T261, T356, less78_out_ga(T356, T358)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
U64_ag(T267, T260, T261, T356, split12_out_aaaa(T260, T261, T273, T266)) → U68_ag(T267, T260, T261, T356, T273, ms25_in_aaa(T267, T266, .(T363, T364)))
U68_ag(T267, T260, T261, T356, T273, ms25_out_aaa(T267, T266, .(T363, T364))) → U69_ag(T267, T260, T261, T356, T363, T364, ms38_in_aa(T273, .(T356, T365)))
U69_ag(T267, T260, T261, T356, T363, T364, ms38_out_aa(T273, .(T356, T365))) → U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_in_ga(T356, T363))
U70_ag(T267, T260, T261, T356, T363, T364, T365, less78_out_ga(T356, T363)) → U71_ag(T267, T260, T261, T356, merge93_in_aa(.(T363, T364), T365))
U71_ag(T267, T260, T261, T356, merge93_out_aa(.(T363, T364), T365)) → ms1_out_ag(.(T267, .(T260, T261)), .(T356, []))
ms1_in_ag(.(T407, .(T405, T406)), T387) → U72_ag(T407, T405, T406, T387, split12_in_aaaa(T405, T406, X523, X522))
U72_ag(T407, T405, T406, T387, split12_out_aaaa(T405, T406, X523, X522)) → ms1_out_ag(.(T407, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U73_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T410, T411))
U73_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T410, T411)) → U74_ag(T412, T405, T406, T387, ms25_in_aaa(T412, T411, X494))
U74_ag(T412, T405, T406, T387, ms25_out_aaa(T412, T411, X494)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T387) → U75_ag(T412, T405, T406, T387, split12_in_aaaa(T405, T406, T420, T411))
U75_ag(T412, T405, T406, T387, split12_out_aaaa(T405, T406, T420, T411)) → U76_ag(T412, T405, T406, T387, T420, ms25_in_aaa(T412, T411, T419))
U76_ag(T412, T405, T406, T387, T420, ms25_out_aaa(T412, T411, T419)) → U77_ag(T412, T405, T406, T387, ms38_in_aa(T420, X495))
U77_ag(T412, T405, T406, T387, ms38_out_aa(T420, X495)) → ms1_out_ag(.(T412, .(T405, T406)), T387)
ms1_in_ag(.(T412, .(T405, T406)), T435) → U78_ag(T412, T405, T406, T435, split12_in_aaaa(T405, T406, T420, T411))
U78_ag(T412, T405, T406, T435, split12_out_aaaa(T405, T406, T420, T411)) → U79_ag(T412, T405, T406, T435, T420, ms25_in_aag(T412, T411, []))
U79_ag(T412, T405, T406, T435, T420, ms25_out_aag(T412, T411, [])) → U80_ag(T412, T405, T406, T435, ms38_in_ag(T420, T435))
U80_ag(T412, T405, T406, T435, ms38_out_ag(T420, T435)) → ms1_out_ag(.(T412, .(T405, T406)), T435)
ms1_in_ag(.(T412, .(T405, T406)), T440) → U81_ag(T412, T405, T406, T440, split12_in_aaaa(T405, T406, T420, T411))
U81_ag(T412, T405, T406, T440, split12_out_aaaa(T405, T406, T420, T411)) → U82_ag(T412, T405, T406, T440, T420, ms25_in_aag(T412, T411, T440))
U82_ag(T412, T405, T406, T440, T420, ms25_out_aag(T412, T411, T440)) → U83_ag(T412, T405, T406, T440, ms38_in_ag(T420, []))
U83_ag(T412, T405, T406, T440, ms38_out_ag(T420, [])) → ms1_out_ag(.(T412, .(T405, T406)), T440)
ms1_in_ag(.(T412, .(T405, T406)), .(T461, T465)) → U84_ag(T412, T405, T406, T461, T465, split12_in_aaaa(T405, T406, T420, T411))
U84_ag(T412, T405, T406, T461, T465, split12_out_aaaa(T405, T406, T420, T411)) → U85_ag(T412, T405, T406, T461, T465, T420, ms25_in_aaa(T412, T411, .(T461, T467)))
U85_ag(T412, T405, T406, T461, T465, T420, ms25_out_aaa(T412, T411, .(T461, T467))) → U86_ag(T412, T405, T406, T461, T465, ms38_in_aa(T420, .(T466, T468)))
U86_ag(T412, T405, T406, T461, T465, ms38_out_aa(T420, .(T466, T468))) → U87_ag(T412, T405, T406, T461, T465, less70_in_ga(T461, T466))
U87_ag(T412, T405, T406, T461, T465, less70_out_ga(T461, T466)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, T465))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491))) → U88_ag(T412, T405, T406, T461, T490, T491, split12_in_aaaa(T405, T406, T420, T411))
U88_ag(T412, T405, T406, T461, T490, T491, split12_out_aaaa(T405, T406, T420, T411)) → U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_in_aag(T412, T411, .(T461, [])))
U89_ag(T412, T405, T406, T461, T490, T491, T420, ms25_out_aag(T412, T411, .(T461, []))) → U90_ag(T412, T405, T406, T461, T490, T491, ms38_in_ag(T420, .(T490, T491)))
U90_ag(T412, T405, T406, T461, T490, T491, ms38_out_ag(T420, .(T490, T491))) → U91_ag(T412, T405, T406, T461, T490, T491, less70_in_gg(T461, T490))
less70_in_gg(0, T154) → less70_out_gg(0, T154)
less70_in_gg(s(T161), T162) → U22_gg(T161, T162, less78_in_gg(T161, T162))
less78_in_gg(0, s(T169)) → less78_out_gg(0, s(T169))
less78_in_gg(s(T176), s(T177)) → U20_gg(T176, T177, less78_in_gg(T176, T177))
U20_gg(T176, T177, less78_out_gg(T176, T177)) → less78_out_gg(s(T176), s(T177))
U22_gg(T161, T162, less78_out_gg(T161, T162)) → less70_out_gg(s(T161), T162)
U91_ag(T412, T405, T406, T461, T490, T491, less70_out_gg(T461, T490)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T490, T491)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517))) → U92_ag(T412, T405, T406, T461, T513, T517, split12_in_aaaa(T405, T406, T420, T411))
U92_ag(T412, T405, T406, T461, T513, T517, split12_out_aaaa(T405, T406, T420, T411)) → U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_in_aaa(T412, T411, .(T461, .(T513, T519))))
U93_ag(T412, T405, T406, T461, T513, T517, T420, ms25_out_aaa(T412, T411, .(T461, .(T513, T519)))) → U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_in_aa(T420, .(T518, T520)))
U94_ag(T412, T405, T406, T461, T513, T517, T519, ms38_out_aa(T420, .(T518, T520))) → U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_in_ga(T461, T518))
U95_ag(T412, T405, T406, T461, T513, T517, T519, T518, T520, less70_out_ga(T461, T518)) → U96_ag(T412, T405, T406, T461, T513, T517, p179_in_gaaag(T513, T518, T519, T520, T517))
p179_in_gaaag(T513, T518, T519, T520, T517) → U23_gaaag(T513, T518, T519, T520, T517, less70_in_ga(T513, T518))
U23_gaaag(T513, T518, T519, T520, T517, less70_out_ga(T513, T518)) → p179_out_gaaag(T513, T518, T519, T520, T517)
p179_in_gaaag(T513, T540, [], T541, .(T540, T541)) → U24_gaaag(T513, T540, T541, less70_in_gg(T513, T540))
U24_gaaag(T513, T540, T541, less70_out_gg(T513, T540)) → p179_out_gaaag(T513, T540, [], T541, .(T540, T541))
p179_in_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567)) → U25_gaaag(T513, T568, T563, T569, T570, T567, less70_in_ga(T513, T568))
U25_gaaag(T513, T568, T563, T569, T570, T567, less70_out_ga(T513, T568)) → U26_gaaag(T513, T568, T563, T569, T570, T567, p179_in_gaaag(T563, T568, T569, T570, T567))
p179_in_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587)) → U27_gaaag(T513, T585, T588, T590, T589, T587, less70_in_gg(T513, T585))
U27_gaaag(T513, T585, T588, T590, T589, T587, less70_out_gg(T513, T585)) → U28_gaaag(T513, T585, T588, T590, T589, T587, p194_in_gaaag(T585, T588, T590, T589, T587))
p194_in_gaaag(T585, T588, T590, T589, T587) → U29_gaaag(T585, T588, T590, T589, T587, less78_in_ga(T585, T588))
U29_gaaag(T585, T588, T590, T589, T587, less78_out_ga(T585, T588)) → p194_out_gaaag(T585, T588, T590, T589, T587)
p194_in_gaaag(T585, T610, T611, [], .(T610, T611)) → U30_gaaag(T585, T610, T611, less78_in_gg(T585, T610))
U30_gaaag(T585, T610, T611, less78_out_gg(T585, T610)) → p194_out_gaaag(T585, T610, T611, [], .(T610, T611))
p194_in_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636)) → U31_gaaag(T585, T632, T638, T637, T639, T636, less78_in_gg(T585, T632))
U31_gaaag(T585, T632, T638, T637, T639, T636, less78_out_gg(T585, T632)) → U32_gaaag(T585, T632, T638, T637, T639, T636, p179_in_gaaag(T632, T637, T638, T639, T636))
U32_gaaag(T585, T632, T638, T637, T639, T636, p179_out_gaaag(T632, T637, T638, T639, T636)) → p194_out_gaaag(T585, T632, T638, .(T637, T639), .(T632, T636))
p194_in_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656)) → U33_gaaag(T585, T657, T659, T654, T658, T656, less78_in_ga(T585, T657))
U33_gaaag(T585, T657, T659, T654, T658, T656, less78_out_ga(T585, T657)) → U34_gaaag(T585, T657, T659, T654, T658, T656, p194_in_gaaag(T654, T657, T659, T658, T656))
U34_gaaag(T585, T657, T659, T654, T658, T656, p194_out_gaaag(T654, T657, T659, T658, T656)) → p194_out_gaaag(T585, T657, T659, .(T654, T658), .(T654, T656))
U28_gaaag(T513, T585, T588, T590, T589, T587, p194_out_gaaag(T585, T588, T590, T589, T587)) → p179_out_gaaag(T513, T585, .(T588, T590), T589, .(T585, T587))
U26_gaaag(T513, T568, T563, T569, T570, T567, p179_out_gaaag(T563, T568, T569, T570, T567)) → p179_out_gaaag(T513, T568, .(T563, T569), T570, .(T563, T567))
U96_ag(T412, T405, T406, T461, T513, T517, p179_out_gaaag(T513, T518, T519, T520, T517)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T513, T517)))
ms1_in_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676))) → U97_ag(T412, T405, T406, T461, T674, T676, split12_in_aaaa(T405, T406, T420, T411))
U97_ag(T412, T405, T406, T461, T674, T676, split12_out_aaaa(T405, T406, T420, T411)) → U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_in_aaa(T412, T411, .(T461, .(T677, T679))))
U98_ag(T412, T405, T406, T461, T674, T676, T420, ms25_out_aaa(T412, T411, .(T461, .(T677, T679)))) → U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_in_aa(T420, .(T674, T678)))
U99_ag(T412, T405, T406, T461, T674, T676, T677, T679, ms38_out_aa(T420, .(T674, T678))) → U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_in_gg(T461, T674))
U100_ag(T412, T405, T406, T461, T674, T676, T677, T679, T678, less70_out_gg(T461, T674)) → U101_ag(T412, T405, T406, T461, T674, T676, p194_in_gaaag(T674, T677, T679, T678, T676))
U101_ag(T412, T405, T406, T461, T674, T676, p194_out_gaaag(T674, T677, T679, T678, T676)) → ms1_out_ag(.(T412, .(T405, T406)), .(T461, .(T674, T676)))
ms1_in_ag(.(T412, .(T405, T406)), .(T694, T696)) → U102_ag(T412, T405, T406, T694, T696, split12_in_aaaa(T405, T406, T420, T411))
U102_ag(T412, T405, T406, T694, T696, split12_out_aaaa(T405, T406, T420, T411)) → U103_ag(T412, T405, T406, T694, T696, T420, ms25_in_aaa(T412, T411, .(T697, T699)))
U103_ag(T412, T405, T406, T694, T696, T420, ms25_out_aaa(T412, T411, .(T697, T699))) → U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_in_aa(T420, .(T694, T698)))
U104_ag(T412, T405, T406, T694, T696, T697, T699, ms38_out_aa(T420, .(T694, T698))) → U105_ag(T412, T405, T406, T694, T696, p194_in_gaaag(T694, T697, T699, T698, T696))
U105_ag(T412, T405, T406, T694, T696, p194_out_gaaag(T694, T697, T699, T698, T696)) → ms1_out_ag(.(T412, .(T405, T406)), .(T694, T696))

The argument filtering Pi contains the following mapping:
ms1_in_ag(x1, x2)  =  ms1_in_ag(x2)
[]  =  []
ms1_out_ag(x1, x2)  =  ms1_out_ag(x2)
U35_ag(x1, x2, x3, x4)  =  U35_ag(x4)
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
U36_ag(x1, x2, x3, x4)  =  U36_ag(x4)
U37_ag(x1, x2, x3, x4)  =  U37_ag(x4)
ms25_in_aaa(x1, x2, x3)  =  ms25_in_aaa
ms25_out_aaa(x1, x2, x3)  =  ms25_out_aaa
U21_aaa(x1, x2, x3, x4, x5)  =  U21_aaa(x5)
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
U38_ag(x1, x2, x3, x4)  =  U38_ag(x4)
U39_ag(x1, x2, x3, x4, x5)  =  U39_ag(x5)
U40_ag(x1, x2, x3, x4)  =  U40_ag(x4)
U41_ag(x1, x2, x3, x4, x5)  =  U41_ag(x5)
U42_ag(x1, x2, x3, x4, x5)  =  U42_ag(x5)
U43_ag(x1, x2, x3, x4)  =  U43_ag(x4)
merge93_in_aa(x1, x2)  =  merge93_in_aa
merge93_out_aa(x1, x2)  =  merge93_out_aa(x1, x2)
.(x1, x2)  =  .(x1, x2)
U44_ag(x1, x2, x3, x4, x5)  =  U44_ag(x4, x5)
U45_ag(x1, x2, x3, x4, x5)  =  U45_ag(x4, x5)
U46_ag(x1, x2, x3, x4, x5)  =  U46_ag(x4, x5)
U47_ag(x1, x2, x3, x4, x5)  =  U47_ag(x4, x5)
U48_ag(x1, x2, x3, x4, x5, x6)  =  U48_ag(x4, x6)
U49_ag(x1, x2, x3, x4, x5)  =  U49_ag(x4, x5)
U50_ag(x1, x2, x3, x4, x5)  =  U50_ag(x4, x5)
U51_ag(x1, x2, x3, x4, x5, x6)  =  U51_ag(x4, x6)
ms25_in_aag(x1, x2, x3)  =  ms25_in_aag(x3)
ms25_out_aag(x1, x2, x3)  =  ms25_out_aag(x3)
U21_aag(x1, x2, x3, x4, x5)  =  U21_aag(x4, x5)
p34_in_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaag(x8)
U3_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaag(x8, x9)
p34_out_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaag(x8)
U4_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaag(x8, x9)
U5_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaag(x8, x9)
U6_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaag(x8, x9)
U7_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaag(x8, x9)
U8_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaag(x8, x9)
U9_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaag(x8, x9)
U10_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaag(x8, x9)
U11_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaag(x8, x9)
U12_aaaaaaag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaag(x8, x9)
merge54_in_aag(x1, x2, x3)  =  merge54_in_aag(x3)
merge54_out_aag(x1, x2, x3)  =  merge54_out_aag(x3)
U14_aag(x1, x2, x3, x4, x5, x6)  =  U14_aag(x1, x5, x6)
less70_in_ga(x1, x2)  =  less70_in_ga(x1)
0  =  0
less70_out_ga(x1, x2)  =  less70_out_ga(x1)
s(x1)  =  s(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
less78_in_ga(x1, x2)  =  less78_in_ga(x1)
less78_out_ga(x1, x2)  =  less78_out_ga(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U15_aag(x1, x2, x3, x4, x5, x6)  =  U15_aag(x1, x5, x6)
U16_aag(x1, x2, x3, x4, x5, x6)  =  U16_aag(x1, x5, x6)
U17_aag(x1, x2, x3, x4, x5, x6)  =  U17_aag(x3, x5, x6)
U18_aag(x1, x2, x3, x4, x5, x6)  =  U18_aag(x3, x5, x6)
U19_aag(x1, x2, x3, x4, x5, x6)  =  U19_aag(x3, x5, x6)
U52_ag(x1, x2, x3, x4, x5)  =  U52_ag(x4, x5)
ms38_in_ag(x1, x2)  =  ms38_in_ag(x2)
ms38_out_ag(x1, x2)  =  ms38_out_ag(x2)
U13_ag(x1, x2, x3, x4, x5)  =  U13_ag(x4, x5)
U53_ag(x1, x2, x3, x4, x5)  =  U53_ag(x4, x5)
U54_ag(x1, x2, x3, x4, x5, x6)  =  U54_ag(x4, x6)
U55_ag(x1, x2, x3, x4, x5)  =  U55_ag(x4, x5)
U56_ag(x1, x2, x3, x4, x5)  =  U56_ag(x4, x5)
U57_ag(x1, x2, x3, x4, x5, x6)  =  U57_ag(x4, x6)
U58_ag(x1, x2, x3, x4, x5)  =  U58_ag(x4, x5)
U59_ag(x1, x2, x3, x4, x5)  =  U59_ag(x4, x5)
U60_ag(x1, x2, x3, x4, x5, x6)  =  U60_ag(x4, x6)
U61_ag(x1, x2, x3, x4, x5, x6)  =  U61_ag(x4, x6)
U62_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U62_ag(x4, x8)
U63_ag(x1, x2, x3, x4, x5)  =  U63_ag(x4, x5)
U64_ag(x1, x2, x3, x4, x5)  =  U64_ag(x4, x5)
U65_ag(x1, x2, x3, x4, x5, x6)  =  U65_ag(x4, x6)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x4, x6)
U67_ag(x1, x2, x3, x4, x5)  =  U67_ag(x4, x5)
U68_ag(x1, x2, x3, x4, x5, x6)  =  U68_ag(x4, x6)
U69_ag(x1, x2, x3, x4, x5, x6, x7)  =  U69_ag(x4, x7)
U70_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U70_ag(x4, x8)
U71_ag(x1, x2, x3, x4, x5)  =  U71_ag(x4, x5)
U72_ag(x1, x2, x3, x4, x5)  =  U72_ag(x4, x5)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x4, x5)
U74_ag(x1, x2, x3, x4, x5)  =  U74_ag(x4, x5)
U75_ag(x1, x2, x3, x4, x5)  =  U75_ag(x4, x5)
U76_ag(x1, x2, x3, x4, x5, x6)  =  U76_ag(x4, x6)
U77_ag(x1, x2, x3, x4, x5)  =  U77_ag(x4, x5)
U78_ag(x1, x2, x3, x4, x5)  =  U78_ag(x4, x5)
U79_ag(x1, x2, x3, x4, x5, x6)  =  U79_ag(x4, x6)
U80_ag(x1, x2, x3, x4, x5)  =  U80_ag(x4, x5)
U81_ag(x1, x2, x3, x4, x5)  =  U81_ag(x4, x5)
U82_ag(x1, x2, x3, x4, x5, x6)  =  U82_ag(x4, x6)
U83_ag(x1, x2, x3, x4, x5)  =  U83_ag(x4, x5)
U84_ag(x1, x2, x3, x4, x5, x6)  =  U84_ag(x4, x5, x6)
U85_ag(x1, x2, x3, x4, x5, x6, x7)  =  U85_ag(x4, x5, x7)
U86_ag(x1, x2, x3, x4, x5, x6)  =  U86_ag(x4, x5, x6)
U87_ag(x1, x2, x3, x4, x5, x6)  =  U87_ag(x4, x5, x6)
U88_ag(x1, x2, x3, x4, x5, x6, x7)  =  U88_ag(x4, x5, x6, x7)
U89_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U89_ag(x4, x5, x6, x8)
U90_ag(x1, x2, x3, x4, x5, x6, x7)  =  U90_ag(x4, x5, x6, x7)
U91_ag(x1, x2, x3, x4, x5, x6, x7)  =  U91_ag(x4, x5, x6, x7)
less70_in_gg(x1, x2)  =  less70_in_gg(x1, x2)
less70_out_gg(x1, x2)  =  less70_out_gg(x1, x2)
U22_gg(x1, x2, x3)  =  U22_gg(x1, x2, x3)
less78_in_gg(x1, x2)  =  less78_in_gg(x1, x2)
less78_out_gg(x1, x2)  =  less78_out_gg(x1, x2)
U20_gg(x1, x2, x3)  =  U20_gg(x1, x2, x3)
U92_ag(x1, x2, x3, x4, x5, x6, x7)  =  U92_ag(x4, x5, x6, x7)
U93_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U93_ag(x4, x5, x6, x8)
U94_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U94_ag(x4, x5, x6, x8)
U95_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U95_ag(x4, x5, x6, x10)
U96_ag(x1, x2, x3, x4, x5, x6, x7)  =  U96_ag(x4, x5, x6, x7)
p179_in_gaaag(x1, x2, x3, x4, x5)  =  p179_in_gaaag(x1, x5)
U23_gaaag(x1, x2, x3, x4, x5, x6)  =  U23_gaaag(x1, x5, x6)
p179_out_gaaag(x1, x2, x3, x4, x5)  =  p179_out_gaaag(x1, x5)
U24_gaaag(x1, x2, x3, x4)  =  U24_gaaag(x1, x2, x3, x4)
U25_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U25_gaaag(x1, x3, x6, x7)
U26_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U26_gaaag(x1, x3, x6, x7)
U27_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U27_gaaag(x1, x2, x6, x7)
U28_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U28_gaaag(x1, x2, x6, x7)
p194_in_gaaag(x1, x2, x3, x4, x5)  =  p194_in_gaaag(x1, x5)
U29_gaaag(x1, x2, x3, x4, x5, x6)  =  U29_gaaag(x1, x5, x6)
p194_out_gaaag(x1, x2, x3, x4, x5)  =  p194_out_gaaag(x1, x5)
U30_gaaag(x1, x2, x3, x4)  =  U30_gaaag(x1, x2, x3, x4)
U31_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U31_gaaag(x1, x2, x6, x7)
U32_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U32_gaaag(x1, x2, x6, x7)
U33_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U33_gaaag(x1, x4, x6, x7)
U34_gaaag(x1, x2, x3, x4, x5, x6, x7)  =  U34_gaaag(x1, x4, x6, x7)
U97_ag(x1, x2, x3, x4, x5, x6, x7)  =  U97_ag(x4, x5, x6, x7)
U98_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U98_ag(x4, x5, x6, x8)
U99_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U99_ag(x4, x5, x6, x9)
U100_ag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)  =  U100_ag(x4, x5, x6, x10)
U101_ag(x1, x2, x3, x4, x5, x6, x7)  =  U101_ag(x4, x5, x6, x7)
U102_ag(x1, x2, x3, x4, x5, x6)  =  U102_ag(x4, x5, x6)
U103_ag(x1, x2, x3, x4, x5, x6, x7)  =  U103_ag(x4, x5, x7)
U104_ag(x1, x2, x3, x4, x5, x6, x7, x8)  =  U104_ag(x4, x5, x8)
U105_ag(x1, x2, x3, x4, x5, x6)  =  U105_ag(x4, x5, x6)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAA
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAA(x9)
MS38_IN_AA(x1, x2)  =  MS38_IN_AA
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAA(x9)

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

(147) UsableRulesProof (EQUIVALENT transformation)

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

(148) Obligation:

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

P34_IN_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127) → U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
U4_AAAAAAAA(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → MS38_IN_AA(T78, X125)
MS38_IN_AA(.(T99, .(T100, T101)), X172) → P34_IN_AAAAAAAA(T99, T100, T101, X168, X169, X170, X171, X172)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127) → U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U7_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → MS38_IN_AA(T84, X126)
U6_AAAAAAAA(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T83)
P34_IN_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127) → U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U10_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → MS38_IN_AA(T84, T105)
U9_AAAAAAAA(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → MS38_IN_AA(T78, T106)

The TRS R consists of the following rules:

split12_in_aaaa(T42, T44, .(T42, X71), X72) → U2_aaaa(T42, T44, X71, X72, split16_in_aaa(T44, X72, X71))
ms38_in_aa([], []) → ms38_out_aa([], [])
ms38_in_aa(.(T89, []), .(T89, [])) → ms38_out_aa(.(T89, []), .(T89, []))
ms38_in_aa(.(T99, .(T100, T101)), X172) → U13_aa(T99, T100, T101, X172, p34_in_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172))
U2_aaaa(T42, T44, X71, X72, split16_out_aaa(T44, X72, X71)) → split12_out_aaaa(T42, T44, .(T42, X71), X72)
U13_aa(T99, T100, T101, X172, p34_out_aaaaaaaa(T99, T100, T101, X168, X169, X170, X171, X172)) → ms38_out_aa(.(T99, .(T100, T101)), X172)
split16_in_aaa([], [], []) → split16_out_aaa([], [], [])
split16_in_aaa(.(T49, T51), .(T49, X89), X90) → U1_aaa(T49, T51, X89, X90, split16_in_aaa(T51, X90, X89))
p34_in_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127) → U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), X123, X124))
p34_in_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127) → U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T79))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127) → U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
p34_in_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127) → U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_in_aaaa(T72, .(T73, T74), T78, T84))
U1_aaa(T49, T51, X89, X90, split16_out_aaa(T51, X90, X89)) → split16_out_aaa(.(T49, T51), .(T49, X89), X90)
U3_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), X123, X124)) → p34_out_aaaaaaaa(T72, T73, T74, X123, X124, X125, X126, X127)
U4_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T79)) → U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_in_aa(T78, X125))
U6_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T78, T83))
U9_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, split12_out_aaaa(T72, .(T73, T74), T78, T84)) → U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T78, T106))
U5_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127, ms38_out_aa(T78, X125)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T79, X125, X126, X127)
U7_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T78, T83)) → U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_in_aa(T84, X126))
U10_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T78, T106)) → U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_in_aa(T84, T105))
U8_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127, ms38_out_aa(T84, X126)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T83, X126, X127)
U11_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, ms38_out_aa(T84, T105)) → U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_in_aaa(T106, T105, X127))
U12_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127, merge54_out_aaa(T106, T105, X127)) → p34_out_aaaaaaaa(T72, T73, T74, T78, T84, T106, T105, X127)
merge54_in_aaa([], T113, T113) → merge54_out_aaa([], T113, T113)
merge54_in_aaa(T118, [], T118) → merge54_out_aaa(T118, [], T118)
merge54_in_aaa(.(T139, T141), .(T140, T142), .(T139, X226)) → U14_aaa(T139, T141, T140, T142, X226, less70_in_aa(T139, T140))
merge54_in_aaa(.(T139, T145), .(T146, T147), .(T139, X226)) → U15_aaa(T139, T145, T146, T147, X226, less70_in_aa(T139, T146))
merge54_in_aaa(.(T197, T199), .(T196, T198), .(T196, X287)) → U17_aaa(T197, T199, T196, T198, X287, less78_in_aa(T196, T197))
merge54_in_aaa(.(T202, T203), .(T196, T204), .(T196, X287)) → U18_aaa(T202, T203, T196, T204, X287, less78_in_aa(T196, T202))
U14_aaa(T139, T141, T140, T142, X226, less70_out_aa(T139, T140)) → merge54_out_aaa(.(T139, T141), .(T140, T142), .(T139, X226))
U15_aaa(T139, T145, T146, T147, X226, less70_out_aa(T139, T146)) → U16_aaa(T139, T145, T146, T147, X226, merge54_in_aaa(T145, .(T146, T147), X226))
U17_aaa(T197, T199, T196, T198, X287, less78_out_aa(T196, T197)) → merge54_out_aaa(.(T197, T199), .(T196, T198), .(T196, X287))
U18_aaa(T202, T203, T196, T204, X287, less78_out_aa(T196, T202)) → U19_aaa(T202, T203, T196, T204, X287, merge54_in_aaa(.(T202, T203), T204, X287))
less70_in_aa(0, T154) → less70_out_aa(0, T154)
less70_in_aa(s(T161), T162) → U22_aa(T161, T162, less78_in_aa(T161, T162))
U16_aaa(T139, T145, T146, T147, X226, merge54_out_aaa(T145, .(T146, T147), X226)) → merge54_out_aaa(.(T139, T145), .(T146, T147), .(T139, X226))
less78_in_aa(0, s(T169)) → less78_out_aa(0, s(T169))
less78_in_aa(s(T176), s(T177)) → U20_aa(T176, T177, less78_in_aa(T176, T177))
U19_aaa(T202, T203, T196, T204, X287, merge54_out_aaa(.(T202, T203), T204, X287)) → merge54_out_aaa(.(T202, T203), .(T196, T204), .(T196, X287))
U22_aa(T161, T162, less78_out_aa(T161, T162)) → less70_out_aa(s(T161), T162)
U20_aa(T176, T177, less78_out_aa(T176, T177)) → less78_out_aa(s(T176), s(T177))

The argument filtering Pi contains the following mapping:
[]  =  []
split12_in_aaaa(x1, x2, x3, x4)  =  split12_in_aaaa
U2_aaaa(x1, x2, x3, x4, x5)  =  U2_aaaa(x5)
split16_in_aaa(x1, x2, x3)  =  split16_in_aaa
split16_out_aaa(x1, x2, x3)  =  split16_out_aaa
U1_aaa(x1, x2, x3, x4, x5)  =  U1_aaa(x5)
split12_out_aaaa(x1, x2, x3, x4)  =  split12_out_aaaa
p34_in_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_in_aaaaaaaa
U3_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U3_aaaaaaaa(x9)
p34_out_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8)  =  p34_out_aaaaaaaa
U4_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_aaaaaaaa(x9)
U5_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U5_aaaaaaaa(x9)
ms38_in_aa(x1, x2)  =  ms38_in_aa
ms38_out_aa(x1, x2)  =  ms38_out_aa
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U6_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_aaaaaaaa(x9)
U7_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_aaaaaaaa(x9)
U8_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U8_aaaaaaaa(x9)
U9_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_aaaaaaaa(x9)
U10_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_aaaaaaaa(x9)
U11_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U11_aaaaaaaa(x9)
U12_aaaaaaaa(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U12_aaaaaaaa(x9)
merge54_in_aaa(x1, x2, x3)  =  merge54_in_aaa
merge54_out_aaa(x1, x2, x3)  =  merge54_out_aaa
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
less70_in_aa(x1, x2)  =  less70_in_aa
less70_out_aa(x1, x2)  =  less70_out_aa(x1)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
less78_in_aa(x1, x2)  =  less78_in_aa
less78_out_aa(x1, x2)  =  less78_out_aa(x1)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2, x3, x4, x5, x6)  =  U16_aaa(x6)
U17_aaa(x1, x2, x3, x4, x5, x6)  =  U17_aaa(x6)
U18_aaa(x1, x2, x3, x4, x5, x6)  =  U18_aaa(x6)
U19_aaa(x1, x2, x3, x4, x5, x6)  =  U19_aaa(x6)
.(x1, x2)  =  .(x1, x2)
0  =  0
s(x1)  =  s(x1)
P34_IN_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8)  =  P34_IN_AAAAAAAA
U4_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U4_AAAAAAAA(x9)
MS38_IN_AA(x1, x2)  =  MS38_IN_AA
U6_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U6_AAAAAAAA(x9)
U7_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U7_AAAAAAAA(x9)
U9_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U9_AAAAAAAA(x9)
U10_AAAAAAAA(x1, x2, x3, x4, x5, x6, x7, x8, x9)  =  U10_AAAAAAAA(x9)

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

(149) PiDPToQDPProof (SOUND transformation)

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

(150) Obligation:

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

P34_IN_AAAAAAAAU4_AAAAAAAA(split12_in_aaaa)
U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
P34_IN_AAAAAAAAU6_AAAAAAAA(split12_in_aaaa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_in_aa)
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(151) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P34_IN_AAAAAAAAU4_AAAAAAAA(split12_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))

(152) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
P34_IN_AAAAAAAAU6_AAAAAAAA(split12_in_aaaa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_in_aa)
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(153) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P34_IN_AAAAAAAAU6_AAAAAAAA(split12_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))

(154) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_in_aa)
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(155) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_in_aa) at position [0] we obtained the following new rules [LPAR04]:

U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_out_aa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))

(156) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_out_aa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(157) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P34_IN_AAAAAAAAU9_AAAAAAAA(split12_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

P34_IN_AAAAAAAAU9_AAAAAAAA(U2_aaaa(split16_in_aaa))

(158) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa)
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_out_aa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))
P34_IN_AAAAAAAAU9_AAAAAAAA(U2_aaaa(split16_in_aaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(159) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_in_aa) at position [0] we obtained the following new rules [LPAR04]:

U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_out_aa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))

(160) Obligation:

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

U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
MS38_IN_AAP34_IN_AAAAAAAA
U7_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U6_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
U10_AAAAAAAA(ms38_out_aa) → MS38_IN_AA
U9_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA
P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
P34_IN_AAAAAAAAU6_AAAAAAAA(U2_aaaa(split16_in_aaa))
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(ms38_out_aa)
U6_AAAAAAAA(split12_out_aaaa) → U7_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))
P34_IN_AAAAAAAAU9_AAAAAAAA(U2_aaaa(split16_in_aaa))
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(ms38_out_aa)
U9_AAAAAAAA(split12_out_aaaa) → U10_AAAAAAAA(U13_aa(p34_in_aaaaaaaa))

The TRS R consists of the following rules:

split12_in_aaaaU2_aaaa(split16_in_aaa)
ms38_in_aams38_out_aa
ms38_in_aaU13_aa(p34_in_aaaaaaaa)
U2_aaaa(split16_out_aaa) → split12_out_aaaa
U13_aa(p34_out_aaaaaaaa) → ms38_out_aa
split16_in_aaasplit16_out_aaa
split16_in_aaaU1_aaa(split16_in_aaa)
p34_in_aaaaaaaaU3_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU4_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU6_aaaaaaaa(split12_in_aaaa)
p34_in_aaaaaaaaU9_aaaaaaaa(split12_in_aaaa)
U1_aaa(split16_out_aaa) → split16_out_aaa
U3_aaaaaaaa(split12_out_aaaa) → p34_out_aaaaaaaa
U4_aaaaaaaa(split12_out_aaaa) → U5_aaaaaaaa(ms38_in_aa)
U6_aaaaaaaa(split12_out_aaaa) → U7_aaaaaaaa(ms38_in_aa)
U9_aaaaaaaa(split12_out_aaaa) → U10_aaaaaaaa(ms38_in_aa)
U5_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U7_aaaaaaaa(ms38_out_aa) → U8_aaaaaaaa(ms38_in_aa)
U10_aaaaaaaa(ms38_out_aa) → U11_aaaaaaaa(ms38_in_aa)
U8_aaaaaaaa(ms38_out_aa) → p34_out_aaaaaaaa
U11_aaaaaaaa(ms38_out_aa) → U12_aaaaaaaa(merge54_in_aaa)
U12_aaaaaaaa(merge54_out_aaa) → p34_out_aaaaaaaa
merge54_in_aaamerge54_out_aaa
merge54_in_aaaU14_aaa(less70_in_aa)
merge54_in_aaaU15_aaa(less70_in_aa)
merge54_in_aaaU17_aaa(less78_in_aa)
merge54_in_aaaU18_aaa(less78_in_aa)
U14_aaa(less70_out_aa(T139)) → merge54_out_aaa
U15_aaa(less70_out_aa(T139)) → U16_aaa(merge54_in_aaa)
U17_aaa(less78_out_aa(T196)) → merge54_out_aaa
U18_aaa(less78_out_aa(T196)) → U19_aaa(merge54_in_aaa)
less70_in_aaless70_out_aa(0)
less70_in_aaU22_aa(less78_in_aa)
U16_aaa(merge54_out_aaa) → merge54_out_aaa
less78_in_aaless78_out_aa(0)
less78_in_aaU20_aa(less78_in_aa)
U19_aaa(merge54_out_aaa) → merge54_out_aaa
U22_aa(less78_out_aa(T161)) → less70_out_aa(s(T161))
U20_aa(less78_out_aa(T176)) → less78_out_aa(s(T176))

The set Q consists of the following terms:

split12_in_aaaa
ms38_in_aa
U2_aaaa(x0)
U13_aa(x0)
split16_in_aaa
p34_in_aaaaaaaa
U1_aaa(x0)
U3_aaaaaaaa(x0)
U4_aaaaaaaa(x0)
U6_aaaaaaaa(x0)
U9_aaaaaaaa(x0)
U5_aaaaaaaa(x0)
U7_aaaaaaaa(x0)
U10_aaaaaaaa(x0)
U8_aaaaaaaa(x0)
U11_aaaaaaaa(x0)
U12_aaaaaaaa(x0)
merge54_in_aaa
U14_aaa(x0)
U15_aaa(x0)
U17_aaa(x0)
U18_aaa(x0)
less70_in_aa
U16_aaa(x0)
less78_in_aa
U19_aaa(x0)
U22_aa(x0)
U20_aa(x0)

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

(161) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.
Found a loop by narrowing to the left:

s = U4_AAAAAAAA(U2_aaaa(split16_in_aaa)) evaluates to t =U4_AAAAAAAA(U2_aaaa(split16_in_aaa))

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
  • Matcher: [ ]
  • Semiunifier: [ ]




Rewriting sequence

U4_AAAAAAAA(U2_aaaa(split16_in_aaa))U4_AAAAAAAA(U2_aaaa(split16_out_aaa))
with rule split16_in_aaasplit16_out_aaa at position [0,0] and matcher [ ]

U4_AAAAAAAA(U2_aaaa(split16_out_aaa))U4_AAAAAAAA(split12_out_aaaa)
with rule U2_aaaa(split16_out_aaa) → split12_out_aaaa at position [0] and matcher [ ]

U4_AAAAAAAA(split12_out_aaaa)MS38_IN_AA
with rule U4_AAAAAAAA(split12_out_aaaa) → MS38_IN_AA at position [] and matcher [ ]

MS38_IN_AAP34_IN_AAAAAAAA
with rule MS38_IN_AAP34_IN_AAAAAAAA at position [] and matcher [ ]

P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))
with rule P34_IN_AAAAAAAAU4_AAAAAAAA(U2_aaaa(split16_in_aaa))

Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence


All these steps are and every following step will be a correct step w.r.t to Q.



(162) NO