Left Termination of the query pattern goal_in_3(g, a, a) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

goal(A, B, C) :- ','(s2t(A, T), tapplast(T, B, C)).
tapplast(L, X, Last) :- ','(tappend(L, node(nil, X, nil), LX), tlast(Last, LX)).
tlast(X, node(nil, X, nil)).
tlast(X, node(L, X1, X2)) :- tlast(X, L).
tlast(X, node(X3, X4, R)) :- tlast(X, R).
tappend(nil, Y, Z) :- ','(!, eq(Y, Z)).
tappend(T, T1, node(T1, X, T2)) :- ','(left(T, nil), ','(right(T, T2), value(T, X))).
tappend(T, T2, node(T1, X, T2)) :- ','(left(T, T1), ','(right(T, nil), value(T, X))).
tappend(T, T3, node(U, X, T2)) :- ','(left(T, T1), ','(right(T, T2), ','(value(T, X), tappend(T1, T3, U)))).
tappend(T, T1, node(T1, X, U)) :- ','(left(T, T1), ','(right(T, T2), ','(value(T, X), tappend(T2, T3, U)))).
s2t(0, L) :- ','(!, eq(L, nil)).
s2t(X, node(T, X5, T)) :- ','(p(X, P), s2t(P, T)).
s2t(X, node(nil, X6, T)) :- ','(p(X, P), s2t(P, T)).
s2t(X, node(T, X7, nil)) :- ','(p(X, P), s2t(P, T)).
s2t(X, node(nil, X8, nil)).
left(nil, nil).
left(node(L, X9, X10), L).
right(nil, nil).
right(node(X11, X12, R), R).
value(nil, nil).
value(node(X13, X, X14), X).
p(0, 0).
p(s(X), X).
eq(X, X).

Queries:

goal(g,a,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: goal(T4, T5, T6)\n\nT4 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: goal(T4, T5, T6), SCOPE: 1, CLAUSE: 0\n\nT4 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(s2t(T7, X21), tapplast(X21, T10, T11))\n\nT7 is ground\nX21 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: s2t(T7, X21)\n\nT7 is ground\nX21 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: tapplast(T12, T10, T11)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: s2t(T7, X21), SCOPE: 2, CLAUSE: 10 | s2t(T7, X21), SCOPE: 2, CLAUSE: 11 | s2t(T7, X21), SCOPE: 2, CLAUSE: 12 | s2t(T7, X21), SCOPE: 2, CLAUSE: 13 | s2t(T7, X21), SCOPE: 2, CLAUSE: 14 | ?_2\n\nT7 is ground\nX21 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ','(!_2, eq(X24, nil)) | s2t(0, X21), SCOPE: 2, CLAUSE: 11 | s2t(0, X21), SCOPE: 2, CLAUSE: 12 | s2t(0, X21), SCOPE: 2, CLAUSE: 13 | s2t(0, X21), SCOPE: 2, CLAUSE: 14 | ?_2\n\nX21 is free\nX24 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: s2t(T7, X21), SCOPE: 2, CLAUSE: 11 | s2t(T7, X21), SCOPE: 2, CLAUSE: 12 | s2t(T7, X21), SCOPE: 2, CLAUSE: 13 | s2t(T7, X21), SCOPE: 2, CLAUSE: 14\n\nT7 is ground\nX21 is free; \nX23 is free; \ns2t(T7, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: eq(X24, nil)\n\nX24 is free", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: eq(X24, nil), SCOPE: 3, CLAUSE: 23\n\nX24 is free", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: s2t(T7, X21), SCOPE: 2, CLAUSE: 11\n\nT7 is ground\nX21 is free; \nX23 is free; \ns2t(T7, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: s2t(T7, X21), SCOPE: 2, CLAUSE: 12 | s2t(T7, X21), SCOPE: 2, CLAUSE: 13 | s2t(T7, X21), SCOPE: 2, CLAUSE: 14\n\nT7 is ground\nX21 is free; \nX23 is free; \ns2t(T7, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(p(T13, X37), s2t(X37, X38))\n\nT13 is ground\nX21 is free; \nX23 is free; \nX38 is free; \nX37 is free; \ns2t(T13, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(p(T13, X37), s2t(X37, X38)), SCOPE: 4, CLAUSE: 21 | ','(p(T13, X37), s2t(X37, X38)), SCOPE: 4, CLAUSE: 22\n\nT13 is ground\nX21 is free; \nX23 is free; \nX38 is free; \nX37 is free; \ns2t(T13, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(p(T13, X37), s2t(X37, X38)), SCOPE: 4, CLAUSE: 22\n\nT13 is ground\nX21 is free; \nX23 is free; \nX38 is free; \nX37 is free; \ns2t(T13, X21) !=? s2t(0, X23)\np(T13, X37) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: s2t(T14, X38)\n\nT14 is ground\nX21 is free; \nX23 is free; \nX38 is free; \nX37 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\nX21 is free\nX23 is free; \nX37 is free; \nX41 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: s2t(T7, X21), SCOPE: 2, CLAUSE: 12\n\nT7 is ground\nX21 is free; \nX23 is free; \ns2t(T7, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: s2t(T7, X21), SCOPE: 2, CLAUSE: 13 | s2t(T7, X21), SCOPE: 2, CLAUSE: 14\n\nT7 is ground\nX21 is free; \nX23 is free; \ns2t(T7, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: ','(p(T15, X51), s2t(X51, X53))\n\nT15 is ground\nX21 is free; \nX23 is free; \nX53 is free; \nX51 is free; \ns2t(T15, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(p(T15, X51), s2t(X51, X53)), SCOPE: 5, CLAUSE: 21 | ','(p(T15, X51), s2t(X51, X53)), SCOPE: 5, CLAUSE: 22\n\nT15 is ground\nX21 is free; \nX23 is free; \nX53 is free; \nX51 is free; \ns2t(T15, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: ','(p(T15, X51), s2t(X51, X53)), SCOPE: 5, CLAUSE: 22\n\nT15 is ground\nX21 is free; \nX23 is free; \nX53 is free; \nX51 is free; \ns2t(T15, X21) !=? s2t(0, X23)\np(T15, X51) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: s2t(T16, X53)\n\nT16 is ground\nX21 is free; \nX23 is free; \nX53 is free; \nX51 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\nX21 is free\nX23 is free; \nX51 is free; \nX55 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: s2t(T7, X21), SCOPE: 2, CLAUSE: 13\n\nT7 is ground\nX21 is free; \nX23 is free; \ns2t(T7, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: s2t(T7, X21), SCOPE: 2, CLAUSE: 14\n\nT7 is ground\nX21 is free; \nX23 is free; \ns2t(T7, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(p(T17, X65), s2t(X65, X66))\n\nT17 is ground\nX21 is free; \nX23 is free; \nX66 is free; \nX65 is free; \ns2t(T17, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(p(T17, X65), s2t(X65, X66)), SCOPE: 6, CLAUSE: 21 | ','(p(T17, X65), s2t(X65, X66)), SCOPE: 6, CLAUSE: 22\n\nT17 is ground\nX21 is free; \nX23 is free; \nX66 is free; \nX65 is free; \ns2t(T17, X21) !=? s2t(0, X23)", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(p(T17, X65), s2t(X65, X66)), SCOPE: 6, CLAUSE: 22\n\nT17 is ground\nX21 is free; \nX23 is free; \nX66 is free; \nX65 is free; \ns2t(T17, X21) !=? s2t(0, X23)\np(T17, X65) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: s2t(T18, X66)\n\nT18 is ground\nX21 is free; \nX23 is free; \nX66 is free; \nX65 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\nX21 is free\nX23 is free; \nX65 is free; \nX69 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: true\n\nX21 is free\nX23 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: tapplast(T12, T10, T11), SCOPE: 7, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(tappend(T23, node(nil, T24, nil), X81), tlast(T25, X81))\n\nX81 is free", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: tappend(T23, node(nil, T24, nil), X81)\n\nX81 is free", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: tlast(T27, T26)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 5 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 6 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 7 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 8 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 9 | ?_8\n\nX81 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(!_8, eq(node(nil, T29, nil), X86)) | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 6 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 7 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 8 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 9 | ?_8\n\nX81 is free\nX86 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 6 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 7 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 8 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 9\n\nX81 is free\nX84 is free; \nX85 is free; \ntappend(T23, node(nil, T24, nil), X81) !=? tappend(nil, X84, X85)", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: eq(node(nil, T29, nil), X86)\n\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: eq(node(nil, T29, nil), X86), SCOPE: 9, CLAUSE: 23\n\nX86 is free", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 6\n\nX81 is free\nX84 is free; \nX85 is free; \ntappend(T23, node(nil, T24, nil), X81) !=? tappend(nil, X84, X85)", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 7 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 8 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 9\n\nX81 is free\nX84 is free; \nX85 is free; \ntappend(T23, node(nil, T24, nil), X81) !=? tappend(nil, X84, X85)", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(left(T33, nil), ','(right(T33, X102), value(T33, X101)))\n\nX81 is free\nX84 is free; \nX85 is free; \nX101 is free; \nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 15 | ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(right(nil, X102), value(nil, X101)) | ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; \nleft(T33, nil) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(right(nil, X102), value(nil, X101)), SCOPE: 11, CLAUSE: 17 | ','(right(nil, X102), value(nil, X101)), SCOPE: 11, CLAUSE: 18 | ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: value(nil, X101) | ','(right(nil, X102), value(nil, X101)), SCOPE: 11, CLAUSE: 18 | ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: value(nil, X101), SCOPE: 12, CLAUSE: 19 | value(nil, X101), SCOPE: 12, CLAUSE: 20 | ','(right(nil, X102), value(nil, X101)), SCOPE: 11, CLAUSE: 18 | ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: true | value(nil, X101), SCOPE: 12, CLAUSE: 20 | ','(right(nil, X102), value(nil, X101)), SCOPE: 11, CLAUSE: 18 | ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: value(nil, X101), SCOPE: 12, CLAUSE: 20 | ','(right(nil, X102), value(nil, X101)), SCOPE: 11, CLAUSE: 18 | ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(right(nil, X102), value(nil, X101)), SCOPE: 11, CLAUSE: 18 | ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(left(T33, nil), ','(right(T33, X102), value(T33, X101))), SCOPE: 10, CLAUSE: 16\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(right(node(nil, T37, T38), X102), value(node(nil, T37, T38), X101))\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: \n\nX112 is free\nX113 is free; \nX114 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ','(right(node(nil, T37, T38), X102), value(node(nil, T37, T38), X101)), SCOPE: 13, CLAUSE: 17 | ','(right(node(nil, T37, T38), X102), value(node(nil, T37, T38), X101)), SCOPE: 13, CLAUSE: 18\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(right(node(nil, T37, T38), X102), value(node(nil, T37, T38), X101)), SCOPE: 13, CLAUSE: 18\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: value(node(nil, T41, T42), X101)\n\nX101 is free", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: value(node(nil, T41, T42), X101), SCOPE: 14, CLAUSE: 19 | value(node(nil, T41, T42), X101), SCOPE: 14, CLAUSE: 20\n\nX101 is free", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: value(node(nil, T41, T42), X101), SCOPE: 14, CLAUSE: 20\n\nX101 is free", 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: ','(right(node(nil, T48, T49), X102), value(node(nil, T48, T49), X101))\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: \n\nX130 is free\nX131 is free; \nX132 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(right(node(nil, T48, T49), X102), value(node(nil, T48, T49), X101)), SCOPE: 15, CLAUSE: 17 | ','(right(node(nil, T48, T49), X102), value(node(nil, T48, T49), X101)), SCOPE: 15, CLAUSE: 18\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(right(node(nil, T48, T49), X102), value(node(nil, T48, T49), X101)), SCOPE: 15, CLAUSE: 18\n\nX101 is free\nX102 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: value(node(nil, T52, T53), X101)\n\nX101 is free", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: value(node(nil, T52, T53), X101), SCOPE: 16, CLAUSE: 19 | value(node(nil, T52, T53), X101), SCOPE: 16, CLAUSE: 20\n\nX101 is free", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: value(node(nil, T52, T53), X101), SCOPE: 16, CLAUSE: 20\n\nX101 is free", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 7\n\nX81 is free\nX84 is free; \nX85 is free; \ntappend(T23, node(nil, T24, nil), X81) !=? tappend(nil, X84, X85)", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 8 | tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 9\n\nX81 is free\nX84 is free; \nX85 is free; \ntappend(T23, node(nil, T24, nil), X81) !=? tappend(nil, X84, X85)", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(left(T58, X157), ','(right(T58, nil), value(T58, X158)))\n\nX81 is free\nX84 is free; \nX85 is free; \nX157 is free; \nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 15 | ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: ','(right(nil, nil), value(nil, X158)) | ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; \nleft(T58, X157) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(right(nil, nil), value(nil, X158)), SCOPE: 18, CLAUSE: 17 | ','(right(nil, nil), value(nil, X158)), SCOPE: 18, CLAUSE: 18 | ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: value(nil, X158) | ','(right(nil, nil), value(nil, X158)), SCOPE: 18, CLAUSE: 18 | ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: value(nil, X158), SCOPE: 19, CLAUSE: 19 | value(nil, X158), SCOPE: 19, CLAUSE: 20 | ','(right(nil, nil), value(nil, X158)), SCOPE: 18, CLAUSE: 18 | ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: true | value(nil, X158), SCOPE: 19, CLAUSE: 20 | ','(right(nil, nil), value(nil, X158)), SCOPE: 18, CLAUSE: 18 | ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: value(nil, X158), SCOPE: 19, CLAUSE: 20 | ','(right(nil, nil), value(nil, X158)), SCOPE: 18, CLAUSE: 18 | ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ','(right(nil, nil), value(nil, X158)), SCOPE: 18, CLAUSE: 18 | ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(left(T58, X157), ','(right(T58, nil), value(T58, X158))), SCOPE: 17, CLAUSE: 16\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: ','(right(node(T62, T63, T64), nil), value(node(T62, T63, T64), X158))\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\nX157 is free\nX168 is free; \nX169 is free; \nX170 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(right(node(T62, T63, T64), nil), value(node(T62, T63, T64), X158)), SCOPE: 20, CLAUSE: 17 | ','(right(node(T62, T63, T64), nil), value(node(T62, T63, T64), X158)), SCOPE: 20, CLAUSE: 18\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(right(node(T62, T63, T64), nil), value(node(T62, T63, T64), X158)), SCOPE: 20, CLAUSE: 18\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: value(node(T68, T69, nil), X158)\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\nX174 is free\nX175 is free; \nX176 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: value(node(T68, T69, nil), X158), SCOPE: 21, CLAUSE: 19 | value(node(T68, T69, nil), X158), SCOPE: 21, CLAUSE: 20\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: value(node(T68, T69, nil), X158), SCOPE: 21, CLAUSE: 20\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(right(node(T75, T76, T77), nil), value(node(T75, T76, T77), X158))\n\nX157 is free\nX158 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\nX157 is free\nX186 is free; \nX187 is free; \nX188 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(right(node(T75, T76, T77), nil), value(node(T75, T76, T77), X158)), SCOPE: 22, CLAUSE: 17 | ','(right(node(T75, T76, T77), nil), value(node(T75, T76, T77), X158)), SCOPE: 22, CLAUSE: 18\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(right(node(T75, T76, T77), nil), value(node(T75, T76, T77), X158)), SCOPE: 22, CLAUSE: 18\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: value(node(T81, T82, nil), X158)\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\nX192 is free\nX193 is free; \nX194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: value(node(T81, T82, nil), X158), SCOPE: 23, CLAUSE: 19 | value(node(T81, T82, nil), X158), SCOPE: 23, CLAUSE: 20\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: value(node(T81, T82, nil), X158), SCOPE: 23, CLAUSE: 20\n\nX158 is free", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 8\n\nX81 is free\nX84 is free; \nX85 is free; \ntappend(T23, node(nil, T24, nil), X81) !=? tappend(nil, X84, X85)", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: tappend(T23, node(nil, T24, nil), X81), SCOPE: 8, CLAUSE: 9\n\nX81 is free\nX84 is free; \nX85 is free; \ntappend(T23, node(nil, T24, nil), X81) !=? tappend(nil, X84, X85)", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217))))\n\nX81 is free\nX84 is free; \nX85 is free; \nX217 is free; \nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 15 | ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(right(nil, X219), ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217))) | ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; \nleft(T87, X216) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ','(right(nil, X219), ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217))), SCOPE: 25, CLAUSE: 17 | ','(right(nil, X219), ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217))), SCOPE: 25, CLAUSE: 18 | ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217)) | ','(right(nil, X219), ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217))), SCOPE: 25, CLAUSE: 18 | ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217)), SCOPE: 26, CLAUSE: 19 | ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217)), SCOPE: 26, CLAUSE: 20 | ','(right(nil, X219), ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217))), SCOPE: 25, CLAUSE: 18 | ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: tappend(nil, node(nil, T89, nil), X217) | ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217)), SCOPE: 26, CLAUSE: 20 | ','(right(nil, X219), ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217))), SCOPE: 25, CLAUSE: 18 | ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: tappend(nil, node(nil, T89, nil), X217)\n\nX217 is free", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217)), SCOPE: 26, CLAUSE: 20 | ','(right(nil, X219), ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217))), SCOPE: 25, CLAUSE: 18 | ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(right(nil, X219), ','(value(nil, X218), tappend(nil, node(nil, T89, nil), X217))), SCOPE: 25, CLAUSE: 18 | ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: ','(left(T87, X216), ','(right(T87, X219), ','(value(T87, X218), tappend(X216, node(nil, T88, nil), X217)))), SCOPE: 24, CLAUSE: 16\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(right(node(T93, T94, T95), X219), ','(value(node(T93, T94, T95), X218), tappend(T93, node(nil, T96, nil), X217)))\n\nX217 is free\nX218 is free; \nX219 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\nX216 is free\nX229 is free; \nX230 is free; \nX231 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(right(node(T93, T94, T95), X219), ','(value(node(T93, T94, T95), X218), tappend(T93, node(nil, T96, nil), X217))), SCOPE: 27, CLAUSE: 17 | ','(right(node(T93, T94, T95), X219), ','(value(node(T93, T94, T95), X218), tappend(T93, node(nil, T96, nil), X217))), SCOPE: 27, CLAUSE: 18\n\nX217 is free\nX218 is free; \nX219 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: ','(right(node(T93, T94, T95), X219), ','(value(node(T93, T94, T95), X218), tappend(T93, node(nil, T96, nil), X217))), SCOPE: 27, CLAUSE: 18\n\nX217 is free\nX218 is free; \nX219 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ','(value(node(T100, T101, T102), X218), tappend(T100, node(nil, T103, nil), X217))\n\nX217 is free\nX218 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: ','(value(node(T100, T101, T102), X218), tappend(T100, node(nil, T103, nil), X217)), SCOPE: 28, CLAUSE: 19 | ','(value(node(T100, T101, T102), X218), tappend(T100, node(nil, T103, nil), X217)), SCOPE: 28, CLAUSE: 20\n\nX217 is free\nX218 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ','(value(node(T100, T101, T102), X218), tappend(T100, node(nil, T103, nil), X217)), SCOPE: 28, CLAUSE: 20\n\nX217 is free\nX218 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: tappend(T107, node(nil, T108, nil), X217)\n\nX217 is free", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: ','(right(node(T112, T113, T114), X219), ','(value(node(T112, T113, T114), X218), tappend(T112, node(nil, T115, nil), X217)))\n\nX217 is free\nX218 is free; \nX219 is free; \nX216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\nX216 is free\nX247 is free; \nX248 is free; \nX249 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(right(node(T112, T113, T114), X219), ','(value(node(T112, T113, T114), X218), tappend(T112, node(nil, T115, nil), X217))), SCOPE: 29, CLAUSE: 17 | ','(right(node(T112, T113, T114), X219), ','(value(node(T112, T113, T114), X218), tappend(T112, node(nil, T115, nil), X217))), SCOPE: 29, CLAUSE: 18\n\nX217 is free\nX218 is free; \nX219 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: ','(right(node(T112, T113, T114), X219), ','(value(node(T112, T113, T114), X218), tappend(T112, node(nil, T115, nil), X217))), SCOPE: 29, CLAUSE: 18\n\nX217 is free\nX218 is free; \nX219 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(value(node(T119, T120, T121), X218), tappend(T119, node(nil, T122, nil), X217))\n\nX217 is free\nX218 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(value(node(T119, T120, T121), X218), tappend(T119, node(nil, T122, nil), X217)), SCOPE: 30, CLAUSE: 19 | ','(value(node(T119, T120, T121), X218), tappend(T119, node(nil, T122, nil), X217)), SCOPE: 30, CLAUSE: 20\n\nX217 is free\nX218 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(value(node(T119, T120, T121), X218), tappend(T119, node(nil, T122, nil), X217)), SCOPE: 30, CLAUSE: 20\n\nX217 is free\nX218 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: tappend(T126, node(nil, T127, nil), X217)\n\nX217 is free", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(left(T130, node(nil, T131, nil)), ','(right(T130, X270), ','(value(T130, X272), tappend(X270, X271, X273))))\n\nX81 is free\nX84 is free; \nX85 is free; \nX272 is free; \nX273 is free; \nX270 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(left(T130, node(nil, T131, nil)), ','(right(T130, X270), ','(value(T130, X272), tappend(X270, X271, X273)))), SCOPE: 31, CLAUSE: 15 | ','(left(T130, node(nil, T131, nil)), ','(right(T130, X270), ','(value(T130, X272), tappend(X270, X271, X273)))), SCOPE: 31, CLAUSE: 16\n\nX272 is free\nX273 is free; \nX270 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(left(T130, node(nil, T131, nil)), ','(right(T130, X270), ','(value(T130, X272), tappend(X270, X271, X273)))), SCOPE: 31, CLAUSE: 16\n\nX272 is free\nX273 is free; \nX270 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: ','(right(node(node(nil, T138, nil), T136, T137), X270), ','(value(node(node(nil, T138, nil), T136, T137), X272), tappend(X270, X271, X273)))\n\nX272 is free\nX273 is free; \nX270 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: \n\nX277 is free\nX278 is free; \nX279 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(right(node(node(nil, T138, nil), T136, T137), X270), ','(value(node(node(nil, T138, nil), T136, T137), X272), tappend(X270, X271, X273))), SCOPE: 32, CLAUSE: 17 | ','(right(node(node(nil, T138, nil), T136, T137), X270), ','(value(node(node(nil, T138, nil), T136, T137), X272), tappend(X270, X271, X273))), SCOPE: 32, CLAUSE: 18\n\nX272 is free\nX273 is free; \nX270 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ','(right(node(node(nil, T138, nil), T136, T137), X270), ','(value(node(node(nil, T138, nil), T136, T137), X272), tappend(X270, X271, X273))), SCOPE: 32, CLAUSE: 18\n\nX272 is free\nX273 is free; \nX270 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(value(node(node(nil, T144, nil), T142, T143), X272), tappend(T143, X271, X273))\n\nX272 is free\nX273 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ','(value(node(node(nil, T144, nil), T142, T143), X272), tappend(T143, X271, X273)), SCOPE: 33, CLAUSE: 19 | ','(value(node(node(nil, T144, nil), T142, T143), X272), tappend(T143, X271, X273)), SCOPE: 33, CLAUSE: 20\n\nX272 is free\nX273 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(value(node(node(nil, T144, nil), T142, T143), X272), tappend(T143, X271, X273)), SCOPE: 33, CLAUSE: 20\n\nX272 is free\nX273 is free; \nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: tappend(T148, X271, X273)\n\nX273 is free\nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 5 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 6 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 7 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 8 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 9 | ?_34\n\nX273 is free\nX271 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(!_34, eq(X296, X297)) | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 6 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 7 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 8 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 9 | ?_34\n\nX273 is free\nX271 is free; \nX296 is free; \nX297 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 6 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 7 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 8 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 9\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \ntappend(T148, X271, X273) !=? tappend(nil, X294, X295)", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: eq(X296, X297)\n\nX296 is free\nX297 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: eq(X296, X297), SCOPE: 35, CLAUSE: 23\n\nX296 is free\nX297 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 6\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \ntappend(T148, X271, X273) !=? tappend(nil, X294, X295)", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 7 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 8 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 9\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \ntappend(T148, X271, X273) !=? tappend(nil, X294, X295)", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: ','(left(T150, nil), ','(right(T150, X315), value(T150, X314)))\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \nX314 is free; \nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 15 | ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ','(right(nil, X315), value(nil, X314)) | ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; \nleft(T150, nil) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: ','(right(nil, X315), value(nil, X314)), SCOPE: 37, CLAUSE: 17 | ','(right(nil, X315), value(nil, X314)), SCOPE: 37, CLAUSE: 18 | ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: value(nil, X314) | ','(right(nil, X315), value(nil, X314)), SCOPE: 37, CLAUSE: 18 | ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: value(nil, X314), SCOPE: 38, CLAUSE: 19 | value(nil, X314), SCOPE: 38, CLAUSE: 20 | ','(right(nil, X315), value(nil, X314)), SCOPE: 37, CLAUSE: 18 | ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: true | value(nil, X314), SCOPE: 38, CLAUSE: 20 | ','(right(nil, X315), value(nil, X314)), SCOPE: 37, CLAUSE: 18 | ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: value(nil, X314), SCOPE: 38, CLAUSE: 20 | ','(right(nil, X315), value(nil, X314)), SCOPE: 37, CLAUSE: 18 | ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: ','(right(nil, X315), value(nil, X314)), SCOPE: 37, CLAUSE: 18 | ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: ','(left(T150, nil), ','(right(T150, X315), value(T150, X314))), SCOPE: 36, CLAUSE: 16\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: ','(right(node(nil, T154, T155), X315), value(node(nil, T154, T155), X314))\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: \n\nX325 is free\nX326 is free; \nX327 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: ','(right(node(nil, T154, T155), X315), value(node(nil, T154, T155), X314)), SCOPE: 39, CLAUSE: 17 | ','(right(node(nil, T154, T155), X315), value(node(nil, T154, T155), X314)), SCOPE: 39, CLAUSE: 18\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: ','(right(node(nil, T154, T155), X315), value(node(nil, T154, T155), X314)), SCOPE: 39, CLAUSE: 18\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: value(node(nil, T158, T159), X314)\n\nX314 is free", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: value(node(nil, T158, T159), X314), SCOPE: 40, CLAUSE: 19 | value(node(nil, T158, T159), X314), SCOPE: 40, CLAUSE: 20\n\nX314 is free", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: value(node(nil, T158, T159), X314), SCOPE: 40, CLAUSE: 20\n\nX314 is free", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(right(node(nil, T165, T166), X315), value(node(nil, T165, T166), X314))\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: \n\nX343 is free\nX344 is free; \nX345 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: ','(right(node(nil, T165, T166), X315), value(node(nil, T165, T166), X314)), SCOPE: 41, CLAUSE: 17 | ','(right(node(nil, T165, T166), X315), value(node(nil, T165, T166), X314)), SCOPE: 41, CLAUSE: 18\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: ','(right(node(nil, T165, T166), X315), value(node(nil, T165, T166), X314)), SCOPE: 41, CLAUSE: 18\n\nX314 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: value(node(nil, T169, T170), X314)\n\nX314 is free", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: value(node(nil, T169, T170), X314), SCOPE: 42, CLAUSE: 19 | value(node(nil, T169, T170), X314), SCOPE: 42, CLAUSE: 20\n\nX314 is free", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: value(node(nil, T169, T170), X314), SCOPE: 42, CLAUSE: 20\n\nX314 is free", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 7\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \ntappend(T148, X271, X273) !=? tappend(nil, X294, X295)", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 8 | tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 9\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \ntappend(T148, X271, X273) !=? tappend(nil, X294, X295)", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: ','(left(T174, X371), ','(right(T174, nil), value(T174, X372)))\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \nX371 is free; \nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 15 | ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: ','(right(nil, nil), value(nil, X372)) | ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; \nleft(T174, X371) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: ','(right(nil, nil), value(nil, X372)), SCOPE: 44, CLAUSE: 17 | ','(right(nil, nil), value(nil, X372)), SCOPE: 44, CLAUSE: 18 | ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: value(nil, X372) | ','(right(nil, nil), value(nil, X372)), SCOPE: 44, CLAUSE: 18 | ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: value(nil, X372), SCOPE: 45, CLAUSE: 19 | value(nil, X372), SCOPE: 45, CLAUSE: 20 | ','(right(nil, nil), value(nil, X372)), SCOPE: 44, CLAUSE: 18 | ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: true | value(nil, X372), SCOPE: 45, CLAUSE: 20 | ','(right(nil, nil), value(nil, X372)), SCOPE: 44, CLAUSE: 18 | ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: value(nil, X372), SCOPE: 45, CLAUSE: 20 | ','(right(nil, nil), value(nil, X372)), SCOPE: 44, CLAUSE: 18 | ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(right(nil, nil), value(nil, X372)), SCOPE: 44, CLAUSE: 18 | ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(left(T174, X371), ','(right(T174, nil), value(T174, X372))), SCOPE: 43, CLAUSE: 16\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: ','(right(node(T178, T179, T180), nil), value(node(T178, T179, T180), X372))\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: \n\nX371 is free\nX382 is free; \nX383 is free; \nX384 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: ','(right(node(T178, T179, T180), nil), value(node(T178, T179, T180), X372)), SCOPE: 46, CLAUSE: 17 | ','(right(node(T178, T179, T180), nil), value(node(T178, T179, T180), X372)), SCOPE: 46, CLAUSE: 18\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: ','(right(node(T178, T179, T180), nil), value(node(T178, T179, T180), X372)), SCOPE: 46, CLAUSE: 18\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: value(node(T184, T185, nil), X372)\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: \n\nX388 is free\nX389 is free; \nX390 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: value(node(T184, T185, nil), X372), SCOPE: 47, CLAUSE: 19 | value(node(T184, T185, nil), X372), SCOPE: 47, CLAUSE: 20\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: value(node(T184, T185, nil), X372), SCOPE: 47, CLAUSE: 20\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: ','(right(node(T191, T192, T193), nil), value(node(T191, T192, T193), X372))\n\nX371 is free\nX372 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: \n\nX371 is free\nX400 is free; \nX401 is free; \nX402 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: ','(right(node(T191, T192, T193), nil), value(node(T191, T192, T193), X372)), SCOPE: 48, CLAUSE: 17 | ','(right(node(T191, T192, T193), nil), value(node(T191, T192, T193), X372)), SCOPE: 48, CLAUSE: 18\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: ','(right(node(T191, T192, T193), nil), value(node(T191, T192, T193), X372)), SCOPE: 48, CLAUSE: 18\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: value(node(T197, T198, nil), X372)\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\nX406 is free\nX407 is free; \nX408 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: value(node(T197, T198, nil), X372), SCOPE: 49, CLAUSE: 19 | value(node(T197, T198, nil), X372), SCOPE: 49, CLAUSE: 20\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: value(node(T197, T198, nil), X372), SCOPE: 49, CLAUSE: 20\n\nX372 is free", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 8\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \ntappend(T148, X271, X273) !=? tappend(nil, X294, X295)", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: tappend(T148, X271, X273), SCOPE: 34, CLAUSE: 9\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \ntappend(T148, X271, X273) !=? tappend(nil, X294, X295)", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432))))\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \nX431 is free; \nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 15 | ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: ','(right(nil, X434), ','(value(nil, X433), tappend(nil, X431, X432))) | ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; \nleft(T202, X430) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: ','(right(nil, X434), ','(value(nil, X433), tappend(nil, X431, X432))), SCOPE: 51, CLAUSE: 17 | ','(right(nil, X434), ','(value(nil, X433), tappend(nil, X431, X432))), SCOPE: 51, CLAUSE: 18 | ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: ','(value(nil, X433), tappend(nil, X431, X432)) | ','(right(nil, X434), ','(value(nil, X433), tappend(nil, X431, X432))), SCOPE: 51, CLAUSE: 18 | ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: ','(value(nil, X433), tappend(nil, X431, X432)), SCOPE: 52, CLAUSE: 19 | ','(value(nil, X433), tappend(nil, X431, X432)), SCOPE: 52, CLAUSE: 20 | ','(right(nil, X434), ','(value(nil, X433), tappend(nil, X431, X432))), SCOPE: 51, CLAUSE: 18 | ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: tappend(nil, X431, X432) | ','(value(nil, X433), tappend(nil, X431, X432)), SCOPE: 52, CLAUSE: 20 | ','(right(nil, X434), ','(value(nil, X433), tappend(nil, X431, X432))), SCOPE: 51, CLAUSE: 18 | ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: tappend(nil, X431, X432)\n\nX431 is free\nX432 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: ','(value(nil, X433), tappend(nil, X431, X432)), SCOPE: 52, CLAUSE: 20 | ','(right(nil, X434), ','(value(nil, X433), tappend(nil, X431, X432))), SCOPE: 51, CLAUSE: 18 | ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: ','(right(nil, X434), ','(value(nil, X433), tappend(nil, X431, X432))), SCOPE: 51, CLAUSE: 18 | ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: ','(left(T202, X430), ','(right(T202, X434), ','(value(T202, X433), tappend(X430, X431, X432)))), SCOPE: 50, CLAUSE: 16\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: ','(right(node(T206, T207, T208), X434), ','(value(node(T206, T207, T208), X433), tappend(T206, X431, X432)))\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: \n\nX430 is free\nX444 is free; \nX445 is free; \nX446 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: ','(right(node(T206, T207, T208), X434), ','(value(node(T206, T207, T208), X433), tappend(T206, X431, X432))), SCOPE: 53, CLAUSE: 17 | ','(right(node(T206, T207, T208), X434), ','(value(node(T206, T207, T208), X433), tappend(T206, X431, X432))), SCOPE: 53, CLAUSE: 18\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: ','(right(node(T206, T207, T208), X434), ','(value(node(T206, T207, T208), X433), tappend(T206, X431, X432))), SCOPE: 53, CLAUSE: 18\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: ','(value(node(T212, T213, T214), X433), tappend(T212, X431, X432))\n\nX431 is free\nX432 is free; \nX433 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: ','(value(node(T212, T213, T214), X433), tappend(T212, X431, X432)), SCOPE: 54, CLAUSE: 19 | ','(value(node(T212, T213, T214), X433), tappend(T212, X431, X432)), SCOPE: 54, CLAUSE: 20\n\nX431 is free\nX432 is free; \nX433 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: ','(value(node(T212, T213, T214), X433), tappend(T212, X431, X432)), SCOPE: 54, CLAUSE: 20\n\nX431 is free\nX432 is free; \nX433 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: tappend(T218, X431, X432)\n\nX431 is free\nX432 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: ','(right(node(T222, T223, T224), X434), ','(value(node(T222, T223, T224), X433), tappend(T222, X431, X432)))\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; \nX430 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: \n\nX430 is free\nX462 is free; \nX463 is free; \nX464 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: ','(right(node(T222, T223, T224), X434), ','(value(node(T222, T223, T224), X433), tappend(T222, X431, X432))), SCOPE: 55, CLAUSE: 17 | ','(right(node(T222, T223, T224), X434), ','(value(node(T222, T223, T224), X433), tappend(T222, X431, X432))), SCOPE: 55, CLAUSE: 18\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: ','(right(node(T222, T223, T224), X434), ','(value(node(T222, T223, T224), X433), tappend(T222, X431, X432))), SCOPE: 55, CLAUSE: 18\n\nX431 is free\nX432 is free; \nX433 is free; \nX434 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: ','(value(node(T228, T229, T230), X433), tappend(T228, X431, X432))\n\nX431 is free\nX432 is free; \nX433 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: ','(value(node(T228, T229, T230), X433), tappend(T228, X431, X432)), SCOPE: 56, CLAUSE: 19 | ','(value(node(T228, T229, T230), X433), tappend(T228, X431, X432)), SCOPE: 56, CLAUSE: 20\n\nX431 is free\nX432 is free; \nX433 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: ','(value(node(T228, T229, T230), X433), tappend(T228, X431, X432)), SCOPE: 56, CLAUSE: 20\n\nX431 is free\nX432 is free; \nX433 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: tappend(T234, X431, X432)\n\nX431 is free\nX432 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489))))\n\nX273 is free\nX271 is free; \nX294 is free; \nX295 is free; \nX487 is free; \nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 15 | ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: ','(right(nil, X485), ','(value(nil, X488), tappend(X485, X486, X489))) | ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; \nleft(T236, X487) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: ','(right(nil, X485), ','(value(nil, X488), tappend(X485, X486, X489))), SCOPE: 58, CLAUSE: 17 | ','(right(nil, X485), ','(value(nil, X488), tappend(X485, X486, X489))), SCOPE: 58, CLAUSE: 18 | ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: ','(value(nil, X488), tappend(nil, X486, X489)) | ','(right(nil, X485), ','(value(nil, X488), tappend(X485, X486, X489))), SCOPE: 58, CLAUSE: 18 | ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: ','(value(nil, X488), tappend(nil, X486, X489)), SCOPE: 59, CLAUSE: 19 | ','(value(nil, X488), tappend(nil, X486, X489)), SCOPE: 59, CLAUSE: 20 | ','(right(nil, X485), ','(value(nil, X488), tappend(X485, X486, X489))), SCOPE: 58, CLAUSE: 18 | ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: tappend(nil, X486, X489) | ','(value(nil, X488), tappend(nil, X486, X489)), SCOPE: 59, CLAUSE: 20 | ','(right(nil, X485), ','(value(nil, X488), tappend(X485, X486, X489))), SCOPE: 58, CLAUSE: 18 | ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: tappend(nil, X486, X489)\n\nX489 is free\nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: ','(value(nil, X488), tappend(nil, X486, X489)), SCOPE: 59, CLAUSE: 20 | ','(right(nil, X485), ','(value(nil, X488), tappend(X485, X486, X489))), SCOPE: 58, CLAUSE: 18 | ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: ','(right(nil, X485), ','(value(nil, X488), tappend(X485, X486, X489))), SCOPE: 58, CLAUSE: 18 | ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: ','(left(T236, X487), ','(right(T236, X485), ','(value(T236, X488), tappend(X485, X486, X489)))), SCOPE: 57, CLAUSE: 16\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: ','(right(node(T240, T241, T242), X485), ','(value(node(T240, T241, T242), X488), tappend(X485, X486, X489)))\n\nX488 is free\nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: \n\nX487 is free\nX499 is free; \nX500 is free; \nX501 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: ','(right(node(T240, T241, T242), X485), ','(value(node(T240, T241, T242), X488), tappend(X485, X486, X489))), SCOPE: 60, CLAUSE: 17 | ','(right(node(T240, T241, T242), X485), ','(value(node(T240, T241, T242), X488), tappend(X485, X486, X489))), SCOPE: 60, CLAUSE: 18\n\nX488 is free\nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: ','(right(node(T240, T241, T242), X485), ','(value(node(T240, T241, T242), X488), tappend(X485, X486, X489))), SCOPE: 60, CLAUSE: 18\n\nX488 is free\nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: ','(value(node(T246, T247, T248), X488), tappend(T248, X486, X489))\n\nX488 is free\nX489 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: ','(value(node(T246, T247, T248), X488), tappend(T248, X486, X489)), SCOPE: 61, CLAUSE: 19 | ','(value(node(T246, T247, T248), X488), tappend(T248, X486, X489)), SCOPE: 61, CLAUSE: 20\n\nX488 is free\nX489 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: ','(value(node(T246, T247, T248), X488), tappend(T248, X486, X489)), SCOPE: 61, CLAUSE: 20\n\nX488 is free\nX489 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: tappend(T252, X486, X489)\n\nX489 is free\nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: ','(right(node(T256, T257, T258), X485), ','(value(node(T256, T257, T258), X488), tappend(X485, X486, X489)))\n\nX487 is free\nX488 is free; \nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: \n\nX487 is free\nX517 is free; \nX518 is free; \nX519 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: ','(right(node(T256, T257, T258), X485), ','(value(node(T256, T257, T258), X488), tappend(X485, X486, X489))), SCOPE: 62, CLAUSE: 17 | ','(right(node(T256, T257, T258), X485), ','(value(node(T256, T257, T258), X488), tappend(X485, X486, X489))), SCOPE: 62, CLAUSE: 18\n\nX488 is free\nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: ','(right(node(T256, T257, T258), X485), ','(value(node(T256, T257, T258), X488), tappend(X485, X486, X489))), SCOPE: 62, CLAUSE: 18\n\nX488 is free\nX489 is free; \nX485 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: ','(value(node(T262, T263, T264), X488), tappend(T264, X486, X489))\n\nX488 is free\nX489 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: ','(value(node(T262, T263, T264), X488), tappend(T264, X486, X489)), SCOPE: 63, CLAUSE: 19 | ','(value(node(T262, T263, T264), X488), tappend(T264, X486, X489)), SCOPE: 63, CLAUSE: 20\n\nX488 is free\nX489 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: ','(value(node(T262, T263, T264), X488), tappend(T264, X486, X489)), SCOPE: 63, CLAUSE: 20\n\nX488 is free\nX489 is free; \nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: tappend(T268, X486, X489)\n\nX489 is free\nX486 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: tlast(T27, T26), SCOPE: 64, CLAUSE: 2 | tlast(T27, T26), SCOPE: 64, CLAUSE: 3 | tlast(T27, T26), SCOPE: 64, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: tlast(T27, T26), SCOPE: 64, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: tlast(T27, T26), SCOPE: 64, CLAUSE: 3 | tlast(T27, T26), SCOPE: 64, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: \n\nX534 is free", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: tlast(T27, T26), SCOPE: 64, CLAUSE: 3\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: tlast(T27, T26), SCOPE: 64, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: tlast(T274, T275)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: \n\nX543 is free\nX544 is free; \nX545 is free; \nX546 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
291 [label="291: tlast(T280, T281)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: \n\nX551 is free\nX552 is free; \nX553 is free; \nX554 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 293 [arrowhead = none ];
293 -> 2;

294 [label="EVAL with clause\ngoal(X18, X19, X20) :- ','(s2t(X18, X21), tapplast(X21, X19, X20)).\nand substitution\nT4 -> T7\nX18 -> T7\nT5 -> T10\nX19 -> T10\nT6 -> T11\nX20 -> T11\nT8 -> T10\nT9 -> T11", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 294 [arrowhead = none ];
294 -> 3;

295 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
3 -> 295 [arrowhead = none ];
295 -> 4;

296 [label="SPLIT 2\nreplacements:\nX21 -> T12", fontsize=14, style = filled, fillcolor = violet];
3 -> 296 [arrowhead = none ];
296 -> 5;

297 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4 -> 297 [arrowhead = none ];
297 -> 6;

298 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5 -> 298 [arrowhead = none ];
298 -> 36;

299 [label="EVAL with clause\ns2t(0, X23) :- ','(!, eq(X23, nil)).\nand substitution\nT7 -> 0\nX21 -> X24\nX23 -> X24", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 299 [arrowhead = none ];
299 -> 7;

300 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 300 [arrowhead = none ];
300 -> 8;

301 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 301 [arrowhead = none ];
301 -> 9;

302 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 302 [arrowhead = none ];
302 -> 13;

303 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 303 [arrowhead = none ];
303 -> 14;

304 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 304 [arrowhead = none ];
304 -> 10;

305 [label="EVAL with clause\neq(X26, X26).\nand substitution\nX24 -> nil\nX26 -> nil\nX27 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 305 [arrowhead = none ];
305 -> 11;

306 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 306 [arrowhead = none ];
306 -> 12;

307 [label="EVAL with clause\ns2t(X34, node(X35, X36, X35)) :- ','(p(X34, X37), s2t(X37, X35)).\nand substitution\nT7 -> T13\nX34 -> T13\nX35 -> X38\nX36 -> X39\nX21 -> node(X38, X39, X38)", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 307 [arrowhead = none ];
307 -> 15;

308 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 308 [arrowhead = none ];
308 -> 20;

309 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 309 [arrowhead = none ];
309 -> 21;

310 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 310 [arrowhead = none ];
310 -> 16;

311 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T13, X21), s2t(0, X23))", fontsize=14, style = filled, fillcolor = white];
16 -> 311 [arrowhead = none ];
311 -> 17;

312 [label="EVAL with clause\np(s(X41), X41).\nand substitution\nX41 -> T14\nT13 -> s(T14)\nX37 -> T14", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 312 [arrowhead = none ];
312 -> 18;

313 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 313 [arrowhead = none ];
313 -> 19;

314 [label="INSTANCE with matching:\nT7 -> T14\nX21 -> X38", fontsize=14, style = filled, fillcolor = lightgrey];
18 -> 314 [arrowhead = none , style=dashed];
314 -> 4[style=dashed];

315 [label="EVAL with clause\ns2t(X48, node(nil, X49, X50)) :- ','(p(X48, X51), s2t(X51, X50)).\nand substitution\nT7 -> T15\nX48 -> T15\nX49 -> X52\nX50 -> X53\nX21 -> node(nil, X52, X53)", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 315 [arrowhead = none ];
315 -> 22;

316 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 316 [arrowhead = none ];
316 -> 27;

317 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 317 [arrowhead = none ];
317 -> 28;

318 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
22 -> 318 [arrowhead = none ];
318 -> 23;

319 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T15, X21), s2t(0, X23))", fontsize=14, style = filled, fillcolor = white];
23 -> 319 [arrowhead = none ];
319 -> 24;

320 [label="EVAL with clause\np(s(X55), X55).\nand substitution\nX55 -> T16\nT15 -> s(T16)\nX51 -> T16", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 320 [arrowhead = none ];
320 -> 25;

321 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 321 [arrowhead = none ];
321 -> 26;

322 [label="INSTANCE with matching:\nT7 -> T16\nX21 -> X53", fontsize=14, style = filled, fillcolor = lightgrey];
25 -> 322 [arrowhead = none , style=dashed];
322 -> 4[style=dashed];

323 [label="EVAL with clause\ns2t(X62, node(X63, X64, nil)) :- ','(p(X62, X65), s2t(X65, X63)).\nand substitution\nT7 -> T17\nX62 -> T17\nX63 -> X66\nX64 -> X67\nX21 -> node(X66, X67, nil)", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 323 [arrowhead = none ];
323 -> 29;

324 [label="EVAL with clause\ns2t(X72, node(nil, X73, nil)).\nand substitution\nT7 -> T19\nX72 -> T19\nX73 -> X74\nX21 -> node(nil, X74, nil)", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 324 [arrowhead = none ];
324 -> 34;

325 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
29 -> 325 [arrowhead = none ];
325 -> 30;

326 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T17, X21), s2t(0, X23))", fontsize=14, style = filled, fillcolor = white];
30 -> 326 [arrowhead = none ];
326 -> 31;

327 [label="EVAL with clause\np(s(X69), X69).\nand substitution\nX69 -> T18\nT17 -> s(T18)\nX65 -> T18", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 327 [arrowhead = none ];
327 -> 32;

328 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 328 [arrowhead = none ];
328 -> 33;

329 [label="INSTANCE with matching:\nT7 -> T18\nX21 -> X66", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 329 [arrowhead = none , style=dashed];
329 -> 4[style=dashed];

330 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
34 -> 330 [arrowhead = none ];
330 -> 35;

331 [label="EVAL with clause\ntapplast(X78, X79, X80) :- ','(tappend(X78, node(nil, X79, nil), X81), tlast(X80, X81)).\nand substitution\nT12 -> T23\nX78 -> T23\nT10 -> T24\nX79 -> T24\nT11 -> T25\nX80 -> T25\nT20 -> T23\nT21 -> T24\nT22 -> T25", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 331 [arrowhead = none ];
331 -> 37;

332 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
37 -> 332 [arrowhead = none ];
332 -> 38;

333 [label="SPLIT 2\nreplacements:\nX81 -> T26\nT25 -> T27", fontsize=14, style = filled, fillcolor = violet];
37 -> 333 [arrowhead = none ];
333 -> 39;

334 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
38 -> 334 [arrowhead = none ];
334 -> 40;

335 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
39 -> 335 [arrowhead = none ];
335 -> 281;

336 [label="EVAL with clause\ntappend(nil, X84, X85) :- ','(!, eq(X84, X85)).\nand substitution\nT23 -> nil\nT24 -> T29\nX84 -> node(nil, T29, nil)\nX81 -> X86\nX85 -> X86\nT28 -> T29", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 336 [arrowhead = none ];
336 -> 41;

337 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 337 [arrowhead = none ];
337 -> 42;

338 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 338 [arrowhead = none ];
338 -> 43;

339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
42 -> 339 [arrowhead = none ];
339 -> 47;

340 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
42 -> 340 [arrowhead = none ];
340 -> 48;

341 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
43 -> 341 [arrowhead = none ];
341 -> 44;

342 [label="EVAL with clause\neq(X88, X88).\nand substitution\nT29 -> T30\nX88 -> node(nil, T30, nil)\nX86 -> node(nil, T30, nil)", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 342 [arrowhead = none ];
342 -> 45;

343 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
45 -> 343 [arrowhead = none ];
343 -> 46;

344 [label="EVAL with clause\ntappend(X97, X98, node(X98, X99, X100)) :- ','(left(X97, nil), ','(right(X97, X100), value(X97, X99))).\nand substitution\nT23 -> T33\nX97 -> T33\nT24 -> T32\nX98 -> node(nil, T32, nil)\nX99 -> X101\nX100 -> X102\nX81 -> node(node(nil, T32, nil), X101, X102)\nT31 -> T33", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 344 [arrowhead = none ];
344 -> 49;

345 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
48 -> 345 [arrowhead = none ];
345 -> 78;

346 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
48 -> 346 [arrowhead = none ];
346 -> 79;

347 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
49 -> 347 [arrowhead = none ];
347 -> 50;

348 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT33 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 348 [arrowhead = none ];
348 -> 51;

349 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 349 [arrowhead = none ];
349 -> 52;

350 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
51 -> 350 [arrowhead = none ];
350 -> 53;

351 [label="EVAL with clause\nleft(node(X130, X131, X132), X130).\nand substitution\nX130 -> nil\nX131 -> T48\nX132 -> T49\nT33 -> node(nil, T48, T49)\nT45 -> nil\nT46 -> T48\nT47 -> T49", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 351 [arrowhead = none ];
351 -> 69;

352 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
52 -> 352 [arrowhead = none ];
352 -> 70;

353 [label="EVAL with clause\nright(nil, nil).\nand substitution\nX102 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
53 -> 353 [arrowhead = none ];
353 -> 54;

354 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 354 [arrowhead = none ];
354 -> 55;

355 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX101 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 355 [arrowhead = none ];
355 -> 56;

356 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
56 -> 356 [arrowhead = none ];
356 -> 57;

357 [label="BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
57 -> 357 [arrowhead = none ];
357 -> 58;

358 [label="BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
58 -> 358 [arrowhead = none ];
358 -> 59;

359 [label="EVAL with clause\nleft(node(X112, X113, X114), X112).\nand substitution\nX112 -> nil\nX113 -> T37\nX114 -> T38\nT33 -> node(nil, T37, T38)\nT34 -> nil\nT35 -> T37\nT36 -> T38", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 359 [arrowhead = none ];
359 -> 60;

360 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 360 [arrowhead = none ];
360 -> 61;

361 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
60 -> 361 [arrowhead = none ];
361 -> 62;

362 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
62 -> 362 [arrowhead = none ];
362 -> 63;

363 [label="EVAL with clause\nright(node(X118, X119, X120), X120).\nand substitution\nX118 -> nil\nT37 -> T41\nX119 -> T41\nT38 -> T42\nX120 -> T42\nX102 -> T42\nT39 -> T41\nT40 -> T42", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 363 [arrowhead = none ];
363 -> 64;

364 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
64 -> 364 [arrowhead = none ];
364 -> 65;

365 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
65 -> 365 [arrowhead = none ];
365 -> 66;

366 [label="EVAL with clause\nvalue(node(X124, X125, X126), X125).\nand substitution\nX124 -> nil\nT41 -> T43\nX125 -> T43\nT42 -> T44\nX126 -> T44\nX101 -> T43", fontsize=14, style = filled, fillcolor = lightblue];
66 -> 366 [arrowhead = none ];
366 -> 67;

367 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 367 [arrowhead = none ];
367 -> 68;

368 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
69 -> 368 [arrowhead = none ];
368 -> 71;

369 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
71 -> 369 [arrowhead = none ];
369 -> 72;

370 [label="EVAL with clause\nright(node(X136, X137, X138), X138).\nand substitution\nX136 -> nil\nT48 -> T52\nX137 -> T52\nT49 -> T53\nX138 -> T53\nX102 -> T53\nT50 -> T52\nT51 -> T53", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 370 [arrowhead = none ];
370 -> 73;

371 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
73 -> 371 [arrowhead = none ];
371 -> 74;

372 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
74 -> 372 [arrowhead = none ];
372 -> 75;

373 [label="EVAL with clause\nvalue(node(X142, X143, X144), X143).\nand substitution\nX142 -> nil\nT52 -> T54\nX143 -> T54\nT53 -> T55\nX144 -> T55\nX101 -> T54", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 373 [arrowhead = none ];
373 -> 76;

374 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
76 -> 374 [arrowhead = none ];
374 -> 77;

375 [label="EVAL with clause\ntappend(X153, X154, node(X155, X156, X154)) :- ','(left(X153, X155), ','(right(X153, nil), value(X153, X156))).\nand substitution\nT23 -> T58\nX153 -> T58\nT24 -> T57\nX154 -> node(nil, T57, nil)\nX155 -> X157\nX156 -> X158\nX81 -> node(X157, X158, node(nil, T57, nil))\nT56 -> T58", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 375 [arrowhead = none ];
375 -> 80;

376 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
79 -> 376 [arrowhead = none ];
376 -> 111;

377 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
79 -> 377 [arrowhead = none ];
377 -> 112;

378 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
80 -> 378 [arrowhead = none ];
378 -> 81;

379 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT58 -> nil\nX157 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 379 [arrowhead = none ];
379 -> 82;

380 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 380 [arrowhead = none ];
380 -> 83;

381 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
82 -> 381 [arrowhead = none ];
381 -> 84;

382 [label="EVAL with clause\nleft(node(X186, X187, X188), X186).\nand substitution\nX186 -> T75\nX187 -> T76\nX188 -> T77\nT58 -> node(T75, T76, T77)\nX157 -> T75\nT72 -> T75\nT73 -> T76\nT74 -> T77", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 382 [arrowhead = none ];
382 -> 101;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 383 [arrowhead = none ];
383 -> 102;

384 [label="EVAL with clause\nright(nil, nil).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 384 [arrowhead = none ];
384 -> 85;

385 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
85 -> 385 [arrowhead = none ];
385 -> 86;

386 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX158 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 386 [arrowhead = none ];
386 -> 87;

387 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
87 -> 387 [arrowhead = none ];
387 -> 88;

388 [label="BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
88 -> 388 [arrowhead = none ];
388 -> 89;

389 [label="BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
89 -> 389 [arrowhead = none ];
389 -> 90;

390 [label="EVAL with clause\nleft(node(X168, X169, X170), X168).\nand substitution\nX168 -> T62\nX169 -> T63\nX170 -> T64\nT58 -> node(T62, T63, T64)\nX157 -> T62\nT59 -> T62\nT60 -> T63\nT61 -> T64", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 390 [arrowhead = none ];
390 -> 91;

391 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 391 [arrowhead = none ];
391 -> 92;

392 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 392 [arrowhead = none ];
392 -> 93;

393 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
93 -> 393 [arrowhead = none ];
393 -> 94;

394 [label="EVAL with clause\nright(node(X174, X175, X176), X176).\nand substitution\nT62 -> T68\nX174 -> T68\nT63 -> T69\nX175 -> T69\nT64 -> nil\nX176 -> nil\nT67 -> nil\nT65 -> T68\nT66 -> T69", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 394 [arrowhead = none ];
394 -> 95;

395 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 395 [arrowhead = none ];
395 -> 96;

396 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
95 -> 396 [arrowhead = none ];
396 -> 97;

397 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
97 -> 397 [arrowhead = none ];
397 -> 98;

398 [label="EVAL with clause\nvalue(node(X180, X181, X182), X181).\nand substitution\nT68 -> T70\nX180 -> T70\nT69 -> T71\nX181 -> T71\nX182 -> nil\nX158 -> T71", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 398 [arrowhead = none ];
398 -> 99;

399 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 399 [arrowhead = none ];
399 -> 100;

400 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
101 -> 400 [arrowhead = none ];
400 -> 103;

401 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
103 -> 401 [arrowhead = none ];
401 -> 104;

402 [label="EVAL with clause\nright(node(X192, X193, X194), X194).\nand substitution\nT75 -> T81\nX192 -> T81\nT76 -> T82\nX193 -> T82\nT77 -> nil\nX194 -> nil\nT80 -> nil\nT78 -> T81\nT79 -> T82", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 402 [arrowhead = none ];
402 -> 105;

403 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 403 [arrowhead = none ];
403 -> 106;

404 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
105 -> 404 [arrowhead = none ];
404 -> 107;

405 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
107 -> 405 [arrowhead = none ];
405 -> 108;

406 [label="EVAL with clause\nvalue(node(X198, X199, X200), X199).\nand substitution\nT81 -> T83\nX198 -> T83\nT82 -> T84\nX199 -> T84\nX200 -> nil\nX158 -> T84", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 406 [arrowhead = none ];
406 -> 109;

407 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
109 -> 407 [arrowhead = none ];
407 -> 110;

408 [label="EVAL with clause\ntappend(X211, X212, node(X213, X214, X215)) :- ','(left(X211, X216), ','(right(X211, X215), ','(value(X211, X214), tappend(X216, X212, X213)))).\nand substitution\nT23 -> T87\nX211 -> T87\nT24 -> T88\nX212 -> node(nil, T88, nil)\nX213 -> X217\nX214 -> X218\nX215 -> X219\nX81 -> node(X217, X218, X219)\nT85 -> T87\nT86 -> T88", fontsize=14, style = filled, fillcolor = lightblue];
111 -> 408 [arrowhead = none ];
408 -> 113;

409 [label="EVAL with clause\ntappend(X266, X267, node(X267, X268, X269)) :- ','(left(X266, X267), ','(right(X266, X270), ','(value(X266, X268), tappend(X270, X271, X269)))).\nand substitution\nT23 -> T130\nX266 -> T130\nT24 -> T131\nX267 -> node(nil, T131, nil)\nX268 -> X272\nX269 -> X273\nX81 -> node(node(nil, T131, nil), X272, X273)\nT128 -> T130\nT129 -> T131", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 409 [arrowhead = none ];
409 -> 141;

410 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
113 -> 410 [arrowhead = none ];
410 -> 114;

411 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT87 -> nil\nX216 -> nil\nT88 -> T89", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 411 [arrowhead = none ];
411 -> 115;

412 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 412 [arrowhead = none ];
412 -> 116;

413 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
115 -> 413 [arrowhead = none ];
413 -> 117;

414 [label="EVAL with clause\nleft(node(X247, X248, X249), X247).\nand substitution\nX247 -> T112\nX248 -> T113\nX249 -> T114\nT87 -> node(T112, T113, T114)\nX216 -> T112\nT109 -> T112\nT110 -> T113\nT111 -> T114\nT88 -> T115", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 414 [arrowhead = none ];
414 -> 133;

415 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
116 -> 415 [arrowhead = none ];
415 -> 134;

416 [label="EVAL with clause\nright(nil, nil).\nand substitution\nX219 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
117 -> 416 [arrowhead = none ];
416 -> 118;

417 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
118 -> 417 [arrowhead = none ];
417 -> 119;

418 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX218 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
119 -> 418 [arrowhead = none ];
418 -> 120;

419 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
120 -> 419 [arrowhead = none ];
419 -> 121;

420 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
120 -> 420 [arrowhead = none ];
420 -> 122;

421 [label="INSTANCE with matching:\nT23 -> nil\nT24 -> T89\nX81 -> X217", fontsize=14, style = filled, fillcolor = lightgrey];
121 -> 421 [arrowhead = none , style=dashed];
421 -> 38[style=dashed];

422 [label="BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
122 -> 422 [arrowhead = none ];
422 -> 123;

423 [label="BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
123 -> 423 [arrowhead = none ];
423 -> 124;

424 [label="EVAL with clause\nleft(node(X229, X230, X231), X229).\nand substitution\nX229 -> T93\nX230 -> T94\nX231 -> T95\nT87 -> node(T93, T94, T95)\nX216 -> T93\nT90 -> T93\nT91 -> T94\nT92 -> T95\nT88 -> T96", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 424 [arrowhead = none ];
424 -> 125;

425 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 425 [arrowhead = none ];
425 -> 126;

426 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
125 -> 426 [arrowhead = none ];
426 -> 127;

427 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
127 -> 427 [arrowhead = none ];
427 -> 128;

428 [label="EVAL with clause\nright(node(X235, X236, X237), X237).\nand substitution\nT93 -> T100\nX235 -> T100\nT94 -> T101\nX236 -> T101\nT95 -> T102\nX237 -> T102\nX219 -> T102\nT97 -> T100\nT98 -> T101\nT99 -> T102\nT96 -> T103", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 428 [arrowhead = none ];
428 -> 129;

429 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
129 -> 429 [arrowhead = none ];
429 -> 130;

430 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
130 -> 430 [arrowhead = none ];
430 -> 131;

431 [label="EVAL with clause\nvalue(node(X241, X242, X243), X242).\nand substitution\nT100 -> T107\nX241 -> T107\nT101 -> T105\nX242 -> T105\nT102 -> T106\nX243 -> T106\nX218 -> T105\nT104 -> T107\nT103 -> T108", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 431 [arrowhead = none ];
431 -> 132;

432 [label="INSTANCE with matching:\nT23 -> T107\nT24 -> T108\nX81 -> X217", fontsize=14, style = filled, fillcolor = lightgrey];
132 -> 432 [arrowhead = none , style=dashed];
432 -> 38[style=dashed];

433 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 433 [arrowhead = none ];
433 -> 135;

434 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
135 -> 434 [arrowhead = none ];
434 -> 136;

435 [label="EVAL with clause\nright(node(X253, X254, X255), X255).\nand substitution\nT112 -> T119\nX253 -> T119\nT113 -> T120\nX254 -> T120\nT114 -> T121\nX255 -> T121\nX219 -> T121\nT116 -> T119\nT117 -> T120\nT118 -> T121\nT115 -> T122", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 435 [arrowhead = none ];
435 -> 137;

436 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
137 -> 436 [arrowhead = none ];
436 -> 138;

437 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
138 -> 437 [arrowhead = none ];
437 -> 139;

438 [label="EVAL with clause\nvalue(node(X259, X260, X261), X260).\nand substitution\nT119 -> T126\nX259 -> T126\nT120 -> T124\nX260 -> T124\nT121 -> T125\nX261 -> T125\nX218 -> T124\nT123 -> T126\nT122 -> T127", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 438 [arrowhead = none ];
438 -> 140;

439 [label="INSTANCE with matching:\nT23 -> T126\nT24 -> T127\nX81 -> X217", fontsize=14, style = filled, fillcolor = lightgrey];
140 -> 439 [arrowhead = none , style=dashed];
439 -> 38[style=dashed];

440 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
141 -> 440 [arrowhead = none ];
440 -> 142;

441 [label="BACKTRACK\nfor clause: left(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
142 -> 441 [arrowhead = none ];
441 -> 143;

442 [label="EVAL with clause\nleft(node(X277, X278, X279), X277).\nand substitution\nX277 -> node(nil, T138, nil)\nX278 -> T136\nX279 -> T137\nT130 -> node(node(nil, T138, nil), T136, T137)\nT131 -> T138\nT132 -> node(nil, T138, nil)\nT133 -> T136\nT134 -> T137\nT135 -> T138", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 442 [arrowhead = none ];
442 -> 144;

443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 443 [arrowhead = none ];
443 -> 145;

444 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
144 -> 444 [arrowhead = none ];
444 -> 146;

445 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
146 -> 445 [arrowhead = none ];
445 -> 147;

446 [label="EVAL with clause\nright(node(X283, X284, X285), X285).\nand substitution\nT138 -> T144\nX283 -> node(nil, T144, nil)\nT136 -> T142\nX284 -> T142\nT137 -> T143\nX285 -> T143\nX270 -> T143\nT140 -> T142\nT141 -> T143\nT139 -> T144", fontsize=14, style = filled, fillcolor = lightblue];
147 -> 446 [arrowhead = none ];
446 -> 148;

447 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
148 -> 447 [arrowhead = none ];
447 -> 149;

448 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
149 -> 448 [arrowhead = none ];
448 -> 150;

449 [label="EVAL with clause\nvalue(node(X289, X290, X291), X290).\nand substitution\nT144 -> T145\nX289 -> node(nil, T145, nil)\nT142 -> T146\nX290 -> T146\nT143 -> T148\nX291 -> T148\nX272 -> T146\nT147 -> T148", fontsize=14, style = filled, fillcolor = lightblue];
150 -> 449 [arrowhead = none ];
449 -> 151;

450 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
151 -> 450 [arrowhead = none ];
450 -> 152;

451 [label="EVAL with clause\ntappend(nil, X294, X295) :- ','(!, eq(X294, X295)).\nand substitution\nT148 -> nil\nX271 -> X296\nX294 -> X296\nX273 -> X297\nX295 -> X297", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 451 [arrowhead = none ];
451 -> 153;

452 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 452 [arrowhead = none ];
452 -> 154;

453 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
153 -> 453 [arrowhead = none ];
453 -> 155;

454 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 454 [arrowhead = none ];
454 -> 159;

455 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 455 [arrowhead = none ];
455 -> 160;

456 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
155 -> 456 [arrowhead = none ];
456 -> 156;

457 [label="EVAL with clause\neq(X299, X299).\nand substitution\nX296 -> X300\nX299 -> X300\nX297 -> X300", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 457 [arrowhead = none ];
457 -> 157;

458 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
157 -> 458 [arrowhead = none ];
458 -> 158;

459 [label="EVAL with clause\ntappend(X309, X310, node(X310, X311, X312)) :- ','(left(X309, nil), ','(right(X309, X312), value(X309, X311))).\nand substitution\nT148 -> T150\nX309 -> T150\nX271 -> X313\nX310 -> X313\nX311 -> X314\nX312 -> X315\nX273 -> node(X313, X314, X315)\nT149 -> T150", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 459 [arrowhead = none ];
459 -> 161;

460 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
160 -> 460 [arrowhead = none ];
460 -> 190;

461 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
160 -> 461 [arrowhead = none ];
461 -> 191;

462 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
161 -> 462 [arrowhead = none ];
462 -> 162;

463 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT150 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 463 [arrowhead = none ];
463 -> 163;

464 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 464 [arrowhead = none ];
464 -> 164;

465 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
163 -> 465 [arrowhead = none ];
465 -> 165;

466 [label="EVAL with clause\nleft(node(X343, X344, X345), X343).\nand substitution\nX343 -> nil\nX344 -> T165\nX345 -> T166\nT150 -> node(nil, T165, T166)\nT162 -> nil\nT163 -> T165\nT164 -> T166", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 466 [arrowhead = none ];
466 -> 181;

467 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 467 [arrowhead = none ];
467 -> 182;

468 [label="EVAL with clause\nright(nil, nil).\nand substitution\nX315 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 468 [arrowhead = none ];
468 -> 166;

469 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
166 -> 469 [arrowhead = none ];
469 -> 167;

470 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX314 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
167 -> 470 [arrowhead = none ];
470 -> 168;

471 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
168 -> 471 [arrowhead = none ];
471 -> 169;

472 [label="BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
169 -> 472 [arrowhead = none ];
472 -> 170;

473 [label="BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
170 -> 473 [arrowhead = none ];
473 -> 171;

474 [label="EVAL with clause\nleft(node(X325, X326, X327), X325).\nand substitution\nX325 -> nil\nX326 -> T154\nX327 -> T155\nT150 -> node(nil, T154, T155)\nT151 -> nil\nT152 -> T154\nT153 -> T155", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 474 [arrowhead = none ];
474 -> 172;

475 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 475 [arrowhead = none ];
475 -> 173;

476 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
172 -> 476 [arrowhead = none ];
476 -> 174;

477 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
174 -> 477 [arrowhead = none ];
477 -> 175;

478 [label="EVAL with clause\nright(node(X331, X332, X333), X333).\nand substitution\nX331 -> nil\nT154 -> T158\nX332 -> T158\nT155 -> T159\nX333 -> T159\nX315 -> T159\nT156 -> T158\nT157 -> T159", fontsize=14, style = filled, fillcolor = lightblue];
175 -> 478 [arrowhead = none ];
478 -> 176;

479 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
176 -> 479 [arrowhead = none ];
479 -> 177;

480 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
177 -> 480 [arrowhead = none ];
480 -> 178;

481 [label="EVAL with clause\nvalue(node(X337, X338, X339), X338).\nand substitution\nX337 -> nil\nT158 -> T160\nX338 -> T160\nT159 -> T161\nX339 -> T161\nX314 -> T160", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 481 [arrowhead = none ];
481 -> 179;

482 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
179 -> 482 [arrowhead = none ];
482 -> 180;

483 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
181 -> 483 [arrowhead = none ];
483 -> 183;

484 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
183 -> 484 [arrowhead = none ];
484 -> 184;

485 [label="EVAL with clause\nright(node(X349, X350, X351), X351).\nand substitution\nX349 -> nil\nT165 -> T169\nX350 -> T169\nT166 -> T170\nX351 -> T170\nX315 -> T170\nT167 -> T169\nT168 -> T170", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 485 [arrowhead = none ];
485 -> 185;

486 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
185 -> 486 [arrowhead = none ];
486 -> 186;

487 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
186 -> 487 [arrowhead = none ];
487 -> 187;

488 [label="EVAL with clause\nvalue(node(X355, X356, X357), X356).\nand substitution\nX355 -> nil\nT169 -> T171\nX356 -> T171\nT170 -> T172\nX357 -> T172\nX314 -> T171", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 488 [arrowhead = none ];
488 -> 188;

489 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
188 -> 489 [arrowhead = none ];
489 -> 189;

490 [label="EVAL with clause\ntappend(X366, X367, node(X368, X369, X367)) :- ','(left(X366, X368), ','(right(X366, nil), value(X366, X369))).\nand substitution\nT148 -> T174\nX366 -> T174\nX271 -> X370\nX367 -> X370\nX368 -> X371\nX369 -> X372\nX273 -> node(X371, X372, X370)\nT173 -> T174", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 490 [arrowhead = none ];
490 -> 192;

491 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
191 -> 491 [arrowhead = none ];
491 -> 223;

492 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
191 -> 492 [arrowhead = none ];
492 -> 224;

493 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
192 -> 493 [arrowhead = none ];
493 -> 193;

494 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT174 -> nil\nX371 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 494 [arrowhead = none ];
494 -> 194;

495 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
193 -> 495 [arrowhead = none ];
495 -> 195;

496 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
194 -> 496 [arrowhead = none ];
496 -> 196;

497 [label="EVAL with clause\nleft(node(X400, X401, X402), X400).\nand substitution\nX400 -> T191\nX401 -> T192\nX402 -> T193\nT174 -> node(T191, T192, T193)\nX371 -> T191\nT188 -> T191\nT189 -> T192\nT190 -> T193", fontsize=14, style = filled, fillcolor = lightblue];
195 -> 497 [arrowhead = none ];
497 -> 213;

498 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
195 -> 498 [arrowhead = none ];
498 -> 214;

499 [label="EVAL with clause\nright(nil, nil).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 499 [arrowhead = none ];
499 -> 197;

500 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
197 -> 500 [arrowhead = none ];
500 -> 198;

501 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX372 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
198 -> 501 [arrowhead = none ];
501 -> 199;

502 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
199 -> 502 [arrowhead = none ];
502 -> 200;

503 [label="BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
200 -> 503 [arrowhead = none ];
503 -> 201;

504 [label="BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
201 -> 504 [arrowhead = none ];
504 -> 202;

505 [label="EVAL with clause\nleft(node(X382, X383, X384), X382).\nand substitution\nX382 -> T178\nX383 -> T179\nX384 -> T180\nT174 -> node(T178, T179, T180)\nX371 -> T178\nT175 -> T178\nT176 -> T179\nT177 -> T180", fontsize=14, style = filled, fillcolor = lightblue];
202 -> 505 [arrowhead = none ];
505 -> 203;

506 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
202 -> 506 [arrowhead = none ];
506 -> 204;

507 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
203 -> 507 [arrowhead = none ];
507 -> 205;

508 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
205 -> 508 [arrowhead = none ];
508 -> 206;

509 [label="EVAL with clause\nright(node(X388, X389, X390), X390).\nand substitution\nT178 -> T184\nX388 -> T184\nT179 -> T185\nX389 -> T185\nT180 -> nil\nX390 -> nil\nT183 -> nil\nT181 -> T184\nT182 -> T185", fontsize=14, style = filled, fillcolor = lightblue];
206 -> 509 [arrowhead = none ];
509 -> 207;

510 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
206 -> 510 [arrowhead = none ];
510 -> 208;

511 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
207 -> 511 [arrowhead = none ];
511 -> 209;

512 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
209 -> 512 [arrowhead = none ];
512 -> 210;

513 [label="EVAL with clause\nvalue(node(X394, X395, X396), X395).\nand substitution\nT184 -> T186\nX394 -> T186\nT185 -> T187\nX395 -> T187\nX396 -> nil\nX372 -> T187", fontsize=14, style = filled, fillcolor = lightblue];
210 -> 513 [arrowhead = none ];
513 -> 211;

514 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
211 -> 514 [arrowhead = none ];
514 -> 212;

515 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
213 -> 515 [arrowhead = none ];
515 -> 215;

516 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
215 -> 516 [arrowhead = none ];
516 -> 216;

517 [label="EVAL with clause\nright(node(X406, X407, X408), X408).\nand substitution\nT191 -> T197\nX406 -> T197\nT192 -> T198\nX407 -> T198\nT193 -> nil\nX408 -> nil\nT196 -> nil\nT194 -> T197\nT195 -> T198", fontsize=14, style = filled, fillcolor = lightblue];
216 -> 517 [arrowhead = none ];
517 -> 217;

518 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
216 -> 518 [arrowhead = none ];
518 -> 218;

519 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
217 -> 519 [arrowhead = none ];
519 -> 219;

520 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
219 -> 520 [arrowhead = none ];
520 -> 220;

521 [label="EVAL with clause\nvalue(node(X412, X413, X414), X413).\nand substitution\nT197 -> T199\nX412 -> T199\nT198 -> T200\nX413 -> T200\nX414 -> nil\nX372 -> T200", fontsize=14, style = filled, fillcolor = lightblue];
220 -> 521 [arrowhead = none ];
521 -> 221;

522 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
221 -> 522 [arrowhead = none ];
522 -> 222;

523 [label="EVAL with clause\ntappend(X425, X426, node(X427, X428, X429)) :- ','(left(X425, X430), ','(right(X425, X429), ','(value(X425, X428), tappend(X430, X426, X427)))).\nand substitution\nT148 -> T202\nX425 -> T202\nX271 -> X431\nX426 -> X431\nX427 -> X432\nX428 -> X433\nX429 -> X434\nX273 -> node(X432, X433, X434)\nT201 -> T202", fontsize=14, style = filled, fillcolor = lightblue];
223 -> 523 [arrowhead = none ];
523 -> 225;

524 [label="EVAL with clause\ntappend(X481, X482, node(X482, X483, X484)) :- ','(left(X481, X482), ','(right(X481, X485), ','(value(X481, X483), tappend(X485, X486, X484)))).\nand substitution\nT148 -> T236\nX481 -> T236\nX271 -> X487\nX482 -> X487\nX483 -> X488\nX484 -> X489\nX273 -> node(X487, X488, X489)\nT235 -> T236", fontsize=14, style = filled, fillcolor = lightblue];
224 -> 524 [arrowhead = none ];
524 -> 253;

525 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
225 -> 525 [arrowhead = none ];
525 -> 226;

526 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT202 -> nil\nX430 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
226 -> 526 [arrowhead = none ];
526 -> 227;

527 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
226 -> 527 [arrowhead = none ];
527 -> 228;

528 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
227 -> 528 [arrowhead = none ];
528 -> 229;

529 [label="EVAL with clause\nleft(node(X462, X463, X464), X462).\nand substitution\nX462 -> T222\nX463 -> T223\nX464 -> T224\nT202 -> node(T222, T223, T224)\nX430 -> T222\nT219 -> T222\nT220 -> T223\nT221 -> T224", fontsize=14, style = filled, fillcolor = lightblue];
228 -> 529 [arrowhead = none ];
529 -> 245;

530 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
228 -> 530 [arrowhead = none ];
530 -> 246;

531 [label="EVAL with clause\nright(nil, nil).\nand substitution\nX434 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
229 -> 531 [arrowhead = none ];
531 -> 230;

532 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
230 -> 532 [arrowhead = none ];
532 -> 231;

533 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX433 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
231 -> 533 [arrowhead = none ];
533 -> 232;

534 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
232 -> 534 [arrowhead = none ];
534 -> 233;

535 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
232 -> 535 [arrowhead = none ];
535 -> 234;

536 [label="INSTANCE with matching:\nT148 -> nil\nX271 -> X431\nX273 -> X432", fontsize=14, style = filled, fillcolor = lightgrey];
233 -> 536 [arrowhead = none , style=dashed];
536 -> 151[style=dashed];

537 [label="BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
234 -> 537 [arrowhead = none ];
537 -> 235;

538 [label="BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
235 -> 538 [arrowhead = none ];
538 -> 236;

539 [label="EVAL with clause\nleft(node(X444, X445, X446), X444).\nand substitution\nX444 -> T206\nX445 -> T207\nX446 -> T208\nT202 -> node(T206, T207, T208)\nX430 -> T206\nT203 -> T206\nT204 -> T207\nT205 -> T208", fontsize=14, style = filled, fillcolor = lightblue];
236 -> 539 [arrowhead = none ];
539 -> 237;

540 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
236 -> 540 [arrowhead = none ];
540 -> 238;

541 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
237 -> 541 [arrowhead = none ];
541 -> 239;

542 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
239 -> 542 [arrowhead = none ];
542 -> 240;

543 [label="EVAL with clause\nright(node(X450, X451, X452), X452).\nand substitution\nT206 -> T212\nX450 -> T212\nT207 -> T213\nX451 -> T213\nT208 -> T214\nX452 -> T214\nX434 -> T214\nT209 -> T212\nT210 -> T213\nT211 -> T214", fontsize=14, style = filled, fillcolor = lightblue];
240 -> 543 [arrowhead = none ];
543 -> 241;

544 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
241 -> 544 [arrowhead = none ];
544 -> 242;

545 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
242 -> 545 [arrowhead = none ];
545 -> 243;

546 [label="EVAL with clause\nvalue(node(X456, X457, X458), X457).\nand substitution\nT212 -> T218\nX456 -> T218\nT213 -> T216\nX457 -> T216\nT214 -> T217\nX458 -> T217\nX433 -> T216\nT215 -> T218", fontsize=14, style = filled, fillcolor = lightblue];
243 -> 546 [arrowhead = none ];
546 -> 244;

547 [label="INSTANCE with matching:\nT148 -> T218\nX271 -> X431\nX273 -> X432", fontsize=14, style = filled, fillcolor = lightgrey];
244 -> 547 [arrowhead = none , style=dashed];
547 -> 151[style=dashed];

548 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
245 -> 548 [arrowhead = none ];
548 -> 247;

549 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
247 -> 549 [arrowhead = none ];
549 -> 248;

550 [label="EVAL with clause\nright(node(X468, X469, X470), X470).\nand substitution\nT222 -> T228\nX468 -> T228\nT223 -> T229\nX469 -> T229\nT224 -> T230\nX470 -> T230\nX434 -> T230\nT225 -> T228\nT226 -> T229\nT227 -> T230", fontsize=14, style = filled, fillcolor = lightblue];
248 -> 550 [arrowhead = none ];
550 -> 249;

551 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
249 -> 551 [arrowhead = none ];
551 -> 250;

552 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
250 -> 552 [arrowhead = none ];
552 -> 251;

553 [label="EVAL with clause\nvalue(node(X474, X475, X476), X475).\nand substitution\nT228 -> T234\nX474 -> T234\nT229 -> T232\nX475 -> T232\nT230 -> T233\nX476 -> T233\nX433 -> T232\nT231 -> T234", fontsize=14, style = filled, fillcolor = lightblue];
251 -> 553 [arrowhead = none ];
553 -> 252;

554 [label="INSTANCE with matching:\nT148 -> T234\nX271 -> X431\nX273 -> X432", fontsize=14, style = filled, fillcolor = lightgrey];
252 -> 554 [arrowhead = none , style=dashed];
554 -> 151[style=dashed];

555 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
253 -> 555 [arrowhead = none ];
555 -> 254;

556 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT236 -> nil\nX487 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
254 -> 556 [arrowhead = none ];
556 -> 255;

557 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
254 -> 557 [arrowhead = none ];
557 -> 256;

558 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
255 -> 558 [arrowhead = none ];
558 -> 257;

559 [label="EVAL with clause\nleft(node(X517, X518, X519), X517).\nand substitution\nX517 -> T256\nX518 -> T257\nX519 -> T258\nT236 -> node(T256, T257, T258)\nX487 -> T256\nT253 -> T256\nT254 -> T257\nT255 -> T258", fontsize=14, style = filled, fillcolor = lightblue];
256 -> 559 [arrowhead = none ];
559 -> 273;

560 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
256 -> 560 [arrowhead = none ];
560 -> 274;

561 [label="EVAL with clause\nright(nil, nil).\nand substitution\nX485 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
257 -> 561 [arrowhead = none ];
561 -> 258;

562 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
258 -> 562 [arrowhead = none ];
562 -> 259;

563 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX488 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
259 -> 563 [arrowhead = none ];
563 -> 260;

564 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
260 -> 564 [arrowhead = none ];
564 -> 261;

565 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
260 -> 565 [arrowhead = none ];
565 -> 262;

566 [label="INSTANCE with matching:\nT148 -> nil\nX271 -> X486\nX273 -> X489", fontsize=14, style = filled, fillcolor = lightgrey];
261 -> 566 [arrowhead = none , style=dashed];
566 -> 151[style=dashed];

567 [label="BACKTRACK\nfor clause: value(node(X13, X, X14), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
262 -> 567 [arrowhead = none ];
567 -> 263;

568 [label="BACKTRACK\nfor clause: right(node(X11, X12, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
263 -> 568 [arrowhead = none ];
568 -> 264;

569 [label="EVAL with clause\nleft(node(X499, X500, X501), X499).\nand substitution\nX499 -> T240\nX500 -> T241\nX501 -> T242\nT236 -> node(T240, T241, T242)\nX487 -> T240\nT237 -> T240\nT238 -> T241\nT239 -> T242", fontsize=14, style = filled, fillcolor = lightblue];
264 -> 569 [arrowhead = none ];
569 -> 265;

570 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
264 -> 570 [arrowhead = none ];
570 -> 266;

571 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
265 -> 571 [arrowhead = none ];
571 -> 267;

572 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
267 -> 572 [arrowhead = none ];
572 -> 268;

573 [label="EVAL with clause\nright(node(X505, X506, X507), X507).\nand substitution\nT240 -> T246\nX505 -> T246\nT241 -> T247\nX506 -> T247\nT242 -> T248\nX507 -> T248\nX485 -> T248\nT243 -> T246\nT244 -> T247\nT245 -> T248", fontsize=14, style = filled, fillcolor = lightblue];
268 -> 573 [arrowhead = none ];
573 -> 269;

574 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
269 -> 574 [arrowhead = none ];
574 -> 270;

575 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
270 -> 575 [arrowhead = none ];
575 -> 271;

576 [label="EVAL with clause\nvalue(node(X511, X512, X513), X512).\nand substitution\nT246 -> T249\nX511 -> T249\nT247 -> T250\nX512 -> T250\nT248 -> T252\nX513 -> T252\nX488 -> T250\nT251 -> T252", fontsize=14, style = filled, fillcolor = lightblue];
271 -> 576 [arrowhead = none ];
576 -> 272;

577 [label="INSTANCE with matching:\nT148 -> T252\nX271 -> X486\nX273 -> X489", fontsize=14, style = filled, fillcolor = lightgrey];
272 -> 577 [arrowhead = none , style=dashed];
577 -> 151[style=dashed];

578 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
273 -> 578 [arrowhead = none ];
578 -> 275;

579 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
275 -> 579 [arrowhead = none ];
579 -> 276;

580 [label="EVAL with clause\nright(node(X523, X524, X525), X525).\nand substitution\nT256 -> T262\nX523 -> T262\nT257 -> T263\nX524 -> T263\nT258 -> T264\nX525 -> T264\nX485 -> T264\nT259 -> T262\nT260 -> T263\nT261 -> T264", fontsize=14, style = filled, fillcolor = lightblue];
276 -> 580 [arrowhead = none ];
580 -> 277;

581 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
277 -> 581 [arrowhead = none ];
581 -> 278;

582 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
278 -> 582 [arrowhead = none ];
582 -> 279;

583 [label="EVAL with clause\nvalue(node(X529, X530, X531), X530).\nand substitution\nT262 -> T265\nX529 -> T265\nT263 -> T266\nX530 -> T266\nT264 -> T268\nX531 -> T268\nX488 -> T266\nT267 -> T268", fontsize=14, style = filled, fillcolor = lightblue];
279 -> 583 [arrowhead = none ];
583 -> 280;

584 [label="INSTANCE with matching:\nT148 -> T268\nX271 -> X486\nX273 -> X489", fontsize=14, style = filled, fillcolor = lightgrey];
280 -> 584 [arrowhead = none , style=dashed];
584 -> 151[style=dashed];

585 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
281 -> 585 [arrowhead = none ];
585 -> 282;

586 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
281 -> 586 [arrowhead = none ];
586 -> 283;

587 [label="EVAL with clause\ntlast(X534, node(nil, X534, nil)).\nand substitution\nT27 -> T269\nX534 -> T269\nT26 -> node(nil, T269, nil)", fontsize=14, style = filled, fillcolor = lightblue];
282 -> 587 [arrowhead = none ];
587 -> 284;

588 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
282 -> 588 [arrowhead = none ];
588 -> 285;

589 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
283 -> 589 [arrowhead = none ];
589 -> 287;

590 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
283 -> 590 [arrowhead = none ];
590 -> 288;

591 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
284 -> 591 [arrowhead = none ];
591 -> 286;

592 [label="EVAL with clause\ntlast(X543, node(X544, X545, X546)) :- tlast(X543, X544).\nand substitution\nT27 -> T274\nX543 -> T274\nX544 -> T275\nX545 -> T272\nX546 -> T273\nT26 -> node(T275, T272, T273)\nT270 -> T274\nT271 -> T275", fontsize=14, style = filled, fillcolor = lightblue];
287 -> 592 [arrowhead = none ];
592 -> 289;

593 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
287 -> 593 [arrowhead = none ];
593 -> 290;

594 [label="EVAL with clause\ntlast(X551, node(X552, X553, X554)) :- tlast(X551, X554).\nand substitution\nT27 -> T280\nX551 -> T280\nX552 -> T277\nX553 -> T278\nX554 -> T281\nT26 -> node(T277, T278, T281)\nT276 -> T280\nT279 -> T281", fontsize=14, style = filled, fillcolor = lightblue];
288 -> 594 [arrowhead = none ];
594 -> 291;

595 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
288 -> 595 [arrowhead = none ];
595 -> 292;

596 [label="INSTANCE with matching:\nT27 -> T274\nT26 -> T275", fontsize=14, style = filled, fillcolor = lightgrey];
289 -> 596 [arrowhead = none , style=dashed];
596 -> 39[style=dashed];

597 [label="INSTANCE with matching:\nT27 -> T280\nT26 -> T281", fontsize=14, style = filled, fillcolor = lightgrey];
291 -> 597 [arrowhead = none , style=dashed];
597 -> 39[style=dashed];

}

(2) Obligation:

Clauses:

s2t4(0, nil).
s2t4(s(T14), node(X38, X39, X38)) :- s2t4(T14, X38).
s2t4(s(T16), node(nil, X52, X53)) :- s2t4(T16, X53).
s2t4(s(T18), node(X66, X67, nil)) :- s2t4(T18, X66).
s2t4(T19, node(nil, X74, nil)).
tappend38(nil, T30, node(nil, T30, nil)).
tappend38(nil, T32, node(node(nil, T32, nil), nil, nil)).
tappend38(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)).
tappend38(node(nil, T54, T55), T32, node(node(nil, T32, nil), T54, T55)).
tappend38(nil, T57, node(nil, nil, node(nil, T57, nil))).
tappend38(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))).
tappend38(node(T83, T84, nil), T57, node(T83, T84, node(nil, T57, nil))).
tappend38(nil, T89, node(X217, nil, nil)) :- tappend38(nil, T89, X217).
tappend38(node(T107, T105, T106), T108, node(X217, T105, T106)) :- tappend38(T107, T108, X217).
tappend38(node(T126, T124, T125), T127, node(X217, T124, T125)) :- tappend38(T126, T127, X217).
tappend38(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)).
tappend38(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))).
tappend38(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))).
tappend38(node(node(nil, T145, nil), T146, node(nil, T171, T172)), T145, node(node(nil, T145, nil), T146, node(X313, T171, T172))).
tappend38(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))).
tappend38(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))).
tappend38(node(node(nil, T145, nil), T146, node(T199, T200, nil)), T145, node(node(nil, T145, nil), T146, node(T199, T200, X370))).
tappend38(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) :- tappend151(nil, X431, X432).
tappend38(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) :- tappend151(T218, X431, X432).
tappend38(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) :- tappend151(T234, X431, X432).
tappend38(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) :- tappend151(nil, X486, X489).
tappend38(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) :- tappend151(T252, X486, X489).
tappend38(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) :- tappend151(T268, X486, X489).
tappend151(nil, X300, X300).
tappend151(nil, X313, node(X313, nil, nil)).
tappend151(node(nil, T160, T161), X313, node(X313, T160, T161)).
tappend151(node(nil, T171, T172), X313, node(X313, T171, T172)).
tappend151(nil, X370, node(nil, nil, X370)).
tappend151(node(T186, T187, nil), X370, node(T186, T187, X370)).
tappend151(node(T199, T200, nil), X370, node(T199, T200, X370)).
tappend151(nil, X431, node(X432, nil, nil)) :- tappend151(nil, X431, X432).
tappend151(node(T218, T216, T217), X431, node(X432, T216, T217)) :- tappend151(T218, X431, X432).
tappend151(node(T234, T232, T233), X431, node(X432, T232, T233)) :- tappend151(T234, X431, X432).
tappend151(nil, nil, node(nil, nil, X489)) :- tappend151(nil, X486, X489).
tappend151(node(T249, T250, T252), T249, node(T249, T250, X489)) :- tappend151(T252, X486, X489).
tappend151(node(T265, T266, T268), T265, node(T265, T266, X489)) :- tappend151(T268, X486, X489).
tlast39(T269, node(nil, T269, nil)).
tlast39(T274, node(T275, T272, T273)) :- tlast39(T274, T275).
tlast39(T280, node(T277, T278, T281)) :- tlast39(T280, T281).
goal1(T7, T10, T11) :- s2t4(T7, X21).
goal1(T7, T24, T25) :- ','(s2t4(T7, T23), tappend38(T23, T24, X81)).
goal1(T7, T24, T269) :- ','(s2t4(T7, T23), tappend38(T23, T24, node(nil, T269, nil))).
goal1(T7, T24, T274) :- ','(s2t4(T7, T23), ','(tappend38(T23, T24, node(T275, T272, T273)), tlast39(T274, T275))).
goal1(T7, T24, T280) :- ','(s2t4(T7, T23), ','(tappend38(T23, T24, node(T277, T278, T281)), tlast39(T280, T281))).

Queries:

goal1(g,a,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:
goal1_in: (b,f,f)
s2t4_in: (b,f)
tappend38_in: (f,f,f) (b,f,f)
tappend151_in: (b,f,f) (f,f,f)
tlast39_in: (f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)

(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:

GOAL1_IN_GAA(T7, T10, T11) → U21_GAA(T7, T10, T11, s2t4_in_ga(T7, X21))
GOAL1_IN_GAA(T7, T10, T11) → S2T4_IN_GA(T7, X21)
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → U1_GA(T14, X38, X39, s2t4_in_ga(T14, X38))
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → S2T4_IN_GA(T14, X38)
S2T4_IN_GA(s(T16), node(nil, X52, X53)) → U2_GA(T16, X52, X53, s2t4_in_ga(T16, X53))
S2T4_IN_GA(s(T16), node(nil, X52, X53)) → S2T4_IN_GA(T16, X53)
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → U3_GA(T18, X66, X67, s2t4_in_ga(T18, X66))
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → S2T4_IN_GA(T18, X66)
GOAL1_IN_GAA(T7, T24, T25) → U22_GAA(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_GAA(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_GAA(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
U22_GAA(T7, T24, T25, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, X81)
TAPPEND38_IN_AAA(nil, T89, node(X217, nil, nil)) → U4_AAA(T89, X217, tappend38_in_gaa(nil, T89, X217))
TAPPEND38_IN_AAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)
TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → U4_GAA(T89, X217, tappend38_in_gaa(nil, T89, X217))
TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)
TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_GAA(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_GAA(T107, T108, X217)
TAPPEND38_IN_GAA(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_GAA(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_GAA(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → U13_GAA(X431, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_GAA(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_GAA(T218, X431, X432)
TAPPEND151_IN_GAA(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_GAA(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → U16_GAA(X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_GAA(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND151_IN_GAA(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_GAA(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_GAA(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → TAPPEND151_IN_GAA(T218, X431, X432)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_GAA(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_GAA(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_GAA(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_GAA(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_AAA(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_AAA(T107, T108, X217)
TAPPEND38_IN_AAA(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_AAA(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_AAA(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_AAA(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → TAPPEND151_IN_AAA(T218, X431, X432)
TAPPEND151_IN_AAA(nil, X431, node(X432, nil, nil)) → U13_AAA(X431, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND151_IN_AAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_AAA(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_AAA(T218, X431, X432)
TAPPEND151_IN_AAA(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_AAA(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
TAPPEND151_IN_AAA(nil, nil, node(nil, nil, X489)) → U16_AAA(X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND151_IN_AAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_AAA(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND151_IN_AAA(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_AAA(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_AAA(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_AAA(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_AAA(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_AAA(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
GOAL1_IN_GAA(T7, T24, T269) → U24_GAA(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_GAA(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_GAA(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U24_GAA(T7, T24, T269, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(nil, T269, nil))
GOAL1_IN_GAA(T7, T24, T274) → U26_GAA(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_GAA(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_GAA(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U26_GAA(T7, T24, T274, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(T275, T272, T273))
U27_GAA(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_GAA(T7, T24, T274, tlast39_in_aa(T274, T275))
U27_GAA(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → TLAST39_IN_AA(T274, T275)
TLAST39_IN_AA(T274, node(T275, T272, T273)) → U19_AA(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
TLAST39_IN_AA(T274, node(T275, T272, T273)) → TLAST39_IN_AA(T274, T275)
TLAST39_IN_AA(T280, node(T277, T278, T281)) → U20_AA(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
TLAST39_IN_AA(T280, node(T277, T278, T281)) → TLAST39_IN_AA(T280, T281)
GOAL1_IN_GAA(T7, T24, T280) → U29_GAA(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_GAA(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_GAA(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U29_GAA(T7, T24, T280, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(T277, T278, T281))
U30_GAA(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_GAA(T7, T24, T280, tlast39_in_aa(T280, T281))
U30_GAA(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → TLAST39_IN_AA(T280, T281)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
GOAL1_IN_GAA(x1, x2, x3)  =  GOAL1_IN_GAA(x1)
U21_GAA(x1, x2, x3, x4)  =  U21_GAA(x1, x4)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(x1)
U1_GA(x1, x2, x3, x4)  =  U1_GA(x1, x4)
U2_GA(x1, x2, x3, x4)  =  U2_GA(x1, x4)
U3_GA(x1, x2, x3, x4)  =  U3_GA(x1, x4)
U22_GAA(x1, x2, x3, x4)  =  U22_GAA(x1, x4)
U23_GAA(x1, x2, x3, x4)  =  U23_GAA(x1, x4)
TAPPEND38_IN_AAA(x1, x2, x3)  =  TAPPEND38_IN_AAA
U4_AAA(x1, x2, x3)  =  U4_AAA(x3)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)
U4_GAA(x1, x2, x3)  =  U4_GAA(x3)
U5_GAA(x1, x2, x3, x4, x5, x6)  =  U5_GAA(x1, x2, x3, x6)
U6_GAA(x1, x2, x3, x4, x5, x6)  =  U6_GAA(x1, x2, x3, x6)
U7_GAA(x1, x2, x3, x4)  =  U7_GAA(x1, x2, x4)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)
U13_GAA(x1, x2, x3)  =  U13_GAA(x3)
U14_GAA(x1, x2, x3, x4, x5, x6)  =  U14_GAA(x1, x2, x3, x6)
U15_GAA(x1, x2, x3, x4, x5, x6)  =  U15_GAA(x1, x2, x3, x6)
U16_GAA(x1, x2)  =  U16_GAA(x2)
U17_GAA(x1, x2, x3, x4, x5)  =  U17_GAA(x1, x2, x3, x5)
U18_GAA(x1, x2, x3, x4, x5)  =  U18_GAA(x1, x2, x3, x5)
U8_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U8_GAA(x1, x2, x3, x4, x5, x7)
U9_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U9_GAA(x1, x2, x3, x4, x5, x7)
U10_GAA(x1, x2, x3, x4)  =  U10_GAA(x1, x2, x4)
U11_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U11_GAA(x1, x2, x3, x4, x5, x7)
U12_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U12_GAA(x1, x2, x3, x4, x5, x7)
U5_AAA(x1, x2, x3, x4, x5, x6)  =  U5_AAA(x6)
U6_AAA(x1, x2, x3, x4, x5, x6)  =  U6_AAA(x6)
U7_AAA(x1, x2, x3, x4)  =  U7_AAA(x4)
U8_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U8_AAA(x7)
TAPPEND151_IN_AAA(x1, x2, x3)  =  TAPPEND151_IN_AAA
U13_AAA(x1, x2, x3)  =  U13_AAA(x3)
U14_AAA(x1, x2, x3, x4, x5, x6)  =  U14_AAA(x6)
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U16_AAA(x1, x2)  =  U16_AAA(x2)
U17_AAA(x1, x2, x3, x4, x5)  =  U17_AAA(x5)
U18_AAA(x1, x2, x3, x4, x5)  =  U18_AAA(x5)
U9_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U9_AAA(x7)
U10_AAA(x1, x2, x3, x4)  =  U10_AAA(x4)
U11_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U11_AAA(x7)
U12_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U12_AAA(x7)
U24_GAA(x1, x2, x3, x4)  =  U24_GAA(x1, x4)
U25_GAA(x1, x2, x3, x4)  =  U25_GAA(x1, x4)
U26_GAA(x1, x2, x3, x4)  =  U26_GAA(x1, x4)
U27_GAA(x1, x2, x3, x4)  =  U27_GAA(x1, x4)
U28_GAA(x1, x2, x3, x4)  =  U28_GAA(x1, x4)
TLAST39_IN_AA(x1, x2)  =  TLAST39_IN_AA
U19_AA(x1, x2, x3, x4, x5)  =  U19_AA(x5)
U20_AA(x1, x2, x3, x4, x5)  =  U20_AA(x5)
U29_GAA(x1, x2, x3, x4)  =  U29_GAA(x1, x4)
U30_GAA(x1, x2, x3, x4)  =  U30_GAA(x1, x4)
U31_GAA(x1, x2, x3, x4)  =  U31_GAA(x1, x4)

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

(6) Obligation:

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

GOAL1_IN_GAA(T7, T10, T11) → U21_GAA(T7, T10, T11, s2t4_in_ga(T7, X21))
GOAL1_IN_GAA(T7, T10, T11) → S2T4_IN_GA(T7, X21)
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → U1_GA(T14, X38, X39, s2t4_in_ga(T14, X38))
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → S2T4_IN_GA(T14, X38)
S2T4_IN_GA(s(T16), node(nil, X52, X53)) → U2_GA(T16, X52, X53, s2t4_in_ga(T16, X53))
S2T4_IN_GA(s(T16), node(nil, X52, X53)) → S2T4_IN_GA(T16, X53)
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → U3_GA(T18, X66, X67, s2t4_in_ga(T18, X66))
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → S2T4_IN_GA(T18, X66)
GOAL1_IN_GAA(T7, T24, T25) → U22_GAA(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_GAA(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_GAA(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
U22_GAA(T7, T24, T25, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, X81)
TAPPEND38_IN_AAA(nil, T89, node(X217, nil, nil)) → U4_AAA(T89, X217, tappend38_in_gaa(nil, T89, X217))
TAPPEND38_IN_AAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)
TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → U4_GAA(T89, X217, tappend38_in_gaa(nil, T89, X217))
TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)
TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_GAA(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_GAA(T107, T108, X217)
TAPPEND38_IN_GAA(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_GAA(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_GAA(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → U13_GAA(X431, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_GAA(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_GAA(T218, X431, X432)
TAPPEND151_IN_GAA(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_GAA(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → U16_GAA(X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_GAA(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND151_IN_GAA(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_GAA(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_GAA(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → TAPPEND151_IN_GAA(T218, X431, X432)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_GAA(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_GAA(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_GAA(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_GAA(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_AAA(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_AAA(T107, T108, X217)
TAPPEND38_IN_AAA(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_AAA(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_AAA(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_AAA(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → TAPPEND151_IN_AAA(T218, X431, X432)
TAPPEND151_IN_AAA(nil, X431, node(X432, nil, nil)) → U13_AAA(X431, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND151_IN_AAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_AAA(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_AAA(T218, X431, X432)
TAPPEND151_IN_AAA(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_AAA(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
TAPPEND151_IN_AAA(nil, nil, node(nil, nil, X489)) → U16_AAA(X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND151_IN_AAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_AAA(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND151_IN_AAA(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_AAA(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_AAA(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_AAA(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_AAA(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_AAA(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
GOAL1_IN_GAA(T7, T24, T269) → U24_GAA(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_GAA(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_GAA(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U24_GAA(T7, T24, T269, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(nil, T269, nil))
GOAL1_IN_GAA(T7, T24, T274) → U26_GAA(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_GAA(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_GAA(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U26_GAA(T7, T24, T274, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(T275, T272, T273))
U27_GAA(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_GAA(T7, T24, T274, tlast39_in_aa(T274, T275))
U27_GAA(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → TLAST39_IN_AA(T274, T275)
TLAST39_IN_AA(T274, node(T275, T272, T273)) → U19_AA(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
TLAST39_IN_AA(T274, node(T275, T272, T273)) → TLAST39_IN_AA(T274, T275)
TLAST39_IN_AA(T280, node(T277, T278, T281)) → U20_AA(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
TLAST39_IN_AA(T280, node(T277, T278, T281)) → TLAST39_IN_AA(T280, T281)
GOAL1_IN_GAA(T7, T24, T280) → U29_GAA(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_GAA(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_GAA(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U29_GAA(T7, T24, T280, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(T277, T278, T281))
U30_GAA(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_GAA(T7, T24, T280, tlast39_in_aa(T280, T281))
U30_GAA(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → TLAST39_IN_AA(T280, T281)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
GOAL1_IN_GAA(x1, x2, x3)  =  GOAL1_IN_GAA(x1)
U21_GAA(x1, x2, x3, x4)  =  U21_GAA(x1, x4)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(x1)
U1_GA(x1, x2, x3, x4)  =  U1_GA(x1, x4)
U2_GA(x1, x2, x3, x4)  =  U2_GA(x1, x4)
U3_GA(x1, x2, x3, x4)  =  U3_GA(x1, x4)
U22_GAA(x1, x2, x3, x4)  =  U22_GAA(x1, x4)
U23_GAA(x1, x2, x3, x4)  =  U23_GAA(x1, x4)
TAPPEND38_IN_AAA(x1, x2, x3)  =  TAPPEND38_IN_AAA
U4_AAA(x1, x2, x3)  =  U4_AAA(x3)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)
U4_GAA(x1, x2, x3)  =  U4_GAA(x3)
U5_GAA(x1, x2, x3, x4, x5, x6)  =  U5_GAA(x1, x2, x3, x6)
U6_GAA(x1, x2, x3, x4, x5, x6)  =  U6_GAA(x1, x2, x3, x6)
U7_GAA(x1, x2, x3, x4)  =  U7_GAA(x1, x2, x4)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)
U13_GAA(x1, x2, x3)  =  U13_GAA(x3)
U14_GAA(x1, x2, x3, x4, x5, x6)  =  U14_GAA(x1, x2, x3, x6)
U15_GAA(x1, x2, x3, x4, x5, x6)  =  U15_GAA(x1, x2, x3, x6)
U16_GAA(x1, x2)  =  U16_GAA(x2)
U17_GAA(x1, x2, x3, x4, x5)  =  U17_GAA(x1, x2, x3, x5)
U18_GAA(x1, x2, x3, x4, x5)  =  U18_GAA(x1, x2, x3, x5)
U8_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U8_GAA(x1, x2, x3, x4, x5, x7)
U9_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U9_GAA(x1, x2, x3, x4, x5, x7)
U10_GAA(x1, x2, x3, x4)  =  U10_GAA(x1, x2, x4)
U11_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U11_GAA(x1, x2, x3, x4, x5, x7)
U12_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U12_GAA(x1, x2, x3, x4, x5, x7)
U5_AAA(x1, x2, x3, x4, x5, x6)  =  U5_AAA(x6)
U6_AAA(x1, x2, x3, x4, x5, x6)  =  U6_AAA(x6)
U7_AAA(x1, x2, x3, x4)  =  U7_AAA(x4)
U8_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U8_AAA(x7)
TAPPEND151_IN_AAA(x1, x2, x3)  =  TAPPEND151_IN_AAA
U13_AAA(x1, x2, x3)  =  U13_AAA(x3)
U14_AAA(x1, x2, x3, x4, x5, x6)  =  U14_AAA(x6)
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U16_AAA(x1, x2)  =  U16_AAA(x2)
U17_AAA(x1, x2, x3, x4, x5)  =  U17_AAA(x5)
U18_AAA(x1, x2, x3, x4, x5)  =  U18_AAA(x5)
U9_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U9_AAA(x7)
U10_AAA(x1, x2, x3, x4)  =  U10_AAA(x4)
U11_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U11_AAA(x7)
U12_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U12_AAA(x7)
U24_GAA(x1, x2, x3, x4)  =  U24_GAA(x1, x4)
U25_GAA(x1, x2, x3, x4)  =  U25_GAA(x1, x4)
U26_GAA(x1, x2, x3, x4)  =  U26_GAA(x1, x4)
U27_GAA(x1, x2, x3, x4)  =  U27_GAA(x1, x4)
U28_GAA(x1, x2, x3, x4)  =  U28_GAA(x1, x4)
TLAST39_IN_AA(x1, x2)  =  TLAST39_IN_AA
U19_AA(x1, x2, x3, x4, x5)  =  U19_AA(x5)
U20_AA(x1, x2, x3, x4, x5)  =  U20_AA(x5)
U29_GAA(x1, x2, x3, x4)  =  U29_GAA(x1, x4)
U30_GAA(x1, x2, x3, x4)  =  U30_GAA(x1, x4)
U31_GAA(x1, x2, x3, x4)  =  U31_GAA(x1, x4)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 64 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

TLAST39_IN_AA(T280, node(T277, T278, T281)) → TLAST39_IN_AA(T280, T281)
TLAST39_IN_AA(T274, node(T275, T272, T273)) → TLAST39_IN_AA(T274, T275)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
TLAST39_IN_AA(x1, x2)  =  TLAST39_IN_AA

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:

TLAST39_IN_AA(T280, node(T277, T278, T281)) → TLAST39_IN_AA(T280, T281)
TLAST39_IN_AA(T274, node(T275, T272, T273)) → TLAST39_IN_AA(T274, T275)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TLAST39_IN_AA(x1, x2)  =  TLAST39_IN_AA

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:

TLAST39_IN_AA → TLAST39_IN_AA

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 = TLAST39_IN_AA evaluates to t =TLAST39_IN_AA

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

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from TLAST39_IN_AA to TLAST39_IN_AA.

(15) FALSE

(16) Obligation:

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

TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)

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

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)

R is empty.
The argument filtering Pi contains the following mapping:
nil  =  nil
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)

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

(19) PiDPToQDPProof (SOUND transformation)

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

(20) Obligation:

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

TAPPEND151_IN_GAA(nil) → TAPPEND151_IN_GAA(nil)

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 = TAPPEND151_IN_GAA(nil) evaluates to t =TAPPEND151_IN_GAA(nil)

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 TAPPEND151_IN_GAA(nil) to TAPPEND151_IN_GAA(nil).

(22) FALSE

(23) Obligation:

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

TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_AAA(T218, X431, X432)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
TAPPEND151_IN_AAA(x1, x2, x3)  =  TAPPEND151_IN_AAA

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:

TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_AAA(T218, X431, X432)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND151_IN_AAA(x1, x2, x3)  =  TAPPEND151_IN_AAA

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:

TAPPEND151_IN_AAA → TAPPEND151_IN_AAA

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 = TAPPEND151_IN_AAA evaluates to t =TAPPEND151_IN_AAA

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

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from TAPPEND151_IN_AAA to TAPPEND151_IN_AAA.

(29) FALSE

(30) Obligation:

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

TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_GAA(T218, X431, X432)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)

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:

TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_GAA(T218, X431, X432)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)

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:

TAPPEND151_IN_GAA(node(T249, T250, T252)) → TAPPEND151_IN_GAA(T252)
TAPPEND151_IN_GAA(node(T218, T216, T217)) → TAPPEND151_IN_GAA(T218)

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

(35) QDPSizeChangeProof (EQUIVALENT transformation)

By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

• TAPPEND151_IN_GAA(node(T249, T250, T252)) → TAPPEND151_IN_GAA(T252)
  The graph contains the following edges 1 > 1

• TAPPEND151_IN_GAA(node(T218, T216, T217)) → TAPPEND151_IN_GAA(T218)
  The graph contains the following edges 1 > 1

(36) TRUE

(37) Obligation:

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

TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)

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:

TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)

R is empty.
The argument filtering Pi contains the following mapping:
nil  =  nil
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)

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:

TAPPEND38_IN_GAA(nil) → TAPPEND38_IN_GAA(nil)

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 = TAPPEND38_IN_GAA(nil) evaluates to t =TAPPEND38_IN_GAA(nil)

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 TAPPEND38_IN_GAA(nil) to TAPPEND38_IN_GAA(nil).

(43) FALSE

(44) Obligation:

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

TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_GAA(T107, T108, X217)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)

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:

TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_GAA(T107, T108, X217)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)

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:

TAPPEND38_IN_GAA(node(T107, T105, T106)) → TAPPEND38_IN_GAA(T107)

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

(49) 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:

• TAPPEND38_IN_GAA(node(T107, T105, T106)) → TAPPEND38_IN_GAA(T107)
  The graph contains the following edges 1 > 1

(50) TRUE

(51) Obligation:

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

TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_AAA(T107, T108, X217)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
TAPPEND38_IN_AAA(x1, x2, x3)  =  TAPPEND38_IN_AAA

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

(52) UsableRulesProof (EQUIVALENT transformation)

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

(53) Obligation:

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

TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_AAA(T107, T108, X217)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND38_IN_AAA(x1, x2, x3)  =  TAPPEND38_IN_AAA

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

(54) PiDPToQDPProof (SOUND transformation)

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

(55) Obligation:

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

TAPPEND38_IN_AAA → TAPPEND38_IN_AAA

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

(56) 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 = TAPPEND38_IN_AAA evaluates to t =TAPPEND38_IN_AAA

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

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from TAPPEND38_IN_AAA to TAPPEND38_IN_AAA.

(57) FALSE

(58) Obligation:

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

S2T4_IN_GA(s(T16), node(nil, X52, X53)) → S2T4_IN_GA(T16, X53)
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → S2T4_IN_GA(T14, X38)
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → S2T4_IN_GA(T18, X66)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x1, x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga(x1)
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x1, x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x1, x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa(x1)
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x1, x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x1, x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa(x1)
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x1, x2, x3, x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x1, x2, x3, x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x1, x2, x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa(x1)
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x1, x2, x3, x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x1, x2, x3, x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x1, x2, x3, x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x1, x2, x3, x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x1, x2, x3, x4, x5, x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x1, x2, x3, x4, x5, x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x1, x2, x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x1, x2, x3, x4, x5, x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x1, x2, x3, x4, x5, x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x1, x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x1, x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x1, x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x1, x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x1, x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x1, x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x1, x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x1, x4)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(x1)

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

(59) UsableRulesProof (EQUIVALENT transformation)

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

(60) Obligation:

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

S2T4_IN_GA(s(T16), node(nil, X52, X53)) → S2T4_IN_GA(T16, X53)
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → S2T4_IN_GA(T14, X38)
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → S2T4_IN_GA(T18, X66)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
nil  =  nil
node(x1, x2, x3)  =  node(x1, x2, x3)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(x1)

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

(61) PiDPToQDPProof (SOUND transformation)

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

(62) Obligation:

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

S2T4_IN_GA(s(T16)) → S2T4_IN_GA(T16)

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

(63) 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:

• S2T4_IN_GA(s(T16)) → S2T4_IN_GA(T16)
  The graph contains the following edges 1 > 1

(64) TRUE

(65) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
goal1_in: (b,f,f)
s2t4_in: (b,f)
tappend38_in: (f,f,f) (b,f,f)
tappend151_in: (b,f,f) (f,f,f)
tlast39_in: (f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(66) Obligation:

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

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)

(67) 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:

GOAL1_IN_GAA(T7, T10, T11) → U21_GAA(T7, T10, T11, s2t4_in_ga(T7, X21))
GOAL1_IN_GAA(T7, T10, T11) → S2T4_IN_GA(T7, X21)
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → U1_GA(T14, X38, X39, s2t4_in_ga(T14, X38))
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → S2T4_IN_GA(T14, X38)
S2T4_IN_GA(s(T16), node(nil, X52, X53)) → U2_GA(T16, X52, X53, s2t4_in_ga(T16, X53))
S2T4_IN_GA(s(T16), node(nil, X52, X53)) → S2T4_IN_GA(T16, X53)
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → U3_GA(T18, X66, X67, s2t4_in_ga(T18, X66))
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → S2T4_IN_GA(T18, X66)
GOAL1_IN_GAA(T7, T24, T25) → U22_GAA(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_GAA(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_GAA(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
U22_GAA(T7, T24, T25, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, X81)
TAPPEND38_IN_AAA(nil, T89, node(X217, nil, nil)) → U4_AAA(T89, X217, tappend38_in_gaa(nil, T89, X217))
TAPPEND38_IN_AAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)
TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → U4_GAA(T89, X217, tappend38_in_gaa(nil, T89, X217))
TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)
TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_GAA(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_GAA(T107, T108, X217)
TAPPEND38_IN_GAA(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_GAA(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_GAA(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → U13_GAA(X431, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_GAA(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_GAA(T218, X431, X432)
TAPPEND151_IN_GAA(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_GAA(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → U16_GAA(X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_GAA(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND151_IN_GAA(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_GAA(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_GAA(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → TAPPEND151_IN_GAA(T218, X431, X432)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_GAA(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_GAA(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_GAA(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_GAA(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_AAA(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_AAA(T107, T108, X217)
TAPPEND38_IN_AAA(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_AAA(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_AAA(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_AAA(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → TAPPEND151_IN_AAA(T218, X431, X432)
TAPPEND151_IN_AAA(nil, X431, node(X432, nil, nil)) → U13_AAA(X431, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND151_IN_AAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_AAA(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_AAA(T218, X431, X432)
TAPPEND151_IN_AAA(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_AAA(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
TAPPEND151_IN_AAA(nil, nil, node(nil, nil, X489)) → U16_AAA(X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND151_IN_AAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_AAA(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND151_IN_AAA(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_AAA(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_AAA(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_AAA(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_AAA(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_AAA(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
GOAL1_IN_GAA(T7, T24, T269) → U24_GAA(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_GAA(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_GAA(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U24_GAA(T7, T24, T269, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(nil, T269, nil))
GOAL1_IN_GAA(T7, T24, T274) → U26_GAA(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_GAA(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_GAA(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U26_GAA(T7, T24, T274, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(T275, T272, T273))
U27_GAA(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_GAA(T7, T24, T274, tlast39_in_aa(T274, T275))
U27_GAA(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → TLAST39_IN_AA(T274, T275)
TLAST39_IN_AA(T274, node(T275, T272, T273)) → U19_AA(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
TLAST39_IN_AA(T274, node(T275, T272, T273)) → TLAST39_IN_AA(T274, T275)
TLAST39_IN_AA(T280, node(T277, T278, T281)) → U20_AA(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
TLAST39_IN_AA(T280, node(T277, T278, T281)) → TLAST39_IN_AA(T280, T281)
GOAL1_IN_GAA(T7, T24, T280) → U29_GAA(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_GAA(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_GAA(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U29_GAA(T7, T24, T280, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(T277, T278, T281))
U30_GAA(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_GAA(T7, T24, T280, tlast39_in_aa(T280, T281))
U30_GAA(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → TLAST39_IN_AA(T280, T281)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
GOAL1_IN_GAA(x1, x2, x3)  =  GOAL1_IN_GAA(x1)
U21_GAA(x1, x2, x3, x4)  =  U21_GAA(x4)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(x1)
U1_GA(x1, x2, x3, x4)  =  U1_GA(x4)
U2_GA(x1, x2, x3, x4)  =  U2_GA(x4)
U3_GA(x1, x2, x3, x4)  =  U3_GA(x4)
U22_GAA(x1, x2, x3, x4)  =  U22_GAA(x4)
U23_GAA(x1, x2, x3, x4)  =  U23_GAA(x4)
TAPPEND38_IN_AAA(x1, x2, x3)  =  TAPPEND38_IN_AAA
U4_AAA(x1, x2, x3)  =  U4_AAA(x3)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)
U4_GAA(x1, x2, x3)  =  U4_GAA(x3)
U5_GAA(x1, x2, x3, x4, x5, x6)  =  U5_GAA(x6)
U6_GAA(x1, x2, x3, x4, x5, x6)  =  U6_GAA(x6)
U7_GAA(x1, x2, x3, x4)  =  U7_GAA(x4)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)
U13_GAA(x1, x2, x3)  =  U13_GAA(x3)
U14_GAA(x1, x2, x3, x4, x5, x6)  =  U14_GAA(x6)
U15_GAA(x1, x2, x3, x4, x5, x6)  =  U15_GAA(x6)
U16_GAA(x1, x2)  =  U16_GAA(x2)
U17_GAA(x1, x2, x3, x4, x5)  =  U17_GAA(x5)
U18_GAA(x1, x2, x3, x4, x5)  =  U18_GAA(x5)
U8_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U8_GAA(x7)
U9_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U9_GAA(x7)
U10_GAA(x1, x2, x3, x4)  =  U10_GAA(x4)
U11_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U11_GAA(x7)
U12_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U12_GAA(x7)
U5_AAA(x1, x2, x3, x4, x5, x6)  =  U5_AAA(x6)
U6_AAA(x1, x2, x3, x4, x5, x6)  =  U6_AAA(x6)
U7_AAA(x1, x2, x3, x4)  =  U7_AAA(x4)
U8_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U8_AAA(x7)
TAPPEND151_IN_AAA(x1, x2, x3)  =  TAPPEND151_IN_AAA
U13_AAA(x1, x2, x3)  =  U13_AAA(x3)
U14_AAA(x1, x2, x3, x4, x5, x6)  =  U14_AAA(x6)
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U16_AAA(x1, x2)  =  U16_AAA(x2)
U17_AAA(x1, x2, x3, x4, x5)  =  U17_AAA(x5)
U18_AAA(x1, x2, x3, x4, x5)  =  U18_AAA(x5)
U9_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U9_AAA(x7)
U10_AAA(x1, x2, x3, x4)  =  U10_AAA(x4)
U11_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U11_AAA(x7)
U12_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U12_AAA(x7)
U24_GAA(x1, x2, x3, x4)  =  U24_GAA(x4)
U25_GAA(x1, x2, x3, x4)  =  U25_GAA(x4)
U26_GAA(x1, x2, x3, x4)  =  U26_GAA(x4)
U27_GAA(x1, x2, x3, x4)  =  U27_GAA(x4)
U28_GAA(x1, x2, x3, x4)  =  U28_GAA(x4)
TLAST39_IN_AA(x1, x2)  =  TLAST39_IN_AA
U19_AA(x1, x2, x3, x4, x5)  =  U19_AA(x5)
U20_AA(x1, x2, x3, x4, x5)  =  U20_AA(x5)
U29_GAA(x1, x2, x3, x4)  =  U29_GAA(x4)
U30_GAA(x1, x2, x3, x4)  =  U30_GAA(x4)
U31_GAA(x1, x2, x3, x4)  =  U31_GAA(x4)

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

(68) Obligation:

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

GOAL1_IN_GAA(T7, T10, T11) → U21_GAA(T7, T10, T11, s2t4_in_ga(T7, X21))
GOAL1_IN_GAA(T7, T10, T11) → S2T4_IN_GA(T7, X21)
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → U1_GA(T14, X38, X39, s2t4_in_ga(T14, X38))
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → S2T4_IN_GA(T14, X38)
S2T4_IN_GA(s(T16), node(nil, X52, X53)) → U2_GA(T16, X52, X53, s2t4_in_ga(T16, X53))
S2T4_IN_GA(s(T16), node(nil, X52, X53)) → S2T4_IN_GA(T16, X53)
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → U3_GA(T18, X66, X67, s2t4_in_ga(T18, X66))
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → S2T4_IN_GA(T18, X66)
GOAL1_IN_GAA(T7, T24, T25) → U22_GAA(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_GAA(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_GAA(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
U22_GAA(T7, T24, T25, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, X81)
TAPPEND38_IN_AAA(nil, T89, node(X217, nil, nil)) → U4_AAA(T89, X217, tappend38_in_gaa(nil, T89, X217))
TAPPEND38_IN_AAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)
TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → U4_GAA(T89, X217, tappend38_in_gaa(nil, T89, X217))
TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)
TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_GAA(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_GAA(T107, T108, X217)
TAPPEND38_IN_GAA(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_GAA(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_GAA(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → U13_GAA(X431, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_GAA(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_GAA(T218, X431, X432)
TAPPEND151_IN_GAA(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_GAA(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → U16_GAA(X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_GAA(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND151_IN_GAA(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_GAA(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_GAA(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → TAPPEND151_IN_GAA(T218, X431, X432)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_GAA(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_GAA(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_GAA(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND38_IN_GAA(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_GAA(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_AAA(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_AAA(T107, T108, X217)
TAPPEND38_IN_AAA(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_AAA(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_AAA(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_AAA(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → TAPPEND151_IN_AAA(T218, X431, X432)
TAPPEND151_IN_AAA(nil, X431, node(X432, nil, nil)) → U13_AAA(X431, X432, tappend151_in_gaa(nil, X431, X432))
TAPPEND151_IN_AAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_AAA(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_AAA(T218, X431, X432)
TAPPEND151_IN_AAA(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_AAA(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
TAPPEND151_IN_AAA(nil, nil, node(nil, nil, X489)) → U16_AAA(X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND151_IN_AAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_AAA(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND151_IN_AAA(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_AAA(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_AAA(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_AAA(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_AAA(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND38_IN_AAA(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_AAA(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
GOAL1_IN_GAA(T7, T24, T269) → U24_GAA(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_GAA(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_GAA(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U24_GAA(T7, T24, T269, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(nil, T269, nil))
GOAL1_IN_GAA(T7, T24, T274) → U26_GAA(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_GAA(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_GAA(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U26_GAA(T7, T24, T274, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(T275, T272, T273))
U27_GAA(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_GAA(T7, T24, T274, tlast39_in_aa(T274, T275))
U27_GAA(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → TLAST39_IN_AA(T274, T275)
TLAST39_IN_AA(T274, node(T275, T272, T273)) → U19_AA(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
TLAST39_IN_AA(T274, node(T275, T272, T273)) → TLAST39_IN_AA(T274, T275)
TLAST39_IN_AA(T280, node(T277, T278, T281)) → U20_AA(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
TLAST39_IN_AA(T280, node(T277, T278, T281)) → TLAST39_IN_AA(T280, T281)
GOAL1_IN_GAA(T7, T24, T280) → U29_GAA(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_GAA(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_GAA(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U29_GAA(T7, T24, T280, s2t4_out_ga(T7, T23)) → TAPPEND38_IN_AAA(T23, T24, node(T277, T278, T281))
U30_GAA(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_GAA(T7, T24, T280, tlast39_in_aa(T280, T281))
U30_GAA(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → TLAST39_IN_AA(T280, T281)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
GOAL1_IN_GAA(x1, x2, x3)  =  GOAL1_IN_GAA(x1)
U21_GAA(x1, x2, x3, x4)  =  U21_GAA(x4)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(x1)
U1_GA(x1, x2, x3, x4)  =  U1_GA(x4)
U2_GA(x1, x2, x3, x4)  =  U2_GA(x4)
U3_GA(x1, x2, x3, x4)  =  U3_GA(x4)
U22_GAA(x1, x2, x3, x4)  =  U22_GAA(x4)
U23_GAA(x1, x2, x3, x4)  =  U23_GAA(x4)
TAPPEND38_IN_AAA(x1, x2, x3)  =  TAPPEND38_IN_AAA
U4_AAA(x1, x2, x3)  =  U4_AAA(x3)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)
U4_GAA(x1, x2, x3)  =  U4_GAA(x3)
U5_GAA(x1, x2, x3, x4, x5, x6)  =  U5_GAA(x6)
U6_GAA(x1, x2, x3, x4, x5, x6)  =  U6_GAA(x6)
U7_GAA(x1, x2, x3, x4)  =  U7_GAA(x4)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)
U13_GAA(x1, x2, x3)  =  U13_GAA(x3)
U14_GAA(x1, x2, x3, x4, x5, x6)  =  U14_GAA(x6)
U15_GAA(x1, x2, x3, x4, x5, x6)  =  U15_GAA(x6)
U16_GAA(x1, x2)  =  U16_GAA(x2)
U17_GAA(x1, x2, x3, x4, x5)  =  U17_GAA(x5)
U18_GAA(x1, x2, x3, x4, x5)  =  U18_GAA(x5)
U8_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U8_GAA(x7)
U9_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U9_GAA(x7)
U10_GAA(x1, x2, x3, x4)  =  U10_GAA(x4)
U11_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U11_GAA(x7)
U12_GAA(x1, x2, x3, x4, x5, x6, x7)  =  U12_GAA(x7)
U5_AAA(x1, x2, x3, x4, x5, x6)  =  U5_AAA(x6)
U6_AAA(x1, x2, x3, x4, x5, x6)  =  U6_AAA(x6)
U7_AAA(x1, x2, x3, x4)  =  U7_AAA(x4)
U8_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U8_AAA(x7)
TAPPEND151_IN_AAA(x1, x2, x3)  =  TAPPEND151_IN_AAA
U13_AAA(x1, x2, x3)  =  U13_AAA(x3)
U14_AAA(x1, x2, x3, x4, x5, x6)  =  U14_AAA(x6)
U15_AAA(x1, x2, x3, x4, x5, x6)  =  U15_AAA(x6)
U16_AAA(x1, x2)  =  U16_AAA(x2)
U17_AAA(x1, x2, x3, x4, x5)  =  U17_AAA(x5)
U18_AAA(x1, x2, x3, x4, x5)  =  U18_AAA(x5)
U9_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U9_AAA(x7)
U10_AAA(x1, x2, x3, x4)  =  U10_AAA(x4)
U11_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U11_AAA(x7)
U12_AAA(x1, x2, x3, x4, x5, x6, x7)  =  U12_AAA(x7)
U24_GAA(x1, x2, x3, x4)  =  U24_GAA(x4)
U25_GAA(x1, x2, x3, x4)  =  U25_GAA(x4)
U26_GAA(x1, x2, x3, x4)  =  U26_GAA(x4)
U27_GAA(x1, x2, x3, x4)  =  U27_GAA(x4)
U28_GAA(x1, x2, x3, x4)  =  U28_GAA(x4)
TLAST39_IN_AA(x1, x2)  =  TLAST39_IN_AA
U19_AA(x1, x2, x3, x4, x5)  =  U19_AA(x5)
U20_AA(x1, x2, x3, x4, x5)  =  U20_AA(x5)
U29_GAA(x1, x2, x3, x4)  =  U29_GAA(x4)
U30_GAA(x1, x2, x3, x4)  =  U30_GAA(x4)
U31_GAA(x1, x2, x3, x4)  =  U31_GAA(x4)

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

(69) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 8 SCCs with 64 less nodes.

(70) Complex Obligation (AND)

(71) Obligation:

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

TLAST39_IN_AA(T280, node(T277, T278, T281)) → TLAST39_IN_AA(T280, T281)
TLAST39_IN_AA(T274, node(T275, T272, T273)) → TLAST39_IN_AA(T274, T275)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
TLAST39_IN_AA(x1, x2)  =  TLAST39_IN_AA

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

(72) UsableRulesProof (EQUIVALENT transformation)

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

(73) Obligation:

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

TLAST39_IN_AA(T280, node(T277, T278, T281)) → TLAST39_IN_AA(T280, T281)
TLAST39_IN_AA(T274, node(T275, T272, T273)) → TLAST39_IN_AA(T274, T275)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TLAST39_IN_AA(x1, x2)  =  TLAST39_IN_AA

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

(74) PiDPToQDPProof (SOUND transformation)

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

(75) Obligation:

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

TLAST39_IN_AA → TLAST39_IN_AA

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

(76) 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 = TLAST39_IN_AA evaluates to t =TLAST39_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 TLAST39_IN_AA to TLAST39_IN_AA.

(77) FALSE

(78) Obligation:

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

TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)

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

(79) UsableRulesProof (EQUIVALENT transformation)

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

(80) Obligation:

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

TAPPEND151_IN_GAA(nil, nil, node(nil, nil, X489)) → TAPPEND151_IN_GAA(nil, X486, X489)
TAPPEND151_IN_GAA(nil, X431, node(X432, nil, nil)) → TAPPEND151_IN_GAA(nil, X431, X432)

R is empty.
The argument filtering Pi contains the following mapping:
nil  =  nil
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)

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

(81) PiDPToQDPProof (SOUND transformation)

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

(82) Obligation:

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

TAPPEND151_IN_GAA(nil) → TAPPEND151_IN_GAA(nil)

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

(83) 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 = TAPPEND151_IN_GAA(nil) evaluates to t =TAPPEND151_IN_GAA(nil)

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 TAPPEND151_IN_GAA(nil) to TAPPEND151_IN_GAA(nil).

(84) FALSE

(85) Obligation:

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

TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_AAA(T218, X431, X432)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
TAPPEND151_IN_AAA(x1, x2, x3)  =  TAPPEND151_IN_AAA

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

(86) UsableRulesProof (EQUIVALENT transformation)

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

(87) Obligation:

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

TAPPEND151_IN_AAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_AAA(T252, X486, X489)
TAPPEND151_IN_AAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_AAA(T218, X431, X432)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND151_IN_AAA(x1, x2, x3)  =  TAPPEND151_IN_AAA

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

(88) PiDPToQDPProof (SOUND transformation)

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

(89) Obligation:

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

TAPPEND151_IN_AAA → TAPPEND151_IN_AAA

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

(90) 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 = TAPPEND151_IN_AAA evaluates to t =TAPPEND151_IN_AAA

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

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from TAPPEND151_IN_AAA to TAPPEND151_IN_AAA.

(91) FALSE

(92) Obligation:

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

TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_GAA(T218, X431, X432)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)

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

(93) UsableRulesProof (EQUIVALENT transformation)

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

(94) Obligation:

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

TAPPEND151_IN_GAA(node(T249, T250, T252), T249, node(T249, T250, X489)) → TAPPEND151_IN_GAA(T252, X486, X489)
TAPPEND151_IN_GAA(node(T218, T216, T217), X431, node(X432, T216, T217)) → TAPPEND151_IN_GAA(T218, X431, X432)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND151_IN_GAA(x1, x2, x3)  =  TAPPEND151_IN_GAA(x1)

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

(95) PiDPToQDPProof (SOUND transformation)

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

(96) Obligation:

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

TAPPEND151_IN_GAA(node(T249, T250, T252)) → TAPPEND151_IN_GAA(T252)
TAPPEND151_IN_GAA(node(T218, T216, T217)) → TAPPEND151_IN_GAA(T218)

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

(97) 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:

• TAPPEND151_IN_GAA(node(T249, T250, T252)) → TAPPEND151_IN_GAA(T252)
  The graph contains the following edges 1 > 1

• TAPPEND151_IN_GAA(node(T218, T216, T217)) → TAPPEND151_IN_GAA(T218)
  The graph contains the following edges 1 > 1

(98) TRUE

(99) Obligation:

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

TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)

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

(100) UsableRulesProof (EQUIVALENT transformation)

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

(101) Obligation:

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

TAPPEND38_IN_GAA(nil, T89, node(X217, nil, nil)) → TAPPEND38_IN_GAA(nil, T89, X217)

R is empty.
The argument filtering Pi contains the following mapping:
nil  =  nil
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)

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

(102) PiDPToQDPProof (SOUND transformation)

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

(103) Obligation:

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

TAPPEND38_IN_GAA(nil) → TAPPEND38_IN_GAA(nil)

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

(104) 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 = TAPPEND38_IN_GAA(nil) evaluates to t =TAPPEND38_IN_GAA(nil)

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 TAPPEND38_IN_GAA(nil) to TAPPEND38_IN_GAA(nil).

(105) FALSE

(106) Obligation:

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

TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_GAA(T107, T108, X217)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)

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

(107) UsableRulesProof (EQUIVALENT transformation)

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

(108) Obligation:

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

TAPPEND38_IN_GAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_GAA(T107, T108, X217)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND38_IN_GAA(x1, x2, x3)  =  TAPPEND38_IN_GAA(x1)

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

(109) PiDPToQDPProof (SOUND transformation)

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

(110) Obligation:

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

TAPPEND38_IN_GAA(node(T107, T105, T106)) → TAPPEND38_IN_GAA(T107)

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

(111) 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:

• TAPPEND38_IN_GAA(node(T107, T105, T106)) → TAPPEND38_IN_GAA(T107)
  The graph contains the following edges 1 > 1

(112) TRUE

(113) Obligation:

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

TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_AAA(T107, T108, X217)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
TAPPEND38_IN_AAA(x1, x2, x3)  =  TAPPEND38_IN_AAA

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

(114) UsableRulesProof (EQUIVALENT transformation)

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

(115) Obligation:

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

TAPPEND38_IN_AAA(node(T107, T105, T106), T108, node(X217, T105, T106)) → TAPPEND38_IN_AAA(T107, T108, X217)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND38_IN_AAA(x1, x2, x3)  =  TAPPEND38_IN_AAA

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

(116) PiDPToQDPProof (SOUND transformation)

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

(117) Obligation:

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

TAPPEND38_IN_AAA → TAPPEND38_IN_AAA

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

(118) 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 = TAPPEND38_IN_AAA evaluates to t =TAPPEND38_IN_AAA

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

• Matcher: [ ]
• Semiunifier: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from TAPPEND38_IN_AAA to TAPPEND38_IN_AAA.

(119) FALSE

(120) Obligation:

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

S2T4_IN_GA(s(T16), node(nil, X52, X53)) → S2T4_IN_GA(T16, X53)
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → S2T4_IN_GA(T14, X38)
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → S2T4_IN_GA(T18, X66)

The TRS R consists of the following rules:

goal1_in_gaa(T7, T10, T11) → U21_gaa(T7, T10, T11, s2t4_in_ga(T7, X21))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T14), node(X38, X39, X38)) → U1_ga(T14, X38, X39, s2t4_in_ga(T14, X38))
s2t4_in_ga(s(T16), node(nil, X52, X53)) → U2_ga(T16, X52, X53, s2t4_in_ga(T16, X53))
s2t4_in_ga(s(T18), node(X66, X67, nil)) → U3_ga(T18, X66, X67, s2t4_in_ga(T18, X66))
s2t4_in_ga(T19, node(nil, X74, nil)) → s2t4_out_ga(T19, node(nil, X74, nil))
U3_ga(T18, X66, X67, s2t4_out_ga(T18, X66)) → s2t4_out_ga(s(T18), node(X66, X67, nil))
U2_ga(T16, X52, X53, s2t4_out_ga(T16, X53)) → s2t4_out_ga(s(T16), node(nil, X52, X53))
U1_ga(T14, X38, X39, s2t4_out_ga(T14, X38)) → s2t4_out_ga(s(T14), node(X38, X39, X38))
U21_gaa(T7, T10, T11, s2t4_out_ga(T7, X21)) → goal1_out_gaa(T7, T10, T11)
goal1_in_gaa(T7, T24, T25) → U22_gaa(T7, T24, T25, s2t4_in_ga(T7, T23))
U22_gaa(T7, T24, T25, s2t4_out_ga(T7, T23)) → U23_gaa(T7, T24, T25, tappend38_in_aaa(T23, T24, X81))
tappend38_in_aaa(nil, T30, node(nil, T30, nil)) → tappend38_out_aaa(nil, T30, node(nil, T30, nil))
tappend38_in_aaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_aaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_aaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_aaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_aaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_aaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_aaa(nil, T89, node(X217, nil, nil)) → U4_aaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(nil, T30, node(nil, T30, nil)) → tappend38_out_gaa(nil, T30, node(nil, T30, nil))
tappend38_in_gaa(nil, T32, node(node(nil, T32, nil), nil, nil)) → tappend38_out_gaa(nil, T32, node(node(nil, T32, nil), nil, nil))
tappend38_in_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44)) → tappend38_out_gaa(node(nil, T43, T44), T32, node(node(nil, T32, nil), T43, T44))
tappend38_in_gaa(nil, T57, node(nil, nil, node(nil, T57, nil))) → tappend38_out_gaa(nil, T57, node(nil, nil, node(nil, T57, nil)))
tappend38_in_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil))) → tappend38_out_gaa(node(T70, T71, nil), T57, node(T70, T71, node(nil, T57, nil)))
tappend38_in_gaa(nil, T89, node(X217, nil, nil)) → U4_gaa(T89, X217, tappend38_in_gaa(nil, T89, X217))
tappend38_in_gaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_gaa(T107, T105, T106, T108, X217, tappend38_in_gaa(T107, T108, X217))
tappend38_in_gaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_gaa(T126, T124, T125, T127, X217, tappend38_in_gaa(T126, T127, X217))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_gaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(nil, X300, X300) → tappend151_out_gaa(nil, X300, X300)
tappend151_in_gaa(nil, X313, node(X313, nil, nil)) → tappend151_out_gaa(nil, X313, node(X313, nil, nil))
tappend151_in_gaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_gaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_gaa(nil, X370, node(nil, nil, X370)) → tappend151_out_gaa(nil, X370, node(nil, nil, X370))
tappend151_in_gaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_gaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_gaa(nil, X431, node(X432, nil, nil)) → U13_gaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
tappend151_in_gaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_gaa(T218, T216, T217, X431, X432, tappend151_in_gaa(T218, X431, X432))
tappend151_in_gaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_gaa(T234, T232, T233, X431, X432, tappend151_in_gaa(T234, X431, X432))
tappend151_in_gaa(nil, nil, node(nil, nil, X489)) → U16_gaa(X489, tappend151_in_gaa(nil, X486, X489))
tappend151_in_gaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_gaa(T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
tappend151_in_gaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_gaa(T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U18_gaa(T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend151_out_gaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_gaa(T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend151_out_gaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U16_gaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_gaa(nil, nil, node(nil, nil, X489))
U15_gaa(T234, T232, T233, X431, X432, tappend151_out_gaa(T234, X431, X432)) → tappend151_out_gaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_gaa(T218, T216, T217, X431, X432, tappend151_out_gaa(T218, X431, X432)) → tappend151_out_gaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U13_gaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_gaa(nil, X431, node(X432, nil, nil))
U7_gaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_in_gaa(T218, X431, X432))
U8_gaa(T145, T146, T218, T216, T217, X432, tappend151_out_gaa(T218, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_in_gaa(T234, X431, X432))
U9_gaa(T145, T146, T234, T232, T233, X432, tappend151_out_gaa(T234, X431, X432)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_gaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_gaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_in_gaa(T252, X486, X489))
U11_gaa(T145, T146, T249, T250, T252, X489, tappend151_out_gaa(T252, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_in_gaa(T268, X486, X489))
U12_gaa(T145, T146, T265, T266, T268, X489, tappend151_out_gaa(T268, X486, X489)) → tappend38_out_gaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_gaa(T126, T124, T125, T127, X217, tappend38_out_gaa(T126, T127, X217)) → tappend38_out_gaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_gaa(T107, T105, T106, T108, X217, tappend38_out_gaa(T107, T108, X217)) → tappend38_out_gaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U4_gaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_gaa(nil, T89, node(X217, nil, nil))
U4_aaa(T89, X217, tappend38_out_gaa(nil, T89, X217)) → tappend38_out_aaa(nil, T89, node(X217, nil, nil))
tappend38_in_aaa(node(T107, T105, T106), T108, node(X217, T105, T106)) → U5_aaa(T107, T105, T106, T108, X217, tappend38_in_aaa(T107, T108, X217))
tappend38_in_aaa(node(T126, T124, T125), T127, node(X217, T124, T125)) → U6_aaa(T126, T124, T125, T127, X217, tappend38_in_aaa(T126, T127, X217))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, X300))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X313, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(nil, T160, T161)), T145, node(node(nil, T145, nil), T146, node(X313, T160, T161)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370))) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T186, T187, nil)), T145, node(node(nil, T145, nil), T146, node(T186, T187, X370)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil))) → U7_aaa(T145, T146, X432, tappend151_in_gaa(nil, X431, X432))
U7_aaa(T145, T146, X432, tappend151_out_gaa(nil, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(X432, nil, nil)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217))) → U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(nil, X300, X300) → tappend151_out_aaa(nil, X300, X300)
tappend151_in_aaa(nil, X313, node(X313, nil, nil)) → tappend151_out_aaa(nil, X313, node(X313, nil, nil))
tappend151_in_aaa(node(nil, T160, T161), X313, node(X313, T160, T161)) → tappend151_out_aaa(node(nil, T160, T161), X313, node(X313, T160, T161))
tappend151_in_aaa(nil, X370, node(nil, nil, X370)) → tappend151_out_aaa(nil, X370, node(nil, nil, X370))
tappend151_in_aaa(node(T186, T187, nil), X370, node(T186, T187, X370)) → tappend151_out_aaa(node(T186, T187, nil), X370, node(T186, T187, X370))
tappend151_in_aaa(nil, X431, node(X432, nil, nil)) → U13_aaa(X431, X432, tappend151_in_gaa(nil, X431, X432))
U13_aaa(X431, X432, tappend151_out_gaa(nil, X431, X432)) → tappend151_out_aaa(nil, X431, node(X432, nil, nil))
tappend151_in_aaa(node(T218, T216, T217), X431, node(X432, T216, T217)) → U14_aaa(T218, T216, T217, X431, X432, tappend151_in_aaa(T218, X431, X432))
tappend151_in_aaa(node(T234, T232, T233), X431, node(X432, T232, T233)) → U15_aaa(T234, T232, T233, X431, X432, tappend151_in_aaa(T234, X431, X432))
tappend151_in_aaa(nil, nil, node(nil, nil, X489)) → U16_aaa(X489, tappend151_in_gaa(nil, X486, X489))
U16_aaa(X489, tappend151_out_gaa(nil, X486, X489)) → tappend151_out_aaa(nil, nil, node(nil, nil, X489))
tappend151_in_aaa(node(T249, T250, T252), T249, node(T249, T250, X489)) → U17_aaa(T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
tappend151_in_aaa(node(T265, T266, T268), T265, node(T265, T266, X489)) → U18_aaa(T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U18_aaa(T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend151_out_aaa(node(T265, T266, T268), T265, node(T265, T266, X489))
U17_aaa(T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend151_out_aaa(node(T249, T250, T252), T249, node(T249, T250, X489))
U15_aaa(T234, T232, T233, X431, X432, tappend151_out_aaa(T234, X431, X432)) → tappend151_out_aaa(node(T234, T232, T233), X431, node(X432, T232, T233))
U14_aaa(T218, T216, T217, X431, X432, tappend151_out_aaa(T218, X431, X432)) → tappend151_out_aaa(node(T218, T216, T217), X431, node(X432, T216, T217))
U8_aaa(T145, T146, T218, T216, T217, X432, tappend151_out_aaa(T218, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T218, T216, T217)), T145, node(node(nil, T145, nil), T146, node(X432, T216, T217)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233))) → U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_in_aaa(T234, X431, X432))
U9_aaa(T145, T146, T234, T232, T233, X432, tappend151_out_aaa(T234, X431, X432)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T234, T232, T233)), T145, node(node(nil, T145, nil), T146, node(X432, T232, T233)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489))) → U10_aaa(T145, T146, X489, tappend151_in_gaa(nil, X486, X489))
U10_aaa(T145, T146, X489, tappend151_out_gaa(nil, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, nil), T145, node(node(nil, T145, nil), T146, node(nil, nil, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489))) → U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_in_aaa(T252, X486, X489))
U11_aaa(T145, T146, T249, T250, T252, X489, tappend151_out_aaa(T252, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T249, T250, T252)), T145, node(node(nil, T145, nil), T146, node(T249, T250, X489)))
tappend38_in_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489))) → U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_in_aaa(T268, X486, X489))
U12_aaa(T145, T146, T265, T266, T268, X489, tappend151_out_aaa(T268, X486, X489)) → tappend38_out_aaa(node(node(nil, T145, nil), T146, node(T265, T266, T268)), T145, node(node(nil, T145, nil), T146, node(T265, T266, X489)))
U6_aaa(T126, T124, T125, T127, X217, tappend38_out_aaa(T126, T127, X217)) → tappend38_out_aaa(node(T126, T124, T125), T127, node(X217, T124, T125))
U5_aaa(T107, T105, T106, T108, X217, tappend38_out_aaa(T107, T108, X217)) → tappend38_out_aaa(node(T107, T105, T106), T108, node(X217, T105, T106))
U23_gaa(T7, T24, T25, tappend38_out_aaa(T23, T24, X81)) → goal1_out_gaa(T7, T24, T25)
goal1_in_gaa(T7, T24, T269) → U24_gaa(T7, T24, T269, s2t4_in_ga(T7, T23))
U24_gaa(T7, T24, T269, s2t4_out_ga(T7, T23)) → U25_gaa(T7, T24, T269, tappend38_in_aaa(T23, T24, node(nil, T269, nil)))
U25_gaa(T7, T24, T269, tappend38_out_aaa(T23, T24, node(nil, T269, nil))) → goal1_out_gaa(T7, T24, T269)
goal1_in_gaa(T7, T24, T274) → U26_gaa(T7, T24, T274, s2t4_in_ga(T7, T23))
U26_gaa(T7, T24, T274, s2t4_out_ga(T7, T23)) → U27_gaa(T7, T24, T274, tappend38_in_aaa(T23, T24, node(T275, T272, T273)))
U27_gaa(T7, T24, T274, tappend38_out_aaa(T23, T24, node(T275, T272, T273))) → U28_gaa(T7, T24, T274, tlast39_in_aa(T274, T275))
tlast39_in_aa(T269, node(nil, T269, nil)) → tlast39_out_aa(T269, node(nil, T269, nil))
tlast39_in_aa(T274, node(T275, T272, T273)) → U19_aa(T274, T275, T272, T273, tlast39_in_aa(T274, T275))
tlast39_in_aa(T280, node(T277, T278, T281)) → U20_aa(T280, T277, T278, T281, tlast39_in_aa(T280, T281))
U20_aa(T280, T277, T278, T281, tlast39_out_aa(T280, T281)) → tlast39_out_aa(T280, node(T277, T278, T281))
U19_aa(T274, T275, T272, T273, tlast39_out_aa(T274, T275)) → tlast39_out_aa(T274, node(T275, T272, T273))
U28_gaa(T7, T24, T274, tlast39_out_aa(T274, T275)) → goal1_out_gaa(T7, T24, T274)
goal1_in_gaa(T7, T24, T280) → U29_gaa(T7, T24, T280, s2t4_in_ga(T7, T23))
U29_gaa(T7, T24, T280, s2t4_out_ga(T7, T23)) → U30_gaa(T7, T24, T280, tappend38_in_aaa(T23, T24, node(T277, T278, T281)))
U30_gaa(T7, T24, T280, tappend38_out_aaa(T23, T24, node(T277, T278, T281))) → U31_gaa(T7, T24, T280, tlast39_in_aa(T280, T281))
U31_gaa(T7, T24, T280, tlast39_out_aa(T280, T281)) → goal1_out_gaa(T7, T24, T280)

The argument filtering Pi contains the following mapping:
goal1_in_gaa(x1, x2, x3)  =  goal1_in_gaa(x1)
U21_gaa(x1, x2, x3, x4)  =  U21_gaa(x4)
s2t4_in_ga(x1, x2)  =  s2t4_in_ga(x1)
0  =  0
s2t4_out_ga(x1, x2)  =  s2t4_out_ga
s(x1)  =  s(x1)
U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)
U2_ga(x1, x2, x3, x4)  =  U2_ga(x4)
U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)
goal1_out_gaa(x1, x2, x3)  =  goal1_out_gaa
U22_gaa(x1, x2, x3, x4)  =  U22_gaa(x4)
U23_gaa(x1, x2, x3, x4)  =  U23_gaa(x4)
tappend38_in_aaa(x1, x2, x3)  =  tappend38_in_aaa
tappend38_out_aaa(x1, x2, x3)  =  tappend38_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
tappend38_in_gaa(x1, x2, x3)  =  tappend38_in_gaa(x1)
nil  =  nil
tappend38_out_gaa(x1, x2, x3)  =  tappend38_out_gaa
node(x1, x2, x3)  =  node(x1, x2, x3)
U4_gaa(x1, x2, x3)  =  U4_gaa(x3)
U5_gaa(x1, x2, x3, x4, x5, x6)  =  U5_gaa(x6)
U6_gaa(x1, x2, x3, x4, x5, x6)  =  U6_gaa(x6)
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
tappend151_in_gaa(x1, x2, x3)  =  tappend151_in_gaa(x1)
tappend151_out_gaa(x1, x2, x3)  =  tappend151_out_gaa
U13_gaa(x1, x2, x3)  =  U13_gaa(x3)
U14_gaa(x1, x2, x3, x4, x5, x6)  =  U14_gaa(x6)
U15_gaa(x1, x2, x3, x4, x5, x6)  =  U15_gaa(x6)
U16_gaa(x1, x2)  =  U16_gaa(x2)
U17_gaa(x1, x2, x3, x4, x5)  =  U17_gaa(x5)
U18_gaa(x1, x2, x3, x4, x5)  =  U18_gaa(x5)
U8_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_gaa(x7)
U9_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_gaa(x7)
U10_gaa(x1, x2, x3, x4)  =  U10_gaa(x4)
U11_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_gaa(x7)
U12_gaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_gaa(x7)
U5_aaa(x1, x2, x3, x4, x5, x6)  =  U5_aaa(x6)
U6_aaa(x1, x2, x3, x4, x5, x6)  =  U6_aaa(x6)
U7_aaa(x1, x2, x3, x4)  =  U7_aaa(x4)
U8_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U8_aaa(x7)
tappend151_in_aaa(x1, x2, x3)  =  tappend151_in_aaa
tappend151_out_aaa(x1, x2, x3)  =  tappend151_out_aaa
U13_aaa(x1, x2, x3)  =  U13_aaa(x3)
U14_aaa(x1, x2, x3, x4, x5, x6)  =  U14_aaa(x6)
U15_aaa(x1, x2, x3, x4, x5, x6)  =  U15_aaa(x6)
U16_aaa(x1, x2)  =  U16_aaa(x2)
U17_aaa(x1, x2, x3, x4, x5)  =  U17_aaa(x5)
U18_aaa(x1, x2, x3, x4, x5)  =  U18_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U9_aaa(x7)
U10_aaa(x1, x2, x3, x4)  =  U10_aaa(x4)
U11_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U11_aaa(x7)
U12_aaa(x1, x2, x3, x4, x5, x6, x7)  =  U12_aaa(x7)
U24_gaa(x1, x2, x3, x4)  =  U24_gaa(x4)
U25_gaa(x1, x2, x3, x4)  =  U25_gaa(x4)
U26_gaa(x1, x2, x3, x4)  =  U26_gaa(x4)
U27_gaa(x1, x2, x3, x4)  =  U27_gaa(x4)
U28_gaa(x1, x2, x3, x4)  =  U28_gaa(x4)
tlast39_in_aa(x1, x2)  =  tlast39_in_aa
tlast39_out_aa(x1, x2)  =  tlast39_out_aa
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3, x4, x5)  =  U20_aa(x5)
U29_gaa(x1, x2, x3, x4)  =  U29_gaa(x4)
U30_gaa(x1, x2, x3, x4)  =  U30_gaa(x4)
U31_gaa(x1, x2, x3, x4)  =  U31_gaa(x4)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(x1)

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

(121) UsableRulesProof (EQUIVALENT transformation)

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

(122) Obligation:

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

S2T4_IN_GA(s(T16), node(nil, X52, X53)) → S2T4_IN_GA(T16, X53)
S2T4_IN_GA(s(T14), node(X38, X39, X38)) → S2T4_IN_GA(T14, X38)
S2T4_IN_GA(s(T18), node(X66, X67, nil)) → S2T4_IN_GA(T18, X66)

R is empty.
The argument filtering Pi contains the following mapping:
s(x1)  =  s(x1)
nil  =  nil
node(x1, x2, x3)  =  node(x1, x2, x3)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(x1)

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

(123) PiDPToQDPProof (SOUND transformation)

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

(124) Obligation:

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

S2T4_IN_GA(s(T16)) → S2T4_IN_GA(T16)

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

(125) 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:

• S2T4_IN_GA(s(T16)) → S2T4_IN_GA(T16)
  The graph contains the following edges 1 > 1

(126) TRUE