Left Termination of the query pattern qs_in_2(g, a) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

qs([], []).
qs(cons(X, L), S) :- ','(split(L, X, L1, L2), ','(qs(L1, S1), ','(qs(L2, S2), append(S1, cons(X, S2), S)))).
append([], L, L).
append(cons(X, L1), L2, cons(X, L3)) :- append(L1, L2, L3).
split([], X, [], []).
split(cons(X, L), Y, cons(X, L1), L2) :- ','(less(X, Y), split(L, Y, L1, L2)).
split(cons(X, L), Y, L1, cons(X, L2)) :- ','(geq(X, Y), split(L, Y, L1, L2)).
less(0, s(X)).
less(s(X), s(Y)) :- less(X, Y).
geq(X, X).
geq(s(X), 0).
geq(s(X), s(Y)) :- geq(X, Y).

Queries:

qs(g,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: qs(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: qs(T1, T2), SCOPE: 1, CLAUSE: 0 | qs(T1, T2), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | qs([], T2), SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: qs(T1, T2), SCOPE: 1, CLAUSE: 1\n\nT1 is ground\nqs(T1, T2) !=? qs([], [])", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: qs([], T2), SCOPE: 1, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9))))\n\nT6 is ground\nT7 is ground\nX10 is free; \nX11 is free; \nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9)))), SCOPE: 2, CLAUSE: 4 | ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9)))), SCOPE: 2, CLAUSE: 5 | ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9)))), SCOPE: 2, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free; \nX11 is free; \nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9)))), SCOPE: 2, CLAUSE: 4\n\nT6 is ground\nT7 is ground\nX10 is free; \nX11 is free; \nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9)))), SCOPE: 2, CLAUSE: 5 | ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9)))), SCOPE: 2, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free; \nX11 is free; \nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(qs([], X12), ','(qs([], X13), append(X12, cons(T14, X13), T9)))\n\nT14 is ground\nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: qs([], X12)\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(qs([], X13), append(T17, cons(T14, X13), T9))\n\nT14 is ground\nT17 is ground\nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: qs([], X12), SCOPE: 3, CLAUSE: 0 | qs([], X12), SCOPE: 3, CLAUSE: 1\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: qs([], X12), SCOPE: 3, CLAUSE: 0\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: qs([], X12), SCOPE: 3, CLAUSE: 1\n\nX12 is free", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: qs([], X13)\n\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: append(T17, cons(T14, T20), T9)\n\nT14 is ground\nT17 is ground\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: append(T17, cons(T14, T20), T9), SCOPE: 4, CLAUSE: 2 | append(T17, cons(T14, T20), T9), SCOPE: 4, CLAUSE: 3\n\nT14 is ground\nT17 is ground\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: append(T17, cons(T14, T20), T9), SCOPE: 4, CLAUSE: 2\n\nT14 is ground\nT17 is ground\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: append(T17, cons(T14, T20), T9), SCOPE: 4, CLAUSE: 3\n\nT14 is ground\nT17 is ground\nT20 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: append(T46, cons(T47, T48), T50)\n\nT46 is ground\nT47 is ground\nT48 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9)))), SCOPE: 2, CLAUSE: 5\n\nT6 is ground\nT7 is ground\nX10 is free; \nX11 is free; \nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(split(T7, T6, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(T6, X13), T9)))), SCOPE: 2, CLAUSE: 6\n\nT6 is ground\nT7 is ground\nX10 is free; \nX11 is free; \nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(less(T67, T69), ','(split(T68, T69, X93, X94), ','(qs(cons(T67, X93), X12), ','(qs(X94, X13), append(X12, cons(T69, X13), T9)))))\n\nT67 is ground\nT68 is ground\nT69 is ground\nX12 is free; \nX13 is free; \nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: less(T67, T69)\n\nT67 is ground\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(split(T68, T69, X93, X94), ','(qs(cons(T67, X93), X12), ','(qs(X94, X13), append(X12, cons(T69, X13), T9))))\n\nT67 is ground\nT68 is ground\nT69 is ground\nX12 is free; \nX13 is free; \nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: less(T67, T69), SCOPE: 5, CLAUSE: 7 | less(T67, T69), SCOPE: 5, CLAUSE: 8\n\nT67 is ground\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: less(T67, T69), SCOPE: 5, CLAUSE: 7\n\nT67 is ground\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: less(T67, T69), SCOPE: 5, CLAUSE: 8\n\nT67 is ground\nT69 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: less(T83, T84)\n\nT83 is ground\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: split(T68, T69, X93, X94)\n\nT68 is ground\nT69 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(qs(cons(T67, T89), X12), ','(qs(T90, X13), append(X12, cons(T69, X13), T9)))\n\nT67 is ground\nT69 is ground\nT89 is ground\nT90 is ground\nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: split(T68, T69, X93, X94), SCOPE: 6, CLAUSE: 4 | split(T68, T69, X93, X94), SCOPE: 6, CLAUSE: 5 | split(T68, T69, X93, X94), SCOPE: 6, CLAUSE: 6\n\nT68 is ground\nT69 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: split(T68, T69, X93, X94), SCOPE: 6, CLAUSE: 4\n\nT68 is ground\nT69 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: split(T68, T69, X93, X94), SCOPE: 6, CLAUSE: 5 | split(T68, T69, X93, X94), SCOPE: 6, CLAUSE: 6\n\nT68 is ground\nT69 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: split(T68, T69, X93, X94), SCOPE: 6, CLAUSE: 5\n\nT68 is ground\nT69 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: split(T68, T69, X93, X94), SCOPE: 6, CLAUSE: 6\n\nT68 is ground\nT69 is ground\nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(less(T110, T112), split(T111, T112, X163, X164))\n\nT110 is ground\nT111 is ground\nT112 is ground\nX163 is free; \nX164 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: less(T110, T112)\n\nT110 is ground\nT112 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: split(T111, T112, X163, X164)\n\nT111 is ground\nT112 is ground\nX163 is free; \nX164 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(geq(T125, T127), split(T126, T127, X195, X196))\n\nT125 is ground\nT126 is ground\nT127 is ground\nX195 is free; \nX196 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: geq(T125, T127)\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: split(T126, T127, X195, X196)\n\nT126 is ground\nT127 is ground\nX195 is free; \nX196 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: geq(T125, T127), SCOPE: 7, CLAUSE: 9 | geq(T125, T127), SCOPE: 7, CLAUSE: 10 | geq(T125, T127), SCOPE: 7, CLAUSE: 11\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: geq(T125, T127), SCOPE: 7, CLAUSE: 9\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: geq(T125, T127), SCOPE: 7, CLAUSE: 10 | geq(T125, T127), SCOPE: 7, CLAUSE: 11\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: geq(T125, T127), SCOPE: 7, CLAUSE: 10\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: geq(T125, T127), SCOPE: 7, CLAUSE: 11\n\nT125 is ground\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: geq(T146, T147)\n\nT146 is ground\nT147 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: qs(cons(T67, T89), X12)\n\nT67 is ground\nT89 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(qs(T90, X13), append(T154, cons(T69, X13), T9))\n\nT69 is ground\nT90 is ground\nT154 is ground\nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: qs(T90, X13)\n\nT90 is ground\nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: append(T154, cons(T69, T157), T9)\n\nT69 is ground\nT154 is ground\nT157 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: qs(T90, X13), SCOPE: 8, CLAUSE: 0 | qs(T90, X13), SCOPE: 8, CLAUSE: 1\n\nT90 is ground\nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: qs(T90, X13), SCOPE: 8, CLAUSE: 0\n\nT90 is ground\nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: qs(T90, X13), SCOPE: 8, CLAUSE: 1\n\nT90 is ground\nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: ','(split(T163, T162, X261, X262), ','(qs(X261, X263), ','(qs(X262, X264), append(X263, cons(T162, X264), X265))))\n\nT162 is ground\nT163 is ground\nX265 is free; \nX261 is free; \nX262 is free; \nX263 is free; \nX264 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: split(T163, T162, X261, X262)\n\nT162 is ground\nT163 is ground\nX261 is free; \nX262 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(qs(T166, X263), ','(qs(T167, X264), append(X263, cons(T162, X264), X265)))\n\nT162 is ground\nT166 is ground\nT167 is ground\nX265 is free; \nX263 is free; \nX264 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: qs(T166, X263)\n\nT166 is ground\nX263 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ','(qs(T167, X264), append(T170, cons(T162, X264), X265))\n\nT162 is ground\nT167 is ground\nT170 is ground\nX265 is free; \nX264 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: qs(T167, X264)\n\nT167 is ground\nX264 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: append(T170, cons(T162, T171), X265)\n\nT162 is ground\nT170 is ground\nT171 is ground\nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: append(T170, cons(T162, T171), X265), SCOPE: 9, CLAUSE: 2 | append(T170, cons(T162, T171), X265), SCOPE: 9, CLAUSE: 3\n\nT162 is ground\nT170 is ground\nT171 is ground\nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: append(T170, cons(T162, T171), X265), SCOPE: 9, CLAUSE: 2\n\nT162 is ground\nT170 is ground\nT171 is ground\nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: append(T170, cons(T162, T171), X265), SCOPE: 9, CLAUSE: 3\n\nT162 is ground\nT170 is ground\nT171 is ground\nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: append(T195, cons(T196, T197), X295)\n\nT195 is ground\nT196 is ground\nT197 is ground\nX295 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(geq(T212, T214), ','(split(T213, T214, X323, X324), ','(qs(X323, X12), ','(qs(cons(T212, X324), X13), append(X12, cons(T214, X13), T9)))))\n\nT212 is ground\nT213 is ground\nT214 is ground\nX12 is free; \nX13 is free; \nX323 is free; \nX324 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: geq(T212, T214)\n\nT212 is ground\nT214 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(split(T213, T214, X323, X324), ','(qs(X323, X12), ','(qs(cons(T212, X324), X13), append(X12, cons(T214, X13), T9))))\n\nT212 is ground\nT213 is ground\nT214 is ground\nX12 is free; \nX13 is free; \nX323 is free; \nX324 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: split(T213, T214, X323, X324)\n\nT213 is ground\nT214 is ground\nX323 is free; \nX324 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: ','(qs(T221, X12), ','(qs(cons(T212, T222), X13), append(X12, cons(T214, X13), T9)))\n\nT212 is ground\nT214 is ground\nT221 is ground\nT222 is ground\nX12 is free; \nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: qs(T221, X12)\n\nT221 is ground\nX12 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(qs(cons(T212, T222), X13), append(T225, cons(T214, X13), T9))\n\nT212 is ground\nT214 is ground\nT222 is ground\nT225 is ground\nX13 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 111 [arrowhead = none ];
111 -> 2;

112 [label="EVAL with clause\nqs([], []).\nand substitution\nT1 -> []\nT2 -> []", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 112 [arrowhead = none ];
112 -> 3;

113 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 113 [arrowhead = none ];
113 -> 4;

114 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 114 [arrowhead = none ];
114 -> 5;

115 [label="EVAL with clause\nqs(cons(X7, X8), X9) :- ','(split(X8, X7, X10, X11), ','(qs(X10, X12), ','(qs(X11, X13), append(X12, cons(X7, X13), X9)))).\nand substitution\nX7 -> T6\nX8 -> T7\nT1 -> cons(T6, T7)\nT2 -> T9\nX9 -> T9\nT8 -> T9", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 115 [arrowhead = none ];
115 -> 7;

116 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 116 [arrowhead = none ];
116 -> 8;

117 [label="BACKTRACK\nfor clause: qs(cons(X, L), S) :- ','(split(L, X, L1, L2), ','(qs(L1, S1), ','(qs(L2, S2), append(S1, cons(X, S2), S))))because of non-unification", fontsize=14, style = filled, fillcolor = white];
5 -> 117 [arrowhead = none ];
117 -> 6;

118 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 118 [arrowhead = none ];
118 -> 9;

119 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
9 -> 119 [arrowhead = none ];
119 -> 10;

120 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
9 -> 120 [arrowhead = none ];
120 -> 11;

121 [label="EVAL with clause\nsplit([], X21, [], []).\nand substitution\nT7 -> []\nT6 -> T14\nX21 -> T14\nX10 -> []\nX11 -> []", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 121 [arrowhead = none ];
121 -> 12;

122 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 122 [arrowhead = none ];
122 -> 13;

123 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 123 [arrowhead = none ];
123 -> 32;

124 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 124 [arrowhead = none ];
124 -> 33;

125 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
12 -> 125 [arrowhead = none ];
125 -> 14;

126 [label="SPLIT 2\nnew knowledge:\nT17 is ground\nreplacements:\nX12 -> T17", fontsize=14, style = filled, fillcolor = violet];
12 -> 126 [arrowhead = none ];
126 -> 15;

127 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
14 -> 127 [arrowhead = none ];
127 -> 16;

128 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
15 -> 128 [arrowhead = none ];
128 -> 22;

129 [label="SPLIT 2\nnew knowledge:\nT20 is ground\nreplacements:\nX13 -> T20", fontsize=14, style = filled, fillcolor = violet];
15 -> 129 [arrowhead = none ];
129 -> 23;

130 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
16 -> 130 [arrowhead = none ];
130 -> 17;

131 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
16 -> 131 [arrowhead = none ];
131 -> 18;

132 [label="ONLY EVAL with clause\nqs([], []).\nand substitution\nX12 -> []", fontsize=14, style = filled, fillcolor = white];
17 -> 132 [arrowhead = none ];
132 -> 19;

133 [label="BACKTRACK\nfor clause: qs(cons(X, L), S) :- ','(split(L, X, L1, L2), ','(qs(L1, S1), ','(qs(L2, S2), append(S1, cons(X, S2), S))))because of non-unification", fontsize=14, style = filled, fillcolor = white];
18 -> 133 [arrowhead = none ];
133 -> 21;

134 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 134 [arrowhead = none ];
134 -> 20;

135 [label="INSTANCE with matching:\nX12 -> X13", fontsize=14, style = filled, fillcolor = lightgrey];
22 -> 135 [arrowhead = none , style=dashed];
135 -> 14[style=dashed];

136 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
23 -> 136 [arrowhead = none ];
136 -> 24;

137 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 137 [arrowhead = none ];
137 -> 25;

138 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 138 [arrowhead = none ];
138 -> 26;

139 [label="EVAL with clause\nappend([], X40, X40).\nand substitution\nT17 -> []\nT14 -> T33\nT20 -> T34\nX40 -> cons(T33, T34)\nT9 -> cons(T33, T34)", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 139 [arrowhead = none ];
139 -> 27;

140 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
25 -> 140 [arrowhead = none ];
140 -> 28;

141 [label="EVAL with clause\nappend(cons(X50, X51), X52, cons(X50, X53)) :- append(X51, X52, X53).\nand substitution\nX50 -> T45\nX51 -> T46\nT17 -> cons(T45, T46)\nT14 -> T47\nT20 -> T48\nX52 -> cons(T47, T48)\nX53 -> T50\nT9 -> cons(T45, T50)\nT49 -> T50", fontsize=14, style = filled, fillcolor = lightblue];
26 -> 141 [arrowhead = none ];
141 -> 30;

142 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
26 -> 142 [arrowhead = none ];
142 -> 31;

143 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
27 -> 143 [arrowhead = none ];
143 -> 29;

144 [label="INSTANCE with matching:\nT17 -> T46\nT14 -> T47\nT20 -> T48\nT9 -> T50", fontsize=14, style = filled, fillcolor = lightgrey];
30 -> 144 [arrowhead = none , style=dashed];
144 -> 23[style=dashed];

145 [label="EVAL with clause\nsplit(cons(X88, X89), X90, cons(X88, X91), X92) :- ','(less(X88, X90), split(X89, X90, X91, X92)).\nand substitution\nX88 -> T67\nX89 -> T68\nT7 -> cons(T67, T68)\nT6 -> T69\nX90 -> T69\nX91 -> X93\nX10 -> cons(T67, X93)\nX11 -> X94\nX92 -> X94", fontsize=14, style = filled, fillcolor = lightblue];
32 -> 145 [arrowhead = none ];
145 -> 34;

146 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
32 -> 146 [arrowhead = none ];
146 -> 35;

147 [label="EVAL with clause\nsplit(cons(X318, X319), X320, X321, cons(X318, X322)) :- ','(geq(X318, X320), split(X319, X320, X321, X322)).\nand substitution\nX318 -> T212\nX319 -> T213\nT7 -> cons(T212, T213)\nT6 -> T214\nX320 -> T214\nX10 -> X323\nX321 -> X323\nX322 -> X324\nX11 -> cons(T212, X324)", fontsize=14, style = filled, fillcolor = lightblue];
33 -> 147 [arrowhead = none ];
147 -> 103;

148 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
33 -> 148 [arrowhead = none ];
148 -> 104;

149 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
34 -> 149 [arrowhead = none ];
149 -> 36;

150 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
34 -> 150 [arrowhead = none ];
150 -> 37;

151 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
36 -> 151 [arrowhead = none ];
151 -> 38;

152 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
37 -> 152 [arrowhead = none ];
152 -> 46;

153 [label="SPLIT 2\nnew knowledge:\nT89 is ground\nT90 is ground\nreplacements:\nX93 -> T89\nX94 -> T90", fontsize=14, style = filled, fillcolor = violet];
37 -> 153 [arrowhead = none ];
153 -> 47;

154 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 154 [arrowhead = none ];
154 -> 39;

155 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 155 [arrowhead = none ];
155 -> 40;

156 [label="EVAL with clause\nless(0, s(X108)).\nand substitution\nT67 -> 0\nX108 -> T78\nT69 -> s(T78)", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 156 [arrowhead = none ];
156 -> 41;

157 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 157 [arrowhead = none ];
157 -> 42;

158 [label="EVAL with clause\nless(s(X114), s(X115)) :- less(X114, X115).\nand substitution\nX114 -> T83\nT67 -> s(T83)\nX115 -> T84\nT69 -> s(T84)", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 158 [arrowhead = none ];
158 -> 44;

159 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 159 [arrowhead = none ];
159 -> 45;

160 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 160 [arrowhead = none ];
160 -> 43;

161 [label="INSTANCE with matching:\nT67 -> T83\nT69 -> T84", fontsize=14, style = filled, fillcolor = lightgrey];
44 -> 161 [arrowhead = none , style=dashed];
161 -> 36[style=dashed];

162 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
46 -> 162 [arrowhead = none ];
162 -> 48;

163 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
47 -> 163 [arrowhead = none ];
163 -> 77;

164 [label="SPLIT 2\nnew knowledge:\nT154 is ground\nreplacements:\nX12 -> T154", fontsize=14, style = filled, fillcolor = violet];
47 -> 164 [arrowhead = none ];
164 -> 78;

165 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
48 -> 165 [arrowhead = none ];
165 -> 49;

166 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
48 -> 166 [arrowhead = none ];
166 -> 50;

167 [label="EVAL with clause\nsplit([], X128, [], []).\nand substitution\nT68 -> []\nT69 -> T97\nX128 -> T97\nX93 -> []\nX94 -> []", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 167 [arrowhead = none ];
167 -> 51;

168 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 168 [arrowhead = none ];
168 -> 52;

169 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 169 [arrowhead = none ];
169 -> 54;

170 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 170 [arrowhead = none ];
170 -> 55;

171 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
51 -> 171 [arrowhead = none ];
171 -> 53;

172 [label="EVAL with clause\nsplit(cons(X158, X159), X160, cons(X158, X161), X162) :- ','(less(X158, X160), split(X159, X160, X161, X162)).\nand substitution\nX158 -> T110\nX159 -> T111\nT68 -> cons(T110, T111)\nT69 -> T112\nX160 -> T112\nX161 -> X163\nX93 -> cons(T110, X163)\nX94 -> X164\nX162 -> X164", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 172 [arrowhead = none ];
172 -> 56;

173 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
54 -> 173 [arrowhead = none ];
173 -> 57;

174 [label="EVAL with clause\nsplit(cons(X190, X191), X192, X193, cons(X190, X194)) :- ','(geq(X190, X192), split(X191, X192, X193, X194)).\nand substitution\nX190 -> T125\nX191 -> T126\nT68 -> cons(T125, T126)\nT69 -> T127\nX192 -> T127\nX93 -> X195\nX193 -> X195\nX194 -> X196\nX94 -> cons(T125, X196)", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 174 [arrowhead = none ];
174 -> 60;

175 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 175 [arrowhead = none ];
175 -> 61;

176 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
56 -> 176 [arrowhead = none ];
176 -> 58;

177 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
56 -> 177 [arrowhead = none ];
177 -> 59;

178 [label="INSTANCE with matching:\nT67 -> T110\nT69 -> T112", fontsize=14, style = filled, fillcolor = lightgrey];
58 -> 178 [arrowhead = none , style=dashed];
178 -> 36[style=dashed];

179 [label="INSTANCE with matching:\nT68 -> T111\nT69 -> T112\nX93 -> X163\nX94 -> X164", fontsize=14, style = filled, fillcolor = lightgrey];
59 -> 179 [arrowhead = none , style=dashed];
179 -> 46[style=dashed];

180 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
60 -> 180 [arrowhead = none ];
180 -> 62;

181 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
60 -> 181 [arrowhead = none ];
181 -> 63;

182 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
62 -> 182 [arrowhead = none ];
182 -> 64;

183 [label="INSTANCE with matching:\nT68 -> T126\nT69 -> T127\nX93 -> X195\nX94 -> X196", fontsize=14, style = filled, fillcolor = lightgrey];
63 -> 183 [arrowhead = none , style=dashed];
183 -> 46[style=dashed];

184 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
64 -> 184 [arrowhead = none ];
184 -> 65;

185 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
64 -> 185 [arrowhead = none ];
185 -> 66;

186 [label="EVAL with clause\ngeq(X210, X210).\nand substitution\nT125 -> T136\nX210 -> T136\nT127 -> T136", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 186 [arrowhead = none ];
186 -> 67;

187 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 187 [arrowhead = none ];
187 -> 68;

188 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 188 [arrowhead = none ];
188 -> 70;

189 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 189 [arrowhead = none ];
189 -> 71;

190 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 190 [arrowhead = none ];
190 -> 69;

191 [label="EVAL with clause\ngeq(s(X216), 0).\nand substitution\nX216 -> T141\nT125 -> s(T141)\nT127 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 191 [arrowhead = none ];
191 -> 72;

192 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
70 -> 192 [arrowhead = none ];
192 -> 73;

193 [label="EVAL with clause\ngeq(s(X222), s(X223)) :- geq(X222, X223).\nand substitution\nX222 -> T146\nT125 -> s(T146)\nX223 -> T147\nT127 -> s(T147)", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 193 [arrowhead = none ];
193 -> 75;

194 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 194 [arrowhead = none ];
194 -> 76;

195 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
72 -> 195 [arrowhead = none ];
195 -> 74;

196 [label="INSTANCE with matching:\nT125 -> T146\nT127 -> T147", fontsize=14, style = filled, fillcolor = lightgrey];
75 -> 196 [arrowhead = none , style=dashed];
196 -> 62[style=dashed];

197 [label="INSTANCE with matching:\nT1 -> cons(T67, T89)\nT2 -> X12", fontsize=14, style = filled, fillcolor = lightgrey];
77 -> 197 [arrowhead = none , style=dashed];
197 -> 1[style=dashed];

198 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
78 -> 198 [arrowhead = none ];
198 -> 79;

199 [label="SPLIT 2\nnew knowledge:\nT157 is ground\nreplacements:\nX13 -> T157", fontsize=14, style = filled, fillcolor = violet];
78 -> 199 [arrowhead = none ];
199 -> 80;

200 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
79 -> 200 [arrowhead = none ];
200 -> 81;

201 [label="INSTANCE with matching:\nT17 -> T154\nT14 -> T69\nT20 -> T157", fontsize=14, style = filled, fillcolor = lightgrey];
80 -> 201 [arrowhead = none , style=dashed];
201 -> 23[style=dashed];

202 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 202 [arrowhead = none ];
202 -> 82;

203 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
81 -> 203 [arrowhead = none ];
203 -> 83;

204 [label="EVAL with clause\nqs([], []).\nand substitution\nT90 -> []\nX13 -> []", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 204 [arrowhead = none ];
204 -> 84;

205 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 205 [arrowhead = none ];
205 -> 85;

206 [label="EVAL with clause\nqs(cons(X258, X259), X260) :- ','(split(X259, X258, X261, X262), ','(qs(X261, X263), ','(qs(X262, X264), append(X263, cons(X258, X264), X260)))).\nand substitution\nX258 -> T162\nX259 -> T163\nT90 -> cons(T162, T163)\nX13 -> X265\nX260 -> X265", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 206 [arrowhead = none ];
206 -> 87;

207 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 207 [arrowhead = none ];
207 -> 88;

208 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
84 -> 208 [arrowhead = none ];
208 -> 86;

209 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
87 -> 209 [arrowhead = none ];
209 -> 89;

210 [label="SPLIT 2\nnew knowledge:\nT166 is ground\nT167 is ground\nreplacements:\nX261 -> T166\nX262 -> T167", fontsize=14, style = filled, fillcolor = violet];
87 -> 210 [arrowhead = none ];
210 -> 90;

211 [label="INSTANCE with matching:\nT68 -> T163\nT69 -> T162\nX93 -> X261\nX94 -> X262", fontsize=14, style = filled, fillcolor = lightgrey];
89 -> 211 [arrowhead = none , style=dashed];
211 -> 46[style=dashed];

212 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
90 -> 212 [arrowhead = none ];
212 -> 91;

213 [label="SPLIT 2\nnew knowledge:\nT170 is ground\nreplacements:\nX263 -> T170", fontsize=14, style = filled, fillcolor = violet];
90 -> 213 [arrowhead = none ];
213 -> 92;

214 [label="INSTANCE with matching:\nT90 -> T166\nX13 -> X263", fontsize=14, style = filled, fillcolor = lightgrey];
91 -> 214 [arrowhead = none , style=dashed];
214 -> 79[style=dashed];

215 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
92 -> 215 [arrowhead = none ];
215 -> 93;

216 [label="SPLIT 2\nnew knowledge:\nT171 is ground\nreplacements:\nX264 -> T171", fontsize=14, style = filled, fillcolor = violet];
92 -> 216 [arrowhead = none ];
216 -> 94;

217 [label="INSTANCE with matching:\nT90 -> T167\nX13 -> X264", fontsize=14, style = filled, fillcolor = lightgrey];
93 -> 217 [arrowhead = none , style=dashed];
217 -> 79[style=dashed];

218 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
94 -> 218 [arrowhead = none ];
218 -> 95;

219 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
95 -> 219 [arrowhead = none ];
219 -> 96;

220 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
95 -> 220 [arrowhead = none ];
220 -> 97;

221 [label="EVAL with clause\nappend([], X279, X279).\nand substitution\nT170 -> []\nT162 -> T184\nT171 -> T185\nX279 -> cons(T184, T185)\nX265 -> cons(T184, T185)", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 221 [arrowhead = none ];
221 -> 98;

222 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 222 [arrowhead = none ];
222 -> 99;

223 [label="EVAL with clause\nappend(cons(X291, X292), X293, cons(X291, X294)) :- append(X292, X293, X294).\nand substitution\nX291 -> T194\nX292 -> T195\nT170 -> cons(T194, T195)\nT162 -> T196\nT171 -> T197\nX293 -> cons(T196, T197)\nX294 -> X295\nX265 -> cons(T194, X295)", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 223 [arrowhead = none ];
223 -> 101;

224 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 224 [arrowhead = none ];
224 -> 102;

225 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
98 -> 225 [arrowhead = none ];
225 -> 100;

226 [label="INSTANCE with matching:\nT170 -> T195\nT162 -> T196\nT171 -> T197\nX265 -> X295", fontsize=14, style = filled, fillcolor = lightgrey];
101 -> 226 [arrowhead = none , style=dashed];
226 -> 94[style=dashed];

227 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
103 -> 227 [arrowhead = none ];
227 -> 105;

228 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
103 -> 228 [arrowhead = none ];
228 -> 106;

229 [label="INSTANCE with matching:\nT125 -> T212\nT127 -> T214", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 229 [arrowhead = none , style=dashed];
229 -> 62[style=dashed];

230 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
106 -> 230 [arrowhead = none ];
230 -> 107;

231 [label="SPLIT 2\nnew knowledge:\nT221 is ground\nT222 is ground\nreplacements:\nX323 -> T221\nX324 -> T222", fontsize=14, style = filled, fillcolor = violet];
106 -> 231 [arrowhead = none ];
231 -> 108;

232 [label="INSTANCE with matching:\nT68 -> T213\nT69 -> T214\nX93 -> X323\nX94 -> X324", fontsize=14, style = filled, fillcolor = lightgrey];
107 -> 232 [arrowhead = none , style=dashed];
232 -> 46[style=dashed];

233 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
108 -> 233 [arrowhead = none ];
233 -> 109;

234 [label="SPLIT 2\nnew knowledge:\nT225 is ground\nreplacements:\nX12 -> T225", fontsize=14, style = filled, fillcolor = violet];
108 -> 234 [arrowhead = none ];
234 -> 110;

235 [label="INSTANCE with matching:\nT90 -> T221\nX13 -> X12", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 235 [arrowhead = none , style=dashed];
235 -> 79[style=dashed];

236 [label="INSTANCE with matching:\nT90 -> cons(T212, T222)\nT154 -> T225\nT69 -> T214", fontsize=14, style = filled, fillcolor = lightgrey];
110 -> 236 [arrowhead = none , style=dashed];
236 -> 78[style=dashed];

}

(2) Obligation:

Clauses:

qs14([]).
append23([], T33, T34, cons(T33, T34)).
append23(cons(T45, T46), T47, T48, cons(T45, T50)) :- append23(T46, T47, T48, T50).
less36(0, s(T78)).
less36(s(T83), s(T84)) :- less36(T83, T84).
split46([], T97, [], []).
split46(cons(T110, T111), T112, cons(T110, X163), X164) :- less36(T110, T112).
split46(cons(T110, T111), T112, cons(T110, X163), X164) :- ','(less36(T110, T112), split46(T111, T112, X163, X164)).
split46(cons(T125, T126), T127, X195, cons(T125, X196)) :- geq62(T125, T127).
split46(cons(T125, T126), T127, X195, cons(T125, X196)) :- ','(geq62(T125, T127), split46(T126, T127, X195, X196)).
geq62(T136, T136).
geq62(s(T141), 0).
geq62(s(T146), s(T147)) :- geq62(T146, T147).
qs79([], []).
qs79(cons(T162, T163), X265) :- split46(T163, T162, X261, X262).
qs79(cons(T162, T163), X265) :- ','(split46(T163, T162, T166, T167), qs79(T166, X263)).
qs79(cons(T162, T163), X265) :- ','(split46(T163, T162, T166, T167), ','(qs79(T166, T170), qs79(T167, X264))).
qs79(cons(T162, T163), X265) :- ','(split46(T163, T162, T166, T167), ','(qs79(T166, T170), ','(qs79(T167, T171), append94(T170, T162, T171, X265)))).
append94([], T184, T185, cons(T184, T185)).
append94(cons(T194, T195), T196, T197, cons(T194, X295)) :- append94(T195, T196, T197, X295).
p78(T90, X13, T154, T69, T9) :- qs79(T90, X13).
p78(T90, T157, T154, T69, T9) :- ','(qs79(T90, T157), append23(T154, T69, T157, T9)).
qs1([], []).
qs1(cons(T14, []), T9) :- qs14(X12).
qs1(cons(T14, []), T9) :- ','(qs14(T17), qs14(X13)).
qs1(cons(T14, []), T9) :- ','(qs14(T17), ','(qs14(T20), append23(T17, T14, T20, T9))).
qs1(cons(T69, cons(T67, T68)), T9) :- less36(T67, T69).
qs1(cons(T69, cons(T67, T68)), T9) :- ','(less36(T67, T69), split46(T68, T69, X93, X94)).
qs1(cons(T69, cons(T67, T68)), T9) :- ','(less36(T67, T69), ','(split46(T68, T69, T89, T90), qs1(cons(T67, T89), X12))).
qs1(cons(T69, cons(T67, T68)), T9) :- ','(less36(T67, T69), ','(split46(T68, T69, T89, T90), ','(qs1(cons(T67, T89), T154), p78(T90, X13, T154, T69, T9)))).
qs1(cons(T214, cons(T212, T213)), T9) :- geq62(T212, T214).
qs1(cons(T214, cons(T212, T213)), T9) :- ','(geq62(T212, T214), split46(T213, T214, X323, X324)).
qs1(cons(T214, cons(T212, T213)), T9) :- ','(geq62(T212, T214), ','(split46(T213, T214, T221, T222), qs79(T221, X12))).
qs1(cons(T214, cons(T212, T213)), T9) :- ','(geq62(T212, T214), ','(split46(T213, T214, T221, T222), ','(qs79(T221, T225), p78(cons(T212, T222), X13, T225, T214, T9)))).

Queries:

qs1(g,a).

(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:
qs1_in: (b,f) (f,f)
append23_in: (b,b,b,f) (b,f,b,f) (f,f,f,f) (f,b,f,f)
less36_in: (b,b) (f,f)
split46_in: (b,b,f,f) (f,f,f,f)
geq62_in: (b,b) (f,f)
qs79_in: (f,f)
append94_in: (f,f,f,f)
p78_in: (f,f,f,f,f) (f,f,f,b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)

(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:

QS1_IN_GA(cons(T14, []), T9) → U19_GA(T14, T9, qs14_in_a(X12))
QS1_IN_GA(cons(T14, []), T9) → QS14_IN_A(X12)
QS1_IN_GA(cons(T14, []), T9) → U20_GA(T14, T9, qs14_in_a(T17))
U20_GA(T14, T9, qs14_out_a(T17)) → U21_GA(T14, T9, qs14_in_a(X13))
U20_GA(T14, T9, qs14_out_a(T17)) → QS14_IN_A(X13)
U20_GA(T14, T9, qs14_out_a(T17)) → U22_GA(T14, T9, T17, qs14_in_a(T20))
U22_GA(T14, T9, T17, qs14_out_a(T20)) → U23_GA(T14, T9, append23_in_ggga(T17, T14, T20, T9))
U22_GA(T14, T9, T17, qs14_out_a(T20)) → APPEND23_IN_GGGA(T17, T14, T20, T9)
APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_GGGA(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GGGA(T46, T47, T48, T50)
QS1_IN_GA(cons(T69, cons(T67, T68)), T9) → U24_GA(T69, T67, T68, T9, less36_in_gg(T67, T69))
QS1_IN_GA(cons(T69, cons(T67, T68)), T9) → LESS36_IN_GG(T67, T69)
LESS36_IN_GG(s(T83), s(T84)) → U2_GG(T83, T84, less36_in_gg(T83, T84))
LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_GA(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → SPLIT46_IN_GGAA(T68, T69, X93, X94)
SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_GGAA(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → LESS36_IN_GG(T110, T112)
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_GGAA(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112, X163, X164)
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_GGAA(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → GEQ62_IN_GG(T125, T127)
GEQ62_IN_GG(s(T146), s(T147)) → U7_GG(T146, T147, geq62_in_gg(T146, T147))
GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_GGAA(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127, X195, X196)
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_GA(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_GA(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)
QS1_IN_AA(cons(T14, []), T9) → U19_AA(T14, T9, qs14_in_a(X12))
QS1_IN_AA(cons(T14, []), T9) → QS14_IN_A(X12)
QS1_IN_AA(cons(T14, []), T9) → U20_AA(T14, T9, qs14_in_a(T17))
U20_AA(T14, T9, qs14_out_a(T17)) → U21_AA(T14, T9, qs14_in_a(X13))
U20_AA(T14, T9, qs14_out_a(T17)) → QS14_IN_A(X13)
U20_AA(T14, T9, qs14_out_a(T17)) → U22_AA(T14, T9, T17, qs14_in_a(T20))
U22_AA(T14, T9, T17, qs14_out_a(T20)) → U23_AA(T14, T9, append23_in_gaga(T17, T14, T20, T9))
U22_AA(T14, T9, T17, qs14_out_a(T20)) → APPEND23_IN_GAGA(T17, T14, T20, T9)
APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_GAGA(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GAGA(T46, T47, T48, T50)
QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → U24_AA(T69, T67, T68, T9, less36_in_aa(T67, T69))
QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → LESS36_IN_AA(T67, T69)
LESS36_IN_AA(s(T83), s(T84)) → U2_AA(T83, T84, less36_in_aa(T83, T84))
LESS36_IN_AA(s(T83), s(T84)) → LESS36_IN_AA(T83, T84)
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → SPLIT46_IN_AAAA(T68, T69, X93, X94)
SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_AAAA(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → LESS36_IN_AA(T110, T112)
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_AAAA(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → SPLIT46_IN_AAAA(T111, T112, X163, X164)
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_AAAA(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → GEQ62_IN_AA(T125, T127)
GEQ62_IN_AA(s(T146), s(T147)) → U7_AA(T146, T147, geq62_in_aa(T146, T147))
GEQ62_IN_AA(s(T146), s(T147)) → GEQ62_IN_AA(T146, T147)
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_AAAA(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → SPLIT46_IN_AAAA(T126, T127, X195, X196)
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_AA(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)
QS1_IN_AA(cons(T214, cons(T212, T213)), T9) → U30_AA(T214, T212, T213, T9, geq62_in_aa(T212, T214))
QS1_IN_AA(cons(T214, cons(T212, T213)), T9) → GEQ62_IN_AA(T212, T214)
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_AA(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → SPLIT46_IN_AAAA(T213, T214, X323, X324)
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_AA(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_AA(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → QS79_IN_AA(T221, X12)
QS79_IN_AA(cons(T162, T163), X265) → U8_AA(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
QS79_IN_AA(cons(T162, T163), X265) → SPLIT46_IN_AAAA(T163, T162, X261, X262)
QS79_IN_AA(cons(T162, T163), X265) → U9_AA(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_AA(T162, T163, X265, qs79_in_aa(T166, X263))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → QS79_IN_AA(T166, X263)
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_AA(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_AA(T162, T163, X265, qs79_in_aa(T167, X264))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → QS79_IN_AA(T167, X264)
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_AA(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_AA(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_AA(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
U13_AA(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → APPEND94_IN_AAAA(T170, T162, T171, X265)
APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_AAAA(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → APPEND94_IN_AAAA(T195, T196, T197, X295)
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_AA(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_AA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_AA(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
U34_AA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → P78_IN_AAAAA(cons(T212, T222), X13, T225, T214, T9)
P78_IN_AAAAA(T90, X13, T154, T69, T9) → U16_AAAAA(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
P78_IN_AAAAA(T90, X13, T154, T69, T9) → QS79_IN_AA(T90, X13)
P78_IN_AAAAA(T90, T157, T154, T69, T9) → U17_AAAAA(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_AAAAA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_AAAAA(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
U17_AAAAA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → APPEND23_IN_AAAA(T154, T69, T157, T9)
APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_AAAA(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AAAA(T46, T47, T48, T50)
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_AA(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_AA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_AA(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U28_AA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → P78_IN_AAAAA(T90, X13, T154, T69, T9)
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_GA(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_GA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_GA(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
U28_GA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → P78_IN_AAAGA(T90, X13, T154, T69, T9)
P78_IN_AAAGA(T90, X13, T154, T69, T9) → U16_AAAGA(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
P78_IN_AAAGA(T90, X13, T154, T69, T9) → QS79_IN_AA(T90, X13)
P78_IN_AAAGA(T90, T157, T154, T69, T9) → U17_AAAGA(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_AAAGA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_AAAGA(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
U17_AAAGA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → APPEND23_IN_AGAA(T154, T69, T157, T9)
APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_AGAA(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AGAA(T46, T47, T48, T50)
QS1_IN_GA(cons(T214, cons(T212, T213)), T9) → U30_GA(T214, T212, T213, T9, geq62_in_gg(T212, T214))
QS1_IN_GA(cons(T214, cons(T212, T213)), T9) → GEQ62_IN_GG(T212, T214)
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_GA(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → SPLIT46_IN_GGAA(T213, T214, X323, X324)
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_GA(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_GA(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → QS79_IN_AA(T221, X12)
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_GA(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_GA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_GA(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U34_GA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → P78_IN_AAAGA(cons(T212, T222), X13, T225, T214, T9)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
QS1_IN_GA(x1, x2)  =  QS1_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x1, x3)
QS14_IN_A(x1)  =  QS14_IN_A
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x3)
U22_GA(x1, x2, x3, x4)  =  U22_GA(x1, x3, x4)
U23_GA(x1, x2, x3)  =  U23_GA(x1, x3)
APPEND23_IN_GGGA(x1, x2, x3, x4)  =  APPEND23_IN_GGGA(x1, x2, x3)
U1_GGGA(x1, x2, x3, x4, x5, x6)  =  U1_GGGA(x1, x2, x3, x4, x6)
U24_GA(x1, x2, x3, x4, x5)  =  U24_GA(x1, x2, x3, x5)
LESS36_IN_GG(x1, x2)  =  LESS36_IN_GG(x1, x2)
U2_GG(x1, x2, x3)  =  U2_GG(x1, x2, x3)
U25_GA(x1, x2, x3, x4, x5)  =  U25_GA(x1, x2, x3, x5)
SPLIT46_IN_GGAA(x1, x2, x3, x4)  =  SPLIT46_IN_GGAA(x1, x2)
U3_GGAA(x1, x2, x3, x4, x5, x6)  =  U3_GGAA(x1, x2, x3, x6)
U4_GGAA(x1, x2, x3, x4, x5, x6)  =  U4_GGAA(x1, x2, x3, x6)
U5_GGAA(x1, x2, x3, x4, x5, x6)  =  U5_GGAA(x1, x2, x3, x6)
GEQ62_IN_GG(x1, x2)  =  GEQ62_IN_GG(x1, x2)
U7_GG(x1, x2, x3)  =  U7_GG(x1, x2, x3)
U6_GGAA(x1, x2, x3, x4, x5, x6)  =  U6_GGAA(x1, x2, x3, x6)
U26_GA(x1, x2, x3, x4, x5)  =  U26_GA(x1, x2, x3, x5)
U27_GA(x1, x2, x3, x4, x5)  =  U27_GA(x1, x2, x3, x5)
QS1_IN_AA(x1, x2)  =  QS1_IN_AA
U19_AA(x1, x2, x3)  =  U19_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U22_AA(x1, x2, x3, x4)  =  U22_AA(x3, x4)
U23_AA(x1, x2, x3)  =  U23_AA(x3)
APPEND23_IN_GAGA(x1, x2, x3, x4)  =  APPEND23_IN_GAGA(x1, x3)
U1_GAGA(x1, x2, x3, x4, x5, x6)  =  U1_GAGA(x1, x2, x4, x6)
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
LESS36_IN_AA(x1, x2)  =  LESS36_IN_AA
U2_AA(x1, x2, x3)  =  U2_AA(x3)
U25_AA(x1, x2, x3, x4, x5)  =  U25_AA(x5)
SPLIT46_IN_AAAA(x1, x2, x3, x4)  =  SPLIT46_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5, x6)  =  U3_AAAA(x6)
U4_AAAA(x1, x2, x3, x4, x5, x6)  =  U4_AAAA(x6)
U5_AAAA(x1, x2, x3, x4, x5, x6)  =  U5_AAAA(x6)
GEQ62_IN_AA(x1, x2)  =  GEQ62_IN_AA
U7_AA(x1, x2, x3)  =  U7_AA(x3)
U6_AAAA(x1, x2, x3, x4, x5, x6)  =  U6_AAAA(x6)
U26_AA(x1, x2, x3, x4, x5)  =  U26_AA(x5)
U27_AA(x1, x2, x3, x4, x5)  =  U27_AA(x5)
U30_AA(x1, x2, x3, x4, x5)  =  U30_AA(x5)
U31_AA(x1, x2, x3, x4, x5)  =  U31_AA(x5)
U32_AA(x1, x2, x3, x4, x5)  =  U32_AA(x5)
U33_AA(x1, x2, x3, x4, x5)  =  U33_AA(x5)
QS79_IN_AA(x1, x2)  =  QS79_IN_AA
U8_AA(x1, x2, x3, x4)  =  U8_AA(x4)
U9_AA(x1, x2, x3, x4)  =  U9_AA(x4)
U10_AA(x1, x2, x3, x4)  =  U10_AA(x4)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)
U12_AA(x1, x2, x3, x4)  =  U12_AA(x4)
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U14_AA(x1, x2, x3, x4)  =  U14_AA(x4)
APPEND94_IN_AAAA(x1, x2, x3, x4)  =  APPEND94_IN_AAAA
U15_AAAA(x1, x2, x3, x4, x5, x6)  =  U15_AAAA(x6)
U34_AA(x1, x2, x3, x4, x5, x6)  =  U34_AA(x6)
U35_AA(x1, x2, x3, x4, x5)  =  U35_AA(x5)
P78_IN_AAAAA(x1, x2, x3, x4, x5)  =  P78_IN_AAAAA
U16_AAAAA(x1, x2, x3, x4, x5, x6)  =  U16_AAAAA(x6)
U17_AAAAA(x1, x2, x3, x4, x5, x6)  =  U17_AAAAA(x6)
U18_AAAAA(x1, x2, x3, x4, x5, x6)  =  U18_AAAAA(x6)
APPEND23_IN_AAAA(x1, x2, x3, x4)  =  APPEND23_IN_AAAA
U1_AAAA(x1, x2, x3, x4, x5, x6)  =  U1_AAAA(x6)
U28_AA(x1, x2, x3, x4, x5, x6)  =  U28_AA(x6)
U29_AA(x1, x2, x3, x4, x5)  =  U29_AA(x5)
U28_GA(x1, x2, x3, x4, x5, x6)  =  U28_GA(x1, x2, x3, x6)
U29_GA(x1, x2, x3, x4, x5)  =  U29_GA(x1, x2, x3, x5)
P78_IN_AAAGA(x1, x2, x3, x4, x5)  =  P78_IN_AAAGA(x4)
U16_AAAGA(x1, x2, x3, x4, x5, x6)  =  U16_AAAGA(x4, x6)
U17_AAAGA(x1, x2, x3, x4, x5, x6)  =  U17_AAAGA(x4, x6)
U18_AAAGA(x1, x2, x3, x4, x5, x6)  =  U18_AAAGA(x4, x6)
APPEND23_IN_AGAA(x1, x2, x3, x4)  =  APPEND23_IN_AGAA(x2)
U1_AGAA(x1, x2, x3, x4, x5, x6)  =  U1_AGAA(x3, x6)
U30_GA(x1, x2, x3, x4, x5)  =  U30_GA(x1, x2, x3, x5)
U31_GA(x1, x2, x3, x4, x5)  =  U31_GA(x1, x2, x3, x5)
U32_GA(x1, x2, x3, x4, x5)  =  U32_GA(x1, x2, x3, x5)
U33_GA(x1, x2, x3, x4, x5)  =  U33_GA(x1, x2, x3, x5)
U34_GA(x1, x2, x3, x4, x5, x6)  =  U34_GA(x1, x2, x3, x6)
U35_GA(x1, x2, x3, x4, x5)  =  U35_GA(x1, x2, x3, x5)

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

(6) Obligation:

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

QS1_IN_GA(cons(T14, []), T9) → U19_GA(T14, T9, qs14_in_a(X12))
QS1_IN_GA(cons(T14, []), T9) → QS14_IN_A(X12)
QS1_IN_GA(cons(T14, []), T9) → U20_GA(T14, T9, qs14_in_a(T17))
U20_GA(T14, T9, qs14_out_a(T17)) → U21_GA(T14, T9, qs14_in_a(X13))
U20_GA(T14, T9, qs14_out_a(T17)) → QS14_IN_A(X13)
U20_GA(T14, T9, qs14_out_a(T17)) → U22_GA(T14, T9, T17, qs14_in_a(T20))
U22_GA(T14, T9, T17, qs14_out_a(T20)) → U23_GA(T14, T9, append23_in_ggga(T17, T14, T20, T9))
U22_GA(T14, T9, T17, qs14_out_a(T20)) → APPEND23_IN_GGGA(T17, T14, T20, T9)
APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_GGGA(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GGGA(T46, T47, T48, T50)
QS1_IN_GA(cons(T69, cons(T67, T68)), T9) → U24_GA(T69, T67, T68, T9, less36_in_gg(T67, T69))
QS1_IN_GA(cons(T69, cons(T67, T68)), T9) → LESS36_IN_GG(T67, T69)
LESS36_IN_GG(s(T83), s(T84)) → U2_GG(T83, T84, less36_in_gg(T83, T84))
LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_GA(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → SPLIT46_IN_GGAA(T68, T69, X93, X94)
SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_GGAA(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → LESS36_IN_GG(T110, T112)
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_GGAA(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112, X163, X164)
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_GGAA(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → GEQ62_IN_GG(T125, T127)
GEQ62_IN_GG(s(T146), s(T147)) → U7_GG(T146, T147, geq62_in_gg(T146, T147))
GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_GGAA(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127, X195, X196)
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_GA(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_GA(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)
QS1_IN_AA(cons(T14, []), T9) → U19_AA(T14, T9, qs14_in_a(X12))
QS1_IN_AA(cons(T14, []), T9) → QS14_IN_A(X12)
QS1_IN_AA(cons(T14, []), T9) → U20_AA(T14, T9, qs14_in_a(T17))
U20_AA(T14, T9, qs14_out_a(T17)) → U21_AA(T14, T9, qs14_in_a(X13))
U20_AA(T14, T9, qs14_out_a(T17)) → QS14_IN_A(X13)
U20_AA(T14, T9, qs14_out_a(T17)) → U22_AA(T14, T9, T17, qs14_in_a(T20))
U22_AA(T14, T9, T17, qs14_out_a(T20)) → U23_AA(T14, T9, append23_in_gaga(T17, T14, T20, T9))
U22_AA(T14, T9, T17, qs14_out_a(T20)) → APPEND23_IN_GAGA(T17, T14, T20, T9)
APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_GAGA(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GAGA(T46, T47, T48, T50)
QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → U24_AA(T69, T67, T68, T9, less36_in_aa(T67, T69))
QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → LESS36_IN_AA(T67, T69)
LESS36_IN_AA(s(T83), s(T84)) → U2_AA(T83, T84, less36_in_aa(T83, T84))
LESS36_IN_AA(s(T83), s(T84)) → LESS36_IN_AA(T83, T84)
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → SPLIT46_IN_AAAA(T68, T69, X93, X94)
SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_AAAA(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → LESS36_IN_AA(T110, T112)
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_AAAA(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → SPLIT46_IN_AAAA(T111, T112, X163, X164)
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_AAAA(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → GEQ62_IN_AA(T125, T127)
GEQ62_IN_AA(s(T146), s(T147)) → U7_AA(T146, T147, geq62_in_aa(T146, T147))
GEQ62_IN_AA(s(T146), s(T147)) → GEQ62_IN_AA(T146, T147)
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_AAAA(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → SPLIT46_IN_AAAA(T126, T127, X195, X196)
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_AA(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)
QS1_IN_AA(cons(T214, cons(T212, T213)), T9) → U30_AA(T214, T212, T213, T9, geq62_in_aa(T212, T214))
QS1_IN_AA(cons(T214, cons(T212, T213)), T9) → GEQ62_IN_AA(T212, T214)
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_AA(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → SPLIT46_IN_AAAA(T213, T214, X323, X324)
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_AA(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_AA(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → QS79_IN_AA(T221, X12)
QS79_IN_AA(cons(T162, T163), X265) → U8_AA(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
QS79_IN_AA(cons(T162, T163), X265) → SPLIT46_IN_AAAA(T163, T162, X261, X262)
QS79_IN_AA(cons(T162, T163), X265) → U9_AA(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_AA(T162, T163, X265, qs79_in_aa(T166, X263))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → QS79_IN_AA(T166, X263)
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_AA(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_AA(T162, T163, X265, qs79_in_aa(T167, X264))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → QS79_IN_AA(T167, X264)
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_AA(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_AA(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_AA(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
U13_AA(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → APPEND94_IN_AAAA(T170, T162, T171, X265)
APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_AAAA(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → APPEND94_IN_AAAA(T195, T196, T197, X295)
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_AA(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_AA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_AA(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
U34_AA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → P78_IN_AAAAA(cons(T212, T222), X13, T225, T214, T9)
P78_IN_AAAAA(T90, X13, T154, T69, T9) → U16_AAAAA(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
P78_IN_AAAAA(T90, X13, T154, T69, T9) → QS79_IN_AA(T90, X13)
P78_IN_AAAAA(T90, T157, T154, T69, T9) → U17_AAAAA(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_AAAAA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_AAAAA(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
U17_AAAAA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → APPEND23_IN_AAAA(T154, T69, T157, T9)
APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_AAAA(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AAAA(T46, T47, T48, T50)
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_AA(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_AA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_AA(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U28_AA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → P78_IN_AAAAA(T90, X13, T154, T69, T9)
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_GA(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_GA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_GA(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
U28_GA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → P78_IN_AAAGA(T90, X13, T154, T69, T9)
P78_IN_AAAGA(T90, X13, T154, T69, T9) → U16_AAAGA(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
P78_IN_AAAGA(T90, X13, T154, T69, T9) → QS79_IN_AA(T90, X13)
P78_IN_AAAGA(T90, T157, T154, T69, T9) → U17_AAAGA(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_AAAGA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_AAAGA(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
U17_AAAGA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → APPEND23_IN_AGAA(T154, T69, T157, T9)
APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_AGAA(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AGAA(T46, T47, T48, T50)
QS1_IN_GA(cons(T214, cons(T212, T213)), T9) → U30_GA(T214, T212, T213, T9, geq62_in_gg(T212, T214))
QS1_IN_GA(cons(T214, cons(T212, T213)), T9) → GEQ62_IN_GG(T212, T214)
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_GA(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → SPLIT46_IN_GGAA(T213, T214, X323, X324)
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_GA(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_GA(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → QS79_IN_AA(T221, X12)
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_GA(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_GA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_GA(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U34_GA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → P78_IN_AAAGA(cons(T212, T222), X13, T225, T214, T9)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
QS1_IN_GA(x1, x2)  =  QS1_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x1, x3)
QS14_IN_A(x1)  =  QS14_IN_A
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x3)
U22_GA(x1, x2, x3, x4)  =  U22_GA(x1, x3, x4)
U23_GA(x1, x2, x3)  =  U23_GA(x1, x3)
APPEND23_IN_GGGA(x1, x2, x3, x4)  =  APPEND23_IN_GGGA(x1, x2, x3)
U1_GGGA(x1, x2, x3, x4, x5, x6)  =  U1_GGGA(x1, x2, x3, x4, x6)
U24_GA(x1, x2, x3, x4, x5)  =  U24_GA(x1, x2, x3, x5)
LESS36_IN_GG(x1, x2)  =  LESS36_IN_GG(x1, x2)
U2_GG(x1, x2, x3)  =  U2_GG(x1, x2, x3)
U25_GA(x1, x2, x3, x4, x5)  =  U25_GA(x1, x2, x3, x5)
SPLIT46_IN_GGAA(x1, x2, x3, x4)  =  SPLIT46_IN_GGAA(x1, x2)
U3_GGAA(x1, x2, x3, x4, x5, x6)  =  U3_GGAA(x1, x2, x3, x6)
U4_GGAA(x1, x2, x3, x4, x5, x6)  =  U4_GGAA(x1, x2, x3, x6)
U5_GGAA(x1, x2, x3, x4, x5, x6)  =  U5_GGAA(x1, x2, x3, x6)
GEQ62_IN_GG(x1, x2)  =  GEQ62_IN_GG(x1, x2)
U7_GG(x1, x2, x3)  =  U7_GG(x1, x2, x3)
U6_GGAA(x1, x2, x3, x4, x5, x6)  =  U6_GGAA(x1, x2, x3, x6)
U26_GA(x1, x2, x3, x4, x5)  =  U26_GA(x1, x2, x3, x5)
U27_GA(x1, x2, x3, x4, x5)  =  U27_GA(x1, x2, x3, x5)
QS1_IN_AA(x1, x2)  =  QS1_IN_AA
U19_AA(x1, x2, x3)  =  U19_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U22_AA(x1, x2, x3, x4)  =  U22_AA(x3, x4)
U23_AA(x1, x2, x3)  =  U23_AA(x3)
APPEND23_IN_GAGA(x1, x2, x3, x4)  =  APPEND23_IN_GAGA(x1, x3)
U1_GAGA(x1, x2, x3, x4, x5, x6)  =  U1_GAGA(x1, x2, x4, x6)
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
LESS36_IN_AA(x1, x2)  =  LESS36_IN_AA
U2_AA(x1, x2, x3)  =  U2_AA(x3)
U25_AA(x1, x2, x3, x4, x5)  =  U25_AA(x5)
SPLIT46_IN_AAAA(x1, x2, x3, x4)  =  SPLIT46_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5, x6)  =  U3_AAAA(x6)
U4_AAAA(x1, x2, x3, x4, x5, x6)  =  U4_AAAA(x6)
U5_AAAA(x1, x2, x3, x4, x5, x6)  =  U5_AAAA(x6)
GEQ62_IN_AA(x1, x2)  =  GEQ62_IN_AA
U7_AA(x1, x2, x3)  =  U7_AA(x3)
U6_AAAA(x1, x2, x3, x4, x5, x6)  =  U6_AAAA(x6)
U26_AA(x1, x2, x3, x4, x5)  =  U26_AA(x5)
U27_AA(x1, x2, x3, x4, x5)  =  U27_AA(x5)
U30_AA(x1, x2, x3, x4, x5)  =  U30_AA(x5)
U31_AA(x1, x2, x3, x4, x5)  =  U31_AA(x5)
U32_AA(x1, x2, x3, x4, x5)  =  U32_AA(x5)
U33_AA(x1, x2, x3, x4, x5)  =  U33_AA(x5)
QS79_IN_AA(x1, x2)  =  QS79_IN_AA
U8_AA(x1, x2, x3, x4)  =  U8_AA(x4)
U9_AA(x1, x2, x3, x4)  =  U9_AA(x4)
U10_AA(x1, x2, x3, x4)  =  U10_AA(x4)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)
U12_AA(x1, x2, x3, x4)  =  U12_AA(x4)
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U14_AA(x1, x2, x3, x4)  =  U14_AA(x4)
APPEND94_IN_AAAA(x1, x2, x3, x4)  =  APPEND94_IN_AAAA
U15_AAAA(x1, x2, x3, x4, x5, x6)  =  U15_AAAA(x6)
U34_AA(x1, x2, x3, x4, x5, x6)  =  U34_AA(x6)
U35_AA(x1, x2, x3, x4, x5)  =  U35_AA(x5)
P78_IN_AAAAA(x1, x2, x3, x4, x5)  =  P78_IN_AAAAA
U16_AAAAA(x1, x2, x3, x4, x5, x6)  =  U16_AAAAA(x6)
U17_AAAAA(x1, x2, x3, x4, x5, x6)  =  U17_AAAAA(x6)
U18_AAAAA(x1, x2, x3, x4, x5, x6)  =  U18_AAAAA(x6)
APPEND23_IN_AAAA(x1, x2, x3, x4)  =  APPEND23_IN_AAAA
U1_AAAA(x1, x2, x3, x4, x5, x6)  =  U1_AAAA(x6)
U28_AA(x1, x2, x3, x4, x5, x6)  =  U28_AA(x6)
U29_AA(x1, x2, x3, x4, x5)  =  U29_AA(x5)
U28_GA(x1, x2, x3, x4, x5, x6)  =  U28_GA(x1, x2, x3, x6)
U29_GA(x1, x2, x3, x4, x5)  =  U29_GA(x1, x2, x3, x5)
P78_IN_AAAGA(x1, x2, x3, x4, x5)  =  P78_IN_AAAGA(x4)
U16_AAAGA(x1, x2, x3, x4, x5, x6)  =  U16_AAAGA(x4, x6)
U17_AAAGA(x1, x2, x3, x4, x5, x6)  =  U17_AAAGA(x4, x6)
U18_AAAGA(x1, x2, x3, x4, x5, x6)  =  U18_AAAGA(x4, x6)
APPEND23_IN_AGAA(x1, x2, x3, x4)  =  APPEND23_IN_AGAA(x2)
U1_AGAA(x1, x2, x3, x4, x5, x6)  =  U1_AGAA(x3, x6)
U30_GA(x1, x2, x3, x4, x5)  =  U30_GA(x1, x2, x3, x5)
U31_GA(x1, x2, x3, x4, x5)  =  U31_GA(x1, x2, x3, x5)
U32_GA(x1, x2, x3, x4, x5)  =  U32_GA(x1, x2, x3, x5)
U33_GA(x1, x2, x3, x4, x5)  =  U33_GA(x1, x2, x3, x5)
U34_GA(x1, x2, x3, x4, x5, x6)  =  U34_GA(x1, x2, x3, x6)
U35_GA(x1, x2, x3, x4, x5)  =  U35_GA(x1, x2, x3, x5)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 13 SCCs with 87 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AGAA(T46, T47, T48, T50)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
APPEND23_IN_AGAA(x1, x2, x3, x4)  =  APPEND23_IN_AGAA(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:

APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AGAA(T46, T47, T48, T50)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND23_IN_AGAA(x1, x2, x3, x4)  =  APPEND23_IN_AGAA(x2)

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

(12) PiDPToQDPProof (SOUND 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:

APPEND23_IN_AGAA(T47) → APPEND23_IN_AGAA(T47)

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

(14) 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 = APPEND23_IN_AGAA(T47) evaluates to t =APPEND23_IN_AGAA(T47)

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 APPEND23_IN_AGAA(T47) to APPEND23_IN_AGAA(T47).

(15) NO

(16) Obligation:

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

APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AAAA(T46, T47, T48, T50)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
APPEND23_IN_AAAA(x1, x2, x3, x4)  =  APPEND23_IN_AAAA

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:

APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AAAA(T46, T47, T48, T50)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND23_IN_AAAA(x1, x2, x3, x4)  =  APPEND23_IN_AAAA

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:

APPEND23_IN_AAAA → APPEND23_IN_AAAA

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

(21) 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 = APPEND23_IN_AAAA evaluates to t =APPEND23_IN_AAAA

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 APPEND23_IN_AAAA to APPEND23_IN_AAAA.

(22) NO

(23) Obligation:

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

APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → APPEND94_IN_AAAA(T195, T196, T197, X295)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
APPEND94_IN_AAAA(x1, x2, x3, x4)  =  APPEND94_IN_AAAA

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:

APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → APPEND94_IN_AAAA(T195, T196, T197, X295)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND94_IN_AAAA(x1, x2, x3, x4)  =  APPEND94_IN_AAAA

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:

APPEND94_IN_AAAA → APPEND94_IN_AAAA

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

(28) 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 = APPEND94_IN_AAAA evaluates to t =APPEND94_IN_AAAA

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 APPEND94_IN_AAAA to APPEND94_IN_AAAA.

(29) NO

(30) Obligation:

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

GEQ62_IN_AA(s(T146), s(T147)) → GEQ62_IN_AA(T146, T147)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
GEQ62_IN_AA(x1, x2)  =  GEQ62_IN_AA

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:

GEQ62_IN_AA(s(T146), s(T147)) → GEQ62_IN_AA(T146, T147)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
GEQ62_IN_AA(x1, x2)  =  GEQ62_IN_AA

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:

GEQ62_IN_AA → GEQ62_IN_AA

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

(35) 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 = GEQ62_IN_AA evaluates to t =GEQ62_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 GEQ62_IN_AA to GEQ62_IN_AA.

(36) NO

(37) Obligation:

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

LESS36_IN_AA(s(T83), s(T84)) → LESS36_IN_AA(T83, T84)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
LESS36_IN_AA(x1, x2)  =  LESS36_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:

LESS36_IN_AA(s(T83), s(T84)) → LESS36_IN_AA(T83, T84)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LESS36_IN_AA(x1, x2)  =  LESS36_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:

LESS36_IN_AA → LESS36_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 = LESS36_IN_AA evaluates to t =LESS36_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 LESS36_IN_AA to LESS36_IN_AA.

(43) NO

(44) Obligation:

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

SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_AAAA(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → SPLIT46_IN_AAAA(T111, T112, X163, X164)
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_AAAA(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → SPLIT46_IN_AAAA(T126, T127, X195, X196)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
SPLIT46_IN_AAAA(x1, x2, x3, x4)  =  SPLIT46_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5, x6)  =  U3_AAAA(x6)
U5_AAAA(x1, x2, x3, x4, x5, x6)  =  U5_AAAA(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:

SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_AAAA(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → SPLIT46_IN_AAAA(T111, T112, X163, X164)
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_AAAA(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → SPLIT46_IN_AAAA(T126, T127, X195, X196)

The TRS R consists of the following rules:

less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))

The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
SPLIT46_IN_AAAA(x1, x2, x3, x4)  =  SPLIT46_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5, x6)  =  U3_AAAA(x6)
U5_AAAA(x1, x2, x3, x4, x5, x6)  =  U5_AAAA(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:

SPLIT46_IN_AAAA → U3_AAAA(less36_in_aa)
U3_AAAA(less36_out_aa(T110)) → SPLIT46_IN_AAAA
SPLIT46_IN_AAAA → U5_AAAA(geq62_in_aa)
U5_AAAA(geq62_out_aa) → SPLIT46_IN_AAAA

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
geq62_in_aa
U2_aa(x0)
U7_aa(x0)

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

(49) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule SPLIT46_IN_AAAA → U3_AAAA(less36_in_aa) at position [0] we obtained the following new rules [LPAR04]:

SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0))
SPLIT46_IN_AAAA → U3_AAAA(U2_aa(less36_in_aa))

(50) Obligation:

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

U3_AAAA(less36_out_aa(T110)) → SPLIT46_IN_AAAA
SPLIT46_IN_AAAA → U5_AAAA(geq62_in_aa)
U5_AAAA(geq62_out_aa) → SPLIT46_IN_AAAA
SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0))
SPLIT46_IN_AAAA → U3_AAAA(U2_aa(less36_in_aa))

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
geq62_in_aa
U2_aa(x0)
U7_aa(x0)

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

(51) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule SPLIT46_IN_AAAA → U5_AAAA(geq62_in_aa) at position [0] we obtained the following new rules [LPAR04]:

SPLIT46_IN_AAAA → U5_AAAA(geq62_out_aa)
SPLIT46_IN_AAAA → U5_AAAA(U7_aa(geq62_in_aa))

(52) Obligation:

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

U3_AAAA(less36_out_aa(T110)) → SPLIT46_IN_AAAA
U5_AAAA(geq62_out_aa) → SPLIT46_IN_AAAA
SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0))
SPLIT46_IN_AAAA → U3_AAAA(U2_aa(less36_in_aa))
SPLIT46_IN_AAAA → U5_AAAA(geq62_out_aa)
SPLIT46_IN_AAAA → U5_AAAA(U7_aa(geq62_in_aa))

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
geq62_in_aa
U2_aa(x0)
U7_aa(x0)

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

(53) 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 = SPLIT46_IN_AAAA evaluates to t =SPLIT46_IN_AAAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0))
with rule SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0)) at position [] and matcher [ ]

U3_AAAA(less36_out_aa(0)) → SPLIT46_IN_AAAA
with rule U3_AAAA(less36_out_aa(T110)) → SPLIT46_IN_AAAA

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.

(54) NO

(55) Obligation:

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

QS79_IN_AA(cons(T162, T163), X265) → U9_AA(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → QS79_IN_AA(T166, X263)
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_AA(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → QS79_IN_AA(T167, X264)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
QS79_IN_AA(x1, x2)  =  QS79_IN_AA
U9_AA(x1, x2, x3, x4)  =  U9_AA(x4)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)

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

(56) UsableRulesProof (EQUIVALENT transformation)

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

(57) Obligation:

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

QS79_IN_AA(cons(T162, T163), X265) → U9_AA(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → QS79_IN_AA(T166, X263)
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_AA(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → QS79_IN_AA(T167, X264)

The TRS R consists of the following rules:

split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))

The argument filtering Pi contains the following mapping:
[]  =  []
cons(x1, x2)  =  cons(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
QS79_IN_AA(x1, x2)  =  QS79_IN_AA
U9_AA(x1, x2, x3, x4)  =  U9_AA(x4)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)

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

(58) PiDPToQDPProof (SOUND transformation)

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

(59) Obligation:

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

QS79_IN_AA → U9_AA(split46_in_aaaa)
U9_AA(split46_out_aaaa) → QS79_IN_AA
U9_AA(split46_out_aaaa) → U11_AA(qs79_in_aa)
U11_AA(qs79_out_aa) → QS79_IN_AA

The TRS R consists of the following rules:

split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
qs79_in_aa → qs79_out_aa
qs79_in_aa → U8_aa(split46_in_aaaa)
qs79_in_aa → U9_aa(split46_in_aaaa)
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U8_aa(split46_out_aaaa) → qs79_out_aa
U9_aa(split46_out_aaaa) → U10_aa(qs79_in_aa)
U9_aa(split46_out_aaaa) → U11_aa(qs79_in_aa)
less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U10_aa(qs79_out_aa) → qs79_out_aa
U11_aa(qs79_out_aa) → U12_aa(qs79_in_aa)
U11_aa(qs79_out_aa) → U13_aa(qs79_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa
U12_aa(qs79_out_aa) → qs79_out_aa
U13_aa(qs79_out_aa) → U14_aa(append94_in_aaaa)
U14_aa(append94_out_aaaa) → qs79_out_aa
append94_in_aaaa → append94_out_aaaa
append94_in_aaaa → U15_aaaa(append94_in_aaaa)
U15_aaaa(append94_out_aaaa) → append94_out_aaaa

The set Q consists of the following terms:

split46_in_aaaa
qs79_in_aa
U3_aaaa(x0)
U5_aaaa(x0)
U8_aa(x0)
U9_aa(x0)
less36_in_aa
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U10_aa(x0)
U11_aa(x0)
U2_aa(x0)
U7_aa(x0)
U12_aa(x0)
U13_aa(x0)
U14_aa(x0)
append94_in_aaaa
U15_aaaa(x0)

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

(60) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule QS79_IN_AA → U9_AA(split46_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

QS79_IN_AA → U9_AA(split46_out_aaaa)
QS79_IN_AA → U9_AA(U3_aaaa(less36_in_aa))
QS79_IN_AA → U9_AA(U5_aaaa(geq62_in_aa))

(61) Obligation:

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

U9_AA(split46_out_aaaa) → QS79_IN_AA
U9_AA(split46_out_aaaa) → U11_AA(qs79_in_aa)
U11_AA(qs79_out_aa) → QS79_IN_AA
QS79_IN_AA → U9_AA(split46_out_aaaa)
QS79_IN_AA → U9_AA(U3_aaaa(less36_in_aa))
QS79_IN_AA → U9_AA(U5_aaaa(geq62_in_aa))

The TRS R consists of the following rules:

split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
qs79_in_aa → qs79_out_aa
qs79_in_aa → U8_aa(split46_in_aaaa)
qs79_in_aa → U9_aa(split46_in_aaaa)
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U8_aa(split46_out_aaaa) → qs79_out_aa
U9_aa(split46_out_aaaa) → U10_aa(qs79_in_aa)
U9_aa(split46_out_aaaa) → U11_aa(qs79_in_aa)
less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U10_aa(qs79_out_aa) → qs79_out_aa
U11_aa(qs79_out_aa) → U12_aa(qs79_in_aa)
U11_aa(qs79_out_aa) → U13_aa(qs79_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa
U12_aa(qs79_out_aa) → qs79_out_aa
U13_aa(qs79_out_aa) → U14_aa(append94_in_aaaa)
U14_aa(append94_out_aaaa) → qs79_out_aa
append94_in_aaaa → append94_out_aaaa
append94_in_aaaa → U15_aaaa(append94_in_aaaa)
U15_aaaa(append94_out_aaaa) → append94_out_aaaa

The set Q consists of the following terms:

split46_in_aaaa
qs79_in_aa
U3_aaaa(x0)
U5_aaaa(x0)
U8_aa(x0)
U9_aa(x0)
less36_in_aa
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U10_aa(x0)
U11_aa(x0)
U2_aa(x0)
U7_aa(x0)
U12_aa(x0)
U13_aa(x0)
U14_aa(x0)
append94_in_aaaa
U15_aaaa(x0)

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

(62) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U9_AA(split46_out_aaaa) → U11_AA(qs79_in_aa) at position [0] we obtained the following new rules [LPAR04]:

U9_AA(split46_out_aaaa) → U11_AA(qs79_out_aa)
U9_AA(split46_out_aaaa) → U11_AA(U8_aa(split46_in_aaaa))
U9_AA(split46_out_aaaa) → U11_AA(U9_aa(split46_in_aaaa))

(63) Obligation:

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

U9_AA(split46_out_aaaa) → QS79_IN_AA
U11_AA(qs79_out_aa) → QS79_IN_AA
QS79_IN_AA → U9_AA(split46_out_aaaa)
QS79_IN_AA → U9_AA(U3_aaaa(less36_in_aa))
QS79_IN_AA → U9_AA(U5_aaaa(geq62_in_aa))
U9_AA(split46_out_aaaa) → U11_AA(qs79_out_aa)
U9_AA(split46_out_aaaa) → U11_AA(U8_aa(split46_in_aaaa))
U9_AA(split46_out_aaaa) → U11_AA(U9_aa(split46_in_aaaa))

The TRS R consists of the following rules:

split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
qs79_in_aa → qs79_out_aa
qs79_in_aa → U8_aa(split46_in_aaaa)
qs79_in_aa → U9_aa(split46_in_aaaa)
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U8_aa(split46_out_aaaa) → qs79_out_aa
U9_aa(split46_out_aaaa) → U10_aa(qs79_in_aa)
U9_aa(split46_out_aaaa) → U11_aa(qs79_in_aa)
less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U10_aa(qs79_out_aa) → qs79_out_aa
U11_aa(qs79_out_aa) → U12_aa(qs79_in_aa)
U11_aa(qs79_out_aa) → U13_aa(qs79_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa
U12_aa(qs79_out_aa) → qs79_out_aa
U13_aa(qs79_out_aa) → U14_aa(append94_in_aaaa)
U14_aa(append94_out_aaaa) → qs79_out_aa
append94_in_aaaa → append94_out_aaaa
append94_in_aaaa → U15_aaaa(append94_in_aaaa)
U15_aaaa(append94_out_aaaa) → append94_out_aaaa

The set Q consists of the following terms:

split46_in_aaaa
qs79_in_aa
U3_aaaa(x0)
U5_aaaa(x0)
U8_aa(x0)
U9_aa(x0)
less36_in_aa
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U10_aa(x0)
U11_aa(x0)
U2_aa(x0)
U7_aa(x0)
U12_aa(x0)
U13_aa(x0)
U14_aa(x0)
append94_in_aaaa
U15_aaaa(x0)

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 narrowing to the left:

s = QS79_IN_AA evaluates to t =QS79_IN_AA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

QS79_IN_AA → U9_AA(split46_out_aaaa)
with rule QS79_IN_AA → U9_AA(split46_out_aaaa) at position [] and matcher [ ]

U9_AA(split46_out_aaaa) → QS79_IN_AA
with rule U9_AA(split46_out_aaaa) → QS79_IN_AA

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.

(65) NO

(66) Obligation:

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

APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GAGA(T46, T47, T48, T50)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
APPEND23_IN_GAGA(x1, x2, x3, x4)  =  APPEND23_IN_GAGA(x1, x3)

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:

APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GAGA(T46, T47, T48, T50)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND23_IN_GAGA(x1, x2, x3, x4)  =  APPEND23_IN_GAGA(x1, x3)

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:

APPEND23_IN_GAGA(cons(T45, T46), T48) → APPEND23_IN_GAGA(T46, T48)

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

(71) 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:

• APPEND23_IN_GAGA(cons(T45, T46), T48) → APPEND23_IN_GAGA(T46, T48)
  The graph contains the following edges 1 > 1, 2 >= 2

(72) YES

(73) Obligation:

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

QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → U24_AA(T69, T67, T68, T9, less36_in_aa(T67, T69))
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
QS1_IN_AA(x1, x2)  =  QS1_IN_AA
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
U26_AA(x1, x2, x3, x4, x5)  =  U26_AA(x5)

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

(74) UsableRulesProof (EQUIVALENT transformation)

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

(75) Obligation:

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

QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → U24_AA(T69, T67, T68, T9, less36_in_aa(T67, T69))
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)

The TRS R consists of the following rules:

less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))

The argument filtering Pi contains the following mapping:
[]  =  []
cons(x1, x2)  =  cons(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
QS1_IN_AA(x1, x2)  =  QS1_IN_AA
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
U26_AA(x1, x2, x3, x4, x5)  =  U26_AA(x5)

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

(76) PiDPToQDPProof (SOUND transformation)

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

(77) Obligation:

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

QS1_IN_AA → U24_AA(less36_in_aa)
U24_AA(less36_out_aa(T67)) → U26_AA(split46_in_aaaa)
U26_AA(split46_out_aaaa) → QS1_IN_AA

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
split46_in_aaaa
U2_aa(x0)
U3_aaaa(x0)
U5_aaaa(x0)
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U7_aa(x0)

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

(78) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule QS1_IN_AA → U24_AA(less36_in_aa) at position [0] we obtained the following new rules [LPAR04]:

QS1_IN_AA → U24_AA(less36_out_aa(0))
QS1_IN_AA → U24_AA(U2_aa(less36_in_aa))

(79) Obligation:

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

U24_AA(less36_out_aa(T67)) → U26_AA(split46_in_aaaa)
U26_AA(split46_out_aaaa) → QS1_IN_AA
QS1_IN_AA → U24_AA(less36_out_aa(0))
QS1_IN_AA → U24_AA(U2_aa(less36_in_aa))

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
split46_in_aaaa
U2_aa(x0)
U3_aaaa(x0)
U5_aaaa(x0)
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U7_aa(x0)

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

(80) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U24_AA(less36_out_aa(T67)) → U26_AA(split46_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

U24_AA(less36_out_aa(y0)) → U26_AA(split46_out_aaaa)
U24_AA(less36_out_aa(y0)) → U26_AA(U3_aaaa(less36_in_aa))
U24_AA(less36_out_aa(y0)) → U26_AA(U5_aaaa(geq62_in_aa))

(81) Obligation:

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

U26_AA(split46_out_aaaa) → QS1_IN_AA
QS1_IN_AA → U24_AA(less36_out_aa(0))
QS1_IN_AA → U24_AA(U2_aa(less36_in_aa))
U24_AA(less36_out_aa(y0)) → U26_AA(split46_out_aaaa)
U24_AA(less36_out_aa(y0)) → U26_AA(U3_aaaa(less36_in_aa))
U24_AA(less36_out_aa(y0)) → U26_AA(U5_aaaa(geq62_in_aa))

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
split46_in_aaaa
U2_aa(x0)
U3_aaaa(x0)
U5_aaaa(x0)
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U7_aa(x0)

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

(82) 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 = QS1_IN_AA evaluates to t =QS1_IN_AA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

QS1_IN_AA → U24_AA(less36_out_aa(0))
with rule QS1_IN_AA → U24_AA(less36_out_aa(0)) at position [] and matcher [ ]

U24_AA(less36_out_aa(0)) → U26_AA(split46_out_aaaa)
with rule U24_AA(less36_out_aa(y0)) → U26_AA(split46_out_aaaa) at position [] and matcher [y0 / 0]

U26_AA(split46_out_aaaa) → QS1_IN_AA
with rule U26_AA(split46_out_aaaa) → QS1_IN_AA

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.

(83) NO

(84) Obligation:

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

GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
GEQ62_IN_GG(x1, x2)  =  GEQ62_IN_GG(x1, x2)

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

(85) UsableRulesProof (EQUIVALENT transformation)

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

(86) Obligation:

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

GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)

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

(87) PiDPToQDPProof (EQUIVALENT transformation)

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

(88) Obligation:

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

GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)

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

(89) 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:

• GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)
  The graph contains the following edges 1 > 1, 2 > 2

(90) YES

(91) Obligation:

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

LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
LESS36_IN_GG(x1, x2)  =  LESS36_IN_GG(x1, x2)

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

(92) UsableRulesProof (EQUIVALENT transformation)

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

(93) Obligation:

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

LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)

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

(94) PiDPToQDPProof (EQUIVALENT transformation)

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

(95) Obligation:

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

LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)

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

(96) 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:

• LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)
  The graph contains the following edges 1 > 1, 2 > 2

(97) YES

(98) Obligation:

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

SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_GGAA(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112, X163, X164)
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_GGAA(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127, X195, X196)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
SPLIT46_IN_GGAA(x1, x2, x3, x4)  =  SPLIT46_IN_GGAA(x1, x2)
U3_GGAA(x1, x2, x3, x4, x5, x6)  =  U3_GGAA(x1, x2, x3, x6)
U5_GGAA(x1, x2, x3, x4, x5, x6)  =  U5_GGAA(x1, x2, x3, x6)

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

(99) UsableRulesProof (EQUIVALENT transformation)

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

(100) Obligation:

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

SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_GGAA(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112, X163, X164)
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_GGAA(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127, X195, X196)

The TRS R consists of the following rules:

less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))

The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
SPLIT46_IN_GGAA(x1, x2, x3, x4)  =  SPLIT46_IN_GGAA(x1, x2)
U3_GGAA(x1, x2, x3, x4, x5, x6)  =  U3_GGAA(x1, x2, x3, x6)
U5_GGAA(x1, x2, x3, x4, x5, x6)  =  U5_GGAA(x1, x2, x3, x6)

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

(101) PiDPToQDPProof (SOUND transformation)

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

(102) Obligation:

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

SPLIT46_IN_GGAA(cons(T110, T111), T112) → U3_GGAA(T110, T111, T112, less36_in_gg(T110, T112))
U3_GGAA(T110, T111, T112, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112)
SPLIT46_IN_GGAA(cons(T125, T126), T127) → U5_GGAA(T125, T126, T127, geq62_in_gg(T125, T127))
U5_GGAA(T125, T126, T127, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127)

The TRS R consists of the following rules:

less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))

The set Q consists of the following terms:

less36_in_gg(x0, x1)
geq62_in_gg(x0, x1)
U2_gg(x0, x1, x2)
U7_gg(x0, x1, x2)

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

(103) 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:

• U3_GGAA(T110, T111, T112, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112)
  The graph contains the following edges 2 >= 1, 3 >= 2, 4 > 2

• U5_GGAA(T125, T126, T127, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127)
  The graph contains the following edges 2 >= 1, 3 >= 2, 4 > 2

• SPLIT46_IN_GGAA(cons(T110, T111), T112) → U3_GGAA(T110, T111, T112, less36_in_gg(T110, T112))
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3

• SPLIT46_IN_GGAA(cons(T125, T126), T127) → U5_GGAA(T125, T126, T127, geq62_in_gg(T125, T127))
  The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3

(104) YES

(105) Obligation:

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

APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GGGA(T46, T47, T48, T50)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga(x1)
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x1, x2, x3, x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x2, x3, x4, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg(x1, x2)
U2_gg(x1, x2, x3)  =  U2_gg(x1, x2, x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x1, x2, x3, x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa(x1, x2)
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x1, x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x1, x2, x3, x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x1, x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg(x1, x2)
U7_gg(x1, x2, x3)  =  U7_gg(x1, x2, x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x1, x2, x3, x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x2, x3, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x1, x2, x3, x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga(x1, x3)
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x1, x2, x4, x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x2, x3, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x1, x2, x3, x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x4, x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga(x4)
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x4, x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa(x2)
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x3, x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x3, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x3, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x3, x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x2, x3, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x3, x5)
APPEND23_IN_GGGA(x1, x2, x3, x4)  =  APPEND23_IN_GGGA(x1, x2, x3)

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

(106) UsableRulesProof (EQUIVALENT transformation)

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

(107) Obligation:

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

APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GGGA(T46, T47, T48, T50)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND23_IN_GGGA(x1, x2, x3, x4)  =  APPEND23_IN_GGGA(x1, x2, x3)

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

(108) PiDPToQDPProof (SOUND transformation)

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

(109) Obligation:

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

APPEND23_IN_GGGA(cons(T45, T46), T47, T48) → APPEND23_IN_GGGA(T46, T47, T48)

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

(110) 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:

• APPEND23_IN_GGGA(cons(T45, T46), T47, T48) → APPEND23_IN_GGGA(T46, T47, T48)
  The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3

(111) YES

(112) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
qs1_in: (b,f) (f,f)
append23_in: (b,b,b,f) (b,f,b,f) (f,f,f,f) (f,b,f,f)
less36_in: (b,b) (f,f)
split46_in: (b,b,f,f) (f,f,f,f)
geq62_in: (b,b) (f,f)
qs79_in: (f,f)
append94_in: (f,f,f,f)
p78_in: (f,f,f,f,f) (f,f,f,b,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(113) Obligation:

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

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)

(114) 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:

QS1_IN_GA(cons(T14, []), T9) → U19_GA(T14, T9, qs14_in_a(X12))
QS1_IN_GA(cons(T14, []), T9) → QS14_IN_A(X12)
QS1_IN_GA(cons(T14, []), T9) → U20_GA(T14, T9, qs14_in_a(T17))
U20_GA(T14, T9, qs14_out_a(T17)) → U21_GA(T14, T9, qs14_in_a(X13))
U20_GA(T14, T9, qs14_out_a(T17)) → QS14_IN_A(X13)
U20_GA(T14, T9, qs14_out_a(T17)) → U22_GA(T14, T9, T17, qs14_in_a(T20))
U22_GA(T14, T9, T17, qs14_out_a(T20)) → U23_GA(T14, T9, append23_in_ggga(T17, T14, T20, T9))
U22_GA(T14, T9, T17, qs14_out_a(T20)) → APPEND23_IN_GGGA(T17, T14, T20, T9)
APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_GGGA(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GGGA(T46, T47, T48, T50)
QS1_IN_GA(cons(T69, cons(T67, T68)), T9) → U24_GA(T69, T67, T68, T9, less36_in_gg(T67, T69))
QS1_IN_GA(cons(T69, cons(T67, T68)), T9) → LESS36_IN_GG(T67, T69)
LESS36_IN_GG(s(T83), s(T84)) → U2_GG(T83, T84, less36_in_gg(T83, T84))
LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_GA(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → SPLIT46_IN_GGAA(T68, T69, X93, X94)
SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_GGAA(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → LESS36_IN_GG(T110, T112)
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_GGAA(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112, X163, X164)
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_GGAA(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → GEQ62_IN_GG(T125, T127)
GEQ62_IN_GG(s(T146), s(T147)) → U7_GG(T146, T147, geq62_in_gg(T146, T147))
GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_GGAA(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127, X195, X196)
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_GA(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_GA(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)
QS1_IN_AA(cons(T14, []), T9) → U19_AA(T14, T9, qs14_in_a(X12))
QS1_IN_AA(cons(T14, []), T9) → QS14_IN_A(X12)
QS1_IN_AA(cons(T14, []), T9) → U20_AA(T14, T9, qs14_in_a(T17))
U20_AA(T14, T9, qs14_out_a(T17)) → U21_AA(T14, T9, qs14_in_a(X13))
U20_AA(T14, T9, qs14_out_a(T17)) → QS14_IN_A(X13)
U20_AA(T14, T9, qs14_out_a(T17)) → U22_AA(T14, T9, T17, qs14_in_a(T20))
U22_AA(T14, T9, T17, qs14_out_a(T20)) → U23_AA(T14, T9, append23_in_gaga(T17, T14, T20, T9))
U22_AA(T14, T9, T17, qs14_out_a(T20)) → APPEND23_IN_GAGA(T17, T14, T20, T9)
APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_GAGA(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GAGA(T46, T47, T48, T50)
QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → U24_AA(T69, T67, T68, T9, less36_in_aa(T67, T69))
QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → LESS36_IN_AA(T67, T69)
LESS36_IN_AA(s(T83), s(T84)) → U2_AA(T83, T84, less36_in_aa(T83, T84))
LESS36_IN_AA(s(T83), s(T84)) → LESS36_IN_AA(T83, T84)
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → SPLIT46_IN_AAAA(T68, T69, X93, X94)
SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_AAAA(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → LESS36_IN_AA(T110, T112)
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_AAAA(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → SPLIT46_IN_AAAA(T111, T112, X163, X164)
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_AAAA(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → GEQ62_IN_AA(T125, T127)
GEQ62_IN_AA(s(T146), s(T147)) → U7_AA(T146, T147, geq62_in_aa(T146, T147))
GEQ62_IN_AA(s(T146), s(T147)) → GEQ62_IN_AA(T146, T147)
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_AAAA(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → SPLIT46_IN_AAAA(T126, T127, X195, X196)
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_AA(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)
QS1_IN_AA(cons(T214, cons(T212, T213)), T9) → U30_AA(T214, T212, T213, T9, geq62_in_aa(T212, T214))
QS1_IN_AA(cons(T214, cons(T212, T213)), T9) → GEQ62_IN_AA(T212, T214)
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_AA(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → SPLIT46_IN_AAAA(T213, T214, X323, X324)
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_AA(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_AA(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → QS79_IN_AA(T221, X12)
QS79_IN_AA(cons(T162, T163), X265) → U8_AA(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
QS79_IN_AA(cons(T162, T163), X265) → SPLIT46_IN_AAAA(T163, T162, X261, X262)
QS79_IN_AA(cons(T162, T163), X265) → U9_AA(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_AA(T162, T163, X265, qs79_in_aa(T166, X263))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → QS79_IN_AA(T166, X263)
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_AA(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_AA(T162, T163, X265, qs79_in_aa(T167, X264))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → QS79_IN_AA(T167, X264)
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_AA(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_AA(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_AA(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
U13_AA(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → APPEND94_IN_AAAA(T170, T162, T171, X265)
APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_AAAA(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → APPEND94_IN_AAAA(T195, T196, T197, X295)
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_AA(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_AA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_AA(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
U34_AA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → P78_IN_AAAAA(cons(T212, T222), X13, T225, T214, T9)
P78_IN_AAAAA(T90, X13, T154, T69, T9) → U16_AAAAA(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
P78_IN_AAAAA(T90, X13, T154, T69, T9) → QS79_IN_AA(T90, X13)
P78_IN_AAAAA(T90, T157, T154, T69, T9) → U17_AAAAA(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_AAAAA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_AAAAA(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
U17_AAAAA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → APPEND23_IN_AAAA(T154, T69, T157, T9)
APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_AAAA(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AAAA(T46, T47, T48, T50)
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_AA(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_AA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_AA(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U28_AA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → P78_IN_AAAAA(T90, X13, T154, T69, T9)
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_GA(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_GA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_GA(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
U28_GA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → P78_IN_AAAGA(T90, X13, T154, T69, T9)
P78_IN_AAAGA(T90, X13, T154, T69, T9) → U16_AAAGA(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
P78_IN_AAAGA(T90, X13, T154, T69, T9) → QS79_IN_AA(T90, X13)
P78_IN_AAAGA(T90, T157, T154, T69, T9) → U17_AAAGA(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_AAAGA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_AAAGA(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
U17_AAAGA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → APPEND23_IN_AGAA(T154, T69, T157, T9)
APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_AGAA(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AGAA(T46, T47, T48, T50)
QS1_IN_GA(cons(T214, cons(T212, T213)), T9) → U30_GA(T214, T212, T213, T9, geq62_in_gg(T212, T214))
QS1_IN_GA(cons(T214, cons(T212, T213)), T9) → GEQ62_IN_GG(T212, T214)
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_GA(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → SPLIT46_IN_GGAA(T213, T214, X323, X324)
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_GA(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_GA(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → QS79_IN_AA(T221, X12)
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_GA(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_GA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_GA(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U34_GA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → P78_IN_AAAGA(cons(T212, T222), X13, T225, T214, T9)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
QS1_IN_GA(x1, x2)  =  QS1_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x3)
QS14_IN_A(x1)  =  QS14_IN_A
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x3)
U22_GA(x1, x2, x3, x4)  =  U22_GA(x1, x3, x4)
U23_GA(x1, x2, x3)  =  U23_GA(x3)
APPEND23_IN_GGGA(x1, x2, x3, x4)  =  APPEND23_IN_GGGA(x1, x2, x3)
U1_GGGA(x1, x2, x3, x4, x5, x6)  =  U1_GGGA(x1, x6)
U24_GA(x1, x2, x3, x4, x5)  =  U24_GA(x1, x3, x5)
LESS36_IN_GG(x1, x2)  =  LESS36_IN_GG(x1, x2)
U2_GG(x1, x2, x3)  =  U2_GG(x3)
U25_GA(x1, x2, x3, x4, x5)  =  U25_GA(x5)
SPLIT46_IN_GGAA(x1, x2, x3, x4)  =  SPLIT46_IN_GGAA(x1, x2)
U3_GGAA(x1, x2, x3, x4, x5, x6)  =  U3_GGAA(x2, x3, x6)
U4_GGAA(x1, x2, x3, x4, x5, x6)  =  U4_GGAA(x6)
U5_GGAA(x1, x2, x3, x4, x5, x6)  =  U5_GGAA(x2, x3, x6)
GEQ62_IN_GG(x1, x2)  =  GEQ62_IN_GG(x1, x2)
U7_GG(x1, x2, x3)  =  U7_GG(x3)
U6_GGAA(x1, x2, x3, x4, x5, x6)  =  U6_GGAA(x6)
U26_GA(x1, x2, x3, x4, x5)  =  U26_GA(x1, x5)
U27_GA(x1, x2, x3, x4, x5)  =  U27_GA(x5)
QS1_IN_AA(x1, x2)  =  QS1_IN_AA
U19_AA(x1, x2, x3)  =  U19_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U22_AA(x1, x2, x3, x4)  =  U22_AA(x3, x4)
U23_AA(x1, x2, x3)  =  U23_AA(x3)
APPEND23_IN_GAGA(x1, x2, x3, x4)  =  APPEND23_IN_GAGA(x1, x3)
U1_GAGA(x1, x2, x3, x4, x5, x6)  =  U1_GAGA(x6)
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
LESS36_IN_AA(x1, x2)  =  LESS36_IN_AA
U2_AA(x1, x2, x3)  =  U2_AA(x3)
U25_AA(x1, x2, x3, x4, x5)  =  U25_AA(x5)
SPLIT46_IN_AAAA(x1, x2, x3, x4)  =  SPLIT46_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5, x6)  =  U3_AAAA(x6)
U4_AAAA(x1, x2, x3, x4, x5, x6)  =  U4_AAAA(x6)
U5_AAAA(x1, x2, x3, x4, x5, x6)  =  U5_AAAA(x6)
GEQ62_IN_AA(x1, x2)  =  GEQ62_IN_AA
U7_AA(x1, x2, x3)  =  U7_AA(x3)
U6_AAAA(x1, x2, x3, x4, x5, x6)  =  U6_AAAA(x6)
U26_AA(x1, x2, x3, x4, x5)  =  U26_AA(x5)
U27_AA(x1, x2, x3, x4, x5)  =  U27_AA(x5)
U30_AA(x1, x2, x3, x4, x5)  =  U30_AA(x5)
U31_AA(x1, x2, x3, x4, x5)  =  U31_AA(x5)
U32_AA(x1, x2, x3, x4, x5)  =  U32_AA(x5)
U33_AA(x1, x2, x3, x4, x5)  =  U33_AA(x5)
QS79_IN_AA(x1, x2)  =  QS79_IN_AA
U8_AA(x1, x2, x3, x4)  =  U8_AA(x4)
U9_AA(x1, x2, x3, x4)  =  U9_AA(x4)
U10_AA(x1, x2, x3, x4)  =  U10_AA(x4)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)
U12_AA(x1, x2, x3, x4)  =  U12_AA(x4)
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U14_AA(x1, x2, x3, x4)  =  U14_AA(x4)
APPEND94_IN_AAAA(x1, x2, x3, x4)  =  APPEND94_IN_AAAA
U15_AAAA(x1, x2, x3, x4, x5, x6)  =  U15_AAAA(x6)
U34_AA(x1, x2, x3, x4, x5, x6)  =  U34_AA(x6)
U35_AA(x1, x2, x3, x4, x5)  =  U35_AA(x5)
P78_IN_AAAAA(x1, x2, x3, x4, x5)  =  P78_IN_AAAAA
U16_AAAAA(x1, x2, x3, x4, x5, x6)  =  U16_AAAAA(x6)
U17_AAAAA(x1, x2, x3, x4, x5, x6)  =  U17_AAAAA(x6)
U18_AAAAA(x1, x2, x3, x4, x5, x6)  =  U18_AAAAA(x6)
APPEND23_IN_AAAA(x1, x2, x3, x4)  =  APPEND23_IN_AAAA
U1_AAAA(x1, x2, x3, x4, x5, x6)  =  U1_AAAA(x6)
U28_AA(x1, x2, x3, x4, x5, x6)  =  U28_AA(x6)
U29_AA(x1, x2, x3, x4, x5)  =  U29_AA(x5)
U28_GA(x1, x2, x3, x4, x5, x6)  =  U28_GA(x1, x6)
U29_GA(x1, x2, x3, x4, x5)  =  U29_GA(x5)
P78_IN_AAAGA(x1, x2, x3, x4, x5)  =  P78_IN_AAAGA(x4)
U16_AAAGA(x1, x2, x3, x4, x5, x6)  =  U16_AAAGA(x6)
U17_AAAGA(x1, x2, x3, x4, x5, x6)  =  U17_AAAGA(x4, x6)
U18_AAAGA(x1, x2, x3, x4, x5, x6)  =  U18_AAAGA(x6)
APPEND23_IN_AGAA(x1, x2, x3, x4)  =  APPEND23_IN_AGAA(x2)
U1_AGAA(x1, x2, x3, x4, x5, x6)  =  U1_AGAA(x6)
U30_GA(x1, x2, x3, x4, x5)  =  U30_GA(x1, x3, x5)
U31_GA(x1, x2, x3, x4, x5)  =  U31_GA(x5)
U32_GA(x1, x2, x3, x4, x5)  =  U32_GA(x1, x5)
U33_GA(x1, x2, x3, x4, x5)  =  U33_GA(x5)
U34_GA(x1, x2, x3, x4, x5, x6)  =  U34_GA(x1, x6)
U35_GA(x1, x2, x3, x4, x5)  =  U35_GA(x5)

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

(115) Obligation:

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

QS1_IN_GA(cons(T14, []), T9) → U19_GA(T14, T9, qs14_in_a(X12))
QS1_IN_GA(cons(T14, []), T9) → QS14_IN_A(X12)
QS1_IN_GA(cons(T14, []), T9) → U20_GA(T14, T9, qs14_in_a(T17))
U20_GA(T14, T9, qs14_out_a(T17)) → U21_GA(T14, T9, qs14_in_a(X13))
U20_GA(T14, T9, qs14_out_a(T17)) → QS14_IN_A(X13)
U20_GA(T14, T9, qs14_out_a(T17)) → U22_GA(T14, T9, T17, qs14_in_a(T20))
U22_GA(T14, T9, T17, qs14_out_a(T20)) → U23_GA(T14, T9, append23_in_ggga(T17, T14, T20, T9))
U22_GA(T14, T9, T17, qs14_out_a(T20)) → APPEND23_IN_GGGA(T17, T14, T20, T9)
APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_GGGA(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GGGA(T46, T47, T48, T50)
QS1_IN_GA(cons(T69, cons(T67, T68)), T9) → U24_GA(T69, T67, T68, T9, less36_in_gg(T67, T69))
QS1_IN_GA(cons(T69, cons(T67, T68)), T9) → LESS36_IN_GG(T67, T69)
LESS36_IN_GG(s(T83), s(T84)) → U2_GG(T83, T84, less36_in_gg(T83, T84))
LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_GA(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → SPLIT46_IN_GGAA(T68, T69, X93, X94)
SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_GGAA(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → LESS36_IN_GG(T110, T112)
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_GGAA(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112, X163, X164)
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_GGAA(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → GEQ62_IN_GG(T125, T127)
GEQ62_IN_GG(s(T146), s(T147)) → U7_GG(T146, T147, geq62_in_gg(T146, T147))
GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_GGAA(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127, X195, X196)
U24_GA(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_GA(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_GA(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)
QS1_IN_AA(cons(T14, []), T9) → U19_AA(T14, T9, qs14_in_a(X12))
QS1_IN_AA(cons(T14, []), T9) → QS14_IN_A(X12)
QS1_IN_AA(cons(T14, []), T9) → U20_AA(T14, T9, qs14_in_a(T17))
U20_AA(T14, T9, qs14_out_a(T17)) → U21_AA(T14, T9, qs14_in_a(X13))
U20_AA(T14, T9, qs14_out_a(T17)) → QS14_IN_A(X13)
U20_AA(T14, T9, qs14_out_a(T17)) → U22_AA(T14, T9, T17, qs14_in_a(T20))
U22_AA(T14, T9, T17, qs14_out_a(T20)) → U23_AA(T14, T9, append23_in_gaga(T17, T14, T20, T9))
U22_AA(T14, T9, T17, qs14_out_a(T20)) → APPEND23_IN_GAGA(T17, T14, T20, T9)
APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_GAGA(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GAGA(T46, T47, T48, T50)
QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → U24_AA(T69, T67, T68, T9, less36_in_aa(T67, T69))
QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → LESS36_IN_AA(T67, T69)
LESS36_IN_AA(s(T83), s(T84)) → U2_AA(T83, T84, less36_in_aa(T83, T84))
LESS36_IN_AA(s(T83), s(T84)) → LESS36_IN_AA(T83, T84)
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → SPLIT46_IN_AAAA(T68, T69, X93, X94)
SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_AAAA(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → LESS36_IN_AA(T110, T112)
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_AAAA(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → SPLIT46_IN_AAAA(T111, T112, X163, X164)
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_AAAA(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → GEQ62_IN_AA(T125, T127)
GEQ62_IN_AA(s(T146), s(T147)) → U7_AA(T146, T147, geq62_in_aa(T146, T147))
GEQ62_IN_AA(s(T146), s(T147)) → GEQ62_IN_AA(T146, T147)
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_AAAA(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → SPLIT46_IN_AAAA(T126, T127, X195, X196)
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_AA(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)
QS1_IN_AA(cons(T214, cons(T212, T213)), T9) → U30_AA(T214, T212, T213, T9, geq62_in_aa(T212, T214))
QS1_IN_AA(cons(T214, cons(T212, T213)), T9) → GEQ62_IN_AA(T212, T214)
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_AA(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → SPLIT46_IN_AAAA(T213, T214, X323, X324)
U30_AA(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_AA(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_AA(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → QS79_IN_AA(T221, X12)
QS79_IN_AA(cons(T162, T163), X265) → U8_AA(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
QS79_IN_AA(cons(T162, T163), X265) → SPLIT46_IN_AAAA(T163, T162, X261, X262)
QS79_IN_AA(cons(T162, T163), X265) → U9_AA(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_AA(T162, T163, X265, qs79_in_aa(T166, X263))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → QS79_IN_AA(T166, X263)
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_AA(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_AA(T162, T163, X265, qs79_in_aa(T167, X264))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → QS79_IN_AA(T167, X264)
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_AA(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_AA(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_AA(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
U13_AA(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → APPEND94_IN_AAAA(T170, T162, T171, X265)
APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_AAAA(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → APPEND94_IN_AAAA(T195, T196, T197, X295)
U32_AA(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_AA(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_AA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_AA(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
U34_AA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → P78_IN_AAAAA(cons(T212, T222), X13, T225, T214, T9)
P78_IN_AAAAA(T90, X13, T154, T69, T9) → U16_AAAAA(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
P78_IN_AAAAA(T90, X13, T154, T69, T9) → QS79_IN_AA(T90, X13)
P78_IN_AAAAA(T90, T157, T154, T69, T9) → U17_AAAAA(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_AAAAA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_AAAAA(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
U17_AAAAA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → APPEND23_IN_AAAA(T154, T69, T157, T9)
APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_AAAA(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AAAA(T46, T47, T48, T50)
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_AA(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_AA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_AA(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U28_AA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → P78_IN_AAAAA(T90, X13, T154, T69, T9)
U26_GA(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_GA(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_GA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_GA(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
U28_GA(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → P78_IN_AAAGA(T90, X13, T154, T69, T9)
P78_IN_AAAGA(T90, X13, T154, T69, T9) → U16_AAAGA(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
P78_IN_AAAGA(T90, X13, T154, T69, T9) → QS79_IN_AA(T90, X13)
P78_IN_AAAGA(T90, T157, T154, T69, T9) → U17_AAAGA(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_AAAGA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_AAAGA(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
U17_AAAGA(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → APPEND23_IN_AGAA(T154, T69, T157, T9)
APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_AGAA(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AGAA(T46, T47, T48, T50)
QS1_IN_GA(cons(T214, cons(T212, T213)), T9) → U30_GA(T214, T212, T213, T9, geq62_in_gg(T212, T214))
QS1_IN_GA(cons(T214, cons(T212, T213)), T9) → GEQ62_IN_GG(T212, T214)
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_GA(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → SPLIT46_IN_GGAA(T213, T214, X323, X324)
U30_GA(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_GA(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_GA(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → QS79_IN_AA(T221, X12)
U32_GA(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_GA(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_GA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_GA(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U34_GA(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → P78_IN_AAAGA(cons(T212, T222), X13, T225, T214, T9)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
QS1_IN_GA(x1, x2)  =  QS1_IN_GA(x1)
U19_GA(x1, x2, x3)  =  U19_GA(x3)
QS14_IN_A(x1)  =  QS14_IN_A
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x3)
U22_GA(x1, x2, x3, x4)  =  U22_GA(x1, x3, x4)
U23_GA(x1, x2, x3)  =  U23_GA(x3)
APPEND23_IN_GGGA(x1, x2, x3, x4)  =  APPEND23_IN_GGGA(x1, x2, x3)
U1_GGGA(x1, x2, x3, x4, x5, x6)  =  U1_GGGA(x1, x6)
U24_GA(x1, x2, x3, x4, x5)  =  U24_GA(x1, x3, x5)
LESS36_IN_GG(x1, x2)  =  LESS36_IN_GG(x1, x2)
U2_GG(x1, x2, x3)  =  U2_GG(x3)
U25_GA(x1, x2, x3, x4, x5)  =  U25_GA(x5)
SPLIT46_IN_GGAA(x1, x2, x3, x4)  =  SPLIT46_IN_GGAA(x1, x2)
U3_GGAA(x1, x2, x3, x4, x5, x6)  =  U3_GGAA(x2, x3, x6)
U4_GGAA(x1, x2, x3, x4, x5, x6)  =  U4_GGAA(x6)
U5_GGAA(x1, x2, x3, x4, x5, x6)  =  U5_GGAA(x2, x3, x6)
GEQ62_IN_GG(x1, x2)  =  GEQ62_IN_GG(x1, x2)
U7_GG(x1, x2, x3)  =  U7_GG(x3)
U6_GGAA(x1, x2, x3, x4, x5, x6)  =  U6_GGAA(x6)
U26_GA(x1, x2, x3, x4, x5)  =  U26_GA(x1, x5)
U27_GA(x1, x2, x3, x4, x5)  =  U27_GA(x5)
QS1_IN_AA(x1, x2)  =  QS1_IN_AA
U19_AA(x1, x2, x3)  =  U19_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U22_AA(x1, x2, x3, x4)  =  U22_AA(x3, x4)
U23_AA(x1, x2, x3)  =  U23_AA(x3)
APPEND23_IN_GAGA(x1, x2, x3, x4)  =  APPEND23_IN_GAGA(x1, x3)
U1_GAGA(x1, x2, x3, x4, x5, x6)  =  U1_GAGA(x6)
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
LESS36_IN_AA(x1, x2)  =  LESS36_IN_AA
U2_AA(x1, x2, x3)  =  U2_AA(x3)
U25_AA(x1, x2, x3, x4, x5)  =  U25_AA(x5)
SPLIT46_IN_AAAA(x1, x2, x3, x4)  =  SPLIT46_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5, x6)  =  U3_AAAA(x6)
U4_AAAA(x1, x2, x3, x4, x5, x6)  =  U4_AAAA(x6)
U5_AAAA(x1, x2, x3, x4, x5, x6)  =  U5_AAAA(x6)
GEQ62_IN_AA(x1, x2)  =  GEQ62_IN_AA
U7_AA(x1, x2, x3)  =  U7_AA(x3)
U6_AAAA(x1, x2, x3, x4, x5, x6)  =  U6_AAAA(x6)
U26_AA(x1, x2, x3, x4, x5)  =  U26_AA(x5)
U27_AA(x1, x2, x3, x4, x5)  =  U27_AA(x5)
U30_AA(x1, x2, x3, x4, x5)  =  U30_AA(x5)
U31_AA(x1, x2, x3, x4, x5)  =  U31_AA(x5)
U32_AA(x1, x2, x3, x4, x5)  =  U32_AA(x5)
U33_AA(x1, x2, x3, x4, x5)  =  U33_AA(x5)
QS79_IN_AA(x1, x2)  =  QS79_IN_AA
U8_AA(x1, x2, x3, x4)  =  U8_AA(x4)
U9_AA(x1, x2, x3, x4)  =  U9_AA(x4)
U10_AA(x1, x2, x3, x4)  =  U10_AA(x4)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)
U12_AA(x1, x2, x3, x4)  =  U12_AA(x4)
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U14_AA(x1, x2, x3, x4)  =  U14_AA(x4)
APPEND94_IN_AAAA(x1, x2, x3, x4)  =  APPEND94_IN_AAAA
U15_AAAA(x1, x2, x3, x4, x5, x6)  =  U15_AAAA(x6)
U34_AA(x1, x2, x3, x4, x5, x6)  =  U34_AA(x6)
U35_AA(x1, x2, x3, x4, x5)  =  U35_AA(x5)
P78_IN_AAAAA(x1, x2, x3, x4, x5)  =  P78_IN_AAAAA
U16_AAAAA(x1, x2, x3, x4, x5, x6)  =  U16_AAAAA(x6)
U17_AAAAA(x1, x2, x3, x4, x5, x6)  =  U17_AAAAA(x6)
U18_AAAAA(x1, x2, x3, x4, x5, x6)  =  U18_AAAAA(x6)
APPEND23_IN_AAAA(x1, x2, x3, x4)  =  APPEND23_IN_AAAA
U1_AAAA(x1, x2, x3, x4, x5, x6)  =  U1_AAAA(x6)
U28_AA(x1, x2, x3, x4, x5, x6)  =  U28_AA(x6)
U29_AA(x1, x2, x3, x4, x5)  =  U29_AA(x5)
U28_GA(x1, x2, x3, x4, x5, x6)  =  U28_GA(x1, x6)
U29_GA(x1, x2, x3, x4, x5)  =  U29_GA(x5)
P78_IN_AAAGA(x1, x2, x3, x4, x5)  =  P78_IN_AAAGA(x4)
U16_AAAGA(x1, x2, x3, x4, x5, x6)  =  U16_AAAGA(x6)
U17_AAAGA(x1, x2, x3, x4, x5, x6)  =  U17_AAAGA(x4, x6)
U18_AAAGA(x1, x2, x3, x4, x5, x6)  =  U18_AAAGA(x6)
APPEND23_IN_AGAA(x1, x2, x3, x4)  =  APPEND23_IN_AGAA(x2)
U1_AGAA(x1, x2, x3, x4, x5, x6)  =  U1_AGAA(x6)
U30_GA(x1, x2, x3, x4, x5)  =  U30_GA(x1, x3, x5)
U31_GA(x1, x2, x3, x4, x5)  =  U31_GA(x5)
U32_GA(x1, x2, x3, x4, x5)  =  U32_GA(x1, x5)
U33_GA(x1, x2, x3, x4, x5)  =  U33_GA(x5)
U34_GA(x1, x2, x3, x4, x5, x6)  =  U34_GA(x1, x6)
U35_GA(x1, x2, x3, x4, x5)  =  U35_GA(x5)

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

(116) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 13 SCCs with 87 less nodes.

(117) Complex Obligation (AND)

(118) Obligation:

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

APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AGAA(T46, T47, T48, T50)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
APPEND23_IN_AGAA(x1, x2, x3, x4)  =  APPEND23_IN_AGAA(x2)

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

(119) UsableRulesProof (EQUIVALENT transformation)

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

(120) Obligation:

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

APPEND23_IN_AGAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AGAA(T46, T47, T48, T50)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND23_IN_AGAA(x1, x2, x3, x4)  =  APPEND23_IN_AGAA(x2)

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

(121) PiDPToQDPProof (SOUND transformation)

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

(122) Obligation:

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

APPEND23_IN_AGAA(T47) → APPEND23_IN_AGAA(T47)

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

(123) 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 = APPEND23_IN_AGAA(T47) evaluates to t =APPEND23_IN_AGAA(T47)

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 APPEND23_IN_AGAA(T47) to APPEND23_IN_AGAA(T47).

(124) NO

(125) Obligation:

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

APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AAAA(T46, T47, T48, T50)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
APPEND23_IN_AAAA(x1, x2, x3, x4)  =  APPEND23_IN_AAAA

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

(126) UsableRulesProof (EQUIVALENT transformation)

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

(127) Obligation:

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

APPEND23_IN_AAAA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_AAAA(T46, T47, T48, T50)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND23_IN_AAAA(x1, x2, x3, x4)  =  APPEND23_IN_AAAA

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

(128) PiDPToQDPProof (SOUND transformation)

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

(129) Obligation:

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

APPEND23_IN_AAAA → APPEND23_IN_AAAA

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

(130) 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 = APPEND23_IN_AAAA evaluates to t =APPEND23_IN_AAAA

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 APPEND23_IN_AAAA to APPEND23_IN_AAAA.

(131) NO

(132) Obligation:

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

APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → APPEND94_IN_AAAA(T195, T196, T197, X295)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
APPEND94_IN_AAAA(x1, x2, x3, x4)  =  APPEND94_IN_AAAA

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

(133) UsableRulesProof (EQUIVALENT transformation)

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

(134) Obligation:

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

APPEND94_IN_AAAA(cons(T194, T195), T196, T197, cons(T194, X295)) → APPEND94_IN_AAAA(T195, T196, T197, X295)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND94_IN_AAAA(x1, x2, x3, x4)  =  APPEND94_IN_AAAA

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

(135) PiDPToQDPProof (SOUND transformation)

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

(136) Obligation:

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

APPEND94_IN_AAAA → APPEND94_IN_AAAA

R is empty.
Q is empty.
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 semiunifying a rule from P directly.

s = APPEND94_IN_AAAA evaluates to t =APPEND94_IN_AAAA

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 APPEND94_IN_AAAA to APPEND94_IN_AAAA.

(138) NO

(139) Obligation:

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

GEQ62_IN_AA(s(T146), s(T147)) → GEQ62_IN_AA(T146, T147)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
GEQ62_IN_AA(x1, x2)  =  GEQ62_IN_AA

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:

GEQ62_IN_AA(s(T146), s(T147)) → GEQ62_IN_AA(T146, T147)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
GEQ62_IN_AA(x1, x2)  =  GEQ62_IN_AA

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:

GEQ62_IN_AA → GEQ62_IN_AA

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 = GEQ62_IN_AA evaluates to t =GEQ62_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 GEQ62_IN_AA to GEQ62_IN_AA.

(145) NO

(146) Obligation:

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

LESS36_IN_AA(s(T83), s(T84)) → LESS36_IN_AA(T83, T84)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
LESS36_IN_AA(x1, x2)  =  LESS36_IN_AA

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:

LESS36_IN_AA(s(T83), s(T84)) → LESS36_IN_AA(T83, T84)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
LESS36_IN_AA(x1, x2)  =  LESS36_IN_AA

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:

LESS36_IN_AA → LESS36_IN_AA

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

(151) 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 = LESS36_IN_AA evaluates to t =LESS36_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 LESS36_IN_AA to LESS36_IN_AA.

(152) NO

(153) Obligation:

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

SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_AAAA(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → SPLIT46_IN_AAAA(T111, T112, X163, X164)
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_AAAA(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → SPLIT46_IN_AAAA(T126, T127, X195, X196)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
SPLIT46_IN_AAAA(x1, x2, x3, x4)  =  SPLIT46_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5, x6)  =  U3_AAAA(x6)
U5_AAAA(x1, x2, x3, x4, x5, x6)  =  U5_AAAA(x6)

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

(154) UsableRulesProof (EQUIVALENT transformation)

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

(155) Obligation:

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

SPLIT46_IN_AAAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_AAAA(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_AAAA(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → SPLIT46_IN_AAAA(T111, T112, X163, X164)
SPLIT46_IN_AAAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_AAAA(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
U5_AAAA(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → SPLIT46_IN_AAAA(T126, T127, X195, X196)

The TRS R consists of the following rules:

less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))

The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
SPLIT46_IN_AAAA(x1, x2, x3, x4)  =  SPLIT46_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5, x6)  =  U3_AAAA(x6)
U5_AAAA(x1, x2, x3, x4, x5, x6)  =  U5_AAAA(x6)

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

(156) PiDPToQDPProof (SOUND transformation)

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

(157) Obligation:

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

SPLIT46_IN_AAAA → U3_AAAA(less36_in_aa)
U3_AAAA(less36_out_aa(T110)) → SPLIT46_IN_AAAA
SPLIT46_IN_AAAA → U5_AAAA(geq62_in_aa)
U5_AAAA(geq62_out_aa) → SPLIT46_IN_AAAA

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
geq62_in_aa
U2_aa(x0)
U7_aa(x0)

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

(158) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule SPLIT46_IN_AAAA → U3_AAAA(less36_in_aa) at position [0] we obtained the following new rules [LPAR04]:

SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0))
SPLIT46_IN_AAAA → U3_AAAA(U2_aa(less36_in_aa))

(159) Obligation:

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

U3_AAAA(less36_out_aa(T110)) → SPLIT46_IN_AAAA
SPLIT46_IN_AAAA → U5_AAAA(geq62_in_aa)
U5_AAAA(geq62_out_aa) → SPLIT46_IN_AAAA
SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0))
SPLIT46_IN_AAAA → U3_AAAA(U2_aa(less36_in_aa))

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
geq62_in_aa
U2_aa(x0)
U7_aa(x0)

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

(160) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule SPLIT46_IN_AAAA → U5_AAAA(geq62_in_aa) at position [0] we obtained the following new rules [LPAR04]:

SPLIT46_IN_AAAA → U5_AAAA(geq62_out_aa)
SPLIT46_IN_AAAA → U5_AAAA(U7_aa(geq62_in_aa))

(161) Obligation:

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

U3_AAAA(less36_out_aa(T110)) → SPLIT46_IN_AAAA
U5_AAAA(geq62_out_aa) → SPLIT46_IN_AAAA
SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0))
SPLIT46_IN_AAAA → U3_AAAA(U2_aa(less36_in_aa))
SPLIT46_IN_AAAA → U5_AAAA(geq62_out_aa)
SPLIT46_IN_AAAA → U5_AAAA(U7_aa(geq62_in_aa))

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
geq62_in_aa
U2_aa(x0)
U7_aa(x0)

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

(162) 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 = SPLIT46_IN_AAAA evaluates to t =SPLIT46_IN_AAAA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0))
with rule SPLIT46_IN_AAAA → U3_AAAA(less36_out_aa(0)) at position [] and matcher [ ]

U3_AAAA(less36_out_aa(0)) → SPLIT46_IN_AAAA
with rule U3_AAAA(less36_out_aa(T110)) → SPLIT46_IN_AAAA

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.

(163) NO

(164) Obligation:

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

QS79_IN_AA(cons(T162, T163), X265) → U9_AA(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → QS79_IN_AA(T166, X263)
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_AA(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → QS79_IN_AA(T167, X264)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
QS79_IN_AA(x1, x2)  =  QS79_IN_AA
U9_AA(x1, x2, x3, x4)  =  U9_AA(x4)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)

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

(165) UsableRulesProof (EQUIVALENT transformation)

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

(166) Obligation:

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

QS79_IN_AA(cons(T162, T163), X265) → U9_AA(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → QS79_IN_AA(T166, X263)
U9_AA(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_AA(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_AA(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → QS79_IN_AA(T167, X264)

The TRS R consists of the following rules:

split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))

The argument filtering Pi contains the following mapping:
[]  =  []
cons(x1, x2)  =  cons(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
QS79_IN_AA(x1, x2)  =  QS79_IN_AA
U9_AA(x1, x2, x3, x4)  =  U9_AA(x4)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)

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

(167) PiDPToQDPProof (SOUND transformation)

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

(168) Obligation:

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

QS79_IN_AA → U9_AA(split46_in_aaaa)
U9_AA(split46_out_aaaa) → QS79_IN_AA
U9_AA(split46_out_aaaa) → U11_AA(qs79_in_aa)
U11_AA(qs79_out_aa) → QS79_IN_AA

The TRS R consists of the following rules:

split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
qs79_in_aa → qs79_out_aa
qs79_in_aa → U8_aa(split46_in_aaaa)
qs79_in_aa → U9_aa(split46_in_aaaa)
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U8_aa(split46_out_aaaa) → qs79_out_aa
U9_aa(split46_out_aaaa) → U10_aa(qs79_in_aa)
U9_aa(split46_out_aaaa) → U11_aa(qs79_in_aa)
less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U10_aa(qs79_out_aa) → qs79_out_aa
U11_aa(qs79_out_aa) → U12_aa(qs79_in_aa)
U11_aa(qs79_out_aa) → U13_aa(qs79_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa
U12_aa(qs79_out_aa) → qs79_out_aa
U13_aa(qs79_out_aa) → U14_aa(append94_in_aaaa)
U14_aa(append94_out_aaaa) → qs79_out_aa
append94_in_aaaa → append94_out_aaaa
append94_in_aaaa → U15_aaaa(append94_in_aaaa)
U15_aaaa(append94_out_aaaa) → append94_out_aaaa

The set Q consists of the following terms:

split46_in_aaaa
qs79_in_aa
U3_aaaa(x0)
U5_aaaa(x0)
U8_aa(x0)
U9_aa(x0)
less36_in_aa
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U10_aa(x0)
U11_aa(x0)
U2_aa(x0)
U7_aa(x0)
U12_aa(x0)
U13_aa(x0)
U14_aa(x0)
append94_in_aaaa
U15_aaaa(x0)

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

(169) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule QS79_IN_AA → U9_AA(split46_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

QS79_IN_AA → U9_AA(split46_out_aaaa)
QS79_IN_AA → U9_AA(U3_aaaa(less36_in_aa))
QS79_IN_AA → U9_AA(U5_aaaa(geq62_in_aa))

(170) Obligation:

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

U9_AA(split46_out_aaaa) → QS79_IN_AA
U9_AA(split46_out_aaaa) → U11_AA(qs79_in_aa)
U11_AA(qs79_out_aa) → QS79_IN_AA
QS79_IN_AA → U9_AA(split46_out_aaaa)
QS79_IN_AA → U9_AA(U3_aaaa(less36_in_aa))
QS79_IN_AA → U9_AA(U5_aaaa(geq62_in_aa))

The TRS R consists of the following rules:

split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
qs79_in_aa → qs79_out_aa
qs79_in_aa → U8_aa(split46_in_aaaa)
qs79_in_aa → U9_aa(split46_in_aaaa)
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U8_aa(split46_out_aaaa) → qs79_out_aa
U9_aa(split46_out_aaaa) → U10_aa(qs79_in_aa)
U9_aa(split46_out_aaaa) → U11_aa(qs79_in_aa)
less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U10_aa(qs79_out_aa) → qs79_out_aa
U11_aa(qs79_out_aa) → U12_aa(qs79_in_aa)
U11_aa(qs79_out_aa) → U13_aa(qs79_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa
U12_aa(qs79_out_aa) → qs79_out_aa
U13_aa(qs79_out_aa) → U14_aa(append94_in_aaaa)
U14_aa(append94_out_aaaa) → qs79_out_aa
append94_in_aaaa → append94_out_aaaa
append94_in_aaaa → U15_aaaa(append94_in_aaaa)
U15_aaaa(append94_out_aaaa) → append94_out_aaaa

The set Q consists of the following terms:

split46_in_aaaa
qs79_in_aa
U3_aaaa(x0)
U5_aaaa(x0)
U8_aa(x0)
U9_aa(x0)
less36_in_aa
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U10_aa(x0)
U11_aa(x0)
U2_aa(x0)
U7_aa(x0)
U12_aa(x0)
U13_aa(x0)
U14_aa(x0)
append94_in_aaaa
U15_aaaa(x0)

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

(171) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U9_AA(split46_out_aaaa) → U11_AA(qs79_in_aa) at position [0] we obtained the following new rules [LPAR04]:

U9_AA(split46_out_aaaa) → U11_AA(qs79_out_aa)
U9_AA(split46_out_aaaa) → U11_AA(U8_aa(split46_in_aaaa))
U9_AA(split46_out_aaaa) → U11_AA(U9_aa(split46_in_aaaa))

(172) Obligation:

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

U9_AA(split46_out_aaaa) → QS79_IN_AA
U11_AA(qs79_out_aa) → QS79_IN_AA
QS79_IN_AA → U9_AA(split46_out_aaaa)
QS79_IN_AA → U9_AA(U3_aaaa(less36_in_aa))
QS79_IN_AA → U9_AA(U5_aaaa(geq62_in_aa))
U9_AA(split46_out_aaaa) → U11_AA(qs79_out_aa)
U9_AA(split46_out_aaaa) → U11_AA(U8_aa(split46_in_aaaa))
U9_AA(split46_out_aaaa) → U11_AA(U9_aa(split46_in_aaaa))

The TRS R consists of the following rules:

split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
qs79_in_aa → qs79_out_aa
qs79_in_aa → U8_aa(split46_in_aaaa)
qs79_in_aa → U9_aa(split46_in_aaaa)
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U8_aa(split46_out_aaaa) → qs79_out_aa
U9_aa(split46_out_aaaa) → U10_aa(qs79_in_aa)
U9_aa(split46_out_aaaa) → U11_aa(qs79_in_aa)
less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U10_aa(qs79_out_aa) → qs79_out_aa
U11_aa(qs79_out_aa) → U12_aa(qs79_in_aa)
U11_aa(qs79_out_aa) → U13_aa(qs79_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U7_aa(geq62_out_aa) → geq62_out_aa
U12_aa(qs79_out_aa) → qs79_out_aa
U13_aa(qs79_out_aa) → U14_aa(append94_in_aaaa)
U14_aa(append94_out_aaaa) → qs79_out_aa
append94_in_aaaa → append94_out_aaaa
append94_in_aaaa → U15_aaaa(append94_in_aaaa)
U15_aaaa(append94_out_aaaa) → append94_out_aaaa

The set Q consists of the following terms:

split46_in_aaaa
qs79_in_aa
U3_aaaa(x0)
U5_aaaa(x0)
U8_aa(x0)
U9_aa(x0)
less36_in_aa
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U10_aa(x0)
U11_aa(x0)
U2_aa(x0)
U7_aa(x0)
U12_aa(x0)
U13_aa(x0)
U14_aa(x0)
append94_in_aaaa
U15_aaaa(x0)

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

(173) 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 = QS79_IN_AA evaluates to t =QS79_IN_AA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

QS79_IN_AA → U9_AA(split46_out_aaaa)
with rule QS79_IN_AA → U9_AA(split46_out_aaaa) at position [] and matcher [ ]

U9_AA(split46_out_aaaa) → QS79_IN_AA
with rule U9_AA(split46_out_aaaa) → QS79_IN_AA

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.

(174) NO

(175) Obligation:

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

APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GAGA(T46, T47, T48, T50)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
APPEND23_IN_GAGA(x1, x2, x3, x4)  =  APPEND23_IN_GAGA(x1, x3)

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

(176) UsableRulesProof (EQUIVALENT transformation)

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

(177) Obligation:

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

APPEND23_IN_GAGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GAGA(T46, T47, T48, T50)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND23_IN_GAGA(x1, x2, x3, x4)  =  APPEND23_IN_GAGA(x1, x3)

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

(178) PiDPToQDPProof (SOUND transformation)

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

(179) Obligation:

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

APPEND23_IN_GAGA(cons(T45, T46), T48) → APPEND23_IN_GAGA(T46, T48)

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

(180) 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:

• APPEND23_IN_GAGA(cons(T45, T46), T48) → APPEND23_IN_GAGA(T46, T48)
  The graph contains the following edges 1 > 1, 2 >= 2

(181) YES

(182) Obligation:

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

QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → U24_AA(T69, T67, T68, T9, less36_in_aa(T67, T69))
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
QS1_IN_AA(x1, x2)  =  QS1_IN_AA
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
U26_AA(x1, x2, x3, x4, x5)  =  U26_AA(x5)

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

(183) UsableRulesProof (EQUIVALENT transformation)

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

(184) Obligation:

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

QS1_IN_AA(cons(T69, cons(T67, T68)), T9) → U24_AA(T69, T67, T68, T9, less36_in_aa(T67, T69))
U24_AA(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_AA(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_AA(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → QS1_IN_AA(cons(T67, T89), X12)

The TRS R consists of the following rules:

less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))

The argument filtering Pi contains the following mapping:
[]  =  []
cons(x1, x2)  =  cons(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
QS1_IN_AA(x1, x2)  =  QS1_IN_AA
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
U26_AA(x1, x2, x3, x4, x5)  =  U26_AA(x5)

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

(185) PiDPToQDPProof (SOUND transformation)

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

(186) Obligation:

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

QS1_IN_AA → U24_AA(less36_in_aa)
U24_AA(less36_out_aa(T67)) → U26_AA(split46_in_aaaa)
U26_AA(split46_out_aaaa) → QS1_IN_AA

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
split46_in_aaaa
U2_aa(x0)
U3_aaaa(x0)
U5_aaaa(x0)
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U7_aa(x0)

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

(187) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule QS1_IN_AA → U24_AA(less36_in_aa) at position [0] we obtained the following new rules [LPAR04]:

QS1_IN_AA → U24_AA(less36_out_aa(0))
QS1_IN_AA → U24_AA(U2_aa(less36_in_aa))

(188) Obligation:

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

U24_AA(less36_out_aa(T67)) → U26_AA(split46_in_aaaa)
U26_AA(split46_out_aaaa) → QS1_IN_AA
QS1_IN_AA → U24_AA(less36_out_aa(0))
QS1_IN_AA → U24_AA(U2_aa(less36_in_aa))

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
split46_in_aaaa
U2_aa(x0)
U3_aaaa(x0)
U5_aaaa(x0)
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U7_aa(x0)

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

(189) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule U24_AA(less36_out_aa(T67)) → U26_AA(split46_in_aaaa) at position [0] we obtained the following new rules [LPAR04]:

U24_AA(less36_out_aa(y0)) → U26_AA(split46_out_aaaa)
U24_AA(less36_out_aa(y0)) → U26_AA(U3_aaaa(less36_in_aa))
U24_AA(less36_out_aa(y0)) → U26_AA(U5_aaaa(geq62_in_aa))

(190) Obligation:

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

U26_AA(split46_out_aaaa) → QS1_IN_AA
QS1_IN_AA → U24_AA(less36_out_aa(0))
QS1_IN_AA → U24_AA(U2_aa(less36_in_aa))
U24_AA(less36_out_aa(y0)) → U26_AA(split46_out_aaaa)
U24_AA(less36_out_aa(y0)) → U26_AA(U3_aaaa(less36_in_aa))
U24_AA(less36_out_aa(y0)) → U26_AA(U5_aaaa(geq62_in_aa))

The TRS R consists of the following rules:

less36_in_aa → less36_out_aa(0)
less36_in_aa → U2_aa(less36_in_aa)
split46_in_aaaa → split46_out_aaaa
split46_in_aaaa → U3_aaaa(less36_in_aa)
split46_in_aaaa → U5_aaaa(geq62_in_aa)
U2_aa(less36_out_aa(T83)) → less36_out_aa(s(T83))
U3_aaaa(less36_out_aa(T110)) → split46_out_aaaa
U3_aaaa(less36_out_aa(T110)) → U4_aaaa(split46_in_aaaa)
U5_aaaa(geq62_out_aa) → split46_out_aaaa
U5_aaaa(geq62_out_aa) → U6_aaaa(split46_in_aaaa)
U4_aaaa(split46_out_aaaa) → split46_out_aaaa
geq62_in_aa → geq62_out_aa
geq62_in_aa → U7_aa(geq62_in_aa)
U6_aaaa(split46_out_aaaa) → split46_out_aaaa
U7_aa(geq62_out_aa) → geq62_out_aa

The set Q consists of the following terms:

less36_in_aa
split46_in_aaaa
U2_aa(x0)
U3_aaaa(x0)
U5_aaaa(x0)
U4_aaaa(x0)
geq62_in_aa
U6_aaaa(x0)
U7_aa(x0)

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

(191) 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 = QS1_IN_AA evaluates to t =QS1_IN_AA

Thus s starts an infinite chain as s semiunifies with t with the following substitutions:

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

QS1_IN_AA → U24_AA(less36_out_aa(0))
with rule QS1_IN_AA → U24_AA(less36_out_aa(0)) at position [] and matcher [ ]

U24_AA(less36_out_aa(0)) → U26_AA(split46_out_aaaa)
with rule U24_AA(less36_out_aa(y0)) → U26_AA(split46_out_aaaa) at position [] and matcher [y0 / 0]

U26_AA(split46_out_aaaa) → QS1_IN_AA
with rule U26_AA(split46_out_aaaa) → QS1_IN_AA

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.

(192) NO

(193) Obligation:

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

GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
GEQ62_IN_GG(x1, x2)  =  GEQ62_IN_GG(x1, x2)

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

(194) UsableRulesProof (EQUIVALENT transformation)

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

(195) Obligation:

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

GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)

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

(196) PiDPToQDPProof (EQUIVALENT transformation)

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

(197) Obligation:

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

GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)

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

(198) 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:

• GEQ62_IN_GG(s(T146), s(T147)) → GEQ62_IN_GG(T146, T147)
  The graph contains the following edges 1 > 1, 2 > 2

(199) YES

(200) Obligation:

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

LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
LESS36_IN_GG(x1, x2)  =  LESS36_IN_GG(x1, x2)

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

(201) UsableRulesProof (EQUIVALENT transformation)

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

(202) Obligation:

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

LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)

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

(203) PiDPToQDPProof (EQUIVALENT transformation)

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

(204) Obligation:

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

LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)

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

(205) 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:

• LESS36_IN_GG(s(T83), s(T84)) → LESS36_IN_GG(T83, T84)
  The graph contains the following edges 1 > 1, 2 > 2

(206) YES

(207) Obligation:

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

SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_GGAA(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112, X163, X164)
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_GGAA(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127, X195, X196)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
SPLIT46_IN_GGAA(x1, x2, x3, x4)  =  SPLIT46_IN_GGAA(x1, x2)
U3_GGAA(x1, x2, x3, x4, x5, x6)  =  U3_GGAA(x2, x3, x6)
U5_GGAA(x1, x2, x3, x4, x5, x6)  =  U5_GGAA(x2, x3, x6)

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

(208) UsableRulesProof (EQUIVALENT transformation)

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

(209) Obligation:

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

SPLIT46_IN_GGAA(cons(T110, T111), T112, cons(T110, X163), X164) → U3_GGAA(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_GGAA(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → SPLIT46_IN_GGAA(T111, T112, X163, X164)
SPLIT46_IN_GGAA(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_GGAA(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
U5_GGAA(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → SPLIT46_IN_GGAA(T126, T127, X195, X196)

The TRS R consists of the following rules:

less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))

The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
SPLIT46_IN_GGAA(x1, x2, x3, x4)  =  SPLIT46_IN_GGAA(x1, x2)
U3_GGAA(x1, x2, x3, x4, x5, x6)  =  U3_GGAA(x2, x3, x6)
U5_GGAA(x1, x2, x3, x4, x5, x6)  =  U5_GGAA(x2, x3, x6)

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

(210) PiDPToQDPProof (SOUND transformation)

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

(211) Obligation:

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

SPLIT46_IN_GGAA(cons(T110, T111), T112) → U3_GGAA(T111, T112, less36_in_gg(T110, T112))
U3_GGAA(T111, T112, less36_out_gg) → SPLIT46_IN_GGAA(T111, T112)
SPLIT46_IN_GGAA(cons(T125, T126), T127) → U5_GGAA(T126, T127, geq62_in_gg(T125, T127))
U5_GGAA(T126, T127, geq62_out_gg) → SPLIT46_IN_GGAA(T126, T127)

The TRS R consists of the following rules:

less36_in_gg(0, s(T78)) → less36_out_gg
less36_in_gg(s(T83), s(T84)) → U2_gg(less36_in_gg(T83, T84))
geq62_in_gg(T136, T136) → geq62_out_gg
geq62_in_gg(s(T141), 0) → geq62_out_gg
geq62_in_gg(s(T146), s(T147)) → U7_gg(geq62_in_gg(T146, T147))
U2_gg(less36_out_gg) → less36_out_gg
U7_gg(geq62_out_gg) → geq62_out_gg

The set Q consists of the following terms:

less36_in_gg(x0, x1)
geq62_in_gg(x0, x1)
U2_gg(x0)
U7_gg(x0)

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

(212) 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:

• U3_GGAA(T111, T112, less36_out_gg) → SPLIT46_IN_GGAA(T111, T112)
  The graph contains the following edges 1 >= 1, 2 >= 2

• U5_GGAA(T126, T127, geq62_out_gg) → SPLIT46_IN_GGAA(T126, T127)
  The graph contains the following edges 1 >= 1, 2 >= 2

• SPLIT46_IN_GGAA(cons(T110, T111), T112) → U3_GGAA(T111, T112, less36_in_gg(T110, T112))
  The graph contains the following edges 1 > 1, 2 >= 2

• SPLIT46_IN_GGAA(cons(T125, T126), T127) → U5_GGAA(T126, T127, geq62_in_gg(T125, T127))
  The graph contains the following edges 1 > 1, 2 >= 2

(213) YES

(214) Obligation:

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

APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GGGA(T46, T47, T48, T50)

The TRS R consists of the following rules:

qs1_in_ga([], []) → qs1_out_ga([], [])
qs1_in_ga(cons(T14, []), T9) → U19_ga(T14, T9, qs14_in_a(X12))
qs14_in_a([]) → qs14_out_a([])
U19_ga(T14, T9, qs14_out_a(X12)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T14, []), T9) → U20_ga(T14, T9, qs14_in_a(T17))
U20_ga(T14, T9, qs14_out_a(T17)) → U21_ga(T14, T9, qs14_in_a(X13))
U21_ga(T14, T9, qs14_out_a(X13)) → qs1_out_ga(cons(T14, []), T9)
U20_ga(T14, T9, qs14_out_a(T17)) → U22_ga(T14, T9, T17, qs14_in_a(T20))
U22_ga(T14, T9, T17, qs14_out_a(T20)) → U23_ga(T14, T9, append23_in_ggga(T17, T14, T20, T9))
append23_in_ggga([], T33, T34, cons(T33, T34)) → append23_out_ggga([], T33, T34, cons(T33, T34))
append23_in_ggga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_ggga(T45, T46, T47, T48, T50, append23_in_ggga(T46, T47, T48, T50))
U1_ggga(T45, T46, T47, T48, T50, append23_out_ggga(T46, T47, T48, T50)) → append23_out_ggga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_ga(T14, T9, append23_out_ggga(T17, T14, T20, T9)) → qs1_out_ga(cons(T14, []), T9)
qs1_in_ga(cons(T69, cons(T67, T68)), T9) → U24_ga(T69, T67, T68, T9, less36_in_gg(T67, T69))
less36_in_gg(0, s(T78)) → less36_out_gg(0, s(T78))
less36_in_gg(s(T83), s(T84)) → U2_gg(T83, T84, less36_in_gg(T83, T84))
U2_gg(T83, T84, less36_out_gg(T83, T84)) → less36_out_gg(s(T83), s(T84))
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U25_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, X93, X94))
split46_in_ggaa([], T97, [], []) → split46_out_ggaa([], T97, [], [])
split46_in_ggaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_ggaa(T110, T111, T112, X163, X164, less36_in_gg(T110, T112))
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_ggaa(T110, T111, T112, X163, X164, less36_out_gg(T110, T112)) → U4_ggaa(T110, T111, T112, X163, X164, split46_in_ggaa(T111, T112, X163, X164))
split46_in_ggaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_ggaa(T125, T126, T127, X195, X196, geq62_in_gg(T125, T127))
geq62_in_gg(T136, T136) → geq62_out_gg(T136, T136)
geq62_in_gg(s(T141), 0) → geq62_out_gg(s(T141), 0)
geq62_in_gg(s(T146), s(T147)) → U7_gg(T146, T147, geq62_in_gg(T146, T147))
U7_gg(T146, T147, geq62_out_gg(T146, T147)) → geq62_out_gg(s(T146), s(T147))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_ggaa(T125, T126, T127, X195, X196, geq62_out_gg(T125, T127)) → U6_ggaa(T125, T126, T127, X195, X196, split46_in_ggaa(T126, T127, X195, X196))
U6_ggaa(T125, T126, T127, X195, X196, split46_out_ggaa(T126, T127, X195, X196)) → split46_out_ggaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_ggaa(T110, T111, T112, X163, X164, split46_out_ggaa(T111, T112, X163, X164)) → split46_out_ggaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, X93, X94)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U24_ga(T69, T67, T68, T9, less36_out_gg(T67, T69)) → U26_ga(T69, T67, T68, T9, split46_in_ggaa(T68, T69, T89, T90))
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U27_ga(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa([], []) → qs1_out_aa([], [])
qs1_in_aa(cons(T14, []), T9) → U19_aa(T14, T9, qs14_in_a(X12))
U19_aa(T14, T9, qs14_out_a(X12)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T14, []), T9) → U20_aa(T14, T9, qs14_in_a(T17))
U20_aa(T14, T9, qs14_out_a(T17)) → U21_aa(T14, T9, qs14_in_a(X13))
U21_aa(T14, T9, qs14_out_a(X13)) → qs1_out_aa(cons(T14, []), T9)
U20_aa(T14, T9, qs14_out_a(T17)) → U22_aa(T14, T9, T17, qs14_in_a(T20))
U22_aa(T14, T9, T17, qs14_out_a(T20)) → U23_aa(T14, T9, append23_in_gaga(T17, T14, T20, T9))
append23_in_gaga([], T33, T34, cons(T33, T34)) → append23_out_gaga([], T33, T34, cons(T33, T34))
append23_in_gaga(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_gaga(T45, T46, T47, T48, T50, append23_in_gaga(T46, T47, T48, T50))
U1_gaga(T45, T46, T47, T48, T50, append23_out_gaga(T46, T47, T48, T50)) → append23_out_gaga(cons(T45, T46), T47, T48, cons(T45, T50))
U23_aa(T14, T9, append23_out_gaga(T17, T14, T20, T9)) → qs1_out_aa(cons(T14, []), T9)
qs1_in_aa(cons(T69, cons(T67, T68)), T9) → U24_aa(T69, T67, T68, T9, less36_in_aa(T67, T69))
less36_in_aa(0, s(T78)) → less36_out_aa(0, s(T78))
less36_in_aa(s(T83), s(T84)) → U2_aa(T83, T84, less36_in_aa(T83, T84))
U2_aa(T83, T84, less36_out_aa(T83, T84)) → less36_out_aa(s(T83), s(T84))
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U25_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, X93, X94))
split46_in_aaaa([], T97, [], []) → split46_out_aaaa([], T97, [], [])
split46_in_aaaa(cons(T110, T111), T112, cons(T110, X163), X164) → U3_aaaa(T110, T111, T112, X163, X164, less36_in_aa(T110, T112))
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U3_aaaa(T110, T111, T112, X163, X164, less36_out_aa(T110, T112)) → U4_aaaa(T110, T111, T112, X163, X164, split46_in_aaaa(T111, T112, X163, X164))
split46_in_aaaa(cons(T125, T126), T127, X195, cons(T125, X196)) → U5_aaaa(T125, T126, T127, X195, X196, geq62_in_aa(T125, T127))
geq62_in_aa(T136, T136) → geq62_out_aa(T136, T136)
geq62_in_aa(s(T141), 0) → geq62_out_aa(s(T141), 0)
geq62_in_aa(s(T146), s(T147)) → U7_aa(T146, T147, geq62_in_aa(T146, T147))
U7_aa(T146, T147, geq62_out_aa(T146, T147)) → geq62_out_aa(s(T146), s(T147))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U5_aaaa(T125, T126, T127, X195, X196, geq62_out_aa(T125, T127)) → U6_aaaa(T125, T126, T127, X195, X196, split46_in_aaaa(T126, T127, X195, X196))
U6_aaaa(T125, T126, T127, X195, X196, split46_out_aaaa(T126, T127, X195, X196)) → split46_out_aaaa(cons(T125, T126), T127, X195, cons(T125, X196))
U4_aaaa(T110, T111, T112, X163, X164, split46_out_aaaa(T111, T112, X163, X164)) → split46_out_aaaa(cons(T110, T111), T112, cons(T110, X163), X164)
U25_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, X93, X94)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U24_aa(T69, T67, T68, T9, less36_out_aa(T67, T69)) → U26_aa(T69, T67, T68, T9, split46_in_aaaa(T68, T69, T89, T90))
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U27_aa(T69, T67, T68, T9, qs1_in_aa(cons(T67, T89), X12))
qs1_in_aa(cons(T214, cons(T212, T213)), T9) → U30_aa(T214, T212, T213, T9, geq62_in_aa(T212, T214))
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U31_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, X323, X324))
U31_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, X323, X324)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U30_aa(T214, T212, T213, T9, geq62_out_aa(T212, T214)) → U32_aa(T214, T212, T213, T9, split46_in_aaaa(T213, T214, T221, T222))
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U33_aa(T214, T212, T213, T9, qs79_in_aa(T221, X12))
qs79_in_aa([], []) → qs79_out_aa([], [])
qs79_in_aa(cons(T162, T163), X265) → U8_aa(T162, T163, X265, split46_in_aaaa(T163, T162, X261, X262))
U8_aa(T162, T163, X265, split46_out_aaaa(T163, T162, X261, X262)) → qs79_out_aa(cons(T162, T163), X265)
qs79_in_aa(cons(T162, T163), X265) → U9_aa(T162, T163, X265, split46_in_aaaa(T163, T162, T166, T167))
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U10_aa(T162, T163, X265, qs79_in_aa(T166, X263))
U10_aa(T162, T163, X265, qs79_out_aa(T166, X263)) → qs79_out_aa(cons(T162, T163), X265)
U9_aa(T162, T163, X265, split46_out_aaaa(T163, T162, T166, T167)) → U11_aa(T162, T163, X265, T167, qs79_in_aa(T166, T170))
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U12_aa(T162, T163, X265, qs79_in_aa(T167, X264))
U12_aa(T162, T163, X265, qs79_out_aa(T167, X264)) → qs79_out_aa(cons(T162, T163), X265)
U11_aa(T162, T163, X265, T167, qs79_out_aa(T166, T170)) → U13_aa(T162, T163, X265, T170, qs79_in_aa(T167, T171))
U13_aa(T162, T163, X265, T170, qs79_out_aa(T167, T171)) → U14_aa(T162, T163, X265, append94_in_aaaa(T170, T162, T171, X265))
append94_in_aaaa([], T184, T185, cons(T184, T185)) → append94_out_aaaa([], T184, T185, cons(T184, T185))
append94_in_aaaa(cons(T194, T195), T196, T197, cons(T194, X295)) → U15_aaaa(T194, T195, T196, T197, X295, append94_in_aaaa(T195, T196, T197, X295))
U15_aaaa(T194, T195, T196, T197, X295, append94_out_aaaa(T195, T196, T197, X295)) → append94_out_aaaa(cons(T194, T195), T196, T197, cons(T194, X295))
U14_aa(T162, T163, X265, append94_out_aaaa(T170, T162, T171, X265)) → qs79_out_aa(cons(T162, T163), X265)
U33_aa(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U32_aa(T214, T212, T213, T9, split46_out_aaaa(T213, T214, T221, T222)) → U34_aa(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_aa(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_aa(T214, T212, T213, T9, p78_in_aaaaa(cons(T212, T222), X13, T225, T214, T9))
p78_in_aaaaa(T90, X13, T154, T69, T9) → U16_aaaaa(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaaa(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaaa(T90, X13, T154, T69, T9)
p78_in_aaaaa(T90, T157, T154, T69, T9) → U17_aaaaa(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaaa(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaaa(T90, T157, T154, T69, T9, append23_in_aaaa(T154, T69, T157, T9))
append23_in_aaaa([], T33, T34, cons(T33, T34)) → append23_out_aaaa([], T33, T34, cons(T33, T34))
append23_in_aaaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_aaaa(T45, T46, T47, T48, T50, append23_in_aaaa(T46, T47, T48, T50))
U1_aaaa(T45, T46, T47, T48, T50, append23_out_aaaa(T46, T47, T48, T50)) → append23_out_aaaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaaa(T90, T157, T154, T69, T9, append23_out_aaaa(T154, T69, T157, T9)) → p78_out_aaaaa(T90, T157, T154, T69, T9)
U35_aa(T214, T212, T213, T9, p78_out_aaaaa(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_aa(cons(T214, cons(T212, T213)), T9)
U27_aa(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U26_aa(T69, T67, T68, T9, split46_out_aaaa(T68, T69, T89, T90)) → U28_aa(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_aa(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_aa(T69, T67, T68, T9, p78_in_aaaaa(T90, X13, T154, T69, T9))
U29_aa(T69, T67, T68, T9, p78_out_aaaaa(T90, X13, T154, T69, T9)) → qs1_out_aa(cons(T69, cons(T67, T68)), T9)
U27_ga(T69, T67, T68, T9, qs1_out_aa(cons(T67, T89), X12)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
U26_ga(T69, T67, T68, T9, split46_out_ggaa(T68, T69, T89, T90)) → U28_ga(T69, T67, T68, T9, T90, qs1_in_aa(cons(T67, T89), T154))
U28_ga(T69, T67, T68, T9, T90, qs1_out_aa(cons(T67, T89), T154)) → U29_ga(T69, T67, T68, T9, p78_in_aaaga(T90, X13, T154, T69, T9))
p78_in_aaaga(T90, X13, T154, T69, T9) → U16_aaaga(T90, X13, T154, T69, T9, qs79_in_aa(T90, X13))
U16_aaaga(T90, X13, T154, T69, T9, qs79_out_aa(T90, X13)) → p78_out_aaaga(T90, X13, T154, T69, T9)
p78_in_aaaga(T90, T157, T154, T69, T9) → U17_aaaga(T90, T157, T154, T69, T9, qs79_in_aa(T90, T157))
U17_aaaga(T90, T157, T154, T69, T9, qs79_out_aa(T90, T157)) → U18_aaaga(T90, T157, T154, T69, T9, append23_in_agaa(T154, T69, T157, T9))
append23_in_agaa([], T33, T34, cons(T33, T34)) → append23_out_agaa([], T33, T34, cons(T33, T34))
append23_in_agaa(cons(T45, T46), T47, T48, cons(T45, T50)) → U1_agaa(T45, T46, T47, T48, T50, append23_in_agaa(T46, T47, T48, T50))
U1_agaa(T45, T46, T47, T48, T50, append23_out_agaa(T46, T47, T48, T50)) → append23_out_agaa(cons(T45, T46), T47, T48, cons(T45, T50))
U18_aaaga(T90, T157, T154, T69, T9, append23_out_agaa(T154, T69, T157, T9)) → p78_out_aaaga(T90, T157, T154, T69, T9)
U29_ga(T69, T67, T68, T9, p78_out_aaaga(T90, X13, T154, T69, T9)) → qs1_out_ga(cons(T69, cons(T67, T68)), T9)
qs1_in_ga(cons(T214, cons(T212, T213)), T9) → U30_ga(T214, T212, T213, T9, geq62_in_gg(T212, T214))
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U31_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, X323, X324))
U31_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, X323, X324)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U30_ga(T214, T212, T213, T9, geq62_out_gg(T212, T214)) → U32_ga(T214, T212, T213, T9, split46_in_ggaa(T213, T214, T221, T222))
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U33_ga(T214, T212, T213, T9, qs79_in_aa(T221, X12))
U33_ga(T214, T212, T213, T9, qs79_out_aa(T221, X12)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)
U32_ga(T214, T212, T213, T9, split46_out_ggaa(T213, T214, T221, T222)) → U34_ga(T214, T212, T213, T9, T222, qs79_in_aa(T221, T225))
U34_ga(T214, T212, T213, T9, T222, qs79_out_aa(T221, T225)) → U35_ga(T214, T212, T213, T9, p78_in_aaaga(cons(T212, T222), X13, T225, T214, T9))
U35_ga(T214, T212, T213, T9, p78_out_aaaga(cons(T212, T222), X13, T225, T214, T9)) → qs1_out_ga(cons(T214, cons(T212, T213)), T9)

The argument filtering Pi contains the following mapping:
qs1_in_ga(x1, x2)  =  qs1_in_ga(x1)
[]  =  []
qs1_out_ga(x1, x2)  =  qs1_out_ga
cons(x1, x2)  =  cons(x1, x2)
U19_ga(x1, x2, x3)  =  U19_ga(x3)
qs14_in_a(x1)  =  qs14_in_a
qs14_out_a(x1)  =  qs14_out_a(x1)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3, x4)  =  U22_ga(x1, x3, x4)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
append23_in_ggga(x1, x2, x3, x4)  =  append23_in_ggga(x1, x2, x3)
append23_out_ggga(x1, x2, x3, x4)  =  append23_out_ggga(x4)
U1_ggga(x1, x2, x3, x4, x5, x6)  =  U1_ggga(x1, x6)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x3, x5)
less36_in_gg(x1, x2)  =  less36_in_gg(x1, x2)
0  =  0
s(x1)  =  s(x1)
less36_out_gg(x1, x2)  =  less36_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
U25_ga(x1, x2, x3, x4, x5)  =  U25_ga(x5)
split46_in_ggaa(x1, x2, x3, x4)  =  split46_in_ggaa(x1, x2)
split46_out_ggaa(x1, x2, x3, x4)  =  split46_out_ggaa
U3_ggaa(x1, x2, x3, x4, x5, x6)  =  U3_ggaa(x2, x3, x6)
U4_ggaa(x1, x2, x3, x4, x5, x6)  =  U4_ggaa(x6)
U5_ggaa(x1, x2, x3, x4, x5, x6)  =  U5_ggaa(x2, x3, x6)
geq62_in_gg(x1, x2)  =  geq62_in_gg(x1, x2)
geq62_out_gg(x1, x2)  =  geq62_out_gg
U7_gg(x1, x2, x3)  =  U7_gg(x3)
U6_ggaa(x1, x2, x3, x4, x5, x6)  =  U6_ggaa(x6)
U26_ga(x1, x2, x3, x4, x5)  =  U26_ga(x1, x5)
U27_ga(x1, x2, x3, x4, x5)  =  U27_ga(x5)
qs1_in_aa(x1, x2)  =  qs1_in_aa
qs1_out_aa(x1, x2)  =  qs1_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3, x4)  =  U22_aa(x3, x4)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
append23_in_gaga(x1, x2, x3, x4)  =  append23_in_gaga(x1, x3)
append23_out_gaga(x1, x2, x3, x4)  =  append23_out_gaga
U1_gaga(x1, x2, x3, x4, x5, x6)  =  U1_gaga(x6)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
less36_in_aa(x1, x2)  =  less36_in_aa
less36_out_aa(x1, x2)  =  less36_out_aa(x1)
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U25_aa(x1, x2, x3, x4, x5)  =  U25_aa(x5)
split46_in_aaaa(x1, x2, x3, x4)  =  split46_in_aaaa
split46_out_aaaa(x1, x2, x3, x4)  =  split46_out_aaaa
U3_aaaa(x1, x2, x3, x4, x5, x6)  =  U3_aaaa(x6)
U4_aaaa(x1, x2, x3, x4, x5, x6)  =  U4_aaaa(x6)
U5_aaaa(x1, x2, x3, x4, x5, x6)  =  U5_aaaa(x6)
geq62_in_aa(x1, x2)  =  geq62_in_aa
geq62_out_aa(x1, x2)  =  geq62_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U6_aaaa(x1, x2, x3, x4, x5, x6)  =  U6_aaaa(x6)
U26_aa(x1, x2, x3, x4, x5)  =  U26_aa(x5)
U27_aa(x1, x2, x3, x4, x5)  =  U27_aa(x5)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
qs79_in_aa(x1, x2)  =  qs79_in_aa
qs79_out_aa(x1, x2)  =  qs79_out_aa
U8_aa(x1, x2, x3, x4)  =  U8_aa(x4)
U9_aa(x1, x2, x3, x4)  =  U9_aa(x4)
U10_aa(x1, x2, x3, x4)  =  U10_aa(x4)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4)  =  U12_aa(x4)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4)  =  U14_aa(x4)
append94_in_aaaa(x1, x2, x3, x4)  =  append94_in_aaaa
append94_out_aaaa(x1, x2, x3, x4)  =  append94_out_aaaa
U15_aaaa(x1, x2, x3, x4, x5, x6)  =  U15_aaaa(x6)
U34_aa(x1, x2, x3, x4, x5, x6)  =  U34_aa(x6)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
p78_in_aaaaa(x1, x2, x3, x4, x5)  =  p78_in_aaaaa
U16_aaaaa(x1, x2, x3, x4, x5, x6)  =  U16_aaaaa(x6)
p78_out_aaaaa(x1, x2, x3, x4, x5)  =  p78_out_aaaaa
U17_aaaaa(x1, x2, x3, x4, x5, x6)  =  U17_aaaaa(x6)
U18_aaaaa(x1, x2, x3, x4, x5, x6)  =  U18_aaaaa(x6)
append23_in_aaaa(x1, x2, x3, x4)  =  append23_in_aaaa
append23_out_aaaa(x1, x2, x3, x4)  =  append23_out_aaaa
U1_aaaa(x1, x2, x3, x4, x5, x6)  =  U1_aaaa(x6)
U28_aa(x1, x2, x3, x4, x5, x6)  =  U28_aa(x6)
U29_aa(x1, x2, x3, x4, x5)  =  U29_aa(x5)
U28_ga(x1, x2, x3, x4, x5, x6)  =  U28_ga(x1, x6)
U29_ga(x1, x2, x3, x4, x5)  =  U29_ga(x5)
p78_in_aaaga(x1, x2, x3, x4, x5)  =  p78_in_aaaga(x4)
U16_aaaga(x1, x2, x3, x4, x5, x6)  =  U16_aaaga(x6)
p78_out_aaaga(x1, x2, x3, x4, x5)  =  p78_out_aaaga
U17_aaaga(x1, x2, x3, x4, x5, x6)  =  U17_aaaga(x4, x6)
U18_aaaga(x1, x2, x3, x4, x5, x6)  =  U18_aaaga(x6)
append23_in_agaa(x1, x2, x3, x4)  =  append23_in_agaa(x2)
append23_out_agaa(x1, x2, x3, x4)  =  append23_out_agaa
U1_agaa(x1, x2, x3, x4, x5, x6)  =  U1_agaa(x6)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x3, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x5)
U34_ga(x1, x2, x3, x4, x5, x6)  =  U34_ga(x1, x6)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
APPEND23_IN_GGGA(x1, x2, x3, x4)  =  APPEND23_IN_GGGA(x1, x2, x3)

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

(215) UsableRulesProof (EQUIVALENT transformation)

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

(216) Obligation:

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

APPEND23_IN_GGGA(cons(T45, T46), T47, T48, cons(T45, T50)) → APPEND23_IN_GGGA(T46, T47, T48, T50)

R is empty.
The argument filtering Pi contains the following mapping:
cons(x1, x2)  =  cons(x1, x2)
APPEND23_IN_GGGA(x1, x2, x3, x4)  =  APPEND23_IN_GGGA(x1, x2, x3)

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

(217) PiDPToQDPProof (SOUND transformation)

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

(218) Obligation:

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

APPEND23_IN_GGGA(cons(T45, T46), T47, T48) → APPEND23_IN_GGGA(T46, T47, T48)

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

(219) 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:

• APPEND23_IN_GGGA(cons(T45, T46), T47, T48) → APPEND23_IN_GGGA(T46, T47, T48)
  The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3

(220) YES