Left Termination of the query pattern goal_in_1(g) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

goal(X) :- ','(s2t(X, T), tappend(T, X1, X2)).
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, X3, T)) :- ','(p(X, P), s2t(P, T)).
s2t(X, node(nil, X4, T)) :- ','(p(X, P), s2t(P, T)).
s2t(X, node(T, X5, nil)) :- ','(p(X, P), s2t(P, T)).
s2t(X, node(nil, X6, nil)).
left(nil, nil).
left(node(L, X7, X8), L).
right(nil, nil).
right(node(X9, X10, R), R).
value(nil, nil).
value(node(X11, X, X12), X).
p(0, 0).
p(s(X), X).
eq(X, X).

Queries:

goal(g).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: goal(T4)\n\nT4 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: goal(T4), SCOPE: 1, CLAUSE: 0\n\nT4 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(s2t(T5, X15), tappend(X15, X16, X17))\n\nT5 is ground\nX15 is free; \nX16 is free; \nX17 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: s2t(T5, X15)\n\nT5 is ground\nX15 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: tappend(T6, X16, X17)\n\nX16 is free\nX17 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: s2t(T5, X15), SCOPE: 2, CLAUSE: 6 | s2t(T5, X15), SCOPE: 2, CLAUSE: 7 | s2t(T5, X15), SCOPE: 2, CLAUSE: 8 | s2t(T5, X15), SCOPE: 2, CLAUSE: 9 | s2t(T5, X15), SCOPE: 2, CLAUSE: 10 | ?_2\n\nT5 is ground\nX15 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: ','(!_2, eq(X20, nil)) | s2t(0, X15), SCOPE: 2, CLAUSE: 7 | s2t(0, X15), SCOPE: 2, CLAUSE: 8 | s2t(0, X15), SCOPE: 2, CLAUSE: 9 | s2t(0, X15), SCOPE: 2, CLAUSE: 10 | ?_2\n\nX15 is free\nX20 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: s2t(T5, X15), SCOPE: 2, CLAUSE: 7 | s2t(T5, X15), SCOPE: 2, CLAUSE: 8 | s2t(T5, X15), SCOPE: 2, CLAUSE: 9 | s2t(T5, X15), SCOPE: 2, CLAUSE: 10\n\nT5 is ground\nX15 is free; \nX19 is free; \ns2t(T5, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: eq(X20, nil)\n\nX20 is free", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: eq(X20, nil), SCOPE: 3, CLAUSE: 19\n\nX20 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(T5, X15), SCOPE: 2, CLAUSE: 7\n\nT5 is ground\nX15 is free; \nX19 is free; \ns2t(T5, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: s2t(T5, X15), SCOPE: 2, CLAUSE: 8 | s2t(T5, X15), SCOPE: 2, CLAUSE: 9 | s2t(T5, X15), SCOPE: 2, CLAUSE: 10\n\nT5 is ground\nX15 is free; \nX19 is free; \ns2t(T5, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(p(T7, X33), s2t(X33, X34))\n\nT7 is ground\nX15 is free; \nX19 is free; \nX34 is free; \nX33 is free; \ns2t(T7, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(p(T7, X33), s2t(X33, X34)), SCOPE: 4, CLAUSE: 17 | ','(p(T7, X33), s2t(X33, X34)), SCOPE: 4, CLAUSE: 18\n\nT7 is ground\nX15 is free; \nX19 is free; \nX34 is free; \nX33 is free; \ns2t(T7, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(p(T7, X33), s2t(X33, X34)), SCOPE: 4, CLAUSE: 18\n\nT7 is ground\nX15 is free; \nX19 is free; \nX34 is free; \nX33 is free; \ns2t(T7, X15) !=? s2t(0, X19)\np(T7, X33) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: s2t(T8, X34)\n\nT8 is ground\nX15 is free; \nX19 is free; \nX34 is free; \nX33 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\nX15 is free\nX19 is free; \nX33 is free; \nX37 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: s2t(T5, X15), SCOPE: 2, CLAUSE: 8\n\nT5 is ground\nX15 is free; \nX19 is free; \ns2t(T5, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: s2t(T5, X15), SCOPE: 2, CLAUSE: 9 | s2t(T5, X15), SCOPE: 2, CLAUSE: 10\n\nT5 is ground\nX15 is free; \nX19 is free; \ns2t(T5, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: ','(p(T9, X47), s2t(X47, X49))\n\nT9 is ground\nX15 is free; \nX19 is free; \nX49 is free; \nX47 is free; \ns2t(T9, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(p(T9, X47), s2t(X47, X49)), SCOPE: 5, CLAUSE: 17 | ','(p(T9, X47), s2t(X47, X49)), SCOPE: 5, CLAUSE: 18\n\nT9 is ground\nX15 is free; \nX19 is free; \nX49 is free; \nX47 is free; \ns2t(T9, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: ','(p(T9, X47), s2t(X47, X49)), SCOPE: 5, CLAUSE: 18\n\nT9 is ground\nX15 is free; \nX19 is free; \nX49 is free; \nX47 is free; \ns2t(T9, X15) !=? s2t(0, X19)\np(T9, X47) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: s2t(T10, X49)\n\nT10 is ground\nX15 is free; \nX19 is free; \nX49 is free; \nX47 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\nX15 is free\nX19 is free; \nX47 is free; \nX51 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: s2t(T5, X15), SCOPE: 2, CLAUSE: 9\n\nT5 is ground\nX15 is free; \nX19 is free; \ns2t(T5, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: s2t(T5, X15), SCOPE: 2, CLAUSE: 10\n\nT5 is ground\nX15 is free; \nX19 is free; \ns2t(T5, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(p(T11, X61), s2t(X61, X62))\n\nT11 is ground\nX15 is free; \nX19 is free; \nX62 is free; \nX61 is free; \ns2t(T11, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ','(p(T11, X61), s2t(X61, X62)), SCOPE: 6, CLAUSE: 17 | ','(p(T11, X61), s2t(X61, X62)), SCOPE: 6, CLAUSE: 18\n\nT11 is ground\nX15 is free; \nX19 is free; \nX62 is free; \nX61 is free; \ns2t(T11, X15) !=? s2t(0, X19)", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(p(T11, X61), s2t(X61, X62)), SCOPE: 6, CLAUSE: 18\n\nT11 is ground\nX15 is free; \nX19 is free; \nX62 is free; \nX61 is free; \ns2t(T11, X15) !=? s2t(0, X19)\np(T11, X61) !=? p(0, 0)", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: s2t(T12, X62)\n\nT12 is ground\nX15 is free; \nX19 is free; \nX62 is free; \nX61 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\nX15 is free\nX19 is free; \nX61 is free; \nX65 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: true\n\nX15 is free\nX19 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 1 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 2 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 3 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 4 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 5 | ?_7\n\nX16 is free\nX17 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: ','(!_7, eq(X75, X76)) | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 2 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 3 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 4 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 5 | ?_7\n\nX16 is free\nX17 is free; \nX75 is free; \nX76 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 2 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 3 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 4 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 5\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \ntappend(T6, X16, X17) !=? tappend(nil, X73, X74)", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: eq(X75, X76)\n\nX75 is free\nX76 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: eq(X75, X76), SCOPE: 8, CLAUSE: 19\n\nX75 is free\nX76 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 2\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \ntappend(T6, X16, X17) !=? tappend(nil, X73, X74)", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 3 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 4 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 5\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \ntappend(T6, X16, X17) !=? tappend(nil, X73, X74)", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(left(T15, nil), ','(right(T15, X94), value(T15, X93)))\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \nX93 is free; \nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 11 | ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(right(nil, X94), value(nil, X93)) | ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; \nleft(T15, nil) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: ','(right(nil, X94), value(nil, X93)), SCOPE: 10, CLAUSE: 13 | ','(right(nil, X94), value(nil, X93)), SCOPE: 10, CLAUSE: 14 | ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: value(nil, X93) | ','(right(nil, X94), value(nil, X93)), SCOPE: 10, CLAUSE: 14 | ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: value(nil, X93), SCOPE: 11, CLAUSE: 15 | value(nil, X93), SCOPE: 11, CLAUSE: 16 | ','(right(nil, X94), value(nil, X93)), SCOPE: 10, CLAUSE: 14 | ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: true | value(nil, X93), SCOPE: 11, CLAUSE: 16 | ','(right(nil, X94), value(nil, X93)), SCOPE: 10, CLAUSE: 14 | ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: value(nil, X93), SCOPE: 11, CLAUSE: 16 | ','(right(nil, X94), value(nil, X93)), SCOPE: 10, CLAUSE: 14 | ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(right(nil, X94), value(nil, X93)), SCOPE: 10, CLAUSE: 14 | ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(left(T15, nil), ','(right(T15, X94), value(T15, X93))), SCOPE: 9, CLAUSE: 12\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(right(node(nil, T19, T20), X94), value(node(nil, T19, T20), X93))\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: \n\nX104 is free\nX105 is free; \nX106 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(right(node(nil, T19, T20), X94), value(node(nil, T19, T20), X93)), SCOPE: 12, CLAUSE: 13 | ','(right(node(nil, T19, T20), X94), value(node(nil, T19, T20), X93)), SCOPE: 12, CLAUSE: 14\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(right(node(nil, T19, T20), X94), value(node(nil, T19, T20), X93)), SCOPE: 12, CLAUSE: 14\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: value(node(nil, T23, T24), X93)\n\nX93 is free", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: value(node(nil, T23, T24), X93), SCOPE: 13, CLAUSE: 15 | value(node(nil, T23, T24), X93), SCOPE: 13, CLAUSE: 16\n\nX93 is free", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: value(node(nil, T23, T24), X93), SCOPE: 13, CLAUSE: 16\n\nX93 is free", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(right(node(nil, T30, T31), X94), value(node(nil, T30, T31), X93))\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: \n\nX122 is free\nX123 is free; \nX124 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(right(node(nil, T30, T31), X94), value(node(nil, T30, T31), X93)), SCOPE: 14, CLAUSE: 13 | ','(right(node(nil, T30, T31), X94), value(node(nil, T30, T31), X93)), SCOPE: 14, CLAUSE: 14\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(right(node(nil, T30, T31), X94), value(node(nil, T30, T31), X93)), SCOPE: 14, CLAUSE: 14\n\nX93 is free\nX94 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: value(node(nil, T34, T35), X93)\n\nX93 is free", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: value(node(nil, T34, T35), X93), SCOPE: 15, CLAUSE: 15 | value(node(nil, T34, T35), X93), SCOPE: 15, CLAUSE: 16\n\nX93 is free", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: value(node(nil, T34, T35), X93), SCOPE: 15, CLAUSE: 16\n\nX93 is free", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 3\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \ntappend(T6, X16, X17) !=? tappend(nil, X73, X74)", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 4 | tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 5\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \ntappend(T6, X16, X17) !=? tappend(nil, X73, X74)", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: ','(left(T39, X150), ','(right(T39, nil), value(T39, X151)))\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \nX150 is free; \nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 11 | ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(right(nil, nil), value(nil, X151)) | ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; \nleft(T39, X150) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: ','(right(nil, nil), value(nil, X151)), SCOPE: 17, CLAUSE: 13 | ','(right(nil, nil), value(nil, X151)), SCOPE: 17, CLAUSE: 14 | ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: value(nil, X151) | ','(right(nil, nil), value(nil, X151)), SCOPE: 17, CLAUSE: 14 | ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: value(nil, X151), SCOPE: 18, CLAUSE: 15 | value(nil, X151), SCOPE: 18, CLAUSE: 16 | ','(right(nil, nil), value(nil, X151)), SCOPE: 17, CLAUSE: 14 | ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: true | value(nil, X151), SCOPE: 18, CLAUSE: 16 | ','(right(nil, nil), value(nil, X151)), SCOPE: 17, CLAUSE: 14 | ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: value(nil, X151), SCOPE: 18, CLAUSE: 16 | ','(right(nil, nil), value(nil, X151)), SCOPE: 17, CLAUSE: 14 | ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ','(right(nil, nil), value(nil, X151)), SCOPE: 17, CLAUSE: 14 | ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(left(T39, X150), ','(right(T39, nil), value(T39, X151))), SCOPE: 16, CLAUSE: 12\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: ','(right(node(T43, T44, T45), nil), value(node(T43, T44, T45), X151))\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: \n\nX150 is free\nX161 is free; \nX162 is free; \nX163 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ','(right(node(T43, T44, T45), nil), value(node(T43, T44, T45), X151)), SCOPE: 19, CLAUSE: 13 | ','(right(node(T43, T44, T45), nil), value(node(T43, T44, T45), X151)), SCOPE: 19, CLAUSE: 14\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(right(node(T43, T44, T45), nil), value(node(T43, T44, T45), X151)), SCOPE: 19, CLAUSE: 14\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: value(node(T49, T50, nil), X151)\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\nX167 is free\nX168 is free; \nX169 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: value(node(T49, T50, nil), X151), SCOPE: 20, CLAUSE: 15 | value(node(T49, T50, nil), X151), SCOPE: 20, CLAUSE: 16\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: value(node(T49, T50, nil), X151), SCOPE: 20, CLAUSE: 16\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(right(node(T56, T57, T58), nil), value(node(T56, T57, T58), X151))\n\nX150 is free\nX151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: \n\nX150 is free\nX179 is free; \nX180 is free; \nX181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: ','(right(node(T56, T57, T58), nil), value(node(T56, T57, T58), X151)), SCOPE: 21, CLAUSE: 13 | ','(right(node(T56, T57, T58), nil), value(node(T56, T57, T58), X151)), SCOPE: 21, CLAUSE: 14\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: ','(right(node(T56, T57, T58), nil), value(node(T56, T57, T58), X151)), SCOPE: 21, CLAUSE: 14\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: value(node(T62, T63, nil), X151)\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\nX185 is free\nX186 is free; \nX187 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: value(node(T62, T63, nil), X151), SCOPE: 22, CLAUSE: 15 | value(node(T62, T63, nil), X151), SCOPE: 22, CLAUSE: 16\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: value(node(T62, T63, nil), X151), SCOPE: 22, CLAUSE: 16\n\nX151 is free", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 4\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \ntappend(T6, X16, X17) !=? tappend(nil, X73, X74)", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: tappend(T6, X16, X17), SCOPE: 7, CLAUSE: 5\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \ntappend(T6, X16, X17) !=? tappend(nil, X73, X74)", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211))))\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \nX210 is free; \nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 11 | ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(right(nil, X213), ','(value(nil, X212), tappend(nil, X210, X211))) | ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; \nleft(T67, X209) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(right(nil, X213), ','(value(nil, X212), tappend(nil, X210, X211))), SCOPE: 24, CLAUSE: 13 | ','(right(nil, X213), ','(value(nil, X212), tappend(nil, X210, X211))), SCOPE: 24, CLAUSE: 14 | ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(value(nil, X212), tappend(nil, X210, X211)) | ','(right(nil, X213), ','(value(nil, X212), tappend(nil, X210, X211))), SCOPE: 24, CLAUSE: 14 | ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(value(nil, X212), tappend(nil, X210, X211)), SCOPE: 25, CLAUSE: 15 | ','(value(nil, X212), tappend(nil, X210, X211)), SCOPE: 25, CLAUSE: 16 | ','(right(nil, X213), ','(value(nil, X212), tappend(nil, X210, X211))), SCOPE: 24, CLAUSE: 14 | ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: tappend(nil, X210, X211) | ','(value(nil, X212), tappend(nil, X210, X211)), SCOPE: 25, CLAUSE: 16 | ','(right(nil, X213), ','(value(nil, X212), tappend(nil, X210, X211))), SCOPE: 24, CLAUSE: 14 | ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: tappend(nil, X210, X211)\n\nX210 is free\nX211 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(value(nil, X212), tappend(nil, X210, X211)), SCOPE: 25, CLAUSE: 16 | ','(right(nil, X213), ','(value(nil, X212), tappend(nil, X210, X211))), SCOPE: 24, CLAUSE: 14 | ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ','(right(nil, X213), ','(value(nil, X212), tappend(nil, X210, X211))), SCOPE: 24, CLAUSE: 14 | ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(left(T67, X209), ','(right(T67, X213), ','(value(T67, X212), tappend(X209, X210, X211)))), SCOPE: 23, CLAUSE: 12\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: ','(right(node(T71, T72, T73), X213), ','(value(node(T71, T72, T73), X212), tappend(T71, X210, X211)))\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: \n\nX209 is free\nX223 is free; \nX224 is free; \nX225 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(right(node(T71, T72, T73), X213), ','(value(node(T71, T72, T73), X212), tappend(T71, X210, X211))), SCOPE: 26, CLAUSE: 13 | ','(right(node(T71, T72, T73), X213), ','(value(node(T71, T72, T73), X212), tappend(T71, X210, X211))), SCOPE: 26, CLAUSE: 14\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: ','(right(node(T71, T72, T73), X213), ','(value(node(T71, T72, T73), X212), tappend(T71, X210, X211))), SCOPE: 26, CLAUSE: 14\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(value(node(T77, T78, T79), X212), tappend(T77, X210, X211))\n\nX210 is free\nX211 is free; \nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: ','(value(node(T77, T78, T79), X212), tappend(T77, X210, X211)), SCOPE: 27, CLAUSE: 15 | ','(value(node(T77, T78, T79), X212), tappend(T77, X210, X211)), SCOPE: 27, CLAUSE: 16\n\nX210 is free\nX211 is free; \nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(value(node(T77, T78, T79), X212), tappend(T77, X210, X211)), SCOPE: 27, CLAUSE: 16\n\nX210 is free\nX211 is free; \nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: tappend(T83, X210, X211)\n\nX210 is free\nX211 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ','(right(node(T87, T88, T89), X213), ','(value(node(T87, T88, T89), X212), tappend(T87, X210, X211)))\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; \nX209 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\nX209 is free\nX241 is free; \nX242 is free; \nX243 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: ','(right(node(T87, T88, T89), X213), ','(value(node(T87, T88, T89), X212), tappend(T87, X210, X211))), SCOPE: 28, CLAUSE: 13 | ','(right(node(T87, T88, T89), X213), ','(value(node(T87, T88, T89), X212), tappend(T87, X210, X211))), SCOPE: 28, CLAUSE: 14\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ','(right(node(T87, T88, T89), X213), ','(value(node(T87, T88, T89), X212), tappend(T87, X210, X211))), SCOPE: 28, CLAUSE: 14\n\nX210 is free\nX211 is free; \nX212 is free; \nX213 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: ','(value(node(T93, T94, T95), X212), tappend(T93, X210, X211))\n\nX210 is free\nX211 is free; \nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(value(node(T93, T94, T95), X212), tappend(T93, X210, X211)), SCOPE: 29, CLAUSE: 15 | ','(value(node(T93, T94, T95), X212), tappend(T93, X210, X211)), SCOPE: 29, CLAUSE: 16\n\nX210 is free\nX211 is free; \nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: ','(value(node(T93, T94, T95), X212), tappend(T93, X210, X211)), SCOPE: 29, CLAUSE: 16\n\nX210 is free\nX211 is free; \nX212 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: tappend(T99, X210, X211)\n\nX210 is free\nX211 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268))))\n\nX16 is free\nX17 is free; \nX73 is free; \nX74 is free; \nX266 is free; \nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 11 | ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(right(nil, X264), ','(value(nil, X267), tappend(X264, X265, X268))) | ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; \nleft(T101, X266) !=? left(nil, nil)", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(right(nil, X264), ','(value(nil, X267), tappend(X264, X265, X268))), SCOPE: 31, CLAUSE: 13 | ','(right(nil, X264), ','(value(nil, X267), tappend(X264, X265, X268))), SCOPE: 31, CLAUSE: 14 | ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(value(nil, X267), tappend(nil, X265, X268)) | ','(right(nil, X264), ','(value(nil, X267), tappend(X264, X265, X268))), SCOPE: 31, CLAUSE: 14 | ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(value(nil, X267), tappend(nil, X265, X268)), SCOPE: 32, CLAUSE: 15 | ','(value(nil, X267), tappend(nil, X265, X268)), SCOPE: 32, CLAUSE: 16 | ','(right(nil, X264), ','(value(nil, X267), tappend(X264, X265, X268))), SCOPE: 31, CLAUSE: 14 | ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: tappend(nil, X265, X268) | ','(value(nil, X267), tappend(nil, X265, X268)), SCOPE: 32, CLAUSE: 16 | ','(right(nil, X264), ','(value(nil, X267), tappend(X264, X265, X268))), SCOPE: 31, CLAUSE: 14 | ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: tappend(nil, X265, X268)\n\nX268 is free\nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: ','(value(nil, X267), tappend(nil, X265, X268)), SCOPE: 32, CLAUSE: 16 | ','(right(nil, X264), ','(value(nil, X267), tappend(X264, X265, X268))), SCOPE: 31, CLAUSE: 14 | ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ','(right(nil, X264), ','(value(nil, X267), tappend(X264, X265, X268))), SCOPE: 31, CLAUSE: 14 | ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(left(T101, X266), ','(right(T101, X264), ','(value(T101, X267), tappend(X264, X265, X268)))), SCOPE: 30, CLAUSE: 12\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ','(right(node(T105, T106, T107), X264), ','(value(node(T105, T106, T107), X267), tappend(X264, X265, X268)))\n\nX267 is free\nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: \n\nX266 is free\nX278 is free; \nX279 is free; \nX280 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: ','(right(node(T105, T106, T107), X264), ','(value(node(T105, T106, T107), X267), tappend(X264, X265, X268))), SCOPE: 33, CLAUSE: 13 | ','(right(node(T105, T106, T107), X264), ','(value(node(T105, T106, T107), X267), tappend(X264, X265, X268))), SCOPE: 33, CLAUSE: 14\n\nX267 is free\nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: ','(right(node(T105, T106, T107), X264), ','(value(node(T105, T106, T107), X267), tappend(X264, X265, X268))), SCOPE: 33, CLAUSE: 14\n\nX267 is free\nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: ','(value(node(T111, T112, T113), X267), tappend(T113, X265, X268))\n\nX267 is free\nX268 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(value(node(T111, T112, T113), X267), tappend(T113, X265, X268)), SCOPE: 34, CLAUSE: 15 | ','(value(node(T111, T112, T113), X267), tappend(T113, X265, X268)), SCOPE: 34, CLAUSE: 16\n\nX267 is free\nX268 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ','(value(node(T111, T112, T113), X267), tappend(T113, X265, X268)), SCOPE: 34, CLAUSE: 16\n\nX267 is free\nX268 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: tappend(T117, X265, X268)\n\nX268 is free\nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(right(node(T121, T122, T123), X264), ','(value(node(T121, T122, T123), X267), tappend(X264, X265, X268)))\n\nX266 is free\nX267 is free; \nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\nX266 is free\nX296 is free; \nX297 is free; \nX298 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(right(node(T121, T122, T123), X264), ','(value(node(T121, T122, T123), X267), tappend(X264, X265, X268))), SCOPE: 35, CLAUSE: 13 | ','(right(node(T121, T122, T123), X264), ','(value(node(T121, T122, T123), X267), tappend(X264, X265, X268))), SCOPE: 35, CLAUSE: 14\n\nX267 is free\nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: ','(right(node(T121, T122, T123), X264), ','(value(node(T121, T122, T123), X267), tappend(X264, X265, X268))), SCOPE: 35, CLAUSE: 14\n\nX267 is free\nX268 is free; \nX264 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: ','(value(node(T127, T128, T129), X267), tappend(T129, X265, X268))\n\nX267 is free\nX268 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(value(node(T127, T128, T129), X267), tappend(T129, X265, X268)), SCOPE: 36, CLAUSE: 15 | ','(value(node(T127, T128, T129), X267), tappend(T129, X265, X268)), SCOPE: 36, CLAUSE: 16\n\nX267 is free\nX268 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ','(value(node(T127, T128, T129), X267), tappend(T129, X265, X268)), SCOPE: 36, CLAUSE: 16\n\nX267 is free\nX268 is free; \nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: tappend(T133, X265, X268)\n\nX268 is free\nX265 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 165 [arrowhead = none ];
165 -> 2;

166 [label="EVAL with clause\ngoal(X14) :- ','(s2t(X14, X15), tappend(X15, X16, X17)).\nand substitution\nT4 -> T5\nX14 -> T5", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 166 [arrowhead = none ];
166 -> 3;

167 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
3 -> 167 [arrowhead = none ];
167 -> 4;

168 [label="SPLIT 2\nreplacements:\nX15 -> T6", fontsize=14, style = filled, fillcolor = violet];
3 -> 168 [arrowhead = none ];
168 -> 5;

169 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
4 -> 169 [arrowhead = none ];
169 -> 6;

170 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
5 -> 170 [arrowhead = none ];
170 -> 36;

171 [label="EVAL with clause\ns2t(0, X19) :- ','(!, eq(X19, nil)).\nand substitution\nT5 -> 0\nX15 -> X20\nX19 -> X20", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 171 [arrowhead = none ];
171 -> 7;

172 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 172 [arrowhead = none ];
172 -> 8;

173 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 173 [arrowhead = none ];
173 -> 9;

174 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 174 [arrowhead = none ];
174 -> 13;

175 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 175 [arrowhead = none ];
175 -> 14;

176 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 176 [arrowhead = none ];
176 -> 10;

177 [label="EVAL with clause\neq(X22, X22).\nand substitution\nX20 -> nil\nX22 -> nil\nX23 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 177 [arrowhead = none ];
177 -> 11;

178 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 178 [arrowhead = none ];
178 -> 12;

179 [label="EVAL with clause\ns2t(X30, node(X31, X32, X31)) :- ','(p(X30, X33), s2t(X33, X31)).\nand substitution\nT5 -> T7\nX30 -> T7\nX31 -> X34\nX32 -> X35\nX15 -> node(X34, X35, X34)", fontsize=14, style = filled, fillcolor = lightblue];
13 -> 179 [arrowhead = none ];
179 -> 15;

180 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 180 [arrowhead = none ];
180 -> 20;

181 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 181 [arrowhead = none ];
181 -> 21;

182 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 182 [arrowhead = none ];
182 -> 16;

183 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T7, X15), s2t(0, X19))", fontsize=14, style = filled, fillcolor = white];
16 -> 183 [arrowhead = none ];
183 -> 17;

184 [label="EVAL with clause\np(s(X37), X37).\nand substitution\nX37 -> T8\nT7 -> s(T8)\nX33 -> T8", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 184 [arrowhead = none ];
184 -> 18;

185 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 185 [arrowhead = none ];
185 -> 19;

186 [label="INSTANCE with matching:\nT5 -> T8\nX15 -> X34", fontsize=14, style = filled, fillcolor = lightgrey];
18 -> 186 [arrowhead = none , style=dashed];
186 -> 4[style=dashed];

187 [label="EVAL with clause\ns2t(X44, node(nil, X45, X46)) :- ','(p(X44, X47), s2t(X47, X46)).\nand substitution\nT5 -> T9\nX44 -> T9\nX45 -> X48\nX46 -> X49\nX15 -> node(nil, X48, X49)", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 187 [arrowhead = none ];
187 -> 22;

188 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 188 [arrowhead = none ];
188 -> 27;

189 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 189 [arrowhead = none ];
189 -> 28;

190 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
22 -> 190 [arrowhead = none ];
190 -> 23;

191 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T9, X15), s2t(0, X19))", fontsize=14, style = filled, fillcolor = white];
23 -> 191 [arrowhead = none ];
191 -> 24;

192 [label="EVAL with clause\np(s(X51), X51).\nand substitution\nX51 -> T10\nT9 -> s(T10)\nX47 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 192 [arrowhead = none ];
192 -> 25;

193 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 193 [arrowhead = none ];
193 -> 26;

194 [label="INSTANCE with matching:\nT5 -> T10\nX15 -> X49", fontsize=14, style = filled, fillcolor = lightgrey];
25 -> 194 [arrowhead = none , style=dashed];
194 -> 4[style=dashed];

195 [label="EVAL with clause\ns2t(X58, node(X59, X60, nil)) :- ','(p(X58, X61), s2t(X61, X59)).\nand substitution\nT5 -> T11\nX58 -> T11\nX59 -> X62\nX60 -> X63\nX15 -> node(X62, X63, nil)", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 195 [arrowhead = none ];
195 -> 29;

196 [label="EVAL with clause\ns2t(X68, node(nil, X69, nil)).\nand substitution\nT5 -> T13\nX68 -> T13\nX69 -> X70\nX15 -> node(nil, X70, nil)", fontsize=14, style = filled, fillcolor = lightblue];
28 -> 196 [arrowhead = none ];
196 -> 34;

197 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
29 -> 197 [arrowhead = none ];
197 -> 30;

198 [label="BACKTRACK\nfor clause: p(0, 0)\nwith clash: (s2t(T11, X15), s2t(0, X19))", fontsize=14, style = filled, fillcolor = white];
30 -> 198 [arrowhead = none ];
198 -> 31;

199 [label="EVAL with clause\np(s(X65), X65).\nand substitution\nX65 -> T12\nT11 -> s(T12)\nX61 -> T12", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 199 [arrowhead = none ];
199 -> 32;

200 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 200 [arrowhead = none ];
200 -> 33;

201 [label="INSTANCE with matching:\nT5 -> T12\nX15 -> X62", fontsize=14, style = filled, fillcolor = lightgrey];
32 -> 201 [arrowhead = none , style=dashed];
201 -> 4[style=dashed];

202 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
34 -> 202 [arrowhead = none ];
202 -> 35;

203 [label="EVAL with clause\ntappend(nil, X73, X74) :- ','(!, eq(X73, X74)).\nand substitution\nT6 -> nil\nX16 -> X75\nX73 -> X75\nX17 -> X76\nX74 -> X76", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 203 [arrowhead = none ];
203 -> 37;

204 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 204 [arrowhead = none ];
204 -> 38;

205 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 205 [arrowhead = none ];
205 -> 39;

206 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 206 [arrowhead = none ];
206 -> 43;

207 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 207 [arrowhead = none ];
207 -> 44;

208 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
39 -> 208 [arrowhead = none ];
208 -> 40;

209 [label="EVAL with clause\neq(X78, X78).\nand substitution\nX75 -> X79\nX78 -> X79\nX76 -> X79", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 209 [arrowhead = none ];
209 -> 41;

210 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 210 [arrowhead = none ];
210 -> 42;

211 [label="EVAL with clause\ntappend(X88, X89, node(X89, X90, X91)) :- ','(left(X88, nil), ','(right(X88, X91), value(X88, X90))).\nand substitution\nT6 -> T15\nX88 -> T15\nX16 -> X92\nX89 -> X92\nX90 -> X93\nX91 -> X94\nX17 -> node(X92, X93, X94)\nT14 -> T15", fontsize=14, style = filled, fillcolor = lightblue];
43 -> 211 [arrowhead = none ];
211 -> 45;

212 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
44 -> 212 [arrowhead = none ];
212 -> 74;

213 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
44 -> 213 [arrowhead = none ];
213 -> 75;

214 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
45 -> 214 [arrowhead = none ];
214 -> 46;

215 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT15 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 215 [arrowhead = none ];
215 -> 47;

216 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 216 [arrowhead = none ];
216 -> 48;

217 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
47 -> 217 [arrowhead = none ];
217 -> 49;

218 [label="EVAL with clause\nleft(node(X122, X123, X124), X122).\nand substitution\nX122 -> nil\nX123 -> T30\nX124 -> T31\nT15 -> node(nil, T30, T31)\nT27 -> nil\nT28 -> T30\nT29 -> T31", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 218 [arrowhead = none ];
218 -> 65;

219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
48 -> 219 [arrowhead = none ];
219 -> 66;

220 [label="EVAL with clause\nright(nil, nil).\nand substitution\nX94 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 220 [arrowhead = none ];
220 -> 50;

221 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
50 -> 221 [arrowhead = none ];
221 -> 51;

222 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX93 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 222 [arrowhead = none ];
222 -> 52;

223 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
52 -> 223 [arrowhead = none ];
223 -> 53;

224 [label="BACKTRACK\nfor clause: value(node(X11, X, X12), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
53 -> 224 [arrowhead = none ];
224 -> 54;

225 [label="BACKTRACK\nfor clause: right(node(X9, X10, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
54 -> 225 [arrowhead = none ];
225 -> 55;

226 [label="EVAL with clause\nleft(node(X104, X105, X106), X104).\nand substitution\nX104 -> nil\nX105 -> T19\nX106 -> T20\nT15 -> node(nil, T19, T20)\nT16 -> nil\nT17 -> T19\nT18 -> T20", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 226 [arrowhead = none ];
226 -> 56;

227 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 227 [arrowhead = none ];
227 -> 57;

228 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
56 -> 228 [arrowhead = none ];
228 -> 58;

229 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
58 -> 229 [arrowhead = none ];
229 -> 59;

230 [label="EVAL with clause\nright(node(X110, X111, X112), X112).\nand substitution\nX110 -> nil\nT19 -> T23\nX111 -> T23\nT20 -> T24\nX112 -> T24\nX94 -> T24\nT21 -> T23\nT22 -> T24", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 230 [arrowhead = none ];
230 -> 60;

231 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
60 -> 231 [arrowhead = none ];
231 -> 61;

232 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
61 -> 232 [arrowhead = none ];
232 -> 62;

233 [label="EVAL with clause\nvalue(node(X116, X117, X118), X117).\nand substitution\nX116 -> nil\nT23 -> T25\nX117 -> T25\nT24 -> T26\nX118 -> T26\nX93 -> T25", fontsize=14, style = filled, fillcolor = lightblue];
62 -> 233 [arrowhead = none ];
233 -> 63;

234 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
63 -> 234 [arrowhead = none ];
234 -> 64;

235 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
65 -> 235 [arrowhead = none ];
235 -> 67;

236 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
67 -> 236 [arrowhead = none ];
236 -> 68;

237 [label="EVAL with clause\nright(node(X128, X129, X130), X130).\nand substitution\nX128 -> nil\nT30 -> T34\nX129 -> T34\nT31 -> T35\nX130 -> T35\nX94 -> T35\nT32 -> T34\nT33 -> T35", fontsize=14, style = filled, fillcolor = lightblue];
68 -> 237 [arrowhead = none ];
237 -> 69;

238 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
69 -> 238 [arrowhead = none ];
238 -> 70;

239 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
70 -> 239 [arrowhead = none ];
239 -> 71;

240 [label="EVAL with clause\nvalue(node(X134, X135, X136), X135).\nand substitution\nX134 -> nil\nT34 -> T36\nX135 -> T36\nT35 -> T37\nX136 -> T37\nX93 -> T36", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 240 [arrowhead = none ];
240 -> 72;

241 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
72 -> 241 [arrowhead = none ];
241 -> 73;

242 [label="EVAL with clause\ntappend(X145, X146, node(X147, X148, X146)) :- ','(left(X145, X147), ','(right(X145, nil), value(X145, X148))).\nand substitution\nT6 -> T39\nX145 -> T39\nX16 -> X149\nX146 -> X149\nX147 -> X150\nX148 -> X151\nX17 -> node(X150, X151, X149)\nT38 -> T39", fontsize=14, style = filled, fillcolor = lightblue];
74 -> 242 [arrowhead = none ];
242 -> 76;

243 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
75 -> 243 [arrowhead = none ];
243 -> 107;

244 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
75 -> 244 [arrowhead = none ];
244 -> 108;

245 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
76 -> 245 [arrowhead = none ];
245 -> 77;

246 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT39 -> nil\nX150 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
77 -> 246 [arrowhead = none ];
246 -> 78;

247 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
77 -> 247 [arrowhead = none ];
247 -> 79;

248 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
78 -> 248 [arrowhead = none ];
248 -> 80;

249 [label="EVAL with clause\nleft(node(X179, X180, X181), X179).\nand substitution\nX179 -> T56\nX180 -> T57\nX181 -> T58\nT39 -> node(T56, T57, T58)\nX150 -> T56\nT53 -> T56\nT54 -> T57\nT55 -> T58", fontsize=14, style = filled, fillcolor = lightblue];
79 -> 249 [arrowhead = none ];
249 -> 97;

250 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
79 -> 250 [arrowhead = none ];
250 -> 98;

251 [label="EVAL with clause\nright(nil, nil).\nand substitution", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 251 [arrowhead = none ];
251 -> 81;

252 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
81 -> 252 [arrowhead = none ];
252 -> 82;

253 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX151 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
82 -> 253 [arrowhead = none ];
253 -> 83;

254 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 254 [arrowhead = none ];
254 -> 84;

255 [label="BACKTRACK\nfor clause: value(node(X11, X, X12), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
84 -> 255 [arrowhead = none ];
255 -> 85;

256 [label="BACKTRACK\nfor clause: right(node(X9, X10, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
85 -> 256 [arrowhead = none ];
256 -> 86;

257 [label="EVAL with clause\nleft(node(X161, X162, X163), X161).\nand substitution\nX161 -> T43\nX162 -> T44\nX163 -> T45\nT39 -> node(T43, T44, T45)\nX150 -> T43\nT40 -> T43\nT41 -> T44\nT42 -> T45", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 257 [arrowhead = none ];
257 -> 87;

258 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 258 [arrowhead = none ];
258 -> 88;

259 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
87 -> 259 [arrowhead = none ];
259 -> 89;

260 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
89 -> 260 [arrowhead = none ];
260 -> 90;

261 [label="EVAL with clause\nright(node(X167, X168, X169), X169).\nand substitution\nT43 -> T49\nX167 -> T49\nT44 -> T50\nX168 -> T50\nT45 -> nil\nX169 -> nil\nT48 -> nil\nT46 -> T49\nT47 -> T50", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 261 [arrowhead = none ];
261 -> 91;

262 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
90 -> 262 [arrowhead = none ];
262 -> 92;

263 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 263 [arrowhead = none ];
263 -> 93;

264 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
93 -> 264 [arrowhead = none ];
264 -> 94;

265 [label="EVAL with clause\nvalue(node(X173, X174, X175), X174).\nand substitution\nT49 -> T51\nX173 -> T51\nT50 -> T52\nX174 -> T52\nX175 -> nil\nX151 -> T52", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 265 [arrowhead = none ];
265 -> 95;

266 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 266 [arrowhead = none ];
266 -> 96;

267 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
97 -> 267 [arrowhead = none ];
267 -> 99;

268 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
99 -> 268 [arrowhead = none ];
268 -> 100;

269 [label="EVAL with clause\nright(node(X185, X186, X187), X187).\nand substitution\nT56 -> T62\nX185 -> T62\nT57 -> T63\nX186 -> T63\nT58 -> nil\nX187 -> nil\nT61 -> nil\nT59 -> T62\nT60 -> T63", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 269 [arrowhead = none ];
269 -> 101;

270 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
100 -> 270 [arrowhead = none ];
270 -> 102;

271 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
101 -> 271 [arrowhead = none ];
271 -> 103;

272 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
103 -> 272 [arrowhead = none ];
272 -> 104;

273 [label="EVAL with clause\nvalue(node(X191, X192, X193), X192).\nand substitution\nT62 -> T64\nX191 -> T64\nT63 -> T65\nX192 -> T65\nX193 -> nil\nX151 -> T65", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 273 [arrowhead = none ];
273 -> 105;

274 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 274 [arrowhead = none ];
274 -> 106;

275 [label="EVAL with clause\ntappend(X204, X205, node(X206, X207, X208)) :- ','(left(X204, X209), ','(right(X204, X208), ','(value(X204, X207), tappend(X209, X205, X206)))).\nand substitution\nT6 -> T67\nX204 -> T67\nX16 -> X210\nX205 -> X210\nX206 -> X211\nX207 -> X212\nX208 -> X213\nX17 -> node(X211, X212, X213)\nT66 -> T67", fontsize=14, style = filled, fillcolor = lightblue];
107 -> 275 [arrowhead = none ];
275 -> 109;

276 [label="EVAL with clause\ntappend(X260, X261, node(X261, X262, X263)) :- ','(left(X260, X261), ','(right(X260, X264), ','(value(X260, X262), tappend(X264, X265, X263)))).\nand substitution\nT6 -> T101\nX260 -> T101\nX16 -> X266\nX261 -> X266\nX262 -> X267\nX263 -> X268\nX17 -> node(X266, X267, X268)\nT100 -> T101", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 276 [arrowhead = none ];
276 -> 137;

277 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
109 -> 277 [arrowhead = none ];
277 -> 110;

278 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT67 -> nil\nX209 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 278 [arrowhead = none ];
278 -> 111;

279 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 279 [arrowhead = none ];
279 -> 112;

280 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
111 -> 280 [arrowhead = none ];
280 -> 113;

281 [label="EVAL with clause\nleft(node(X241, X242, X243), X241).\nand substitution\nX241 -> T87\nX242 -> T88\nX243 -> T89\nT67 -> node(T87, T88, T89)\nX209 -> T87\nT84 -> T87\nT85 -> T88\nT86 -> T89", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 281 [arrowhead = none ];
281 -> 129;

282 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 282 [arrowhead = none ];
282 -> 130;

283 [label="EVAL with clause\nright(nil, nil).\nand substitution\nX213 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
113 -> 283 [arrowhead = none ];
283 -> 114;

284 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
114 -> 284 [arrowhead = none ];
284 -> 115;

285 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX212 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 285 [arrowhead = none ];
285 -> 116;

286 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 286 [arrowhead = none ];
286 -> 117;

287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 287 [arrowhead = none ];
287 -> 118;

288 [label="INSTANCE with matching:\nT6 -> nil\nX16 -> X210\nX17 -> X211", fontsize=14, style = filled, fillcolor = lightgrey];
117 -> 288 [arrowhead = none , style=dashed];
288 -> 5[style=dashed];

289 [label="BACKTRACK\nfor clause: value(node(X11, X, X12), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
118 -> 289 [arrowhead = none ];
289 -> 119;

290 [label="BACKTRACK\nfor clause: right(node(X9, X10, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
119 -> 290 [arrowhead = none ];
290 -> 120;

291 [label="EVAL with clause\nleft(node(X223, X224, X225), X223).\nand substitution\nX223 -> T71\nX224 -> T72\nX225 -> T73\nT67 -> node(T71, T72, T73)\nX209 -> T71\nT68 -> T71\nT69 -> T72\nT70 -> T73", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 291 [arrowhead = none ];
291 -> 121;

292 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 292 [arrowhead = none ];
292 -> 122;

293 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
121 -> 293 [arrowhead = none ];
293 -> 123;

294 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
123 -> 294 [arrowhead = none ];
294 -> 124;

295 [label="EVAL with clause\nright(node(X229, X230, X231), X231).\nand substitution\nT71 -> T77\nX229 -> T77\nT72 -> T78\nX230 -> T78\nT73 -> T79\nX231 -> T79\nX213 -> T79\nT74 -> T77\nT75 -> T78\nT76 -> T79", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 295 [arrowhead = none ];
295 -> 125;

296 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
125 -> 296 [arrowhead = none ];
296 -> 126;

297 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
126 -> 297 [arrowhead = none ];
297 -> 127;

298 [label="EVAL with clause\nvalue(node(X235, X236, X237), X236).\nand substitution\nT77 -> T83\nX235 -> T83\nT78 -> T81\nX236 -> T81\nT79 -> T82\nX237 -> T82\nX212 -> T81\nT80 -> T83", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 298 [arrowhead = none ];
298 -> 128;

299 [label="INSTANCE with matching:\nT6 -> T83\nX16 -> X210\nX17 -> X211", fontsize=14, style = filled, fillcolor = lightgrey];
128 -> 299 [arrowhead = none , style=dashed];
299 -> 5[style=dashed];

300 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
129 -> 300 [arrowhead = none ];
300 -> 131;

301 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
131 -> 301 [arrowhead = none ];
301 -> 132;

302 [label="EVAL with clause\nright(node(X247, X248, X249), X249).\nand substitution\nT87 -> T93\nX247 -> T93\nT88 -> T94\nX248 -> T94\nT89 -> T95\nX249 -> T95\nX213 -> T95\nT90 -> T93\nT91 -> T94\nT92 -> T95", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 302 [arrowhead = none ];
302 -> 133;

303 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 303 [arrowhead = none ];
303 -> 134;

304 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
134 -> 304 [arrowhead = none ];
304 -> 135;

305 [label="EVAL with clause\nvalue(node(X253, X254, X255), X254).\nand substitution\nT93 -> T99\nX253 -> T99\nT94 -> T97\nX254 -> T97\nT95 -> T98\nX255 -> T98\nX212 -> T97\nT96 -> T99", fontsize=14, style = filled, fillcolor = lightblue];
135 -> 305 [arrowhead = none ];
305 -> 136;

306 [label="INSTANCE with matching:\nT6 -> T99\nX16 -> X210\nX17 -> X211", fontsize=14, style = filled, fillcolor = lightgrey];
136 -> 306 [arrowhead = none , style=dashed];
306 -> 5[style=dashed];

307 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
137 -> 307 [arrowhead = none ];
307 -> 138;

308 [label="EVAL with clause\nleft(nil, nil).\nand substitution\nT101 -> nil\nX266 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 308 [arrowhead = none ];
308 -> 139;

309 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
138 -> 309 [arrowhead = none ];
309 -> 140;

310 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
139 -> 310 [arrowhead = none ];
310 -> 141;

311 [label="EVAL with clause\nleft(node(X296, X297, X298), X296).\nand substitution\nX296 -> T121\nX297 -> T122\nX298 -> T123\nT101 -> node(T121, T122, T123)\nX266 -> T121\nT118 -> T121\nT119 -> T122\nT120 -> T123", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 311 [arrowhead = none ];
311 -> 157;

312 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 312 [arrowhead = none ];
312 -> 158;

313 [label="EVAL with clause\nright(nil, nil).\nand substitution\nX264 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
141 -> 313 [arrowhead = none ];
313 -> 142;

314 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
142 -> 314 [arrowhead = none ];
314 -> 143;

315 [label="EVAL with clause\nvalue(nil, nil).\nand substitution\nX267 -> nil", fontsize=14, style = filled, fillcolor = lightblue];
143 -> 315 [arrowhead = none ];
315 -> 144;

316 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
144 -> 316 [arrowhead = none ];
316 -> 145;

317 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
144 -> 317 [arrowhead = none ];
317 -> 146;

318 [label="INSTANCE with matching:\nT6 -> nil\nX16 -> X265\nX17 -> X268", fontsize=14, style = filled, fillcolor = lightgrey];
145 -> 318 [arrowhead = none , style=dashed];
318 -> 5[style=dashed];

319 [label="BACKTRACK\nfor clause: value(node(X11, X, X12), X)because of non-unification", fontsize=14, style = filled, fillcolor = white];
146 -> 319 [arrowhead = none ];
319 -> 147;

320 [label="BACKTRACK\nfor clause: right(node(X9, X10, R), R)because of non-unification", fontsize=14, style = filled, fillcolor = white];
147 -> 320 [arrowhead = none ];
320 -> 148;

321 [label="EVAL with clause\nleft(node(X278, X279, X280), X278).\nand substitution\nX278 -> T105\nX279 -> T106\nX280 -> T107\nT101 -> node(T105, T106, T107)\nX266 -> T105\nT102 -> T105\nT103 -> T106\nT104 -> T107", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 321 [arrowhead = none ];
321 -> 149;

322 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 322 [arrowhead = none ];
322 -> 150;

323 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
149 -> 323 [arrowhead = none ];
323 -> 151;

324 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
151 -> 324 [arrowhead = none ];
324 -> 152;

325 [label="EVAL with clause\nright(node(X284, X285, X286), X286).\nand substitution\nT105 -> T111\nX284 -> T111\nT106 -> T112\nX285 -> T112\nT107 -> T113\nX286 -> T113\nX264 -> T113\nT108 -> T111\nT109 -> T112\nT110 -> T113", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 325 [arrowhead = none ];
325 -> 153;

326 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
153 -> 326 [arrowhead = none ];
326 -> 154;

327 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
154 -> 327 [arrowhead = none ];
327 -> 155;

328 [label="EVAL with clause\nvalue(node(X290, X291, X292), X291).\nand substitution\nT111 -> T114\nX290 -> T114\nT112 -> T115\nX291 -> T115\nT113 -> T117\nX292 -> T117\nX267 -> T115\nT116 -> T117", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 328 [arrowhead = none ];
328 -> 156;

329 [label="INSTANCE with matching:\nT6 -> T117\nX16 -> X265\nX17 -> X268", fontsize=14, style = filled, fillcolor = lightgrey];
156 -> 329 [arrowhead = none , style=dashed];
329 -> 5[style=dashed];

330 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
157 -> 330 [arrowhead = none ];
330 -> 159;

331 [label="BACKTRACK\nfor clause: right(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
159 -> 331 [arrowhead = none ];
331 -> 160;

332 [label="EVAL with clause\nright(node(X302, X303, X304), X304).\nand substitution\nT121 -> T127\nX302 -> T127\nT122 -> T128\nX303 -> T128\nT123 -> T129\nX304 -> T129\nX264 -> T129\nT124 -> T127\nT125 -> T128\nT126 -> T129", fontsize=14, style = filled, fillcolor = lightblue];
160 -> 332 [arrowhead = none ];
332 -> 161;

333 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
161 -> 333 [arrowhead = none ];
333 -> 162;

334 [label="BACKTRACK\nfor clause: value(nil, nil)because of non-unification", fontsize=14, style = filled, fillcolor = white];
162 -> 334 [arrowhead = none ];
334 -> 163;

335 [label="EVAL with clause\nvalue(node(X308, X309, X310), X309).\nand substitution\nT127 -> T130\nX308 -> T130\nT128 -> T131\nX309 -> T131\nT129 -> T133\nX310 -> T133\nX267 -> T131\nT132 -> T133", fontsize=14, style = filled, fillcolor = lightblue];
163 -> 335 [arrowhead = none ];
335 -> 164;

336 [label="INSTANCE with matching:\nT6 -> T133\nX16 -> X265\nX17 -> X268", fontsize=14, style = filled, fillcolor = lightgrey];
164 -> 336 [arrowhead = none , style=dashed];
336 -> 5[style=dashed];

}

(2) Obligation:

Clauses:

s2t4(0, nil).
s2t4(s(T8), node(X34, X35, X34)) :- s2t4(T8, X34).
s2t4(s(T10), node(nil, X48, X49)) :- s2t4(T10, X49).
s2t4(s(T12), node(X62, X63, nil)) :- s2t4(T12, X62).
s2t4(T13, node(nil, X70, nil)).
tappend5(nil, X79, X79).
tappend5(nil, X92, node(X92, nil, nil)).
tappend5(node(nil, T25, T26), X92, node(X92, T25, T26)).
tappend5(node(nil, T36, T37), X92, node(X92, T36, T37)).
tappend5(nil, X149, node(nil, nil, X149)).
tappend5(node(T51, T52, nil), X149, node(T51, T52, X149)).
tappend5(node(T64, T65, nil), X149, node(T64, T65, X149)).
tappend5(nil, X210, node(X211, nil, nil)) :- tappend5(nil, X210, X211).
tappend5(node(T83, T81, T82), X210, node(X211, T81, T82)) :- tappend5(T83, X210, X211).
tappend5(node(T99, T97, T98), X210, node(X211, T97, T98)) :- tappend5(T99, X210, X211).
tappend5(nil, nil, node(nil, nil, X268)) :- tappend5(nil, X265, X268).
tappend5(node(T114, T115, T117), T114, node(T114, T115, X268)) :- tappend5(T117, X265, X268).
tappend5(node(T130, T131, T133), T130, node(T130, T131, X268)) :- tappend5(T133, X265, X268).
goal1(T5) :- s2t4(T5, X15).
goal1(T5) :- s2t4(T5, nil).
goal1(T5) :- s2t4(T5, nil).
goal1(T5) :- s2t4(T5, node(nil, T25, T26)).
goal1(T5) :- s2t4(T5, node(nil, T36, T37)).
goal1(T5) :- s2t4(T5, nil).
goal1(T5) :- s2t4(T5, node(T51, T52, nil)).
goal1(T5) :- s2t4(T5, node(T64, T65, nil)).
goal1(T5) :- ','(s2t4(T5, nil), tappend5(nil, X210, X211)).
goal1(T5) :- ','(s2t4(T5, node(T83, T81, T82)), tappend5(T83, X210, X211)).
goal1(T5) :- ','(s2t4(T5, node(T99, T97, T98)), tappend5(T99, X210, X211)).
goal1(T5) :- ','(s2t4(T5, nil), tappend5(nil, X265, X268)).
goal1(T5) :- ','(s2t4(T5, node(T114, T115, T117)), tappend5(T117, X265, X268)).
goal1(T5) :- ','(s2t4(T5, node(T130, T131, T133)), tappend5(T133, X265, X268)).

Queries:

goal1(g).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
goal1_in: (b)
s2t4_in: (b,f) (b,b)
tappend5_in: (b,f,f) (f,f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)

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_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)

(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_G(T5) → U10_G(T5, s2t4_in_ga(T5, X15))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, X15)
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → U1_GA(T8, X34, X35, s2t4_in_ga(T8, X34))
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → S2T4_IN_GA(T8, X34)
S2T4_IN_GA(s(T10), node(nil, X48, X49)) → U2_GA(T10, X48, X49, s2t4_in_ga(T10, X49))
S2T4_IN_GA(s(T10), node(nil, X48, X49)) → S2T4_IN_GA(T10, X49)
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → U3_GA(T12, X62, X63, s2t4_in_ga(T12, X62))
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → S2T4_IN_GA(T12, X62)
GOAL1_IN_G(T5) → U11_G(T5, s2t4_in_gg(T5, nil))
GOAL1_IN_G(T5) → S2T4_IN_GG(T5, nil)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → U1_GG(T8, X34, X35, s2t4_in_gg(T8, X34))
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T10), node(nil, X48, X49)) → U2_GG(T10, X48, X49, s2t4_in_gg(T10, X49))
S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → U3_GG(T12, X62, X63, s2t4_in_gg(T12, X62))
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)
U11_G(T5, s2t4_out_gg(T5, nil)) → U12_G(T5, tappend5_in_gaa(nil, X210, X211))
U11_G(T5, s2t4_out_gg(T5, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → U4_GAA(X210, X211, tappend5_in_gaa(nil, X210, X211))
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_GAA(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_GAA(T83, X210, X211)
TAPPEND5_IN_GAA(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_GAA(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → U7_GAA(X268, tappend5_in_gaa(nil, X265, X268))
TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_GAA(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_GAA(T117, X265, X268)
TAPPEND5_IN_GAA(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_GAA(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U11_G(T5, s2t4_out_gg(T5, nil)) → U13_G(T5, tappend5_in_gaa(nil, X265, X268))
GOAL1_IN_G(T5) → U14_G(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(nil, T25, T26))
GOAL1_IN_G(T5) → U15_G(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
GOAL1_IN_G(T5) → U16_G(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(T51, T52, nil))
GOAL1_IN_G(T5) → U17_G(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
GOAL1_IN_G(T5) → U18_G(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(T83, T81, T82))
U18_G(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_G(T5, tappend5_in_aaa(T83, X210, X211))
U18_G(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → TAPPEND5_IN_AAA(T83, X210, X211)
TAPPEND5_IN_AAA(nil, X210, node(X211, nil, nil)) → U4_AAA(X210, X211, tappend5_in_gaa(nil, X210, X211))
TAPPEND5_IN_AAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_AAA(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_AAA(T83, X210, X211)
TAPPEND5_IN_AAA(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_AAA(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
TAPPEND5_IN_AAA(nil, nil, node(nil, nil, X268)) → U7_AAA(X268, tappend5_in_gaa(nil, X265, X268))
TAPPEND5_IN_AAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_AAA(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_AAA(T117, X265, X268)
TAPPEND5_IN_AAA(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_AAA(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
GOAL1_IN_G(T5) → U20_G(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_G(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_G(T5, tappend5_in_aaa(T99, X210, X211))
U20_G(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → TAPPEND5_IN_AAA(T99, X210, X211)
GOAL1_IN_G(T5) → U22_G(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_G(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_G(T5, tappend5_in_aaa(T117, X265, X268))
U22_G(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → TAPPEND5_IN_AAA(T117, X265, X268)
GOAL1_IN_G(T5) → U24_G(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_G(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_G(T5, tappend5_in_aaa(T133, X265, X268))
U24_G(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → TAPPEND5_IN_AAA(T133, X265, X268)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)
GOAL1_IN_G(x1)  =  GOAL1_IN_G(x1)
U10_G(x1, x2)  =  U10_G(x2)
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)
U11_G(x1, x2)  =  U11_G(x2)
S2T4_IN_GG(x1, x2)  =  S2T4_IN_GG(x1, x2)
U1_GG(x1, x2, x3, x4)  =  U1_GG(x4)
U2_GG(x1, x2, x3, x4)  =  U2_GG(x4)
U3_GG(x1, x2, x3, x4)  =  U3_GG(x4)
U12_G(x1, x2)  =  U12_G(x2)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_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)  =  U7_GAA(x2)
U8_GAA(x1, x2, x3, x4, x5)  =  U8_GAA(x5)
U9_GAA(x1, x2, x3, x4, x5)  =  U9_GAA(x5)
U13_G(x1, x2)  =  U13_G(x2)
U14_G(x1, x2)  =  U14_G(x2)
U15_G(x1, x2)  =  U15_G(x2)
U16_G(x1, x2)  =  U16_G(x2)
U17_G(x1, x2)  =  U17_G(x2)
U18_G(x1, x2)  =  U18_G(x2)
U19_G(x1, x2)  =  U19_G(x2)
TAPPEND5_IN_AAA(x1, x2, x3)  =  TAPPEND5_IN_AAA
U4_AAA(x1, x2, x3)  =  U4_AAA(x3)
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)  =  U7_AAA(x2)
U8_AAA(x1, x2, x3, x4, x5)  =  U8_AAA(x5)
U9_AAA(x1, x2, x3, x4, x5)  =  U9_AAA(x5)
U20_G(x1, x2)  =  U20_G(x2)
U21_G(x1, x2)  =  U21_G(x2)
U22_G(x1, x2)  =  U22_G(x2)
U23_G(x1, x2)  =  U23_G(x2)
U24_G(x1, x2)  =  U24_G(x2)
U25_G(x1, x2)  =  U25_G(x2)

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

(6) Obligation:

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

GOAL1_IN_G(T5) → U10_G(T5, s2t4_in_ga(T5, X15))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, X15)
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → U1_GA(T8, X34, X35, s2t4_in_ga(T8, X34))
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → S2T4_IN_GA(T8, X34)
S2T4_IN_GA(s(T10), node(nil, X48, X49)) → U2_GA(T10, X48, X49, s2t4_in_ga(T10, X49))
S2T4_IN_GA(s(T10), node(nil, X48, X49)) → S2T4_IN_GA(T10, X49)
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → U3_GA(T12, X62, X63, s2t4_in_ga(T12, X62))
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → S2T4_IN_GA(T12, X62)
GOAL1_IN_G(T5) → U11_G(T5, s2t4_in_gg(T5, nil))
GOAL1_IN_G(T5) → S2T4_IN_GG(T5, nil)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → U1_GG(T8, X34, X35, s2t4_in_gg(T8, X34))
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T10), node(nil, X48, X49)) → U2_GG(T10, X48, X49, s2t4_in_gg(T10, X49))
S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → U3_GG(T12, X62, X63, s2t4_in_gg(T12, X62))
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)
U11_G(T5, s2t4_out_gg(T5, nil)) → U12_G(T5, tappend5_in_gaa(nil, X210, X211))
U11_G(T5, s2t4_out_gg(T5, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → U4_GAA(X210, X211, tappend5_in_gaa(nil, X210, X211))
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_GAA(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_GAA(T83, X210, X211)
TAPPEND5_IN_GAA(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_GAA(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → U7_GAA(X268, tappend5_in_gaa(nil, X265, X268))
TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_GAA(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_GAA(T117, X265, X268)
TAPPEND5_IN_GAA(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_GAA(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U11_G(T5, s2t4_out_gg(T5, nil)) → U13_G(T5, tappend5_in_gaa(nil, X265, X268))
GOAL1_IN_G(T5) → U14_G(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(nil, T25, T26))
GOAL1_IN_G(T5) → U15_G(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
GOAL1_IN_G(T5) → U16_G(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(T51, T52, nil))
GOAL1_IN_G(T5) → U17_G(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
GOAL1_IN_G(T5) → U18_G(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(T83, T81, T82))
U18_G(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_G(T5, tappend5_in_aaa(T83, X210, X211))
U18_G(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → TAPPEND5_IN_AAA(T83, X210, X211)
TAPPEND5_IN_AAA(nil, X210, node(X211, nil, nil)) → U4_AAA(X210, X211, tappend5_in_gaa(nil, X210, X211))
TAPPEND5_IN_AAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_AAA(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_AAA(T83, X210, X211)
TAPPEND5_IN_AAA(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_AAA(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
TAPPEND5_IN_AAA(nil, nil, node(nil, nil, X268)) → U7_AAA(X268, tappend5_in_gaa(nil, X265, X268))
TAPPEND5_IN_AAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_AAA(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_AAA(T117, X265, X268)
TAPPEND5_IN_AAA(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_AAA(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
GOAL1_IN_G(T5) → U20_G(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_G(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_G(T5, tappend5_in_aaa(T99, X210, X211))
U20_G(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → TAPPEND5_IN_AAA(T99, X210, X211)
GOAL1_IN_G(T5) → U22_G(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_G(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_G(T5, tappend5_in_aaa(T117, X265, X268))
U22_G(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → TAPPEND5_IN_AAA(T117, X265, X268)
GOAL1_IN_G(T5) → U24_G(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_G(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_G(T5, tappend5_in_aaa(T133, X265, X268))
U24_G(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → TAPPEND5_IN_AAA(T133, X265, X268)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)
GOAL1_IN_G(x1)  =  GOAL1_IN_G(x1)
U10_G(x1, x2)  =  U10_G(x2)
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)
U11_G(x1, x2)  =  U11_G(x2)
S2T4_IN_GG(x1, x2)  =  S2T4_IN_GG(x1, x2)
U1_GG(x1, x2, x3, x4)  =  U1_GG(x4)
U2_GG(x1, x2, x3, x4)  =  U2_GG(x4)
U3_GG(x1, x2, x3, x4)  =  U3_GG(x4)
U12_G(x1, x2)  =  U12_G(x2)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_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)  =  U7_GAA(x2)
U8_GAA(x1, x2, x3, x4, x5)  =  U8_GAA(x5)
U9_GAA(x1, x2, x3, x4, x5)  =  U9_GAA(x5)
U13_G(x1, x2)  =  U13_G(x2)
U14_G(x1, x2)  =  U14_G(x2)
U15_G(x1, x2)  =  U15_G(x2)
U16_G(x1, x2)  =  U16_G(x2)
U17_G(x1, x2)  =  U17_G(x2)
U18_G(x1, x2)  =  U18_G(x2)
U19_G(x1, x2)  =  U19_G(x2)
TAPPEND5_IN_AAA(x1, x2, x3)  =  TAPPEND5_IN_AAA
U4_AAA(x1, x2, x3)  =  U4_AAA(x3)
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)  =  U7_AAA(x2)
U8_AAA(x1, x2, x3, x4, x5)  =  U8_AAA(x5)
U9_AAA(x1, x2, x3, x4, x5)  =  U9_AAA(x5)
U20_G(x1, x2)  =  U20_G(x2)
U21_G(x1, x2)  =  U21_G(x2)
U22_G(x1, x2)  =  U22_G(x2)
U23_G(x1, x2)  =  U23_G(x2)
U24_G(x1, x2)  =  U24_G(x2)
U25_G(x1, x2)  =  U25_G(x2)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 5 SCCs with 46 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_IN_GAA(x1)

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:

TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)

R is empty.
The argument filtering Pi contains the following mapping:
nil  =  nil
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_IN_GAA(x1)

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:

TAPPEND5_IN_GAA(nil) → TAPPEND5_IN_GAA(nil)

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 = TAPPEND5_IN_GAA(nil) evaluates to t =TAPPEND5_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 TAPPEND5_IN_GAA(nil) to TAPPEND5_IN_GAA(nil).

(15) FALSE

(16) Obligation:

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

TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_AAA(T117, X265, X268)
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_AAA(T83, X210, X211)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)
TAPPEND5_IN_AAA(x1, x2, x3)  =  TAPPEND5_IN_AAA

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:

TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_AAA(T117, X265, X268)
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_AAA(T83, X210, X211)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND5_IN_AAA(x1, x2, x3)  =  TAPPEND5_IN_AAA

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:

TAPPEND5_IN_AAA → TAPPEND5_IN_AAA

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 = TAPPEND5_IN_AAA evaluates to t =TAPPEND5_IN_AAA

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

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from TAPPEND5_IN_AAA to TAPPEND5_IN_AAA.

(22) FALSE

(23) Obligation:

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

TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_GAA(T117, X265, X268)
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_GAA(T83, X210, X211)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_IN_GAA(x1)

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:

TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_GAA(T117, X265, X268)
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_GAA(T83, X210, X211)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_IN_GAA(x1)

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:

TAPPEND5_IN_GAA(node(T114, T115, T117)) → TAPPEND5_IN_GAA(T117)
TAPPEND5_IN_GAA(node(T83, T81, T82)) → TAPPEND5_IN_GAA(T83)

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

(28) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• TAPPEND5_IN_GAA(node(T114, T115, T117)) → TAPPEND5_IN_GAA(T117)
  The graph contains the following edges 1 > 1

• TAPPEND5_IN_GAA(node(T83, T81, T82)) → TAPPEND5_IN_GAA(T83)
  The graph contains the following edges 1 > 1

(29) TRUE

(30) Obligation:

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

S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)
S2T4_IN_GG(x1, x2)  =  S2T4_IN_GG(x1, x2)

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:

S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)

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

(33) PiDPToQDPProof (EQUIVALENT 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:

S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)

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:

• S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
  The graph contains the following edges 1 > 1, 2 > 2

• S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
  The graph contains the following edges 1 > 1, 2 > 2

• S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)
  The graph contains the following edges 1 > 1, 2 > 2

(36) TRUE

(37) Obligation:

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

S2T4_IN_GA(s(T10), node(nil, X48, X49)) → S2T4_IN_GA(T10, X49)
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → S2T4_IN_GA(T8, X34)
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → S2T4_IN_GA(T12, X62)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x2)
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_g(x1)  =  goal1_out_g
U11_g(x1, x2)  =  U11_g(x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x4)
U12_g(x1, x2)  =  U12_g(x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_gaa
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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x5)
U13_g(x1, x2)  =  U13_g(x2)
U14_g(x1, x2)  =  U14_g(x2)
U15_g(x1, x2)  =  U15_g(x2)
U16_g(x1, x2)  =  U16_g(x2)
U17_g(x1, x2)  =  U17_g(x2)
U18_g(x1, x2)  =  U18_g(x2)
U19_g(x1, x2)  =  U19_g(x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x2)
U21_g(x1, x2)  =  U21_g(x2)
U22_g(x1, x2)  =  U22_g(x2)
U23_g(x1, x2)  =  U23_g(x2)
U24_g(x1, x2)  =  U24_g(x2)
U25_g(x1, x2)  =  U25_g(x2)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(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:

S2T4_IN_GA(s(T10), node(nil, X48, X49)) → S2T4_IN_GA(T10, X49)
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → S2T4_IN_GA(T8, X34)
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → S2T4_IN_GA(T12, X62)

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

(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:

S2T4_IN_GA(s(T10)) → S2T4_IN_GA(T10)

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

(42) 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(T10)) → S2T4_IN_GA(T10)
  The graph contains the following edges 1 > 1

(43) TRUE

(44) 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)
s2t4_in: (b,f) (b,b)
tappend5_in: (b,f,f) (f,f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(45) Obligation:

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

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)

(46) 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_G(T5) → U10_G(T5, s2t4_in_ga(T5, X15))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, X15)
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → U1_GA(T8, X34, X35, s2t4_in_ga(T8, X34))
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → S2T4_IN_GA(T8, X34)
S2T4_IN_GA(s(T10), node(nil, X48, X49)) → U2_GA(T10, X48, X49, s2t4_in_ga(T10, X49))
S2T4_IN_GA(s(T10), node(nil, X48, X49)) → S2T4_IN_GA(T10, X49)
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → U3_GA(T12, X62, X63, s2t4_in_ga(T12, X62))
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → S2T4_IN_GA(T12, X62)
GOAL1_IN_G(T5) → U11_G(T5, s2t4_in_gg(T5, nil))
GOAL1_IN_G(T5) → S2T4_IN_GG(T5, nil)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → U1_GG(T8, X34, X35, s2t4_in_gg(T8, X34))
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T10), node(nil, X48, X49)) → U2_GG(T10, X48, X49, s2t4_in_gg(T10, X49))
S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → U3_GG(T12, X62, X63, s2t4_in_gg(T12, X62))
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)
U11_G(T5, s2t4_out_gg(T5, nil)) → U12_G(T5, tappend5_in_gaa(nil, X210, X211))
U11_G(T5, s2t4_out_gg(T5, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → U4_GAA(X210, X211, tappend5_in_gaa(nil, X210, X211))
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_GAA(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_GAA(T83, X210, X211)
TAPPEND5_IN_GAA(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_GAA(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → U7_GAA(X268, tappend5_in_gaa(nil, X265, X268))
TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_GAA(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_GAA(T117, X265, X268)
TAPPEND5_IN_GAA(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_GAA(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U11_G(T5, s2t4_out_gg(T5, nil)) → U13_G(T5, tappend5_in_gaa(nil, X265, X268))
GOAL1_IN_G(T5) → U14_G(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(nil, T25, T26))
GOAL1_IN_G(T5) → U15_G(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
GOAL1_IN_G(T5) → U16_G(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(T51, T52, nil))
GOAL1_IN_G(T5) → U17_G(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
GOAL1_IN_G(T5) → U18_G(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(T83, T81, T82))
U18_G(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_G(T5, tappend5_in_aaa(T83, X210, X211))
U18_G(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → TAPPEND5_IN_AAA(T83, X210, X211)
TAPPEND5_IN_AAA(nil, X210, node(X211, nil, nil)) → U4_AAA(X210, X211, tappend5_in_gaa(nil, X210, X211))
TAPPEND5_IN_AAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_AAA(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_AAA(T83, X210, X211)
TAPPEND5_IN_AAA(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_AAA(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
TAPPEND5_IN_AAA(nil, nil, node(nil, nil, X268)) → U7_AAA(X268, tappend5_in_gaa(nil, X265, X268))
TAPPEND5_IN_AAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_AAA(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_AAA(T117, X265, X268)
TAPPEND5_IN_AAA(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_AAA(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
GOAL1_IN_G(T5) → U20_G(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_G(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_G(T5, tappend5_in_aaa(T99, X210, X211))
U20_G(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → TAPPEND5_IN_AAA(T99, X210, X211)
GOAL1_IN_G(T5) → U22_G(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_G(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_G(T5, tappend5_in_aaa(T117, X265, X268))
U22_G(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → TAPPEND5_IN_AAA(T117, X265, X268)
GOAL1_IN_G(T5) → U24_G(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_G(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_G(T5, tappend5_in_aaa(T133, X265, X268))
U24_G(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → TAPPEND5_IN_AAA(T133, X265, X268)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)
GOAL1_IN_G(x1)  =  GOAL1_IN_G(x1)
U10_G(x1, x2)  =  U10_G(x1, x2)
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)
U11_G(x1, x2)  =  U11_G(x1, x2)
S2T4_IN_GG(x1, x2)  =  S2T4_IN_GG(x1, x2)
U1_GG(x1, x2, x3, x4)  =  U1_GG(x1, x2, x3, x4)
U2_GG(x1, x2, x3, x4)  =  U2_GG(x1, x2, x3, x4)
U3_GG(x1, x2, x3, x4)  =  U3_GG(x1, x2, x3, x4)
U12_G(x1, x2)  =  U12_G(x1, x2)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_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)  =  U7_GAA(x2)
U8_GAA(x1, x2, x3, x4, x5)  =  U8_GAA(x1, x2, x3, x5)
U9_GAA(x1, x2, x3, x4, x5)  =  U9_GAA(x1, x2, x3, x5)
U13_G(x1, x2)  =  U13_G(x1, x2)
U14_G(x1, x2)  =  U14_G(x1, x2)
U15_G(x1, x2)  =  U15_G(x1, x2)
U16_G(x1, x2)  =  U16_G(x1, x2)
U17_G(x1, x2)  =  U17_G(x1, x2)
U18_G(x1, x2)  =  U18_G(x1, x2)
U19_G(x1, x2)  =  U19_G(x1, x2)
TAPPEND5_IN_AAA(x1, x2, x3)  =  TAPPEND5_IN_AAA
U4_AAA(x1, x2, x3)  =  U4_AAA(x3)
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)  =  U7_AAA(x2)
U8_AAA(x1, x2, x3, x4, x5)  =  U8_AAA(x5)
U9_AAA(x1, x2, x3, x4, x5)  =  U9_AAA(x5)
U20_G(x1, x2)  =  U20_G(x1, x2)
U21_G(x1, x2)  =  U21_G(x1, x2)
U22_G(x1, x2)  =  U22_G(x1, x2)
U23_G(x1, x2)  =  U23_G(x1, x2)
U24_G(x1, x2)  =  U24_G(x1, x2)
U25_G(x1, x2)  =  U25_G(x1, x2)

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

(47) Obligation:

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

GOAL1_IN_G(T5) → U10_G(T5, s2t4_in_ga(T5, X15))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, X15)
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → U1_GA(T8, X34, X35, s2t4_in_ga(T8, X34))
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → S2T4_IN_GA(T8, X34)
S2T4_IN_GA(s(T10), node(nil, X48, X49)) → U2_GA(T10, X48, X49, s2t4_in_ga(T10, X49))
S2T4_IN_GA(s(T10), node(nil, X48, X49)) → S2T4_IN_GA(T10, X49)
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → U3_GA(T12, X62, X63, s2t4_in_ga(T12, X62))
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → S2T4_IN_GA(T12, X62)
GOAL1_IN_G(T5) → U11_G(T5, s2t4_in_gg(T5, nil))
GOAL1_IN_G(T5) → S2T4_IN_GG(T5, nil)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → U1_GG(T8, X34, X35, s2t4_in_gg(T8, X34))
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T10), node(nil, X48, X49)) → U2_GG(T10, X48, X49, s2t4_in_gg(T10, X49))
S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → U3_GG(T12, X62, X63, s2t4_in_gg(T12, X62))
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)
U11_G(T5, s2t4_out_gg(T5, nil)) → U12_G(T5, tappend5_in_gaa(nil, X210, X211))
U11_G(T5, s2t4_out_gg(T5, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → U4_GAA(X210, X211, tappend5_in_gaa(nil, X210, X211))
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_GAA(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_GAA(T83, X210, X211)
TAPPEND5_IN_GAA(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_GAA(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → U7_GAA(X268, tappend5_in_gaa(nil, X265, X268))
TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_GAA(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_GAA(T117, X265, X268)
TAPPEND5_IN_GAA(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_GAA(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U11_G(T5, s2t4_out_gg(T5, nil)) → U13_G(T5, tappend5_in_gaa(nil, X265, X268))
GOAL1_IN_G(T5) → U14_G(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(nil, T25, T26))
GOAL1_IN_G(T5) → U15_G(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
GOAL1_IN_G(T5) → U16_G(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(T51, T52, nil))
GOAL1_IN_G(T5) → U17_G(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
GOAL1_IN_G(T5) → U18_G(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
GOAL1_IN_G(T5) → S2T4_IN_GA(T5, node(T83, T81, T82))
U18_G(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_G(T5, tappend5_in_aaa(T83, X210, X211))
U18_G(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → TAPPEND5_IN_AAA(T83, X210, X211)
TAPPEND5_IN_AAA(nil, X210, node(X211, nil, nil)) → U4_AAA(X210, X211, tappend5_in_gaa(nil, X210, X211))
TAPPEND5_IN_AAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_AAA(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_AAA(T83, X210, X211)
TAPPEND5_IN_AAA(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_AAA(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
TAPPEND5_IN_AAA(nil, nil, node(nil, nil, X268)) → U7_AAA(X268, tappend5_in_gaa(nil, X265, X268))
TAPPEND5_IN_AAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_AAA(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_AAA(T117, X265, X268)
TAPPEND5_IN_AAA(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_AAA(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
GOAL1_IN_G(T5) → U20_G(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_G(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_G(T5, tappend5_in_aaa(T99, X210, X211))
U20_G(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → TAPPEND5_IN_AAA(T99, X210, X211)
GOAL1_IN_G(T5) → U22_G(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_G(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_G(T5, tappend5_in_aaa(T117, X265, X268))
U22_G(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → TAPPEND5_IN_AAA(T117, X265, X268)
GOAL1_IN_G(T5) → U24_G(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_G(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_G(T5, tappend5_in_aaa(T133, X265, X268))
U24_G(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → TAPPEND5_IN_AAA(T133, X265, X268)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)
GOAL1_IN_G(x1)  =  GOAL1_IN_G(x1)
U10_G(x1, x2)  =  U10_G(x1, x2)
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)
U11_G(x1, x2)  =  U11_G(x1, x2)
S2T4_IN_GG(x1, x2)  =  S2T4_IN_GG(x1, x2)
U1_GG(x1, x2, x3, x4)  =  U1_GG(x1, x2, x3, x4)
U2_GG(x1, x2, x3, x4)  =  U2_GG(x1, x2, x3, x4)
U3_GG(x1, x2, x3, x4)  =  U3_GG(x1, x2, x3, x4)
U12_G(x1, x2)  =  U12_G(x1, x2)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_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)  =  U7_GAA(x2)
U8_GAA(x1, x2, x3, x4, x5)  =  U8_GAA(x1, x2, x3, x5)
U9_GAA(x1, x2, x3, x4, x5)  =  U9_GAA(x1, x2, x3, x5)
U13_G(x1, x2)  =  U13_G(x1, x2)
U14_G(x1, x2)  =  U14_G(x1, x2)
U15_G(x1, x2)  =  U15_G(x1, x2)
U16_G(x1, x2)  =  U16_G(x1, x2)
U17_G(x1, x2)  =  U17_G(x1, x2)
U18_G(x1, x2)  =  U18_G(x1, x2)
U19_G(x1, x2)  =  U19_G(x1, x2)
TAPPEND5_IN_AAA(x1, x2, x3)  =  TAPPEND5_IN_AAA
U4_AAA(x1, x2, x3)  =  U4_AAA(x3)
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)  =  U7_AAA(x2)
U8_AAA(x1, x2, x3, x4, x5)  =  U8_AAA(x5)
U9_AAA(x1, x2, x3, x4, x5)  =  U9_AAA(x5)
U20_G(x1, x2)  =  U20_G(x1, x2)
U21_G(x1, x2)  =  U21_G(x1, x2)
U22_G(x1, x2)  =  U22_G(x1, x2)
U23_G(x1, x2)  =  U23_G(x1, x2)
U24_G(x1, x2)  =  U24_G(x1, x2)
U25_G(x1, x2)  =  U25_G(x1, x2)

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

(48) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 5 SCCs with 46 less nodes.

(49) Complex Obligation (AND)

(50) Obligation:

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

TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_IN_GAA(x1)

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

(51) UsableRulesProof (EQUIVALENT transformation)

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

(52) Obligation:

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

TAPPEND5_IN_GAA(nil, nil, node(nil, nil, X268)) → TAPPEND5_IN_GAA(nil, X265, X268)
TAPPEND5_IN_GAA(nil, X210, node(X211, nil, nil)) → TAPPEND5_IN_GAA(nil, X210, X211)

R is empty.
The argument filtering Pi contains the following mapping:
nil  =  nil
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_IN_GAA(x1)

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

(53) PiDPToQDPProof (SOUND transformation)

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

(54) Obligation:

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

TAPPEND5_IN_GAA(nil) → TAPPEND5_IN_GAA(nil)

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

(55) 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 = TAPPEND5_IN_GAA(nil) evaluates to t =TAPPEND5_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 TAPPEND5_IN_GAA(nil) to TAPPEND5_IN_GAA(nil).

(56) FALSE

(57) Obligation:

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

TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_AAA(T117, X265, X268)
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_AAA(T83, X210, X211)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)
TAPPEND5_IN_AAA(x1, x2, x3)  =  TAPPEND5_IN_AAA

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

(58) UsableRulesProof (EQUIVALENT transformation)

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

(59) Obligation:

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

TAPPEND5_IN_AAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_AAA(T117, X265, X268)
TAPPEND5_IN_AAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_AAA(T83, X210, X211)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND5_IN_AAA(x1, x2, x3)  =  TAPPEND5_IN_AAA

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

(60) PiDPToQDPProof (SOUND transformation)

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

(61) Obligation:

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

TAPPEND5_IN_AAA → TAPPEND5_IN_AAA

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

(62) 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 = TAPPEND5_IN_AAA evaluates to t =TAPPEND5_IN_AAA

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

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from TAPPEND5_IN_AAA to TAPPEND5_IN_AAA.

(63) FALSE

(64) Obligation:

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

TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_GAA(T117, X265, X268)
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_GAA(T83, X210, X211)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_IN_GAA(x1)

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

(65) UsableRulesProof (EQUIVALENT transformation)

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

(66) Obligation:

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

TAPPEND5_IN_GAA(node(T114, T115, T117), T114, node(T114, T115, X268)) → TAPPEND5_IN_GAA(T117, X265, X268)
TAPPEND5_IN_GAA(node(T83, T81, T82), X210, node(X211, T81, T82)) → TAPPEND5_IN_GAA(T83, X210, X211)

R is empty.
The argument filtering Pi contains the following mapping:
node(x1, x2, x3)  =  node(x1, x2, x3)
TAPPEND5_IN_GAA(x1, x2, x3)  =  TAPPEND5_IN_GAA(x1)

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

(67) PiDPToQDPProof (SOUND transformation)

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

(68) Obligation:

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

TAPPEND5_IN_GAA(node(T114, T115, T117)) → TAPPEND5_IN_GAA(T117)
TAPPEND5_IN_GAA(node(T83, T81, T82)) → TAPPEND5_IN_GAA(T83)

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

(69) 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:

• TAPPEND5_IN_GAA(node(T114, T115, T117)) → TAPPEND5_IN_GAA(T117)
  The graph contains the following edges 1 > 1

• TAPPEND5_IN_GAA(node(T83, T81, T82)) → TAPPEND5_IN_GAA(T83)
  The graph contains the following edges 1 > 1

(70) TRUE

(71) Obligation:

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

S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)
S2T4_IN_GG(x1, x2)  =  S2T4_IN_GG(x1, x2)

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:

S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)

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

(74) PiDPToQDPProof (EQUIVALENT 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:

S2T4_IN_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)

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

(76) 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_GG(s(T10), node(nil, X48, X49)) → S2T4_IN_GG(T10, X49)
  The graph contains the following edges 1 > 1, 2 > 2

• S2T4_IN_GG(s(T8), node(X34, X35, X34)) → S2T4_IN_GG(T8, X34)
  The graph contains the following edges 1 > 1, 2 > 2

• S2T4_IN_GG(s(T12), node(X62, X63, nil)) → S2T4_IN_GG(T12, X62)
  The graph contains the following edges 1 > 1, 2 > 2

(77) TRUE

(78) Obligation:

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

S2T4_IN_GA(s(T10), node(nil, X48, X49)) → S2T4_IN_GA(T10, X49)
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → S2T4_IN_GA(T8, X34)
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → S2T4_IN_GA(T12, X62)

The TRS R consists of the following rules:

goal1_in_g(T5) → U10_g(T5, s2t4_in_ga(T5, X15))
s2t4_in_ga(0, nil) → s2t4_out_ga(0, nil)
s2t4_in_ga(s(T8), node(X34, X35, X34)) → U1_ga(T8, X34, X35, s2t4_in_ga(T8, X34))
s2t4_in_ga(s(T10), node(nil, X48, X49)) → U2_ga(T10, X48, X49, s2t4_in_ga(T10, X49))
s2t4_in_ga(s(T12), node(X62, X63, nil)) → U3_ga(T12, X62, X63, s2t4_in_ga(T12, X62))
s2t4_in_ga(T13, node(nil, X70, nil)) → s2t4_out_ga(T13, node(nil, X70, nil))
U3_ga(T12, X62, X63, s2t4_out_ga(T12, X62)) → s2t4_out_ga(s(T12), node(X62, X63, nil))
U2_ga(T10, X48, X49, s2t4_out_ga(T10, X49)) → s2t4_out_ga(s(T10), node(nil, X48, X49))
U1_ga(T8, X34, X35, s2t4_out_ga(T8, X34)) → s2t4_out_ga(s(T8), node(X34, X35, X34))
U10_g(T5, s2t4_out_ga(T5, X15)) → goal1_out_g(T5)
goal1_in_g(T5) → U11_g(T5, s2t4_in_gg(T5, nil))
s2t4_in_gg(0, nil) → s2t4_out_gg(0, nil)
s2t4_in_gg(s(T8), node(X34, X35, X34)) → U1_gg(T8, X34, X35, s2t4_in_gg(T8, X34))
s2t4_in_gg(s(T10), node(nil, X48, X49)) → U2_gg(T10, X48, X49, s2t4_in_gg(T10, X49))
s2t4_in_gg(s(T12), node(X62, X63, nil)) → U3_gg(T12, X62, X63, s2t4_in_gg(T12, X62))
s2t4_in_gg(T13, node(nil, X70, nil)) → s2t4_out_gg(T13, node(nil, X70, nil))
U3_gg(T12, X62, X63, s2t4_out_gg(T12, X62)) → s2t4_out_gg(s(T12), node(X62, X63, nil))
U2_gg(T10, X48, X49, s2t4_out_gg(T10, X49)) → s2t4_out_gg(s(T10), node(nil, X48, X49))
U1_gg(T8, X34, X35, s2t4_out_gg(T8, X34)) → s2t4_out_gg(s(T8), node(X34, X35, X34))
U11_g(T5, s2t4_out_gg(T5, nil)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U12_g(T5, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(nil, X79, X79) → tappend5_out_gaa(nil, X79, X79)
tappend5_in_gaa(nil, X92, node(X92, nil, nil)) → tappend5_out_gaa(nil, X92, node(X92, nil, nil))
tappend5_in_gaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_gaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_gaa(nil, X149, node(nil, nil, X149)) → tappend5_out_gaa(nil, X149, node(nil, nil, X149))
tappend5_in_gaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_gaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_gaa(nil, X210, node(X211, nil, nil)) → U4_gaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
tappend5_in_gaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_gaa(T83, T81, T82, X210, X211, tappend5_in_gaa(T83, X210, X211))
tappend5_in_gaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_gaa(T99, T97, T98, X210, X211, tappend5_in_gaa(T99, X210, X211))
tappend5_in_gaa(nil, nil, node(nil, nil, X268)) → U7_gaa(X268, tappend5_in_gaa(nil, X265, X268))
tappend5_in_gaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_gaa(T114, T115, T117, X268, tappend5_in_gaa(T117, X265, X268))
tappend5_in_gaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_gaa(T130, T131, T133, X268, tappend5_in_gaa(T133, X265, X268))
U9_gaa(T130, T131, T133, X268, tappend5_out_gaa(T133, X265, X268)) → tappend5_out_gaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_gaa(T114, T115, T117, X268, tappend5_out_gaa(T117, X265, X268)) → tappend5_out_gaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U7_gaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_gaa(nil, nil, node(nil, nil, X268))
U6_gaa(T99, T97, T98, X210, X211, tappend5_out_gaa(T99, X210, X211)) → tappend5_out_gaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_gaa(T83, T81, T82, X210, X211, tappend5_out_gaa(T83, X210, X211)) → tappend5_out_gaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U4_gaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_gaa(nil, X210, node(X211, nil, nil))
U12_g(T5, tappend5_out_gaa(nil, X210, X211)) → goal1_out_g(T5)
U11_g(T5, s2t4_out_gg(T5, nil)) → U13_g(T5, tappend5_in_gaa(nil, X265, X268))
U13_g(T5, tappend5_out_gaa(nil, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U14_g(T5, s2t4_in_ga(T5, node(nil, T25, T26)))
U14_g(T5, s2t4_out_ga(T5, node(nil, T25, T26))) → goal1_out_g(T5)
goal1_in_g(T5) → U15_g(T5, s2t4_in_ga(T5, node(nil, T36, T37)))
U15_g(T5, s2t4_out_ga(T5, node(nil, T36, T37))) → goal1_out_g(T5)
goal1_in_g(T5) → U16_g(T5, s2t4_in_ga(T5, node(T51, T52, nil)))
U16_g(T5, s2t4_out_ga(T5, node(T51, T52, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U17_g(T5, s2t4_in_ga(T5, node(T64, T65, nil)))
U17_g(T5, s2t4_out_ga(T5, node(T64, T65, nil))) → goal1_out_g(T5)
goal1_in_g(T5) → U18_g(T5, s2t4_in_ga(T5, node(T83, T81, T82)))
U18_g(T5, s2t4_out_ga(T5, node(T83, T81, T82))) → U19_g(T5, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(nil, X79, X79) → tappend5_out_aaa(nil, X79, X79)
tappend5_in_aaa(nil, X92, node(X92, nil, nil)) → tappend5_out_aaa(nil, X92, node(X92, nil, nil))
tappend5_in_aaa(node(nil, T25, T26), X92, node(X92, T25, T26)) → tappend5_out_aaa(node(nil, T25, T26), X92, node(X92, T25, T26))
tappend5_in_aaa(nil, X149, node(nil, nil, X149)) → tappend5_out_aaa(nil, X149, node(nil, nil, X149))
tappend5_in_aaa(node(T51, T52, nil), X149, node(T51, T52, X149)) → tappend5_out_aaa(node(T51, T52, nil), X149, node(T51, T52, X149))
tappend5_in_aaa(nil, X210, node(X211, nil, nil)) → U4_aaa(X210, X211, tappend5_in_gaa(nil, X210, X211))
U4_aaa(X210, X211, tappend5_out_gaa(nil, X210, X211)) → tappend5_out_aaa(nil, X210, node(X211, nil, nil))
tappend5_in_aaa(node(T83, T81, T82), X210, node(X211, T81, T82)) → U5_aaa(T83, T81, T82, X210, X211, tappend5_in_aaa(T83, X210, X211))
tappend5_in_aaa(node(T99, T97, T98), X210, node(X211, T97, T98)) → U6_aaa(T99, T97, T98, X210, X211, tappend5_in_aaa(T99, X210, X211))
tappend5_in_aaa(nil, nil, node(nil, nil, X268)) → U7_aaa(X268, tappend5_in_gaa(nil, X265, X268))
U7_aaa(X268, tappend5_out_gaa(nil, X265, X268)) → tappend5_out_aaa(nil, nil, node(nil, nil, X268))
tappend5_in_aaa(node(T114, T115, T117), T114, node(T114, T115, X268)) → U8_aaa(T114, T115, T117, X268, tappend5_in_aaa(T117, X265, X268))
tappend5_in_aaa(node(T130, T131, T133), T130, node(T130, T131, X268)) → U9_aaa(T130, T131, T133, X268, tappend5_in_aaa(T133, X265, X268))
U9_aaa(T130, T131, T133, X268, tappend5_out_aaa(T133, X265, X268)) → tappend5_out_aaa(node(T130, T131, T133), T130, node(T130, T131, X268))
U8_aaa(T114, T115, T117, X268, tappend5_out_aaa(T117, X265, X268)) → tappend5_out_aaa(node(T114, T115, T117), T114, node(T114, T115, X268))
U6_aaa(T99, T97, T98, X210, X211, tappend5_out_aaa(T99, X210, X211)) → tappend5_out_aaa(node(T99, T97, T98), X210, node(X211, T97, T98))
U5_aaa(T83, T81, T82, X210, X211, tappend5_out_aaa(T83, X210, X211)) → tappend5_out_aaa(node(T83, T81, T82), X210, node(X211, T81, T82))
U19_g(T5, tappend5_out_aaa(T83, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U20_g(T5, s2t4_in_ga(T5, node(T99, T97, T98)))
U20_g(T5, s2t4_out_ga(T5, node(T99, T97, T98))) → U21_g(T5, tappend5_in_aaa(T99, X210, X211))
U21_g(T5, tappend5_out_aaa(T99, X210, X211)) → goal1_out_g(T5)
goal1_in_g(T5) → U22_g(T5, s2t4_in_ga(T5, node(T114, T115, T117)))
U22_g(T5, s2t4_out_ga(T5, node(T114, T115, T117))) → U23_g(T5, tappend5_in_aaa(T117, X265, X268))
U23_g(T5, tappend5_out_aaa(T117, X265, X268)) → goal1_out_g(T5)
goal1_in_g(T5) → U24_g(T5, s2t4_in_ga(T5, node(T130, T131, T133)))
U24_g(T5, s2t4_out_ga(T5, node(T130, T131, T133))) → U25_g(T5, tappend5_in_aaa(T133, X265, X268))
U25_g(T5, tappend5_out_aaa(T133, X265, X268)) → goal1_out_g(T5)

The argument filtering Pi contains the following mapping:
goal1_in_g(x1)  =  goal1_in_g(x1)
U10_g(x1, x2)  =  U10_g(x1, x2)
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_g(x1)  =  goal1_out_g(x1)
U11_g(x1, x2)  =  U11_g(x1, x2)
s2t4_in_gg(x1, x2)  =  s2t4_in_gg(x1, x2)
nil  =  nil
s2t4_out_gg(x1, x2)  =  s2t4_out_gg(x1, x2)
node(x1, x2, x3)  =  node(x1, x2, x3)
U1_gg(x1, x2, x3, x4)  =  U1_gg(x1, x2, x3, x4)
U2_gg(x1, x2, x3, x4)  =  U2_gg(x1, x2, x3, x4)
U3_gg(x1, x2, x3, x4)  =  U3_gg(x1, x2, x3, x4)
U12_g(x1, x2)  =  U12_g(x1, x2)
tappend5_in_gaa(x1, x2, x3)  =  tappend5_in_gaa(x1)
tappend5_out_gaa(x1, x2, x3)  =  tappend5_out_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)  =  U7_gaa(x2)
U8_gaa(x1, x2, x3, x4, x5)  =  U8_gaa(x1, x2, x3, x5)
U9_gaa(x1, x2, x3, x4, x5)  =  U9_gaa(x1, x2, x3, x5)
U13_g(x1, x2)  =  U13_g(x1, x2)
U14_g(x1, x2)  =  U14_g(x1, x2)
U15_g(x1, x2)  =  U15_g(x1, x2)
U16_g(x1, x2)  =  U16_g(x1, x2)
U17_g(x1, x2)  =  U17_g(x1, x2)
U18_g(x1, x2)  =  U18_g(x1, x2)
U19_g(x1, x2)  =  U19_g(x1, x2)
tappend5_in_aaa(x1, x2, x3)  =  tappend5_in_aaa
tappend5_out_aaa(x1, x2, x3)  =  tappend5_out_aaa
U4_aaa(x1, x2, x3)  =  U4_aaa(x3)
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)  =  U7_aaa(x2)
U8_aaa(x1, x2, x3, x4, x5)  =  U8_aaa(x5)
U9_aaa(x1, x2, x3, x4, x5)  =  U9_aaa(x5)
U20_g(x1, x2)  =  U20_g(x1, x2)
U21_g(x1, x2)  =  U21_g(x1, x2)
U22_g(x1, x2)  =  U22_g(x1, x2)
U23_g(x1, x2)  =  U23_g(x1, x2)
U24_g(x1, x2)  =  U24_g(x1, x2)
U25_g(x1, x2)  =  U25_g(x1, x2)
S2T4_IN_GA(x1, x2)  =  S2T4_IN_GA(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:

S2T4_IN_GA(s(T10), node(nil, X48, X49)) → S2T4_IN_GA(T10, X49)
S2T4_IN_GA(s(T8), node(X34, X35, X34)) → S2T4_IN_GA(T8, X34)
S2T4_IN_GA(s(T12), node(X62, X63, nil)) → S2T4_IN_GA(T12, X62)

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

(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:

S2T4_IN_GA(s(T10)) → S2T4_IN_GA(T10)

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

(83) 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(T10)) → S2T4_IN_GA(T10)
  The graph contains the following edges 1 > 1

(84) TRUE