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

(0) Obligation:

Clauses:

insert(X, void, tree(X, void, void)).
insert(X, tree(X, Left, Right), tree(X, Left, Right)).
insert(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), insert(X, Left, Left1)).
insert(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), insert(X, Right, Right1)).
less(0, s(X1)).
less(s(X), s(Y)) :- less(X, Y).

Query: insert(a,a,g)

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph ICLP10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: insert(T1, T2, T3)\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\nX3 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 1 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T5, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(less(T20, T17), insert(T20, T21, void)) | insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: insert(T1, T2, tree(T9, void, void)), SCOPE: 1, CLAUSE: 3\n\nT9 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T1, T2, tree(T9, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 4 | ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 4\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 5 | ?_2 | insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: insert(0, T27, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(less(T20, T17), insert(T20, T21, void)), SCOPE: 2, CLAUSE: 5\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ?_2 | insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ','(less(T38, T37), insert(s(T38), T39, void))\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: less(T38, T37)\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: insert(s(T42), T43, void)\n\nT42 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: less(T38, T37), SCOPE: 3, CLAUSE: 4 | less(T38, T37), SCOPE: 3, CLAUSE: 5\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: less(T38, T37), SCOPE: 3, CLAUSE: 4\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: less(T38, T37), SCOPE: 3, CLAUSE: 5\n\nT37 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: less(T57, T56)\n\nT56 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: insert(T1, T2, tree(T17, void, void)), SCOPE: 1, CLAUSE: 3\n\nT17 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(less(T71, T74), insert(T74, T75, void))\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: less(T71, T74)\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: insert(T78, T79, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: less(T71, T74), SCOPE: 4, CLAUSE: 4 | less(T71, T74), SCOPE: 4, CLAUSE: 5\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: less(T71, T74), SCOPE: 4, CLAUSE: 4\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: less(T71, T74), SCOPE: 4, CLAUSE: 5\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: less(T91, T93)\n\nT91 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(less(T103, T106), insert(T106, T107, void))\n\nT103 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T1, T2, tree(T103, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(less(T103, T106), insert(T106, T107, void)), SCOPE: 5, CLAUSE: 4 | ','(less(T103, T106), insert(T106, T107, void)), SCOPE: 5, CLAUSE: 5\n\nT103 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T1, T2, tree(T103, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: ','(less(T103, T106), insert(T106, T107, void)), SCOPE: 5, CLAUSE: 4\n\nT103 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T1, T2, tree(T103, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(less(T103, T106), insert(T106, T107, void)), SCOPE: 5, CLAUSE: 5\n\nT103 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T1, T2, tree(T103, void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: insert(s(T114), T113, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(less(T121, T123), insert(s(T123), T124, void))\n\nT121 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T1, T2, tree(s(T121), void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: less(T121, T123)\n\nT121 is ground\nX15 is free\nX16 is free\nX17 is free\nX18 is free\nX19 is free\ninsert(T1, T2, tree(s(T121), void, void)) !=? insert(X15, tree(X16, X17, X18), tree(X16, X19, X18))", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: insert(s(T127), T128, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: ','(less(T143, T140), insert(T143, T144, void)) | insert(T1, T2, tree(T140, void, void)), SCOPE: 1, CLAUSE: 3\n\nT140 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T140, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: insert(T1, T2, tree(T5, void, void)), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T5, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(less(T143, T140), insert(T143, T144, void)), SCOPE: 6, CLAUSE: 4 | ','(less(T143, T140), insert(T143, T144, void)), SCOPE: 6, CLAUSE: 5 | ?_6 | insert(T1, T2, tree(T140, void, void)), SCOPE: 1, CLAUSE: 3\n\nT140 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T140, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: ','(less(T143, T140), insert(T143, T144, void)), SCOPE: 6, CLAUSE: 4\n\nT140 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T140, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(less(T143, T140), insert(T143, T144, void)), SCOPE: 6, CLAUSE: 5 | ?_6 | insert(T1, T2, tree(T140, void, void)), SCOPE: 1, CLAUSE: 3\n\nT140 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T140, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: insert(0, T150, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(less(T143, T140), insert(T143, T144, void)), SCOPE: 6, CLAUSE: 5\n\nT140 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T140, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: ?_6 | insert(T1, T2, tree(T140, void, void)), SCOPE: 1, CLAUSE: 3\n\nT140 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T140, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(less(T161, T160), insert(s(T161), T162, void))\n\nT160 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(s(T160), void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: insert(T1, T2, tree(T140, void, void)), SCOPE: 1, CLAUSE: 3\n\nT140 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T140, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: ','(less(T174, T177), insert(T177, T178, void))\n\nT174 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T174, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: ','(less(T186, T189), insert(T189, T190, void))\n\nT186 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T186, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: ','(less(T186, T189), insert(T189, T190, void)), SCOPE: 7, CLAUSE: 4 | ','(less(T186, T189), insert(T189, T190, void)), SCOPE: 7, CLAUSE: 5\n\nT186 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T186, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: ','(less(T186, T189), insert(T189, T190, void)), SCOPE: 7, CLAUSE: 4\n\nT186 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T186, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(less(T186, T189), insert(T189, T190, void)), SCOPE: 7, CLAUSE: 5\n\nT186 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(T186, void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: insert(s(T197), T196, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(less(T204, T206), insert(s(T206), T207, void))\n\nT204 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(s(T204), void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: less(T204, T206)\n\nT204 is ground\nX7 is free\nX8 is free\nX9 is free\ninsert(T1, T2, tree(s(T204), void, void)) !=? insert(X7, tree(X7, X8, X9), tree(X7, X8, X9))", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: insert(s(T210), T211, void)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: true | insert(T1, T2, tree(T221, T222, T223)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T221, T222, T223)), SCOPE: 1, CLAUSE: 3\n\nT221 is ground\nT222 is ground\nT223 is ground\nX3 is free\ninsert(T1, T2, tree(T221, T222, T223)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: insert(T1, T2, tree(T221, T222, T223)), SCOPE: 1, CLAUSE: 2 | insert(T1, T2, tree(T221, T222, T223)), SCOPE: 1, CLAUSE: 3\n\nT221 is ground\nT222 is ground\nT223 is ground\nX3 is free\ninsert(T1, T2, tree(T221, T222, T223)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: ','(less(T234, T230), insert(T234, T235, T233)) | insert(T1, T2, tree(T230, T233, T232)), SCOPE: 1, CLAUSE: 3\n\nT230 is ground\nT233 is ground\nT232 is ground\nX3 is free\ninsert(T1, T2, tree(T230, T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: insert(T1, T2, tree(T221, T222, T223)), SCOPE: 1, CLAUSE: 3\n\nT221 is ground\nT222 is ground\nT223 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T1, T2, tree(T221, T222, T223)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T221, T222, T223)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: ','(less(T234, T230), insert(T234, T235, T233)), SCOPE: 8, CLAUSE: 4 | ','(less(T234, T230), insert(T234, T235, T233)), SCOPE: 8, CLAUSE: 5 | ?_8 | insert(T1, T2, tree(T230, T233, T232)), SCOPE: 1, CLAUSE: 3\n\nT230 is ground\nT233 is ground\nT232 is ground\nX3 is free\ninsert(T1, T2, tree(T230, T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: ','(less(T234, T230), insert(T234, T235, T233)), SCOPE: 8, CLAUSE: 4\n\nT230 is ground\nT233 is ground\nT232 is ground\nX3 is free\ninsert(T1, T2, tree(T230, T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: ','(less(T234, T230), insert(T234, T235, T233)), SCOPE: 8, CLAUSE: 5 | ?_8 | insert(T1, T2, tree(T230, T233, T232)), SCOPE: 1, CLAUSE: 3\n\nT230 is ground\nT233 is ground\nT232 is ground\nX3 is free\ninsert(T1, T2, tree(T230, T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: insert(0, T241, T233)\n\nT233 is ground\nT232 is ground\nT240 is ground\nX3 is free\ninsert(T1, T2, tree(s(T240), T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: ','(less(T234, T230), insert(T234, T235, T233)), SCOPE: 8, CLAUSE: 5\n\nT230 is ground\nT233 is ground\nT232 is ground\nX3 is free\ninsert(T1, T2, tree(T230, T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ?_8 | insert(T1, T2, tree(T230, T233, T232)), SCOPE: 1, CLAUSE: 3\n\nT230 is ground\nT233 is ground\nT232 is ground\nX3 is free\ninsert(T1, T2, tree(T230, T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: ','(less(T252, T251), insert(s(T252), T253, T233))\n\nT233 is ground\nT232 is ground\nT251 is ground\nX3 is free\ninsert(T1, T2, tree(s(T251), T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: less(T252, T251)\n\nT233 is ground\nT232 is ground\nT251 is ground\nX3 is free\ninsert(T1, T2, tree(s(T251), T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: insert(s(T256), T257, T233)\n\nT233 is ground\nT232 is ground\nT251 is ground\nT256 is ground\nX3 is free\ninsert(T258, T259, tree(s(T251), T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: insert(T1, T2, tree(T230, T233, T232)), SCOPE: 1, CLAUSE: 3\n\nT230 is ground\nT233 is ground\nT232 is ground\nX3 is free\ninsert(T1, T2, tree(T230, T233, T232)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: ','(less(T275, T279), insert(T279, T280, T278))\n\nT275 is ground\nT276 is ground\nT278 is ground\nX3 is free\ninsert(T1, T2, tree(T275, T276, T278)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: less(T275, T279)\n\nT275 is ground\nT276 is ground\nT278 is ground\nX3 is free\ninsert(T1, T2, tree(T275, T276, T278)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: insert(T283, T284, T278)\n\nT275 is ground\nT276 is ground\nT278 is ground\nX3 is free\ninsert(T285, T286, tree(T275, T276, T278)) !=? insert(X3, void, tree(X3, void, void))", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: ','(less(T297, T301), insert(T301, T302, T300))\n\nT297 is ground\nT298 is ground\nT300 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T1, T2, tree(T297, T298, T300)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T297, T298, T300)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(less(T297, T301), insert(T301, T302, T300)), SCOPE: 9, CLAUSE: 4 | ','(less(T297, T301), insert(T301, T302, T300)), SCOPE: 9, CLAUSE: 5\n\nT297 is ground\nT298 is ground\nT300 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T1, T2, tree(T297, T298, T300)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T297, T298, T300)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(less(T297, T301), insert(T301, T302, T300)), SCOPE: 9, CLAUSE: 4\n\nT297 is ground\nT298 is ground\nT300 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T1, T2, tree(T297, T298, T300)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T297, T298, T300)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(less(T297, T301), insert(T301, T302, T300)), SCOPE: 9, CLAUSE: 5\n\nT297 is ground\nT298 is ground\nT300 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T1, T2, tree(T297, T298, T300)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T297, T298, T300)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: insert(s(T309), T308, T300)\n\nT298 is ground\nT300 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T1, T2, tree(0, T298, T300)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(0, T298, T300)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: ','(less(T316, T318), insert(s(T318), T319, T300))\n\nT298 is ground\nT300 is ground\nT316 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T1, T2, tree(s(T316), T298, T300)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(s(T316), T298, T300)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: less(T316, T318)\n\nT298 is ground\nT300 is ground\nT316 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T1, T2, tree(s(T316), T298, T300)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(s(T316), T298, T300)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: insert(s(T322), T323, T300)\n\nT298 is ground\nT300 is ground\nT316 is ground\nX3 is free\nX205 is free\nX206 is free\nX207 is free\nX208 is free\nX209 is free\ninsert(T324, T325, tree(s(T316), T298, T300)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T324, T325, tree(s(T316), T298, T300)) !=? insert(X205, tree(X206, X207, X208), tree(X206, X209, X208))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(less(T340, T336), insert(T340, T341, T339)) | insert(T1, T2, tree(T336, T339, T338)), SCOPE: 1, CLAUSE: 3\n\nT336 is ground\nT339 is ground\nT338 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: insert(T1, T2, T3), SCOPE: 1, CLAUSE: 3\n\nT3 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, T3) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, T3) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(less(T340, T336), insert(T340, T341, T339)), SCOPE: 10, CLAUSE: 4 | ','(less(T340, T336), insert(T340, T341, T339)), SCOPE: 10, CLAUSE: 5 | ?_10 | insert(T1, T2, tree(T336, T339, T338)), SCOPE: 1, CLAUSE: 3\n\nT336 is ground\nT339 is ground\nT338 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(less(T340, T336), insert(T340, T341, T339)), SCOPE: 10, CLAUSE: 4\n\nT336 is ground\nT339 is ground\nT338 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: ','(less(T340, T336), insert(T340, T341, T339)), SCOPE: 10, CLAUSE: 5 | ?_10 | insert(T1, T2, tree(T336, T339, T338)), SCOPE: 1, CLAUSE: 3\n\nT336 is ground\nT339 is ground\nT338 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: insert(0, T347, T339)\n\nT339 is ground\nT338 is ground\nT346 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(s(T346), T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(s(T346), T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(less(T340, T336), insert(T340, T341, T339)), SCOPE: 10, CLAUSE: 5\n\nT336 is ground\nT339 is ground\nT338 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ?_10 | insert(T1, T2, tree(T336, T339, T338)), SCOPE: 1, CLAUSE: 3\n\nT336 is ground\nT339 is ground\nT338 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(less(T358, T357), insert(s(T358), T359, T339))\n\nT339 is ground\nT338 is ground\nT357 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(s(T357), T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(s(T357), T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: insert(T1, T2, tree(T336, T339, T338)), SCOPE: 1, CLAUSE: 3\n\nT336 is ground\nT339 is ground\nT338 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T336, T339, T338)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(less(T373, T377), insert(T377, T378, T376))\n\nT373 is ground\nT374 is ground\nT376 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T373, T374, T376)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T373, T374, T376)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(less(T387, T391), insert(T391, T392, T390))\n\nT387 is ground\nT388 is ground\nT390 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T387, T388, T390)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T387, T388, T390)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: ','(less(T387, T391), insert(T391, T392, T390)), SCOPE: 11, CLAUSE: 4 | ','(less(T387, T391), insert(T391, T392, T390)), SCOPE: 11, CLAUSE: 5\n\nT387 is ground\nT388 is ground\nT390 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T387, T388, T390)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T387, T388, T390)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: ','(less(T387, T391), insert(T391, T392, T390)), SCOPE: 11, CLAUSE: 4\n\nT387 is ground\nT388 is ground\nT390 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T387, T388, T390)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T387, T388, T390)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ','(less(T387, T391), insert(T391, T392, T390)), SCOPE: 11, CLAUSE: 5\n\nT387 is ground\nT388 is ground\nT390 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(T387, T388, T390)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(T387, T388, T390)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: insert(s(T399), T398, T390)\n\nT388 is ground\nT390 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(0, T388, T390)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(0, T388, T390)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ','(less(T406, T408), insert(s(T408), T409, T390))\n\nT388 is ground\nT390 is ground\nT406 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(s(T406), T388, T390)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(s(T406), T388, T390)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: less(T406, T408)\n\nT388 is ground\nT390 is ground\nT406 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T1, T2, tree(s(T406), T388, T390)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T1, T2, tree(s(T406), T388, T390)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: insert(s(T412), T413, T390)\n\nT388 is ground\nT390 is ground\nT406 is ground\nX3 is free\nX197 is free\nX198 is free\nX199 is free\ninsert(T414, T415, tree(s(T406), T388, T390)) !=? insert(X3, void, tree(X3, void, void))\ninsert(T414, T415, tree(s(T406), T388, T390)) !=? insert(X197, tree(X197, X198, X199), tree(X197, X198, X199))", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 136 [arrowhead = none ];
136 -> 2;

137 [label="EVAL with clause\ninsert(X3, void, tree(X3, void, void)).\nand substitutionT1 -> T5,\nX3 -> T5,\nT2 -> void,\nT3 -> tree(T5, void, void)", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 137 [arrowhead = none ];
137 -> 3;

138 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 138 [arrowhead = none ];
138 -> 4;

139 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 139 [arrowhead = none ];
139 -> 5;

140 [label="EVAL with clause\ninsert(X197, tree(X197, X198, X199), tree(X197, X198, X199)).\nand substitutionT1 -> T221,\nX197 -> T221,\nX198 -> T222,\nX199 -> T223,\nT2 -> tree(T221, T222, T223),\nT3 -> tree(T221, T222, T223)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 140 [arrowhead = none ];
140 -> 79;

141 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 141 [arrowhead = none ];
141 -> 80;

142 [label="EVAL with clause\ninsert(X7, tree(X7, X8, X9), tree(X7, X8, X9)).\nand substitutionT1 -> T9,\nX7 -> T9,\nX8 -> void,\nX9 -> void,\nT2 -> tree(T9, void, void),\nT5 -> T9,\nT10 -> void,\nT11 -> void", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 142 [arrowhead = none ];
142 -> 6;

143 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 143 [arrowhead = none ];
143 -> 7;

144 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 144 [arrowhead = none ];
144 -> 8;

145 [label="EVAL with clause\ninsert(X124, tree(X125, X126, X127), tree(X125, X128, X127)) :- ','(less(X124, X125), insert(X124, X126, X128)).\nand substitutionT1 -> T143,\nX124 -> T143,\nX125 -> T140,\nX126 -> T144,\nX127 -> void,\nT2 -> tree(T140, T144, void),\nT5 -> T140,\nX128 -> void,\nT142 -> void,\nT139 -> T143,\nT141 -> T144", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 145 [arrowhead = none ];
145 -> 54;

146 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 146 [arrowhead = none ];
146 -> 55;

147 [label="EVAL with clause\ninsert(X15, tree(X16, X17, X18), tree(X16, X19, X18)) :- ','(less(X15, X16), insert(X15, X17, X19)).\nand substitutionT1 -> T20,\nX15 -> T20,\nX16 -> T17,\nX17 -> T21,\nX18 -> void,\nT2 -> tree(T17, T21, void),\nT9 -> T17,\nX19 -> void,\nT19 -> void,\nT16 -> T20,\nT18 -> T21", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 147 [arrowhead = none ];
147 -> 9;

148 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 148 [arrowhead = none ];
148 -> 10;

149 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 149 [arrowhead = none ];
149 -> 11;

150 [label="EVAL with clause\ninsert(X95, tree(X96, X97, X98), tree(X96, X97, X99)) :- ','(less(X96, X95), insert(X95, X98, X99)).\nand substitutionT1 -> T106,\nX95 -> T106,\nX96 -> T103,\nX97 -> void,\nX98 -> T107,\nT2 -> tree(T103, void, T107),\nT9 -> T103,\nT104 -> void,\nX99 -> void,\nT102 -> T106,\nT105 -> T107", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 150 [arrowhead = none ];
150 -> 43;

151 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 151 [arrowhead = none ];
151 -> 44;

152 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 152 [arrowhead = none ];
152 -> 12;

153 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 153 [arrowhead = none ];
153 -> 13;

154 [label="EVAL with clause\nless(0, s(X24)).\nand substitutionT20 -> 0,\nX24 -> T26,\nT17 -> s(T26),\nT21 -> T27", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 154 [arrowhead = none ];
154 -> 14;

155 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 155 [arrowhead = none ];
155 -> 15;

156 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 156 [arrowhead = none ];
156 -> 16;

157 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 157 [arrowhead = none ];
157 -> 17;

158 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T27\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
14 -> 158 [arrowhead = none , style=dashed];
158 -> 1[style=dashed];

159 [label="EVAL with clause\nless(s(X35), s(X36)) :- less(X35, X36).\nand substitutionX35 -> T38,\nT20 -> s(T38),\nX36 -> T37,\nT17 -> s(T37),\nT36 -> T38,\nT21 -> T39", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 159 [arrowhead = none ];
159 -> 18;

160 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 160 [arrowhead = none ];
160 -> 19;

161 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 161 [arrowhead = none ];
161 -> 30;

162 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
18 -> 162 [arrowhead = none ];
162 -> 20;

163 [label="SPLIT 2\nnew knowledge:\nT42 is ground\nT37 is ground\nreplacements:T38 -> T42,\nT39 -> T43", fontsize=14, style = filled, fillcolor = violet];
18 -> 163 [arrowhead = none ];
163 -> 21;

164 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
20 -> 164 [arrowhead = none ];
164 -> 22;

165 [label="INSTANCE with matching:\nT1 -> s(T42)\nT2 -> T43\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
21 -> 165 [arrowhead = none , style=dashed];
165 -> 1[style=dashed];

166 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
22 -> 166 [arrowhead = none ];
166 -> 23;

167 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
22 -> 167 [arrowhead = none ];
167 -> 24;

168 [label="EVAL with clause\nless(0, s(X45)).\nand substitutionT38 -> 0,\nX45 -> T50,\nT37 -> s(T50)", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 168 [arrowhead = none ];
168 -> 25;

169 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 169 [arrowhead = none ];
169 -> 26;

170 [label="EVAL with clause\nless(s(X50), s(X51)) :- less(X50, X51).\nand substitutionX50 -> T57,\nT38 -> s(T57),\nX51 -> T56,\nT37 -> s(T56),\nT55 -> T57", fontsize=14, style = filled, fillcolor = lightblue];
24 -> 170 [arrowhead = none ];
170 -> 28;

171 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 171 [arrowhead = none ];
171 -> 29;

172 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
25 -> 172 [arrowhead = none ];
172 -> 27;

173 [label="INSTANCE with matching:\nT38 -> T57\nT37 -> T56", fontsize=14, style = filled, fillcolor = lightgrey];
28 -> 173 [arrowhead = none , style=dashed];
173 -> 20[style=dashed];

174 [label="EVAL with clause\ninsert(X66, tree(X67, X68, X69), tree(X67, X68, X70)) :- ','(less(X67, X66), insert(X66, X69, X70)).\nand substitutionT1 -> T74,\nX66 -> T74,\nX67 -> T71,\nX68 -> void,\nX69 -> T75,\nT2 -> tree(T71, void, T75),\nT17 -> T71,\nT72 -> void,\nX70 -> void,\nT70 -> T74,\nT73 -> T75", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 174 [arrowhead = none ];
174 -> 31;

175 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 175 [arrowhead = none ];
175 -> 32;

176 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
31 -> 176 [arrowhead = none ];
176 -> 33;

177 [label="SPLIT 2\nnew knowledge:\nT71 is ground\nreplacements:T74 -> T78,\nT75 -> T79", fontsize=14, style = filled, fillcolor = violet];
31 -> 177 [arrowhead = none ];
177 -> 34;

178 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
33 -> 178 [arrowhead = none ];
178 -> 35;

179 [label="INSTANCE with matching:\nT1 -> T78\nT2 -> T79\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
34 -> 179 [arrowhead = none , style=dashed];
179 -> 1[style=dashed];

180 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
35 -> 180 [arrowhead = none ];
180 -> 36;

181 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
35 -> 181 [arrowhead = none ];
181 -> 37;

182 [label="EVAL with clause\nless(0, s(X79)).\nand substitutionT71 -> 0,\nX79 -> T86,\nT74 -> s(T86)", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 182 [arrowhead = none ];
182 -> 38;

183 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 183 [arrowhead = none ];
183 -> 39;

184 [label="EVAL with clause\nless(s(X84), s(X85)) :- less(X84, X85).\nand substitutionX84 -> T91,\nT71 -> s(T91),\nX85 -> T93,\nT74 -> s(T93),\nT92 -> T93", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 184 [arrowhead = none ];
184 -> 41;

185 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 185 [arrowhead = none ];
185 -> 42;

186 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 186 [arrowhead = none ];
186 -> 40;

187 [label="INSTANCE with matching:\nT71 -> T91\nT74 -> T93", fontsize=14, style = filled, fillcolor = lightgrey];
41 -> 187 [arrowhead = none , style=dashed];
187 -> 33[style=dashed];

188 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
43 -> 188 [arrowhead = none ];
188 -> 45;

189 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 189 [arrowhead = none ];
189 -> 46;

190 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
45 -> 190 [arrowhead = none ];
190 -> 47;

191 [label="EVAL with clause\nless(0, s(X104)).\nand substitutionT103 -> 0,\nX104 -> T114,\nT106 -> s(T114),\nT107 -> T113,\nT112 -> T114", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 191 [arrowhead = none ];
191 -> 48;

192 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
46 -> 192 [arrowhead = none ];
192 -> 49;

193 [label="EVAL with clause\nless(s(X111), s(X112)) :- less(X111, X112).\nand substitutionX111 -> T121,\nT103 -> s(T121),\nX112 -> T123,\nT106 -> s(T123),\nT122 -> T123,\nT107 -> T124", fontsize=14, style = filled, fillcolor = lightblue];
47 -> 193 [arrowhead = none ];
193 -> 50;

194 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 194 [arrowhead = none ];
194 -> 51;

195 [label="INSTANCE with matching:\nT1 -> s(T114)\nT2 -> T113\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
48 -> 195 [arrowhead = none , style=dashed];
195 -> 1[style=dashed];

196 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
50 -> 196 [arrowhead = none ];
196 -> 52;

197 [label="SPLIT 2\nnew knowledge:\nT121 is ground\nreplacements:T123 -> T127,\nT124 -> T128,\nT1 -> T129,\nT2 -> T130", fontsize=14, style = filled, fillcolor = violet];
50 -> 197 [arrowhead = none ];
197 -> 53;

198 [label="INSTANCE with matching:\nT71 -> T121\nT74 -> T123", fontsize=14, style = filled, fillcolor = lightgrey];
52 -> 198 [arrowhead = none , style=dashed];
198 -> 33[style=dashed];

199 [label="INSTANCE with matching:\nT1 -> s(T127)\nT2 -> T128\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
53 -> 199 [arrowhead = none , style=dashed];
199 -> 1[style=dashed];

200 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
54 -> 200 [arrowhead = none ];
200 -> 56;

201 [label="EVAL with clause\ninsert(X170, tree(X171, X172, X173), tree(X171, X172, X174)) :- ','(less(X171, X170), insert(X170, X173, X174)).\nand substitutionT1 -> T189,\nX170 -> T189,\nX171 -> T186,\nX172 -> void,\nX173 -> T190,\nT2 -> tree(T186, void, T190),\nT5 -> T186,\nT187 -> void,\nX174 -> void,\nT185 -> T189,\nT188 -> T190", fontsize=14, style = filled, fillcolor = lightblue];
55 -> 201 [arrowhead = none ];
201 -> 68;

202 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 202 [arrowhead = none ];
202 -> 69;

203 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 203 [arrowhead = none ];
203 -> 57;

204 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
56 -> 204 [arrowhead = none ];
204 -> 58;

205 [label="EVAL with clause\nless(0, s(X133)).\nand substitutionT143 -> 0,\nX133 -> T149,\nT140 -> s(T149),\nT144 -> T150", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 205 [arrowhead = none ];
205 -> 59;

206 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
57 -> 206 [arrowhead = none ];
206 -> 60;

207 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 207 [arrowhead = none ];
207 -> 61;

208 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 208 [arrowhead = none ];
208 -> 62;

209 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T150\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
59 -> 209 [arrowhead = none , style=dashed];
209 -> 1[style=dashed];

210 [label="EVAL with clause\nless(s(X144), s(X145)) :- less(X144, X145).\nand substitutionX144 -> T161,\nT143 -> s(T161),\nX145 -> T160,\nT140 -> s(T160),\nT159 -> T161,\nT144 -> T162", fontsize=14, style = filled, fillcolor = lightblue];
61 -> 210 [arrowhead = none ];
210 -> 63;

211 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 211 [arrowhead = none ];
211 -> 64;

212 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
62 -> 212 [arrowhead = none ];
212 -> 65;

213 [label="INSTANCE with matching:\nT38 -> T161\nT37 -> T160\nT39 -> T162", fontsize=14, style = filled, fillcolor = lightgrey];
63 -> 213 [arrowhead = none , style=dashed];
213 -> 18[style=dashed];

214 [label="EVAL with clause\ninsert(X158, tree(X159, X160, X161), tree(X159, X160, X162)) :- ','(less(X159, X158), insert(X158, X161, X162)).\nand substitutionT1 -> T177,\nX158 -> T177,\nX159 -> T174,\nX160 -> void,\nX161 -> T178,\nT2 -> tree(T174, void, T178),\nT140 -> T174,\nT175 -> void,\nX162 -> void,\nT173 -> T177,\nT176 -> T178", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 214 [arrowhead = none ];
214 -> 66;

215 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 215 [arrowhead = none ];
215 -> 67;

216 [label="INSTANCE with matching:\nT71 -> T174\nT74 -> T177\nT75 -> T178", fontsize=14, style = filled, fillcolor = lightgrey];
66 -> 216 [arrowhead = none , style=dashed];
216 -> 31[style=dashed];

217 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
68 -> 217 [arrowhead = none ];
217 -> 70;

218 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 218 [arrowhead = none ];
218 -> 71;

219 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 219 [arrowhead = none ];
219 -> 72;

220 [label="EVAL with clause\nless(0, s(X179)).\nand substitutionT186 -> 0,\nX179 -> T197,\nT189 -> s(T197),\nT190 -> T196,\nT195 -> T197", fontsize=14, style = filled, fillcolor = lightblue];
71 -> 220 [arrowhead = none ];
220 -> 73;

221 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 221 [arrowhead = none ];
221 -> 74;

222 [label="EVAL with clause\nless(s(X186), s(X187)) :- less(X186, X187).\nand substitutionX186 -> T204,\nT186 -> s(T204),\nX187 -> T206,\nT189 -> s(T206),\nT205 -> T206,\nT190 -> T207", fontsize=14, style = filled, fillcolor = lightblue];
72 -> 222 [arrowhead = none ];
222 -> 75;

223 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
72 -> 223 [arrowhead = none ];
223 -> 76;

224 [label="INSTANCE with matching:\nT1 -> s(T197)\nT2 -> T196\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
73 -> 224 [arrowhead = none , style=dashed];
224 -> 1[style=dashed];

225 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
75 -> 225 [arrowhead = none ];
225 -> 77;

226 [label="SPLIT 2\nnew knowledge:\nT204 is ground\nreplacements:T206 -> T210,\nT207 -> T211,\nT1 -> T212,\nT2 -> T213", fontsize=14, style = filled, fillcolor = violet];
75 -> 226 [arrowhead = none ];
226 -> 78;

227 [label="INSTANCE with matching:\nT71 -> T204\nT74 -> T206", fontsize=14, style = filled, fillcolor = lightgrey];
77 -> 227 [arrowhead = none , style=dashed];
227 -> 33[style=dashed];

228 [label="INSTANCE with matching:\nT1 -> s(T210)\nT2 -> T211\nT3 -> void", fontsize=14, style = filled, fillcolor = lightgrey];
78 -> 228 [arrowhead = none , style=dashed];
228 -> 1[style=dashed];

229 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
79 -> 229 [arrowhead = none ];
229 -> 81;

230 [label="EVAL with clause\ninsert(X288, tree(X289, X290, X291), tree(X289, X292, X291)) :- ','(less(X288, X289), insert(X288, X290, X292)).\nand substitutionT1 -> T340,\nX288 -> T340,\nX289 -> T336,\nX290 -> T341,\nX291 -> T338,\nT2 -> tree(T336, T341, T338),\nX292 -> T339,\nT3 -> tree(T336, T339, T338),\nT335 -> T340,\nT337 -> T341", fontsize=14, style = filled, fillcolor = lightblue];
80 -> 230 [arrowhead = none ];
230 -> 111;

231 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
80 -> 231 [arrowhead = none ];
231 -> 112;

232 [label="EVAL with clause\ninsert(X205, tree(X206, X207, X208), tree(X206, X209, X208)) :- ','(less(X205, X206), insert(X205, X207, X209)).\nand substitutionT1 -> T234,\nX205 -> T234,\nX206 -> T230,\nX207 -> T235,\nX208 -> T232,\nT2 -> tree(T230, T235, T232),\nT221 -> T230,\nT222 -> T233,\nX209 -> T233,\nT223 -> T232,\nT229 -> T234,\nT231 -> T235", fontsize=14, style = filled, fillcolor = lightblue];
81 -> 232 [arrowhead = none ];
232 -> 82;

233 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 233 [arrowhead = none ];
233 -> 83;

234 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
82 -> 234 [arrowhead = none ];
234 -> 84;

235 [label="EVAL with clause\ninsert(X259, tree(X260, X261, X262), tree(X260, X261, X263)) :- ','(less(X260, X259), insert(X259, X262, X263)).\nand substitutionT1 -> T301,\nX259 -> T301,\nX260 -> T297,\nX261 -> T298,\nX262 -> T302,\nT2 -> tree(T297, T298, T302),\nT221 -> T297,\nT222 -> T298,\nT223 -> T300,\nX263 -> T300,\nT296 -> T301,\nT299 -> T302", fontsize=14, style = filled, fillcolor = lightblue];
83 -> 235 [arrowhead = none ];
235 -> 100;

236 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 236 [arrowhead = none ];
236 -> 101;

237 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 237 [arrowhead = none ];
237 -> 85;

238 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 238 [arrowhead = none ];
238 -> 86;

239 [label="EVAL with clause\nless(0, s(X214)).\nand substitutionT234 -> 0,\nX214 -> T240,\nT230 -> s(T240),\nT235 -> T241", fontsize=14, style = filled, fillcolor = lightblue];
85 -> 239 [arrowhead = none ];
239 -> 87;

240 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
85 -> 240 [arrowhead = none ];
240 -> 88;

241 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 241 [arrowhead = none ];
241 -> 89;

242 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 242 [arrowhead = none ];
242 -> 90;

243 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T241\nT3 -> T233", fontsize=14, style = filled, fillcolor = lightgrey];
87 -> 243 [arrowhead = none , style=dashed];
243 -> 1[style=dashed];

244 [label="EVAL with clause\nless(s(X225), s(X226)) :- less(X225, X226).\nand substitutionX225 -> T252,\nT234 -> s(T252),\nX226 -> T251,\nT230 -> s(T251),\nT250 -> T252,\nT235 -> T253", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 244 [arrowhead = none ];
244 -> 91;

245 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
89 -> 245 [arrowhead = none ];
245 -> 92;

246 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
90 -> 246 [arrowhead = none ];
246 -> 95;

247 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
91 -> 247 [arrowhead = none ];
247 -> 93;

248 [label="SPLIT 2\nnew knowledge:\nT256 is ground\nT251 is ground\nreplacements:T252 -> T256,\nT253 -> T257,\nT1 -> T258,\nT2 -> T259", fontsize=14, style = filled, fillcolor = violet];
91 -> 248 [arrowhead = none ];
248 -> 94;

249 [label="INSTANCE with matching:\nT38 -> T252\nT37 -> T251", fontsize=14, style = filled, fillcolor = lightgrey];
93 -> 249 [arrowhead = none , style=dashed];
249 -> 20[style=dashed];

250 [label="INSTANCE with matching:\nT1 -> s(T256)\nT2 -> T257\nT3 -> T233", fontsize=14, style = filled, fillcolor = lightgrey];
94 -> 250 [arrowhead = none , style=dashed];
250 -> 1[style=dashed];

251 [label="EVAL with clause\ninsert(X243, tree(X244, X245, X246), tree(X244, X245, X247)) :- ','(less(X244, X243), insert(X243, X246, X247)).\nand substitutionT1 -> T279,\nX243 -> T279,\nX244 -> T275,\nX245 -> T276,\nX246 -> T280,\nT2 -> tree(T275, T276, T280),\nT230 -> T275,\nT233 -> T276,\nT232 -> T278,\nX247 -> T278,\nT274 -> T279,\nT277 -> T280", fontsize=14, style = filled, fillcolor = lightblue];
95 -> 251 [arrowhead = none ];
251 -> 96;

252 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
95 -> 252 [arrowhead = none ];
252 -> 97;

253 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
96 -> 253 [arrowhead = none ];
253 -> 98;

254 [label="SPLIT 2\nnew knowledge:\nT275 is ground\nreplacements:T279 -> T283,\nT280 -> T284,\nT1 -> T285,\nT2 -> T286", fontsize=14, style = filled, fillcolor = violet];
96 -> 254 [arrowhead = none ];
254 -> 99;

255 [label="INSTANCE with matching:\nT71 -> T275\nT74 -> T279", fontsize=14, style = filled, fillcolor = lightgrey];
98 -> 255 [arrowhead = none , style=dashed];
255 -> 33[style=dashed];

256 [label="INSTANCE with matching:\nT1 -> T283\nT2 -> T284\nT3 -> T278", fontsize=14, style = filled, fillcolor = lightgrey];
99 -> 256 [arrowhead = none , style=dashed];
256 -> 1[style=dashed];

257 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
100 -> 257 [arrowhead = none ];
257 -> 102;

258 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
102 -> 258 [arrowhead = none ];
258 -> 103;

259 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
102 -> 259 [arrowhead = none ];
259 -> 104;

260 [label="EVAL with clause\nless(0, s(X268)).\nand substitutionT297 -> 0,\nX268 -> T309,\nT301 -> s(T309),\nT302 -> T308,\nT307 -> T309", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 260 [arrowhead = none ];
260 -> 105;

261 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
103 -> 261 [arrowhead = none ];
261 -> 106;

262 [label="EVAL with clause\nless(s(X275), s(X276)) :- less(X275, X276).\nand substitutionX275 -> T316,\nT297 -> s(T316),\nX276 -> T318,\nT301 -> s(T318),\nT317 -> T318,\nT302 -> T319", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 262 [arrowhead = none ];
262 -> 107;

263 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
104 -> 263 [arrowhead = none ];
263 -> 108;

264 [label="INSTANCE with matching:\nT1 -> s(T309)\nT2 -> T308\nT3 -> T300", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 264 [arrowhead = none , style=dashed];
264 -> 1[style=dashed];

265 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
107 -> 265 [arrowhead = none ];
265 -> 109;

266 [label="SPLIT 2\nnew knowledge:\nT316 is ground\nreplacements:T318 -> T322,\nT319 -> T323,\nT1 -> T324,\nT2 -> T325", fontsize=14, style = filled, fillcolor = violet];
107 -> 266 [arrowhead = none ];
266 -> 110;

267 [label="INSTANCE with matching:\nT71 -> T316\nT74 -> T318", fontsize=14, style = filled, fillcolor = lightgrey];
109 -> 267 [arrowhead = none , style=dashed];
267 -> 33[style=dashed];

268 [label="INSTANCE with matching:\nT1 -> s(T322)\nT2 -> T323\nT3 -> T300", fontsize=14, style = filled, fillcolor = lightgrey];
110 -> 268 [arrowhead = none , style=dashed];
268 -> 1[style=dashed];

269 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
111 -> 269 [arrowhead = none ];
269 -> 113;

270 [label="EVAL with clause\ninsert(X334, tree(X335, X336, X337), tree(X335, X336, X338)) :- ','(less(X335, X334), insert(X334, X337, X338)).\nand substitutionT1 -> T391,\nX334 -> T391,\nX335 -> T387,\nX336 -> T388,\nX337 -> T392,\nT2 -> tree(T387, T388, T392),\nX338 -> T390,\nT3 -> tree(T387, T388, T390),\nT386 -> T391,\nT389 -> T392", fontsize=14, style = filled, fillcolor = lightblue];
112 -> 270 [arrowhead = none ];
270 -> 125;

271 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 271 [arrowhead = none ];
271 -> 126;

272 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 272 [arrowhead = none ];
272 -> 114;

273 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 273 [arrowhead = none ];
273 -> 115;

274 [label="EVAL with clause\nless(0, s(X297)).\nand substitutionT340 -> 0,\nX297 -> T346,\nT336 -> s(T346),\nT341 -> T347", fontsize=14, style = filled, fillcolor = lightblue];
114 -> 274 [arrowhead = none ];
274 -> 116;

275 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
114 -> 275 [arrowhead = none ];
275 -> 117;

276 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
115 -> 276 [arrowhead = none ];
276 -> 118;

277 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
115 -> 277 [arrowhead = none ];
277 -> 119;

278 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T347\nT3 -> T339", fontsize=14, style = filled, fillcolor = lightgrey];
116 -> 278 [arrowhead = none , style=dashed];
278 -> 1[style=dashed];

279 [label="EVAL with clause\nless(s(X308), s(X309)) :- less(X308, X309).\nand substitutionX308 -> T358,\nT340 -> s(T358),\nX309 -> T357,\nT336 -> s(T357),\nT356 -> T358,\nT341 -> T359", fontsize=14, style = filled, fillcolor = lightblue];
118 -> 279 [arrowhead = none ];
279 -> 120;

280 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
118 -> 280 [arrowhead = none ];
280 -> 121;

281 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
119 -> 281 [arrowhead = none ];
281 -> 122;

282 [label="INSTANCE with matching:\nT252 -> T358\nT251 -> T357\nT253 -> T359\nT233 -> T339\nT232 -> T338", fontsize=14, style = filled, fillcolor = lightgrey];
120 -> 282 [arrowhead = none , style=dashed];
282 -> 91[style=dashed];

283 [label="EVAL with clause\ninsert(X322, tree(X323, X324, X325), tree(X323, X324, X326)) :- ','(less(X323, X322), insert(X322, X325, X326)).\nand substitutionT1 -> T377,\nX322 -> T377,\nX323 -> T373,\nX324 -> T374,\nX325 -> T378,\nT2 -> tree(T373, T374, T378),\nT336 -> T373,\nT339 -> T374,\nT338 -> T376,\nX326 -> T376,\nT372 -> T377,\nT375 -> T378", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 283 [arrowhead = none ];
283 -> 123;

284 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
122 -> 284 [arrowhead = none ];
284 -> 124;

285 [label="INSTANCE with matching:\nT275 -> T373\nT279 -> T377\nT280 -> T378\nT278 -> T376\nT276 -> T374", fontsize=14, style = filled, fillcolor = lightgrey];
123 -> 285 [arrowhead = none , style=dashed];
285 -> 96[style=dashed];

286 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
125 -> 286 [arrowhead = none ];
286 -> 127;

287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
127 -> 287 [arrowhead = none ];
287 -> 128;

288 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
127 -> 288 [arrowhead = none ];
288 -> 129;

289 [label="EVAL with clause\nless(0, s(X343)).\nand substitutionT387 -> 0,\nX343 -> T399,\nT391 -> s(T399),\nT392 -> T398,\nT397 -> T399", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 289 [arrowhead = none ];
289 -> 130;

290 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
128 -> 290 [arrowhead = none ];
290 -> 131;

291 [label="EVAL with clause\nless(s(X350), s(X351)) :- less(X350, X351).\nand substitutionX350 -> T406,\nT387 -> s(T406),\nX351 -> T408,\nT391 -> s(T408),\nT407 -> T408,\nT392 -> T409", fontsize=14, style = filled, fillcolor = lightblue];
129 -> 291 [arrowhead = none ];
291 -> 132;

292 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 292 [arrowhead = none ];
292 -> 133;

293 [label="INSTANCE with matching:\nT1 -> s(T399)\nT2 -> T398\nT3 -> T390", fontsize=14, style = filled, fillcolor = lightgrey];
130 -> 293 [arrowhead = none , style=dashed];
293 -> 1[style=dashed];

294 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
132 -> 294 [arrowhead = none ];
294 -> 134;

295 [label="SPLIT 2\nnew knowledge:\nT406 is ground\nreplacements:T408 -> T412,\nT409 -> T413,\nT1 -> T414,\nT2 -> T415", fontsize=14, style = filled, fillcolor = violet];
132 -> 295 [arrowhead = none ];
295 -> 135;

296 [label="INSTANCE with matching:\nT71 -> T406\nT74 -> T408", fontsize=14, style = filled, fillcolor = lightgrey];
134 -> 296 [arrowhead = none , style=dashed];
296 -> 33[style=dashed];

297 [label="INSTANCE with matching:\nT1 -> s(T412)\nT2 -> T413\nT3 -> T390", fontsize=14, style = filled, fillcolor = lightgrey];
135 -> 297 [arrowhead = none , style=dashed];
297 -> 1[style=dashed];

}

(2) Obligation:

Clauses:

lessA(0, s(T50)).
lessA(s(T57), s(T56)) :- lessA(T57, T56).
lessB(0, s(T86)).
lessB(s(T91), s(T93)) :- lessB(T91, T93).
pC(T38, T37, T39) :- lessA(T38, T37).
pC(T42, T37, T43) :- ','(lessA(T42, T37), insertD(s(T42), T43, void)).
pE(T71, T74, T75) :- lessB(T71, T74).
pE(T71, T78, T79) :- ','(lessB(T71, T78), insertD(T78, T79, void)).
pF(T252, T251, T253, T233) :- lessA(T252, T251).
pF(T256, T251, T257, T233) :- ','(lessA(T256, T251), insertD(s(T256), T257, T233)).
pG(T275, T279, T280, T278) :- lessB(T275, T279).
pG(T275, T283, T284, T278) :- ','(lessB(T275, T283), insertD(T283, T284, T278)).
insertD(T5, void, tree(T5, void, void)).
insertD(T9, tree(T9, void, void), tree(T9, void, void)).
insertD(0, tree(s(T26), T27, void), tree(s(T26), void, void)) :- insertD(0, T27, void).
insertD(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) :- pC(T38, T37, T39).
insertD(T74, tree(T71, void, T75), tree(T71, void, void)) :- pE(T71, T74, T75).
insertD(s(T114), tree(0, void, T113), tree(0, void, void)) :- insertD(s(T114), T113, void).
insertD(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) :- lessB(T121, T123).
insertD(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) :- ','(lessB(T121, T127), insertD(s(T127), T128, void)).
insertD(0, tree(s(T149), T150, void), tree(s(T149), void, void)) :- insertD(0, T150, void).
insertD(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) :- pC(T161, T160, T162).
insertD(T177, tree(T174, void, T178), tree(T174, void, void)) :- pE(T174, T177, T178).
insertD(s(T197), tree(0, void, T196), tree(0, void, void)) :- insertD(s(T197), T196, void).
insertD(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) :- lessB(T204, T206).
insertD(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) :- ','(lessB(T204, T210), insertD(s(T210), T211, void)).
insertD(T221, tree(T221, T222, T223), tree(T221, T222, T223)).
insertD(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) :- insertD(0, T241, T233).
insertD(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) :- pF(T252, T251, T253, T233).
insertD(T279, tree(T275, T276, T280), tree(T275, T276, T278)) :- pG(T275, T279, T280, T278).
insertD(s(T309), tree(0, T298, T308), tree(0, T298, T300)) :- insertD(s(T309), T308, T300).
insertD(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) :- lessB(T316, T318).
insertD(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) :- ','(lessB(T316, T322), insertD(s(T322), T323, T300)).
insertD(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) :- insertD(0, T347, T339).
insertD(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) :- pF(T358, T357, T359, T339).
insertD(T377, tree(T373, T374, T378), tree(T373, T374, T376)) :- pG(T373, T377, T378, T376).
insertD(s(T399), tree(0, T388, T398), tree(0, T388, T390)) :- insertD(s(T399), T398, T390).
insertD(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) :- lessB(T406, T408).
insertD(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) :- ','(lessB(T406, T412), insertD(s(T412), T413, T390)).

Query: insertD(a,a,g)

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
insertD_in: (f,f,b) (b,f,b)
pC_in: (b,b,f) (f,b,f)
lessA_in: (b,b) (f,b)
pE_in: (b,b,f) (b,f,f)
lessB_in: (b,b) (b,f)
pF_in: (b,b,f,b) (f,b,f,b)
pG_in: (b,b,f,b) (b,f,f,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)

(5) DependencyPairsProof (EQUIVALENT transformation)

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

INSERTD_IN_AAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_AAG(T26, T27, insertD_in_gag(0, T27, void))
INSERTD_IN_AAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → INSERTD_IN_GAG(0, T27, void)
INSERTD_IN_GAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_GAG(T26, T27, insertD_in_gag(0, T27, void))
INSERTD_IN_GAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → INSERTD_IN_GAG(0, T27, void)
INSERTD_IN_GAG(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_GAG(T38, T37, T39, pC_in_gga(T38, T37, T39))
INSERTD_IN_GAG(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → PC_IN_GGA(T38, T37, T39)
PC_IN_GGA(T38, T37, T39) → U3_GGA(T38, T37, T39, lessA_in_gg(T38, T37))
PC_IN_GGA(T38, T37, T39) → LESSA_IN_GG(T38, T37)
LESSA_IN_GG(s(T57), s(T56)) → U1_GG(T57, T56, lessA_in_gg(T57, T56))
LESSA_IN_GG(s(T57), s(T56)) → LESSA_IN_GG(T57, T56)
PC_IN_GGA(T42, T37, T43) → U4_GGA(T42, T37, T43, lessA_in_gg(T42, T37))
U4_GGA(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_GGA(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U4_GGA(T42, T37, T43, lessA_out_gg(T42, T37)) → INSERTD_IN_GAG(s(T42), T43, void)
INSERTD_IN_GAG(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_GAG(T74, T71, T75, pE_in_gga(T71, T74, T75))
INSERTD_IN_GAG(T74, tree(T71, void, T75), tree(T71, void, void)) → PE_IN_GGA(T71, T74, T75)
PE_IN_GGA(T71, T74, T75) → U6_GGA(T71, T74, T75, lessB_in_gg(T71, T74))
PE_IN_GGA(T71, T74, T75) → LESSB_IN_GG(T71, T74)
LESSB_IN_GG(s(T91), s(T93)) → U2_GG(T91, T93, lessB_in_gg(T91, T93))
LESSB_IN_GG(s(T91), s(T93)) → LESSB_IN_GG(T91, T93)
PE_IN_GGA(T71, T78, T79) → U7_GGA(T71, T78, T79, lessB_in_gg(T71, T78))
U7_GGA(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_GGA(T71, T78, T79, insertD_in_gag(T78, T79, void))
U7_GGA(T71, T78, T79, lessB_out_gg(T71, T78)) → INSERTD_IN_GAG(T78, T79, void)
INSERTD_IN_GAG(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_GAG(T114, T113, insertD_in_gag(s(T114), T113, void))
INSERTD_IN_GAG(s(T114), tree(0, void, T113), tree(0, void, void)) → INSERTD_IN_GAG(s(T114), T113, void)
INSERTD_IN_GAG(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_GAG(T123, T121, T124, lessB_in_gg(T121, T123))
INSERTD_IN_GAG(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → LESSB_IN_GG(T121, T123)
INSERTD_IN_GAG(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_GAG(T127, T121, T128, lessB_in_gg(T121, T127))
U20_GAG(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_GAG(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
U20_GAG(T127, T121, T128, lessB_out_gg(T121, T127)) → INSERTD_IN_GAG(s(T127), T128, void)
INSERTD_IN_GAG(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_GAG(T149, T150, insertD_in_gag(0, T150, void))
INSERTD_IN_GAG(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_GAG(T161, T160, T162, pC_in_gga(T161, T160, T162))
INSERTD_IN_GAG(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_GAG(T177, T174, T178, pE_in_gga(T174, T177, T178))
INSERTD_IN_GAG(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_GAG(T197, T196, insertD_in_gag(s(T197), T196, void))
INSERTD_IN_GAG(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_GAG(T206, T204, T207, lessB_in_gg(T204, T206))
INSERTD_IN_GAG(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_GAG(T210, T204, T211, lessB_in_gg(T204, T210))
U27_GAG(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_GAG(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
U27_GAG(T210, T204, T211, lessB_out_gg(T204, T210)) → INSERTD_IN_GAG(s(T210), T211, void)
INSERTD_IN_GAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_GAG(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
INSERTD_IN_GAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → INSERTD_IN_GAG(0, T241, T233)
INSERTD_IN_GAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_GAG(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
INSERTD_IN_GAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → PF_IN_GGAG(T252, T251, T253, T233)
PF_IN_GGAG(T252, T251, T253, T233) → U9_GGAG(T252, T251, T253, T233, lessA_in_gg(T252, T251))
PF_IN_GGAG(T252, T251, T253, T233) → LESSA_IN_GG(T252, T251)
PF_IN_GGAG(T256, T251, T257, T233) → U10_GGAG(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_GGAG(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_GGAG(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U10_GGAG(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → INSERTD_IN_GAG(s(T256), T257, T233)
INSERTD_IN_GAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_GAG(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
INSERTD_IN_GAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → PG_IN_GGAG(T275, T279, T280, T278)
PG_IN_GGAG(T275, T279, T280, T278) → U12_GGAG(T275, T279, T280, T278, lessB_in_gg(T275, T279))
PG_IN_GGAG(T275, T279, T280, T278) → LESSB_IN_GG(T275, T279)
PG_IN_GGAG(T275, T283, T284, T278) → U13_GGAG(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_GGAG(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_GGAG(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
U13_GGAG(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → INSERTD_IN_GAG(T283, T284, T278)
INSERTD_IN_GAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_GAG(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
INSERTD_IN_GAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → INSERTD_IN_GAG(s(T309), T308, T300)
INSERTD_IN_GAG(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_GAG(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
INSERTD_IN_GAG(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → LESSB_IN_GG(T316, T318)
INSERTD_IN_GAG(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_GAG(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_GAG(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_GAG(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
U34_GAG(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → INSERTD_IN_GAG(s(T322), T323, T300)
INSERTD_IN_GAG(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_GAG(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
INSERTD_IN_GAG(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_GAG(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
INSERTD_IN_GAG(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_GAG(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
INSERTD_IN_GAG(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_GAG(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
INSERTD_IN_GAG(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_GAG(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
INSERTD_IN_GAG(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_GAG(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_GAG(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_GAG(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U41_GAG(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → INSERTD_IN_GAG(s(T412), T413, T390)
INSERTD_IN_AAG(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_AAG(T38, T37, T39, pC_in_aga(T38, T37, T39))
INSERTD_IN_AAG(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → PC_IN_AGA(T38, T37, T39)
PC_IN_AGA(T38, T37, T39) → U3_AGA(T38, T37, T39, lessA_in_ag(T38, T37))
PC_IN_AGA(T38, T37, T39) → LESSA_IN_AG(T38, T37)
LESSA_IN_AG(s(T57), s(T56)) → U1_AG(T57, T56, lessA_in_ag(T57, T56))
LESSA_IN_AG(s(T57), s(T56)) → LESSA_IN_AG(T57, T56)
PC_IN_AGA(T42, T37, T43) → U4_AGA(T42, T37, T43, lessA_in_ag(T42, T37))
U4_AGA(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_AGA(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U4_AGA(T42, T37, T43, lessA_out_ag(T42, T37)) → INSERTD_IN_GAG(s(T42), T43, void)
INSERTD_IN_AAG(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_AAG(T74, T71, T75, pE_in_gaa(T71, T74, T75))
INSERTD_IN_AAG(T74, tree(T71, void, T75), tree(T71, void, void)) → PE_IN_GAA(T71, T74, T75)
PE_IN_GAA(T71, T74, T75) → U6_GAA(T71, T74, T75, lessB_in_ga(T71, T74))
PE_IN_GAA(T71, T74, T75) → LESSB_IN_GA(T71, T74)
LESSB_IN_GA(s(T91), s(T93)) → U2_GA(T91, T93, lessB_in_ga(T91, T93))
LESSB_IN_GA(s(T91), s(T93)) → LESSB_IN_GA(T91, T93)
PE_IN_GAA(T71, T78, T79) → U7_GAA(T71, T78, T79, lessB_in_ga(T71, T78))
U7_GAA(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_GAA(T71, T78, T79, insertD_in_aag(T78, T79, void))
U7_GAA(T71, T78, T79, lessB_out_ga(T71, T78)) → INSERTD_IN_AAG(T78, T79, void)
INSERTD_IN_AAG(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_AAG(T114, T113, insertD_in_aag(s(T114), T113, void))
INSERTD_IN_AAG(s(T114), tree(0, void, T113), tree(0, void, void)) → INSERTD_IN_AAG(s(T114), T113, void)
INSERTD_IN_AAG(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_AAG(T123, T121, T124, lessB_in_ga(T121, T123))
INSERTD_IN_AAG(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → LESSB_IN_GA(T121, T123)
INSERTD_IN_AAG(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_AAG(T127, T121, T128, lessB_in_ga(T121, T127))
U20_AAG(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_AAG(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
U20_AAG(T127, T121, T128, lessB_out_ga(T121, T127)) → INSERTD_IN_AAG(s(T127), T128, void)
INSERTD_IN_AAG(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_AAG(T149, T150, insertD_in_gag(0, T150, void))
INSERTD_IN_AAG(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_AAG(T161, T160, T162, pC_in_aga(T161, T160, T162))
INSERTD_IN_AAG(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_AAG(T177, T174, T178, pE_in_gaa(T174, T177, T178))
INSERTD_IN_AAG(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_AAG(T197, T196, insertD_in_aag(s(T197), T196, void))
INSERTD_IN_AAG(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_AAG(T206, T204, T207, lessB_in_ga(T204, T206))
INSERTD_IN_AAG(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_AAG(T210, T204, T211, lessB_in_ga(T204, T210))
U27_AAG(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_AAG(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
U27_AAG(T210, T204, T211, lessB_out_ga(T204, T210)) → INSERTD_IN_AAG(s(T210), T211, void)
INSERTD_IN_AAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_AAG(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
INSERTD_IN_AAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → INSERTD_IN_GAG(0, T241, T233)
INSERTD_IN_AAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_AAG(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
INSERTD_IN_AAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → PF_IN_AGAG(T252, T251, T253, T233)
PF_IN_AGAG(T252, T251, T253, T233) → U9_AGAG(T252, T251, T253, T233, lessA_in_ag(T252, T251))
PF_IN_AGAG(T252, T251, T253, T233) → LESSA_IN_AG(T252, T251)
PF_IN_AGAG(T256, T251, T257, T233) → U10_AGAG(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_AGAG(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_AGAG(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U10_AGAG(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → INSERTD_IN_GAG(s(T256), T257, T233)
INSERTD_IN_AAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_AAG(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
INSERTD_IN_AAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → PG_IN_GAAG(T275, T279, T280, T278)
PG_IN_GAAG(T275, T279, T280, T278) → U12_GAAG(T275, T279, T280, T278, lessB_in_ga(T275, T279))
PG_IN_GAAG(T275, T279, T280, T278) → LESSB_IN_GA(T275, T279)
PG_IN_GAAG(T275, T283, T284, T278) → U13_GAAG(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_GAAG(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_GAAG(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
U13_GAAG(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → INSERTD_IN_AAG(T283, T284, T278)
INSERTD_IN_AAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_AAG(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
INSERTD_IN_AAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → INSERTD_IN_AAG(s(T309), T308, T300)
INSERTD_IN_AAG(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_AAG(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
INSERTD_IN_AAG(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → LESSB_IN_GA(T316, T318)
INSERTD_IN_AAG(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_AAG(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_AAG(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_AAG(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
U34_AAG(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → INSERTD_IN_AAG(s(T322), T323, T300)
INSERTD_IN_AAG(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_AAG(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
INSERTD_IN_AAG(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_AAG(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
INSERTD_IN_AAG(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_AAG(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
INSERTD_IN_AAG(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_AAG(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
INSERTD_IN_AAG(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_AAG(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
INSERTD_IN_AAG(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_AAG(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_AAG(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_AAG(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U41_AAG(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → INSERTD_IN_AAG(s(T412), T413, T390)

The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)
INSERTD_IN_AAG(x1, x2, x3)  =  INSERTD_IN_AAG(x3)
U15_AAG(x1, x2, x3)  =  U15_AAG(x3)
INSERTD_IN_GAG(x1, x2, x3)  =  INSERTD_IN_GAG(x1, x3)
U15_GAG(x1, x2, x3)  =  U15_GAG(x3)
U16_GAG(x1, x2, x3, x4)  =  U16_GAG(x4)
PC_IN_GGA(x1, x2, x3)  =  PC_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4)  =  U3_GGA(x4)
LESSA_IN_GG(x1, x2)  =  LESSA_IN_GG(x1, x2)
U1_GG(x1, x2, x3)  =  U1_GG(x3)
U4_GGA(x1, x2, x3, x4)  =  U4_GGA(x1, x4)
U5_GGA(x1, x2, x3, x4)  =  U5_GGA(x4)
U17_GAG(x1, x2, x3, x4)  =  U17_GAG(x4)
PE_IN_GGA(x1, x2, x3)  =  PE_IN_GGA(x1, x2)
U6_GGA(x1, x2, x3, x4)  =  U6_GGA(x4)
LESSB_IN_GG(x1, x2)  =  LESSB_IN_GG(x1, x2)
U2_GG(x1, x2, x3)  =  U2_GG(x3)
U7_GGA(x1, x2, x3, x4)  =  U7_GGA(x2, x4)
U8_GGA(x1, x2, x3, x4)  =  U8_GGA(x4)
U18_GAG(x1, x2, x3)  =  U18_GAG(x3)
U19_GAG(x1, x2, x3, x4)  =  U19_GAG(x4)
U20_GAG(x1, x2, x3, x4)  =  U20_GAG(x1, x4)
U21_GAG(x1, x2, x3, x4)  =  U21_GAG(x4)
U22_GAG(x1, x2, x3)  =  U22_GAG(x3)
U23_GAG(x1, x2, x3, x4)  =  U23_GAG(x4)
U24_GAG(x1, x2, x3, x4)  =  U24_GAG(x4)
U25_GAG(x1, x2, x3)  =  U25_GAG(x3)
U26_GAG(x1, x2, x3, x4)  =  U26_GAG(x4)
U27_GAG(x1, x2, x3, x4)  =  U27_GAG(x1, x4)
U28_GAG(x1, x2, x3, x4)  =  U28_GAG(x4)
U29_GAG(x1, x2, x3, x4, x5)  =  U29_GAG(x5)
U30_GAG(x1, x2, x3, x4, x5, x6)  =  U30_GAG(x6)
PF_IN_GGAG(x1, x2, x3, x4)  =  PF_IN_GGAG(x1, x2, x4)
U9_GGAG(x1, x2, x3, x4, x5)  =  U9_GGAG(x5)
U10_GGAG(x1, x2, x3, x4, x5)  =  U10_GGAG(x1, x4, x5)
U11_GGAG(x1, x2, x3, x4, x5)  =  U11_GGAG(x5)
U31_GAG(x1, x2, x3, x4, x5, x6)  =  U31_GAG(x6)
PG_IN_GGAG(x1, x2, x3, x4)  =  PG_IN_GGAG(x1, x2, x4)
U12_GGAG(x1, x2, x3, x4, x5)  =  U12_GGAG(x5)
U13_GGAG(x1, x2, x3, x4, x5)  =  U13_GGAG(x2, x4, x5)
U14_GGAG(x1, x2, x3, x4, x5)  =  U14_GGAG(x5)
U32_GAG(x1, x2, x3, x4, x5)  =  U32_GAG(x5)
U33_GAG(x1, x2, x3, x4, x5, x6)  =  U33_GAG(x6)
U34_GAG(x1, x2, x3, x4, x5, x6)  =  U34_GAG(x1, x5, x6)
U35_GAG(x1, x2, x3, x4, x5, x6)  =  U35_GAG(x6)
U36_GAG(x1, x2, x3, x4, x5)  =  U36_GAG(x5)
U37_GAG(x1, x2, x3, x4, x5, x6)  =  U37_GAG(x6)
U38_GAG(x1, x2, x3, x4, x5, x6)  =  U38_GAG(x6)
U39_GAG(x1, x2, x3, x4, x5)  =  U39_GAG(x5)
U40_GAG(x1, x2, x3, x4, x5, x6)  =  U40_GAG(x6)
U41_GAG(x1, x2, x3, x4, x5, x6)  =  U41_GAG(x1, x5, x6)
U42_GAG(x1, x2, x3, x4, x5, x6)  =  U42_GAG(x6)
U16_AAG(x1, x2, x3, x4)  =  U16_AAG(x4)
PC_IN_AGA(x1, x2, x3)  =  PC_IN_AGA(x2)
U3_AGA(x1, x2, x3, x4)  =  U3_AGA(x4)
LESSA_IN_AG(x1, x2)  =  LESSA_IN_AG(x2)
U1_AG(x1, x2, x3)  =  U1_AG(x3)
U4_AGA(x1, x2, x3, x4)  =  U4_AGA(x4)
U5_AGA(x1, x2, x3, x4)  =  U5_AGA(x1, x4)
U17_AAG(x1, x2, x3, x4)  =  U17_AAG(x4)
PE_IN_GAA(x1, x2, x3)  =  PE_IN_GAA(x1)
U6_GAA(x1, x2, x3, x4)  =  U6_GAA(x4)
LESSB_IN_GA(x1, x2)  =  LESSB_IN_GA(x1)
U2_GA(x1, x2, x3)  =  U2_GA(x3)
U7_GAA(x1, x2, x3, x4)  =  U7_GAA(x4)
U8_GAA(x1, x2, x3, x4)  =  U8_GAA(x4)
U18_AAG(x1, x2, x3)  =  U18_AAG(x3)
U19_AAG(x1, x2, x3, x4)  =  U19_AAG(x4)
U20_AAG(x1, x2, x3, x4)  =  U20_AAG(x4)
U21_AAG(x1, x2, x3, x4)  =  U21_AAG(x4)
U22_AAG(x1, x2, x3)  =  U22_AAG(x3)
U23_AAG(x1, x2, x3, x4)  =  U23_AAG(x4)
U24_AAG(x1, x2, x3, x4)  =  U24_AAG(x4)
U25_AAG(x1, x2, x3)  =  U25_AAG(x3)
U26_AAG(x1, x2, x3, x4)  =  U26_AAG(x4)
U27_AAG(x1, x2, x3, x4)  =  U27_AAG(x4)
U28_AAG(x1, x2, x3, x4)  =  U28_AAG(x4)
U29_AAG(x1, x2, x3, x4, x5)  =  U29_AAG(x5)
U30_AAG(x1, x2, x3, x4, x5, x6)  =  U30_AAG(x6)
PF_IN_AGAG(x1, x2, x3, x4)  =  PF_IN_AGAG(x2, x4)
U9_AGAG(x1, x2, x3, x4, x5)  =  U9_AGAG(x5)
U10_AGAG(x1, x2, x3, x4, x5)  =  U10_AGAG(x4, x5)
U11_AGAG(x1, x2, x3, x4, x5)  =  U11_AGAG(x1, x5)
U31_AAG(x1, x2, x3, x4, x5, x6)  =  U31_AAG(x6)
PG_IN_GAAG(x1, x2, x3, x4)  =  PG_IN_GAAG(x1, x4)
U12_GAAG(x1, x2, x3, x4, x5)  =  U12_GAAG(x5)
U13_GAAG(x1, x2, x3, x4, x5)  =  U13_GAAG(x4, x5)
U14_GAAG(x1, x2, x3, x4, x5)  =  U14_GAAG(x5)
U32_AAG(x1, x2, x3, x4, x5)  =  U32_AAG(x5)
U33_AAG(x1, x2, x3, x4, x5, x6)  =  U33_AAG(x6)
U34_AAG(x1, x2, x3, x4, x5, x6)  =  U34_AAG(x5, x6)
U35_AAG(x1, x2, x3, x4, x5, x6)  =  U35_AAG(x6)
U36_AAG(x1, x2, x3, x4, x5)  =  U36_AAG(x5)
U37_AAG(x1, x2, x3, x4, x5, x6)  =  U37_AAG(x6)
U38_AAG(x1, x2, x3, x4, x5, x6)  =  U38_AAG(x6)
U39_AAG(x1, x2, x3, x4, x5)  =  U39_AAG(x5)
U40_AAG(x1, x2, x3, x4, x5, x6)  =  U40_AAG(x6)
U41_AAG(x1, x2, x3, x4, x5, x6)  =  U41_AAG(x5, x6)
U42_AAG(x1, x2, x3, x4, x5, x6)  =  U42_AAG(x6)

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

(6) Obligation:

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

INSERTD_IN_AAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_AAG(T26, T27, insertD_in_gag(0, T27, void))
INSERTD_IN_AAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → INSERTD_IN_GAG(0, T27, void)
INSERTD_IN_GAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_GAG(T26, T27, insertD_in_gag(0, T27, void))
INSERTD_IN_GAG(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → INSERTD_IN_GAG(0, T27, void)
INSERTD_IN_GAG(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_GAG(T38, T37, T39, pC_in_gga(T38, T37, T39))
INSERTD_IN_GAG(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → PC_IN_GGA(T38, T37, T39)
PC_IN_GGA(T38, T37, T39) → U3_GGA(T38, T37, T39, lessA_in_gg(T38, T37))
PC_IN_GGA(T38, T37, T39) → LESSA_IN_GG(T38, T37)
LESSA_IN_GG(s(T57), s(T56)) → U1_GG(T57, T56, lessA_in_gg(T57, T56))
LESSA_IN_GG(s(T57), s(T56)) → LESSA_IN_GG(T57, T56)
PC_IN_GGA(T42, T37, T43) → U4_GGA(T42, T37, T43, lessA_in_gg(T42, T37))
U4_GGA(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_GGA(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U4_GGA(T42, T37, T43, lessA_out_gg(T42, T37)) → INSERTD_IN_GAG(s(T42), T43, void)
INSERTD_IN_GAG(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_GAG(T74, T71, T75, pE_in_gga(T71, T74, T75))
INSERTD_IN_GAG(T74, tree(T71, void, T75), tree(T71, void, void)) → PE_IN_GGA(T71, T74, T75)
PE_IN_GGA(T71, T74, T75) → U6_GGA(T71, T74, T75, lessB_in_gg(T71, T74))
PE_IN_GGA(T71, T74, T75) → LESSB_IN_GG(T71, T74)
LESSB_IN_GG(s(T91), s(T93)) → U2_GG(T91, T93, lessB_in_gg(T91, T93))
LESSB_IN_GG(s(T91), s(T93)) → LESSB_IN_GG(T91, T93)
PE_IN_GGA(T71, T78, T79) → U7_GGA(T71, T78, T79, lessB_in_gg(T71, T78))
U7_GGA(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_GGA(T71, T78, T79, insertD_in_gag(T78, T79, void))
U7_GGA(T71, T78, T79, lessB_out_gg(T71, T78)) → INSERTD_IN_GAG(T78, T79, void)
INSERTD_IN_GAG(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_GAG(T114, T113, insertD_in_gag(s(T114), T113, void))
INSERTD_IN_GAG(s(T114), tree(0, void, T113), tree(0, void, void)) → INSERTD_IN_GAG(s(T114), T113, void)
INSERTD_IN_GAG(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_GAG(T123, T121, T124, lessB_in_gg(T121, T123))
INSERTD_IN_GAG(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → LESSB_IN_GG(T121, T123)
INSERTD_IN_GAG(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_GAG(T127, T121, T128, lessB_in_gg(T121, T127))
U20_GAG(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_GAG(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
U20_GAG(T127, T121, T128, lessB_out_gg(T121, T127)) → INSERTD_IN_GAG(s(T127), T128, void)
INSERTD_IN_GAG(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_GAG(T149, T150, insertD_in_gag(0, T150, void))
INSERTD_IN_GAG(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_GAG(T161, T160, T162, pC_in_gga(T161, T160, T162))
INSERTD_IN_GAG(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_GAG(T177, T174, T178, pE_in_gga(T174, T177, T178))
INSERTD_IN_GAG(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_GAG(T197, T196, insertD_in_gag(s(T197), T196, void))
INSERTD_IN_GAG(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_GAG(T206, T204, T207, lessB_in_gg(T204, T206))
INSERTD_IN_GAG(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_GAG(T210, T204, T211, lessB_in_gg(T204, T210))
U27_GAG(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_GAG(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
U27_GAG(T210, T204, T211, lessB_out_gg(T204, T210)) → INSERTD_IN_GAG(s(T210), T211, void)
INSERTD_IN_GAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_GAG(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
INSERTD_IN_GAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → INSERTD_IN_GAG(0, T241, T233)
INSERTD_IN_GAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_GAG(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
INSERTD_IN_GAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → PF_IN_GGAG(T252, T251, T253, T233)
PF_IN_GGAG(T252, T251, T253, T233) → U9_GGAG(T252, T251, T253, T233, lessA_in_gg(T252, T251))
PF_IN_GGAG(T252, T251, T253, T233) → LESSA_IN_GG(T252, T251)
PF_IN_GGAG(T256, T251, T257, T233) → U10_GGAG(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_GGAG(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_GGAG(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U10_GGAG(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → INSERTD_IN_GAG(s(T256), T257, T233)
INSERTD_IN_GAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_GAG(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
INSERTD_IN_GAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → PG_IN_GGAG(T275, T279, T280, T278)
PG_IN_GGAG(T275, T279, T280, T278) → U12_GGAG(T275, T279, T280, T278, lessB_in_gg(T275, T279))
PG_IN_GGAG(T275, T279, T280, T278) → LESSB_IN_GG(T275, T279)
PG_IN_GGAG(T275, T283, T284, T278) → U13_GGAG(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_GGAG(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_GGAG(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
U13_GGAG(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → INSERTD_IN_GAG(T283, T284, T278)
INSERTD_IN_GAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_GAG(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
INSERTD_IN_GAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → INSERTD_IN_GAG(s(T309), T308, T300)
INSERTD_IN_GAG(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_GAG(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
INSERTD_IN_GAG(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → LESSB_IN_GG(T316, T318)
INSERTD_IN_GAG(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_GAG(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_GAG(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_GAG(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
U34_GAG(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → INSERTD_IN_GAG(s(T322), T323, T300)
INSERTD_IN_GAG(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_GAG(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
INSERTD_IN_GAG(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_GAG(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
INSERTD_IN_GAG(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_GAG(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
INSERTD_IN_GAG(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_GAG(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
INSERTD_IN_GAG(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_GAG(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
INSERTD_IN_GAG(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_GAG(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_GAG(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_GAG(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U41_GAG(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → INSERTD_IN_GAG(s(T412), T413, T390)
INSERTD_IN_AAG(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_AAG(T38, T37, T39, pC_in_aga(T38, T37, T39))
INSERTD_IN_AAG(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → PC_IN_AGA(T38, T37, T39)
PC_IN_AGA(T38, T37, T39) → U3_AGA(T38, T37, T39, lessA_in_ag(T38, T37))
PC_IN_AGA(T38, T37, T39) → LESSA_IN_AG(T38, T37)
LESSA_IN_AG(s(T57), s(T56)) → U1_AG(T57, T56, lessA_in_ag(T57, T56))
LESSA_IN_AG(s(T57), s(T56)) → LESSA_IN_AG(T57, T56)
PC_IN_AGA(T42, T37, T43) → U4_AGA(T42, T37, T43, lessA_in_ag(T42, T37))
U4_AGA(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_AGA(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U4_AGA(T42, T37, T43, lessA_out_ag(T42, T37)) → INSERTD_IN_GAG(s(T42), T43, void)
INSERTD_IN_AAG(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_AAG(T74, T71, T75, pE_in_gaa(T71, T74, T75))
INSERTD_IN_AAG(T74, tree(T71, void, T75), tree(T71, void, void)) → PE_IN_GAA(T71, T74, T75)
PE_IN_GAA(T71, T74, T75) → U6_GAA(T71, T74, T75, lessB_in_ga(T71, T74))
PE_IN_GAA(T71, T74, T75) → LESSB_IN_GA(T71, T74)
LESSB_IN_GA(s(T91), s(T93)) → U2_GA(T91, T93, lessB_in_ga(T91, T93))
LESSB_IN_GA(s(T91), s(T93)) → LESSB_IN_GA(T91, T93)
PE_IN_GAA(T71, T78, T79) → U7_GAA(T71, T78, T79, lessB_in_ga(T71, T78))
U7_GAA(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_GAA(T71, T78, T79, insertD_in_aag(T78, T79, void))
U7_GAA(T71, T78, T79, lessB_out_ga(T71, T78)) → INSERTD_IN_AAG(T78, T79, void)
INSERTD_IN_AAG(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_AAG(T114, T113, insertD_in_aag(s(T114), T113, void))
INSERTD_IN_AAG(s(T114), tree(0, void, T113), tree(0, void, void)) → INSERTD_IN_AAG(s(T114), T113, void)
INSERTD_IN_AAG(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_AAG(T123, T121, T124, lessB_in_ga(T121, T123))
INSERTD_IN_AAG(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → LESSB_IN_GA(T121, T123)
INSERTD_IN_AAG(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_AAG(T127, T121, T128, lessB_in_ga(T121, T127))
U20_AAG(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_AAG(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
U20_AAG(T127, T121, T128, lessB_out_ga(T121, T127)) → INSERTD_IN_AAG(s(T127), T128, void)
INSERTD_IN_AAG(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_AAG(T149, T150, insertD_in_gag(0, T150, void))
INSERTD_IN_AAG(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_AAG(T161, T160, T162, pC_in_aga(T161, T160, T162))
INSERTD_IN_AAG(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_AAG(T177, T174, T178, pE_in_gaa(T174, T177, T178))
INSERTD_IN_AAG(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_AAG(T197, T196, insertD_in_aag(s(T197), T196, void))
INSERTD_IN_AAG(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_AAG(T206, T204, T207, lessB_in_ga(T204, T206))
INSERTD_IN_AAG(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_AAG(T210, T204, T211, lessB_in_ga(T204, T210))
U27_AAG(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_AAG(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
U27_AAG(T210, T204, T211, lessB_out_ga(T204, T210)) → INSERTD_IN_AAG(s(T210), T211, void)
INSERTD_IN_AAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_AAG(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
INSERTD_IN_AAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → INSERTD_IN_GAG(0, T241, T233)
INSERTD_IN_AAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_AAG(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
INSERTD_IN_AAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → PF_IN_AGAG(T252, T251, T253, T233)
PF_IN_AGAG(T252, T251, T253, T233) → U9_AGAG(T252, T251, T253, T233, lessA_in_ag(T252, T251))
PF_IN_AGAG(T252, T251, T253, T233) → LESSA_IN_AG(T252, T251)
PF_IN_AGAG(T256, T251, T257, T233) → U10_AGAG(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_AGAG(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_AGAG(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U10_AGAG(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → INSERTD_IN_GAG(s(T256), T257, T233)
INSERTD_IN_AAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_AAG(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
INSERTD_IN_AAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → PG_IN_GAAG(T275, T279, T280, T278)
PG_IN_GAAG(T275, T279, T280, T278) → U12_GAAG(T275, T279, T280, T278, lessB_in_ga(T275, T279))
PG_IN_GAAG(T275, T279, T280, T278) → LESSB_IN_GA(T275, T279)
PG_IN_GAAG(T275, T283, T284, T278) → U13_GAAG(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_GAAG(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_GAAG(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
U13_GAAG(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → INSERTD_IN_AAG(T283, T284, T278)
INSERTD_IN_AAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_AAG(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
INSERTD_IN_AAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → INSERTD_IN_AAG(s(T309), T308, T300)
INSERTD_IN_AAG(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_AAG(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
INSERTD_IN_AAG(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → LESSB_IN_GA(T316, T318)
INSERTD_IN_AAG(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_AAG(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_AAG(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_AAG(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
U34_AAG(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → INSERTD_IN_AAG(s(T322), T323, T300)
INSERTD_IN_AAG(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_AAG(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
INSERTD_IN_AAG(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_AAG(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
INSERTD_IN_AAG(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_AAG(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
INSERTD_IN_AAG(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_AAG(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
INSERTD_IN_AAG(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_AAG(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
INSERTD_IN_AAG(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_AAG(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_AAG(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_AAG(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U41_AAG(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → INSERTD_IN_AAG(s(T412), T413, T390)

The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)
INSERTD_IN_AAG(x1, x2, x3)  =  INSERTD_IN_AAG(x3)
U15_AAG(x1, x2, x3)  =  U15_AAG(x3)
INSERTD_IN_GAG(x1, x2, x3)  =  INSERTD_IN_GAG(x1, x3)
U15_GAG(x1, x2, x3)  =  U15_GAG(x3)
U16_GAG(x1, x2, x3, x4)  =  U16_GAG(x4)
PC_IN_GGA(x1, x2, x3)  =  PC_IN_GGA(x1, x2)
U3_GGA(x1, x2, x3, x4)  =  U3_GGA(x4)
LESSA_IN_GG(x1, x2)  =  LESSA_IN_GG(x1, x2)
U1_GG(x1, x2, x3)  =  U1_GG(x3)
U4_GGA(x1, x2, x3, x4)  =  U4_GGA(x1, x4)
U5_GGA(x1, x2, x3, x4)  =  U5_GGA(x4)
U17_GAG(x1, x2, x3, x4)  =  U17_GAG(x4)
PE_IN_GGA(x1, x2, x3)  =  PE_IN_GGA(x1, x2)
U6_GGA(x1, x2, x3, x4)  =  U6_GGA(x4)
LESSB_IN_GG(x1, x2)  =  LESSB_IN_GG(x1, x2)
U2_GG(x1, x2, x3)  =  U2_GG(x3)
U7_GGA(x1, x2, x3, x4)  =  U7_GGA(x2, x4)
U8_GGA(x1, x2, x3, x4)  =  U8_GGA(x4)
U18_GAG(x1, x2, x3)  =  U18_GAG(x3)
U19_GAG(x1, x2, x3, x4)  =  U19_GAG(x4)
U20_GAG(x1, x2, x3, x4)  =  U20_GAG(x1, x4)
U21_GAG(x1, x2, x3, x4)  =  U21_GAG(x4)
U22_GAG(x1, x2, x3)  =  U22_GAG(x3)
U23_GAG(x1, x2, x3, x4)  =  U23_GAG(x4)
U24_GAG(x1, x2, x3, x4)  =  U24_GAG(x4)
U25_GAG(x1, x2, x3)  =  U25_GAG(x3)
U26_GAG(x1, x2, x3, x4)  =  U26_GAG(x4)
U27_GAG(x1, x2, x3, x4)  =  U27_GAG(x1, x4)
U28_GAG(x1, x2, x3, x4)  =  U28_GAG(x4)
U29_GAG(x1, x2, x3, x4, x5)  =  U29_GAG(x5)
U30_GAG(x1, x2, x3, x4, x5, x6)  =  U30_GAG(x6)
PF_IN_GGAG(x1, x2, x3, x4)  =  PF_IN_GGAG(x1, x2, x4)
U9_GGAG(x1, x2, x3, x4, x5)  =  U9_GGAG(x5)
U10_GGAG(x1, x2, x3, x4, x5)  =  U10_GGAG(x1, x4, x5)
U11_GGAG(x1, x2, x3, x4, x5)  =  U11_GGAG(x5)
U31_GAG(x1, x2, x3, x4, x5, x6)  =  U31_GAG(x6)
PG_IN_GGAG(x1, x2, x3, x4)  =  PG_IN_GGAG(x1, x2, x4)
U12_GGAG(x1, x2, x3, x4, x5)  =  U12_GGAG(x5)
U13_GGAG(x1, x2, x3, x4, x5)  =  U13_GGAG(x2, x4, x5)
U14_GGAG(x1, x2, x3, x4, x5)  =  U14_GGAG(x5)
U32_GAG(x1, x2, x3, x4, x5)  =  U32_GAG(x5)
U33_GAG(x1, x2, x3, x4, x5, x6)  =  U33_GAG(x6)
U34_GAG(x1, x2, x3, x4, x5, x6)  =  U34_GAG(x1, x5, x6)
U35_GAG(x1, x2, x3, x4, x5, x6)  =  U35_GAG(x6)
U36_GAG(x1, x2, x3, x4, x5)  =  U36_GAG(x5)
U37_GAG(x1, x2, x3, x4, x5, x6)  =  U37_GAG(x6)
U38_GAG(x1, x2, x3, x4, x5, x6)  =  U38_GAG(x6)
U39_GAG(x1, x2, x3, x4, x5)  =  U39_GAG(x5)
U40_GAG(x1, x2, x3, x4, x5, x6)  =  U40_GAG(x6)
U41_GAG(x1, x2, x3, x4, x5, x6)  =  U41_GAG(x1, x5, x6)
U42_GAG(x1, x2, x3, x4, x5, x6)  =  U42_GAG(x6)
U16_AAG(x1, x2, x3, x4)  =  U16_AAG(x4)
PC_IN_AGA(x1, x2, x3)  =  PC_IN_AGA(x2)
U3_AGA(x1, x2, x3, x4)  =  U3_AGA(x4)
LESSA_IN_AG(x1, x2)  =  LESSA_IN_AG(x2)
U1_AG(x1, x2, x3)  =  U1_AG(x3)
U4_AGA(x1, x2, x3, x4)  =  U4_AGA(x4)
U5_AGA(x1, x2, x3, x4)  =  U5_AGA(x1, x4)
U17_AAG(x1, x2, x3, x4)  =  U17_AAG(x4)
PE_IN_GAA(x1, x2, x3)  =  PE_IN_GAA(x1)
U6_GAA(x1, x2, x3, x4)  =  U6_GAA(x4)
LESSB_IN_GA(x1, x2)  =  LESSB_IN_GA(x1)
U2_GA(x1, x2, x3)  =  U2_GA(x3)
U7_GAA(x1, x2, x3, x4)  =  U7_GAA(x4)
U8_GAA(x1, x2, x3, x4)  =  U8_GAA(x4)
U18_AAG(x1, x2, x3)  =  U18_AAG(x3)
U19_AAG(x1, x2, x3, x4)  =  U19_AAG(x4)
U20_AAG(x1, x2, x3, x4)  =  U20_AAG(x4)
U21_AAG(x1, x2, x3, x4)  =  U21_AAG(x4)
U22_AAG(x1, x2, x3)  =  U22_AAG(x3)
U23_AAG(x1, x2, x3, x4)  =  U23_AAG(x4)
U24_AAG(x1, x2, x3, x4)  =  U24_AAG(x4)
U25_AAG(x1, x2, x3)  =  U25_AAG(x3)
U26_AAG(x1, x2, x3, x4)  =  U26_AAG(x4)
U27_AAG(x1, x2, x3, x4)  =  U27_AAG(x4)
U28_AAG(x1, x2, x3, x4)  =  U28_AAG(x4)
U29_AAG(x1, x2, x3, x4, x5)  =  U29_AAG(x5)
U30_AAG(x1, x2, x3, x4, x5, x6)  =  U30_AAG(x6)
PF_IN_AGAG(x1, x2, x3, x4)  =  PF_IN_AGAG(x2, x4)
U9_AGAG(x1, x2, x3, x4, x5)  =  U9_AGAG(x5)
U10_AGAG(x1, x2, x3, x4, x5)  =  U10_AGAG(x4, x5)
U11_AGAG(x1, x2, x3, x4, x5)  =  U11_AGAG(x1, x5)
U31_AAG(x1, x2, x3, x4, x5, x6)  =  U31_AAG(x6)
PG_IN_GAAG(x1, x2, x3, x4)  =  PG_IN_GAAG(x1, x4)
U12_GAAG(x1, x2, x3, x4, x5)  =  U12_GAAG(x5)
U13_GAAG(x1, x2, x3, x4, x5)  =  U13_GAAG(x4, x5)
U14_GAAG(x1, x2, x3, x4, x5)  =  U14_GAAG(x5)
U32_AAG(x1, x2, x3, x4, x5)  =  U32_AAG(x5)
U33_AAG(x1, x2, x3, x4, x5, x6)  =  U33_AAG(x6)
U34_AAG(x1, x2, x3, x4, x5, x6)  =  U34_AAG(x5, x6)
U35_AAG(x1, x2, x3, x4, x5, x6)  =  U35_AAG(x6)
U36_AAG(x1, x2, x3, x4, x5)  =  U36_AAG(x5)
U37_AAG(x1, x2, x3, x4, x5, x6)  =  U37_AAG(x6)
U38_AAG(x1, x2, x3, x4, x5, x6)  =  U38_AAG(x6)
U39_AAG(x1, x2, x3, x4, x5)  =  U39_AAG(x5)
U40_AAG(x1, x2, x3, x4, x5, x6)  =  U40_AAG(x6)
U41_AAG(x1, x2, x3, x4, x5, x6)  =  U41_AAG(x5, x6)
U42_AAG(x1, x2, x3, x4, x5, x6)  =  U42_AAG(x6)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 108 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

LESSB_IN_GA(s(T91), s(T93)) → LESSB_IN_GA(T91, T93)

The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)
LESSB_IN_GA(x1, x2)  =  LESSB_IN_GA(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:

LESSB_IN_GA(s(T91), s(T93)) → LESSB_IN_GA(T91, T93)

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

LESSB_IN_GA(s(T91)) → LESSB_IN_GA(T91)

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

(14) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• LESSB_IN_GA(s(T91)) → LESSB_IN_GA(T91)
  The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

LESSA_IN_AG(s(T57), s(T56)) → LESSA_IN_AG(T57, T56)

The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)
LESSA_IN_AG(x1, x2)  =  LESSA_IN_AG(x2)

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:

LESSA_IN_AG(s(T57), s(T56)) → LESSA_IN_AG(T57, T56)

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

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:

LESSA_IN_AG(s(T56)) → LESSA_IN_AG(T56)

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

(21) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• LESSA_IN_AG(s(T56)) → LESSA_IN_AG(T56)
  The graph contains the following edges 1 > 1

(22) YES

(23) Obligation:

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

LESSB_IN_GG(s(T91), s(T93)) → LESSB_IN_GG(T91, T93)

The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)
LESSB_IN_GG(x1, x2)  =  LESSB_IN_GG(x1, x2)

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:

LESSB_IN_GG(s(T91), s(T93)) → LESSB_IN_GG(T91, T93)

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

(26) PiDPToQDPProof (EQUIVALENT 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:

LESSB_IN_GG(s(T91), s(T93)) → LESSB_IN_GG(T91, T93)

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:

• LESSB_IN_GG(s(T91), s(T93)) → LESSB_IN_GG(T91, T93)
  The graph contains the following edges 1 > 1, 2 > 2

(29) YES

(30) Obligation:

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

LESSA_IN_GG(s(T57), s(T56)) → LESSA_IN_GG(T57, T56)

The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)
LESSA_IN_GG(x1, x2)  =  LESSA_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:

LESSA_IN_GG(s(T57), s(T56)) → LESSA_IN_GG(T57, T56)

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:

LESSA_IN_GG(s(T57), s(T56)) → LESSA_IN_GG(T57, T56)

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:

• LESSA_IN_GG(s(T57), s(T56)) → LESSA_IN_GG(T57, T56)
  The graph contains the following edges 1 > 1, 2 > 2

(36) YES

(37) Obligation:

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

INSERTD_IN_GAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → PG_IN_GGAG(T275, T279, T280, T278)
PG_IN_GGAG(T275, T283, T284, T278) → U13_GGAG(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_GGAG(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → INSERTD_IN_GAG(T283, T284, T278)
INSERTD_IN_GAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → INSERTD_IN_GAG(0, T241, T233)
INSERTD_IN_GAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → PF_IN_GGAG(T252, T251, T253, T233)
PF_IN_GGAG(T256, T251, T257, T233) → U10_GGAG(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_GGAG(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → INSERTD_IN_GAG(s(T256), T257, T233)
INSERTD_IN_GAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → INSERTD_IN_GAG(s(T309), T308, T300)
INSERTD_IN_GAG(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_GAG(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_GAG(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → INSERTD_IN_GAG(s(T322), T323, T300)
INSERTD_IN_GAG(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_GAG(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_GAG(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → INSERTD_IN_GAG(s(T412), T413, T390)

The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)
INSERTD_IN_GAG(x1, x2, x3)  =  INSERTD_IN_GAG(x1, x3)
PF_IN_GGAG(x1, x2, x3, x4)  =  PF_IN_GGAG(x1, x2, x4)
U10_GGAG(x1, x2, x3, x4, x5)  =  U10_GGAG(x1, x4, x5)
PG_IN_GGAG(x1, x2, x3, x4)  =  PG_IN_GGAG(x1, x2, x4)
U13_GGAG(x1, x2, x3, x4, x5)  =  U13_GGAG(x2, x4, x5)
U34_GAG(x1, x2, x3, x4, x5, x6)  =  U34_GAG(x1, x5, x6)
U41_GAG(x1, x2, x3, x4, x5, x6)  =  U41_GAG(x1, x5, x6)

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:

INSERTD_IN_GAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → PG_IN_GGAG(T275, T279, T280, T278)
PG_IN_GGAG(T275, T283, T284, T278) → U13_GGAG(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_GGAG(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → INSERTD_IN_GAG(T283, T284, T278)
INSERTD_IN_GAG(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → INSERTD_IN_GAG(0, T241, T233)
INSERTD_IN_GAG(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → PF_IN_GGAG(T252, T251, T253, T233)
PF_IN_GGAG(T256, T251, T257, T233) → U10_GGAG(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_GGAG(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → INSERTD_IN_GAG(s(T256), T257, T233)
INSERTD_IN_GAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → INSERTD_IN_GAG(s(T309), T308, T300)
INSERTD_IN_GAG(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_GAG(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_GAG(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → INSERTD_IN_GAG(s(T322), T323, T300)
INSERTD_IN_GAG(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_GAG(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_GAG(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → INSERTD_IN_GAG(s(T412), T413, T390)

The TRS R consists of the following rules:

lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3)  =  tree(x1, x2, x3)
s(x1)  =  s(x1)
0  =  0
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
INSERTD_IN_GAG(x1, x2, x3)  =  INSERTD_IN_GAG(x1, x3)
PF_IN_GGAG(x1, x2, x3, x4)  =  PF_IN_GGAG(x1, x2, x4)
U10_GGAG(x1, x2, x3, x4, x5)  =  U10_GGAG(x1, x4, x5)
PG_IN_GGAG(x1, x2, x3, x4)  =  PG_IN_GGAG(x1, x2, x4)
U13_GGAG(x1, x2, x3, x4, x5)  =  U13_GGAG(x2, x4, x5)
U34_GAG(x1, x2, x3, x4, x5, x6)  =  U34_GAG(x1, x5, x6)
U41_GAG(x1, x2, x3, x4, x5, x6)  =  U41_GAG(x1, x5, x6)

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:

INSERTD_IN_GAG(T279, tree(T275, T276, T278)) → PG_IN_GGAG(T275, T279, T278)
PG_IN_GGAG(T275, T283, T278) → U13_GGAG(T283, T278, lessB_in_gg(T275, T283))
U13_GGAG(T283, T278, lessB_out_gg) → INSERTD_IN_GAG(T283, T278)
INSERTD_IN_GAG(0, tree(s(T240), T233, T232)) → INSERTD_IN_GAG(0, T233)
INSERTD_IN_GAG(s(T252), tree(s(T251), T233, T232)) → PF_IN_GGAG(T252, T251, T233)
PF_IN_GGAG(T256, T251, T233) → U10_GGAG(T256, T233, lessA_in_gg(T256, T251))
U10_GGAG(T256, T233, lessA_out_gg) → INSERTD_IN_GAG(s(T256), T233)
INSERTD_IN_GAG(s(T309), tree(0, T298, T300)) → INSERTD_IN_GAG(s(T309), T300)
INSERTD_IN_GAG(s(T322), tree(s(T316), T298, T300)) → U34_GAG(T322, T300, lessB_in_gg(T316, T322))
U34_GAG(T322, T300, lessB_out_gg) → INSERTD_IN_GAG(s(T322), T300)
INSERTD_IN_GAG(s(T412), tree(s(T406), T388, T390)) → U41_GAG(T412, T390, lessB_in_gg(T406, T412))
U41_GAG(T412, T390, lessB_out_gg) → INSERTD_IN_GAG(s(T412), T390)

The TRS R consists of the following rules:

lessB_in_gg(0, s(T86)) → lessB_out_gg
lessB_in_gg(s(T91), s(T93)) → U2_gg(lessB_in_gg(T91, T93))
lessA_in_gg(0, s(T50)) → lessA_out_gg
lessA_in_gg(s(T57), s(T56)) → U1_gg(lessA_in_gg(T57, T56))
U2_gg(lessB_out_gg) → lessB_out_gg
U1_gg(lessA_out_gg) → lessA_out_gg

The set Q consists of the following terms:

lessB_in_gg(x0, x1)
lessA_in_gg(x0, x1)
U2_gg(x0)
U1_gg(x0)

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:

• PG_IN_GGAG(T275, T283, T278) → U13_GGAG(T283, T278, lessB_in_gg(T275, T283))
  The graph contains the following edges 2 >= 1, 3 >= 2

• U13_GGAG(T283, T278, lessB_out_gg) → INSERTD_IN_GAG(T283, T278)
  The graph contains the following edges 1 >= 1, 2 >= 2

• INSERTD_IN_GAG(T279, tree(T275, T276, T278)) → PG_IN_GGAG(T275, T279, T278)
  The graph contains the following edges 2 > 1, 1 >= 2, 2 > 3

• PF_IN_GGAG(T256, T251, T233) → U10_GGAG(T256, T233, lessA_in_gg(T256, T251))
  The graph contains the following edges 1 >= 1, 3 >= 2

• INSERTD_IN_GAG(0, tree(s(T240), T233, T232)) → INSERTD_IN_GAG(0, T233)
  The graph contains the following edges 1 >= 1, 2 > 2

• INSERTD_IN_GAG(s(T309), tree(0, T298, T300)) → INSERTD_IN_GAG(s(T309), T300)
  The graph contains the following edges 1 >= 1, 2 > 2

• U10_GGAG(T256, T233, lessA_out_gg) → INSERTD_IN_GAG(s(T256), T233)
  The graph contains the following edges 2 >= 2

• INSERTD_IN_GAG(s(T252), tree(s(T251), T233, T232)) → PF_IN_GGAG(T252, T251, T233)
  The graph contains the following edges 1 > 1, 2 > 2, 2 > 3

• U34_GAG(T322, T300, lessB_out_gg) → INSERTD_IN_GAG(s(T322), T300)
  The graph contains the following edges 2 >= 2

• U41_GAG(T412, T390, lessB_out_gg) → INSERTD_IN_GAG(s(T412), T390)
  The graph contains the following edges 2 >= 2

• INSERTD_IN_GAG(s(T322), tree(s(T316), T298, T300)) → U34_GAG(T322, T300, lessB_in_gg(T316, T322))
  The graph contains the following edges 1 > 1, 2 > 2

• INSERTD_IN_GAG(s(T412), tree(s(T406), T388, T390)) → U41_GAG(T412, T390, lessB_in_gg(T406, T412))
  The graph contains the following edges 1 > 1, 2 > 2

(43) YES

(44) Obligation:

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

INSERTD_IN_AAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → PG_IN_GAAG(T275, T279, T280, T278)
PG_IN_GAAG(T275, T283, T284, T278) → U13_GAAG(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_GAAG(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → INSERTD_IN_AAG(T283, T284, T278)
INSERTD_IN_AAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → INSERTD_IN_AAG(s(T309), T308, T300)
INSERTD_IN_AAG(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_AAG(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_AAG(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → INSERTD_IN_AAG(s(T322), T323, T300)
INSERTD_IN_AAG(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_AAG(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_AAG(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → INSERTD_IN_AAG(s(T412), T413, T390)

The TRS R consists of the following rules:

insertD_in_aag(T5, void, tree(T5, void, void)) → insertD_out_aag(T5, void, tree(T5, void, void))
insertD_in_aag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_aag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_aag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(T5, void, tree(T5, void, void)) → insertD_out_gag(T5, void, tree(T5, void, void))
insertD_in_gag(T9, tree(T9, void, void), tree(T9, void, void)) → insertD_out_gag(T9, tree(T9, void, void), tree(T9, void, void))
insertD_in_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void)) → U15_gag(T26, T27, insertD_in_gag(0, T27, void))
insertD_in_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_gag(T38, T37, T39, pC_in_gga(T38, T37, T39))
pC_in_gga(T38, T37, T39) → U3_gga(T38, T37, T39, lessA_in_gg(T38, T37))
lessA_in_gg(0, s(T50)) → lessA_out_gg(0, s(T50))
lessA_in_gg(s(T57), s(T56)) → U1_gg(T57, T56, lessA_in_gg(T57, T56))
U1_gg(T57, T56, lessA_out_gg(T57, T56)) → lessA_out_gg(s(T57), s(T56))
U3_gga(T38, T37, T39, lessA_out_gg(T38, T37)) → pC_out_gga(T38, T37, T39)
pC_in_gga(T42, T37, T43) → U4_gga(T42, T37, T43, lessA_in_gg(T42, T37))
U4_gga(T42, T37, T43, lessA_out_gg(T42, T37)) → U5_gga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
insertD_in_gag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_gag(T74, T71, T75, pE_in_gga(T71, T74, T75))
pE_in_gga(T71, T74, T75) → U6_gga(T71, T74, T75, lessB_in_gg(T71, T74))
lessB_in_gg(0, s(T86)) → lessB_out_gg(0, s(T86))
lessB_in_gg(s(T91), s(T93)) → U2_gg(T91, T93, lessB_in_gg(T91, T93))
U2_gg(T91, T93, lessB_out_gg(T91, T93)) → lessB_out_gg(s(T91), s(T93))
U6_gga(T71, T74, T75, lessB_out_gg(T71, T74)) → pE_out_gga(T71, T74, T75)
pE_in_gga(T71, T78, T79) → U7_gga(T71, T78, T79, lessB_in_gg(T71, T78))
U7_gga(T71, T78, T79, lessB_out_gg(T71, T78)) → U8_gga(T71, T78, T79, insertD_in_gag(T78, T79, void))
insertD_in_gag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_gag(T114, T113, insertD_in_gag(s(T114), T113, void))
insertD_in_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_gag(T123, T121, T124, lessB_in_gg(T121, T123))
U19_gag(T123, T121, T124, lessB_out_gg(T121, T123)) → insertD_out_gag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_gag(T127, T121, T128, lessB_in_gg(T121, T127))
U20_gag(T127, T121, T128, lessB_out_gg(T121, T127)) → U21_gag(T127, T121, T128, insertD_in_gag(s(T127), T128, void))
insertD_in_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_gag(T149, T150, insertD_in_gag(0, T150, void))
insertD_in_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_gag(T161, T160, T162, pC_in_gga(T161, T160, T162))
U23_gag(T161, T160, T162, pC_out_gga(T161, T160, T162)) → insertD_out_gag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_gag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_gag(T177, T174, T178, pE_in_gga(T174, T177, T178))
U24_gag(T177, T174, T178, pE_out_gga(T174, T177, T178)) → insertD_out_gag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_gag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_gag(T197, T196, insertD_in_gag(s(T197), T196, void))
insertD_in_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_gag(T206, T204, T207, lessB_in_gg(T204, T206))
U26_gag(T206, T204, T207, lessB_out_gg(T204, T206)) → insertD_out_gag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_gag(T210, T204, T211, lessB_in_gg(T204, T210))
U27_gag(T210, T204, T211, lessB_out_gg(T204, T210)) → U28_gag(T210, T204, T211, insertD_in_gag(s(T210), T211, void))
insertD_in_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_gag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_gag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
insertD_in_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_gag(T252, T251, T253, T232, T233, pF_in_ggag(T252, T251, T253, T233))
pF_in_ggag(T252, T251, T253, T233) → U9_ggag(T252, T251, T253, T233, lessA_in_gg(T252, T251))
U9_ggag(T252, T251, T253, T233, lessA_out_gg(T252, T251)) → pF_out_ggag(T252, T251, T253, T233)
pF_in_ggag(T256, T251, T257, T233) → U10_ggag(T256, T251, T257, T233, lessA_in_gg(T256, T251))
U10_ggag(T256, T251, T257, T233, lessA_out_gg(T256, T251)) → U11_ggag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
insertD_in_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_gag(T279, T275, T276, T280, T278, pG_in_ggag(T275, T279, T280, T278))
pG_in_ggag(T275, T279, T280, T278) → U12_ggag(T275, T279, T280, T278, lessB_in_gg(T275, T279))
U12_ggag(T275, T279, T280, T278, lessB_out_gg(T275, T279)) → pG_out_ggag(T275, T279, T280, T278)
pG_in_ggag(T275, T283, T284, T278) → U13_ggag(T275, T283, T284, T278, lessB_in_gg(T275, T283))
U13_ggag(T275, T283, T284, T278, lessB_out_gg(T275, T283)) → U14_ggag(T275, T283, T284, T278, insertD_in_gag(T283, T284, T278))
insertD_in_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_gag(T309, T298, T308, T300, insertD_in_gag(s(T309), T308, T300))
insertD_in_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_gag(T318, T316, T298, T319, T300, lessB_in_gg(T316, T318))
U33_gag(T318, T316, T298, T319, T300, lessB_out_gg(T316, T318)) → insertD_out_gag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_gag(T322, T316, T298, T323, T300, lessB_in_gg(T316, T322))
U34_gag(T322, T316, T298, T323, T300, lessB_out_gg(T316, T322)) → U35_gag(T322, T316, T298, T323, T300, insertD_in_gag(s(T322), T323, T300))
insertD_in_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_gag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
insertD_in_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_gag(T358, T357, T359, T338, T339, pF_in_ggag(T358, T357, T359, T339))
U37_gag(T358, T357, T359, T338, T339, pF_out_ggag(T358, T357, T359, T339)) → insertD_out_gag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_gag(T377, T373, T374, T378, T376, pG_in_ggag(T373, T377, T378, T376))
U38_gag(T377, T373, T374, T378, T376, pG_out_ggag(T373, T377, T378, T376)) → insertD_out_gag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_gag(T399, T388, T398, T390, insertD_in_gag(s(T399), T398, T390))
insertD_in_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_gag(T408, T406, T388, T409, T390, lessB_in_gg(T406, T408))
U40_gag(T408, T406, T388, T409, T390, lessB_out_gg(T406, T408)) → insertD_out_gag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_gag(T412, T406, T388, T413, T390, lessB_in_gg(T406, T412))
U41_gag(T412, T406, T388, T413, T390, lessB_out_gg(T406, T412)) → U42_gag(T412, T406, T388, T413, T390, insertD_in_gag(s(T412), T413, T390))
U42_gag(T412, T406, T388, T413, T390, insertD_out_gag(s(T412), T413, T390)) → insertD_out_gag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_gag(T399, T388, T398, T390, insertD_out_gag(s(T399), T398, T390)) → insertD_out_gag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U36_gag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_gag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
U35_gag(T322, T316, T298, T323, T300, insertD_out_gag(s(T322), T323, T300)) → insertD_out_gag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_gag(T309, T298, T308, T300, insertD_out_gag(s(T309), T308, T300)) → insertD_out_gag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_ggag(T275, T283, T284, T278, insertD_out_gag(T283, T284, T278)) → pG_out_ggag(T275, T283, T284, T278)
U31_gag(T279, T275, T276, T280, T278, pG_out_ggag(T275, T279, T280, T278)) → insertD_out_gag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U11_ggag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_ggag(T256, T251, T257, T233)
U30_gag(T252, T251, T253, T232, T233, pF_out_ggag(T252, T251, T253, T233)) → insertD_out_gag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
U29_gag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_gag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
U28_gag(T210, T204, T211, insertD_out_gag(s(T210), T211, void)) → insertD_out_gag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_gag(T197, T196, insertD_out_gag(s(T197), T196, void)) → insertD_out_gag(s(T197), tree(0, void, T196), tree(0, void, void))
U22_gag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_gag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
U21_gag(T127, T121, T128, insertD_out_gag(s(T127), T128, void)) → insertD_out_gag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_gag(T114, T113, insertD_out_gag(s(T114), T113, void)) → insertD_out_gag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gga(T71, T78, T79, insertD_out_gag(T78, T79, void)) → pE_out_gga(T71, T78, T79)
U17_gag(T74, T71, T75, pE_out_gga(T71, T74, T75)) → insertD_out_gag(T74, tree(T71, void, T75), tree(T71, void, void))
U5_gga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_gga(T42, T37, T43)
U16_gag(T38, T37, T39, pC_out_gga(T38, T37, T39)) → insertD_out_gag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
U15_gag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_gag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
U15_aag(T26, T27, insertD_out_gag(0, T27, void)) → insertD_out_aag(0, tree(s(T26), T27, void), tree(s(T26), void, void))
insertD_in_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void)) → U16_aag(T38, T37, T39, pC_in_aga(T38, T37, T39))
pC_in_aga(T38, T37, T39) → U3_aga(T38, T37, T39, lessA_in_ag(T38, T37))
lessA_in_ag(0, s(T50)) → lessA_out_ag(0, s(T50))
lessA_in_ag(s(T57), s(T56)) → U1_ag(T57, T56, lessA_in_ag(T57, T56))
U1_ag(T57, T56, lessA_out_ag(T57, T56)) → lessA_out_ag(s(T57), s(T56))
U3_aga(T38, T37, T39, lessA_out_ag(T38, T37)) → pC_out_aga(T38, T37, T39)
pC_in_aga(T42, T37, T43) → U4_aga(T42, T37, T43, lessA_in_ag(T42, T37))
U4_aga(T42, T37, T43, lessA_out_ag(T42, T37)) → U5_aga(T42, T37, T43, insertD_in_gag(s(T42), T43, void))
U5_aga(T42, T37, T43, insertD_out_gag(s(T42), T43, void)) → pC_out_aga(T42, T37, T43)
U16_aag(T38, T37, T39, pC_out_aga(T38, T37, T39)) → insertD_out_aag(s(T38), tree(s(T37), T39, void), tree(s(T37), void, void))
insertD_in_aag(T74, tree(T71, void, T75), tree(T71, void, void)) → U17_aag(T74, T71, T75, pE_in_gaa(T71, T74, T75))
pE_in_gaa(T71, T74, T75) → U6_gaa(T71, T74, T75, lessB_in_ga(T71, T74))
lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))
U6_gaa(T71, T74, T75, lessB_out_ga(T71, T74)) → pE_out_gaa(T71, T74, T75)
pE_in_gaa(T71, T78, T79) → U7_gaa(T71, T78, T79, lessB_in_ga(T71, T78))
U7_gaa(T71, T78, T79, lessB_out_ga(T71, T78)) → U8_gaa(T71, T78, T79, insertD_in_aag(T78, T79, void))
insertD_in_aag(s(T114), tree(0, void, T113), tree(0, void, void)) → U18_aag(T114, T113, insertD_in_aag(s(T114), T113, void))
insertD_in_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void)) → U19_aag(T123, T121, T124, lessB_in_ga(T121, T123))
U19_aag(T123, T121, T124, lessB_out_ga(T121, T123)) → insertD_out_aag(s(T123), tree(s(T121), void, T124), tree(s(T121), void, void))
insertD_in_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void)) → U20_aag(T127, T121, T128, lessB_in_ga(T121, T127))
U20_aag(T127, T121, T128, lessB_out_ga(T121, T127)) → U21_aag(T127, T121, T128, insertD_in_aag(s(T127), T128, void))
insertD_in_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void)) → U22_aag(T149, T150, insertD_in_gag(0, T150, void))
U22_aag(T149, T150, insertD_out_gag(0, T150, void)) → insertD_out_aag(0, tree(s(T149), T150, void), tree(s(T149), void, void))
insertD_in_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void)) → U23_aag(T161, T160, T162, pC_in_aga(T161, T160, T162))
U23_aag(T161, T160, T162, pC_out_aga(T161, T160, T162)) → insertD_out_aag(s(T161), tree(s(T160), T162, void), tree(s(T160), void, void))
insertD_in_aag(T177, tree(T174, void, T178), tree(T174, void, void)) → U24_aag(T177, T174, T178, pE_in_gaa(T174, T177, T178))
U24_aag(T177, T174, T178, pE_out_gaa(T174, T177, T178)) → insertD_out_aag(T177, tree(T174, void, T178), tree(T174, void, void))
insertD_in_aag(s(T197), tree(0, void, T196), tree(0, void, void)) → U25_aag(T197, T196, insertD_in_aag(s(T197), T196, void))
insertD_in_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void)) → U26_aag(T206, T204, T207, lessB_in_ga(T204, T206))
U26_aag(T206, T204, T207, lessB_out_ga(T204, T206)) → insertD_out_aag(s(T206), tree(s(T204), void, T207), tree(s(T204), void, void))
insertD_in_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void)) → U27_aag(T210, T204, T211, lessB_in_ga(T204, T210))
U27_aag(T210, T204, T211, lessB_out_ga(T204, T210)) → U28_aag(T210, T204, T211, insertD_in_aag(s(T210), T211, void))
insertD_in_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223)) → insertD_out_aag(T221, tree(T221, T222, T223), tree(T221, T222, T223))
insertD_in_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232)) → U29_aag(T240, T241, T232, T233, insertD_in_gag(0, T241, T233))
U29_aag(T240, T241, T232, T233, insertD_out_gag(0, T241, T233)) → insertD_out_aag(0, tree(s(T240), T241, T232), tree(s(T240), T233, T232))
insertD_in_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232)) → U30_aag(T252, T251, T253, T232, T233, pF_in_agag(T252, T251, T253, T233))
pF_in_agag(T252, T251, T253, T233) → U9_agag(T252, T251, T253, T233, lessA_in_ag(T252, T251))
U9_agag(T252, T251, T253, T233, lessA_out_ag(T252, T251)) → pF_out_agag(T252, T251, T253, T233)
pF_in_agag(T256, T251, T257, T233) → U10_agag(T256, T251, T257, T233, lessA_in_ag(T256, T251))
U10_agag(T256, T251, T257, T233, lessA_out_ag(T256, T251)) → U11_agag(T256, T251, T257, T233, insertD_in_gag(s(T256), T257, T233))
U11_agag(T256, T251, T257, T233, insertD_out_gag(s(T256), T257, T233)) → pF_out_agag(T256, T251, T257, T233)
U30_aag(T252, T251, T253, T232, T233, pF_out_agag(T252, T251, T253, T233)) → insertD_out_aag(s(T252), tree(s(T251), T253, T232), tree(s(T251), T233, T232))
insertD_in_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → U31_aag(T279, T275, T276, T280, T278, pG_in_gaag(T275, T279, T280, T278))
pG_in_gaag(T275, T279, T280, T278) → U12_gaag(T275, T279, T280, T278, lessB_in_ga(T275, T279))
U12_gaag(T275, T279, T280, T278, lessB_out_ga(T275, T279)) → pG_out_gaag(T275, T279, T280, T278)
pG_in_gaag(T275, T283, T284, T278) → U13_gaag(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_gaag(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → U14_gaag(T275, T283, T284, T278, insertD_in_aag(T283, T284, T278))
insertD_in_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → U32_aag(T309, T298, T308, T300, insertD_in_aag(s(T309), T308, T300))
insertD_in_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300)) → U33_aag(T318, T316, T298, T319, T300, lessB_in_ga(T316, T318))
U33_aag(T318, T316, T298, T319, T300, lessB_out_ga(T316, T318)) → insertD_out_aag(s(T318), tree(s(T316), T298, T319), tree(s(T316), T298, T300))
insertD_in_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_aag(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_aag(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → U35_aag(T322, T316, T298, T323, T300, insertD_in_aag(s(T322), T323, T300))
insertD_in_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338)) → U36_aag(T346, T347, T338, T339, insertD_in_gag(0, T347, T339))
U36_aag(T346, T347, T338, T339, insertD_out_gag(0, T347, T339)) → insertD_out_aag(0, tree(s(T346), T347, T338), tree(s(T346), T339, T338))
insertD_in_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338)) → U37_aag(T358, T357, T359, T338, T339, pF_in_agag(T358, T357, T359, T339))
U37_aag(T358, T357, T359, T338, T339, pF_out_agag(T358, T357, T359, T339)) → insertD_out_aag(s(T358), tree(s(T357), T359, T338), tree(s(T357), T339, T338))
insertD_in_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376)) → U38_aag(T377, T373, T374, T378, T376, pG_in_gaag(T373, T377, T378, T376))
U38_aag(T377, T373, T374, T378, T376, pG_out_gaag(T373, T377, T378, T376)) → insertD_out_aag(T377, tree(T373, T374, T378), tree(T373, T374, T376))
insertD_in_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390)) → U39_aag(T399, T388, T398, T390, insertD_in_aag(s(T399), T398, T390))
insertD_in_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390)) → U40_aag(T408, T406, T388, T409, T390, lessB_in_ga(T406, T408))
U40_aag(T408, T406, T388, T409, T390, lessB_out_ga(T406, T408)) → insertD_out_aag(s(T408), tree(s(T406), T388, T409), tree(s(T406), T388, T390))
insertD_in_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_aag(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_aag(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → U42_aag(T412, T406, T388, T413, T390, insertD_in_aag(s(T412), T413, T390))
U42_aag(T412, T406, T388, T413, T390, insertD_out_aag(s(T412), T413, T390)) → insertD_out_aag(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390))
U39_aag(T399, T388, T398, T390, insertD_out_aag(s(T399), T398, T390)) → insertD_out_aag(s(T399), tree(0, T388, T398), tree(0, T388, T390))
U35_aag(T322, T316, T298, T323, T300, insertD_out_aag(s(T322), T323, T300)) → insertD_out_aag(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300))
U32_aag(T309, T298, T308, T300, insertD_out_aag(s(T309), T308, T300)) → insertD_out_aag(s(T309), tree(0, T298, T308), tree(0, T298, T300))
U14_gaag(T275, T283, T284, T278, insertD_out_aag(T283, T284, T278)) → pG_out_gaag(T275, T283, T284, T278)
U31_aag(T279, T275, T276, T280, T278, pG_out_gaag(T275, T279, T280, T278)) → insertD_out_aag(T279, tree(T275, T276, T280), tree(T275, T276, T278))
U28_aag(T210, T204, T211, insertD_out_aag(s(T210), T211, void)) → insertD_out_aag(s(T210), tree(s(T204), void, T211), tree(s(T204), void, void))
U25_aag(T197, T196, insertD_out_aag(s(T197), T196, void)) → insertD_out_aag(s(T197), tree(0, void, T196), tree(0, void, void))
U21_aag(T127, T121, T128, insertD_out_aag(s(T127), T128, void)) → insertD_out_aag(s(T127), tree(s(T121), void, T128), tree(s(T121), void, void))
U18_aag(T114, T113, insertD_out_aag(s(T114), T113, void)) → insertD_out_aag(s(T114), tree(0, void, T113), tree(0, void, void))
U8_gaa(T71, T78, T79, insertD_out_aag(T78, T79, void)) → pE_out_gaa(T71, T78, T79)
U17_aag(T74, T71, T75, pE_out_gaa(T71, T74, T75)) → insertD_out_aag(T74, tree(T71, void, T75), tree(T71, void, void))

The argument filtering Pi contains the following mapping:
insertD_in_aag(x1, x2, x3)  =  insertD_in_aag(x3)
tree(x1, x2, x3)  =  tree(x1, x2, x3)
void  =  void
insertD_out_aag(x1, x2, x3)  =  insertD_out_aag
s(x1)  =  s(x1)
U15_aag(x1, x2, x3)  =  U15_aag(x3)
insertD_in_gag(x1, x2, x3)  =  insertD_in_gag(x1, x3)
insertD_out_gag(x1, x2, x3)  =  insertD_out_gag
0  =  0
U15_gag(x1, x2, x3)  =  U15_gag(x3)
U16_gag(x1, x2, x3, x4)  =  U16_gag(x4)
pC_in_gga(x1, x2, x3)  =  pC_in_gga(x1, x2)
U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)
lessA_in_gg(x1, x2)  =  lessA_in_gg(x1, x2)
lessA_out_gg(x1, x2)  =  lessA_out_gg
U1_gg(x1, x2, x3)  =  U1_gg(x3)
pC_out_gga(x1, x2, x3)  =  pC_out_gga
U4_gga(x1, x2, x3, x4)  =  U4_gga(x1, x4)
U5_gga(x1, x2, x3, x4)  =  U5_gga(x4)
U17_gag(x1, x2, x3, x4)  =  U17_gag(x4)
pE_in_gga(x1, x2, x3)  =  pE_in_gga(x1, x2)
U6_gga(x1, x2, x3, x4)  =  U6_gga(x4)
lessB_in_gg(x1, x2)  =  lessB_in_gg(x1, x2)
lessB_out_gg(x1, x2)  =  lessB_out_gg
U2_gg(x1, x2, x3)  =  U2_gg(x3)
pE_out_gga(x1, x2, x3)  =  pE_out_gga
U7_gga(x1, x2, x3, x4)  =  U7_gga(x2, x4)
U8_gga(x1, x2, x3, x4)  =  U8_gga(x4)
U18_gag(x1, x2, x3)  =  U18_gag(x3)
U19_gag(x1, x2, x3, x4)  =  U19_gag(x4)
U20_gag(x1, x2, x3, x4)  =  U20_gag(x1, x4)
U21_gag(x1, x2, x3, x4)  =  U21_gag(x4)
U22_gag(x1, x2, x3)  =  U22_gag(x3)
U23_gag(x1, x2, x3, x4)  =  U23_gag(x4)
U24_gag(x1, x2, x3, x4)  =  U24_gag(x4)
U25_gag(x1, x2, x3)  =  U25_gag(x3)
U26_gag(x1, x2, x3, x4)  =  U26_gag(x4)
U27_gag(x1, x2, x3, x4)  =  U27_gag(x1, x4)
U28_gag(x1, x2, x3, x4)  =  U28_gag(x4)
U29_gag(x1, x2, x3, x4, x5)  =  U29_gag(x5)
U30_gag(x1, x2, x3, x4, x5, x6)  =  U30_gag(x6)
pF_in_ggag(x1, x2, x3, x4)  =  pF_in_ggag(x1, x2, x4)
U9_ggag(x1, x2, x3, x4, x5)  =  U9_ggag(x5)
pF_out_ggag(x1, x2, x3, x4)  =  pF_out_ggag
U10_ggag(x1, x2, x3, x4, x5)  =  U10_ggag(x1, x4, x5)
U11_ggag(x1, x2, x3, x4, x5)  =  U11_ggag(x5)
U31_gag(x1, x2, x3, x4, x5, x6)  =  U31_gag(x6)
pG_in_ggag(x1, x2, x3, x4)  =  pG_in_ggag(x1, x2, x4)
U12_ggag(x1, x2, x3, x4, x5)  =  U12_ggag(x5)
pG_out_ggag(x1, x2, x3, x4)  =  pG_out_ggag
U13_ggag(x1, x2, x3, x4, x5)  =  U13_ggag(x2, x4, x5)
U14_ggag(x1, x2, x3, x4, x5)  =  U14_ggag(x5)
U32_gag(x1, x2, x3, x4, x5)  =  U32_gag(x5)
U33_gag(x1, x2, x3, x4, x5, x6)  =  U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6)  =  U34_gag(x1, x5, x6)
U35_gag(x1, x2, x3, x4, x5, x6)  =  U35_gag(x6)
U36_gag(x1, x2, x3, x4, x5)  =  U36_gag(x5)
U37_gag(x1, x2, x3, x4, x5, x6)  =  U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5, x6)  =  U38_gag(x6)
U39_gag(x1, x2, x3, x4, x5)  =  U39_gag(x5)
U40_gag(x1, x2, x3, x4, x5, x6)  =  U40_gag(x6)
U41_gag(x1, x2, x3, x4, x5, x6)  =  U41_gag(x1, x5, x6)
U42_gag(x1, x2, x3, x4, x5, x6)  =  U42_gag(x6)
U16_aag(x1, x2, x3, x4)  =  U16_aag(x4)
pC_in_aga(x1, x2, x3)  =  pC_in_aga(x2)
U3_aga(x1, x2, x3, x4)  =  U3_aga(x4)
lessA_in_ag(x1, x2)  =  lessA_in_ag(x2)
lessA_out_ag(x1, x2)  =  lessA_out_ag(x1)
U1_ag(x1, x2, x3)  =  U1_ag(x3)
pC_out_aga(x1, x2, x3)  =  pC_out_aga(x1)
U4_aga(x1, x2, x3, x4)  =  U4_aga(x4)
U5_aga(x1, x2, x3, x4)  =  U5_aga(x1, x4)
U17_aag(x1, x2, x3, x4)  =  U17_aag(x4)
pE_in_gaa(x1, x2, x3)  =  pE_in_gaa(x1)
U6_gaa(x1, x2, x3, x4)  =  U6_gaa(x4)
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
pE_out_gaa(x1, x2, x3)  =  pE_out_gaa
U7_gaa(x1, x2, x3, x4)  =  U7_gaa(x4)
U8_gaa(x1, x2, x3, x4)  =  U8_gaa(x4)
U18_aag(x1, x2, x3)  =  U18_aag(x3)
U19_aag(x1, x2, x3, x4)  =  U19_aag(x4)
U20_aag(x1, x2, x3, x4)  =  U20_aag(x4)
U21_aag(x1, x2, x3, x4)  =  U21_aag(x4)
U22_aag(x1, x2, x3)  =  U22_aag(x3)
U23_aag(x1, x2, x3, x4)  =  U23_aag(x4)
U24_aag(x1, x2, x3, x4)  =  U24_aag(x4)
U25_aag(x1, x2, x3)  =  U25_aag(x3)
U26_aag(x1, x2, x3, x4)  =  U26_aag(x4)
U27_aag(x1, x2, x3, x4)  =  U27_aag(x4)
U28_aag(x1, x2, x3, x4)  =  U28_aag(x4)
U29_aag(x1, x2, x3, x4, x5)  =  U29_aag(x5)
U30_aag(x1, x2, x3, x4, x5, x6)  =  U30_aag(x6)
pF_in_agag(x1, x2, x3, x4)  =  pF_in_agag(x2, x4)
U9_agag(x1, x2, x3, x4, x5)  =  U9_agag(x5)
pF_out_agag(x1, x2, x3, x4)  =  pF_out_agag(x1)
U10_agag(x1, x2, x3, x4, x5)  =  U10_agag(x4, x5)
U11_agag(x1, x2, x3, x4, x5)  =  U11_agag(x1, x5)
U31_aag(x1, x2, x3, x4, x5, x6)  =  U31_aag(x6)
pG_in_gaag(x1, x2, x3, x4)  =  pG_in_gaag(x1, x4)
U12_gaag(x1, x2, x3, x4, x5)  =  U12_gaag(x5)
pG_out_gaag(x1, x2, x3, x4)  =  pG_out_gaag
U13_gaag(x1, x2, x3, x4, x5)  =  U13_gaag(x4, x5)
U14_gaag(x1, x2, x3, x4, x5)  =  U14_gaag(x5)
U32_aag(x1, x2, x3, x4, x5)  =  U32_aag(x5)
U33_aag(x1, x2, x3, x4, x5, x6)  =  U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6)  =  U34_aag(x5, x6)
U35_aag(x1, x2, x3, x4, x5, x6)  =  U35_aag(x6)
U36_aag(x1, x2, x3, x4, x5)  =  U36_aag(x5)
U37_aag(x1, x2, x3, x4, x5, x6)  =  U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5, x6)  =  U38_aag(x6)
U39_aag(x1, x2, x3, x4, x5)  =  U39_aag(x5)
U40_aag(x1, x2, x3, x4, x5, x6)  =  U40_aag(x6)
U41_aag(x1, x2, x3, x4, x5, x6)  =  U41_aag(x5, x6)
U42_aag(x1, x2, x3, x4, x5, x6)  =  U42_aag(x6)
INSERTD_IN_AAG(x1, x2, x3)  =  INSERTD_IN_AAG(x3)
PG_IN_GAAG(x1, x2, x3, x4)  =  PG_IN_GAAG(x1, x4)
U13_GAAG(x1, x2, x3, x4, x5)  =  U13_GAAG(x4, x5)
U34_AAG(x1, x2, x3, x4, x5, x6)  =  U34_AAG(x5, x6)
U41_AAG(x1, x2, x3, x4, x5, x6)  =  U41_AAG(x5, x6)

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

(45) UsableRulesProof (EQUIVALENT transformation)

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

(46) Obligation:

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

INSERTD_IN_AAG(T279, tree(T275, T276, T280), tree(T275, T276, T278)) → PG_IN_GAAG(T275, T279, T280, T278)
PG_IN_GAAG(T275, T283, T284, T278) → U13_GAAG(T275, T283, T284, T278, lessB_in_ga(T275, T283))
U13_GAAG(T275, T283, T284, T278, lessB_out_ga(T275, T283)) → INSERTD_IN_AAG(T283, T284, T278)
INSERTD_IN_AAG(s(T309), tree(0, T298, T308), tree(0, T298, T300)) → INSERTD_IN_AAG(s(T309), T308, T300)
INSERTD_IN_AAG(s(T322), tree(s(T316), T298, T323), tree(s(T316), T298, T300)) → U34_AAG(T322, T316, T298, T323, T300, lessB_in_ga(T316, T322))
U34_AAG(T322, T316, T298, T323, T300, lessB_out_ga(T316, T322)) → INSERTD_IN_AAG(s(T322), T323, T300)
INSERTD_IN_AAG(s(T412), tree(s(T406), T388, T413), tree(s(T406), T388, T390)) → U41_AAG(T412, T406, T388, T413, T390, lessB_in_ga(T406, T412))
U41_AAG(T412, T406, T388, T413, T390, lessB_out_ga(T406, T412)) → INSERTD_IN_AAG(s(T412), T413, T390)

The TRS R consists of the following rules:

lessB_in_ga(0, s(T86)) → lessB_out_ga(0, s(T86))
lessB_in_ga(s(T91), s(T93)) → U2_ga(T91, T93, lessB_in_ga(T91, T93))
U2_ga(T91, T93, lessB_out_ga(T91, T93)) → lessB_out_ga(s(T91), s(T93))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3)  =  tree(x1, x2, x3)
s(x1)  =  s(x1)
0  =  0
lessB_in_ga(x1, x2)  =  lessB_in_ga(x1)
lessB_out_ga(x1, x2)  =  lessB_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
INSERTD_IN_AAG(x1, x2, x3)  =  INSERTD_IN_AAG(x3)
PG_IN_GAAG(x1, x2, x3, x4)  =  PG_IN_GAAG(x1, x4)
U13_GAAG(x1, x2, x3, x4, x5)  =  U13_GAAG(x4, x5)
U34_AAG(x1, x2, x3, x4, x5, x6)  =  U34_AAG(x5, x6)
U41_AAG(x1, x2, x3, x4, x5, x6)  =  U41_AAG(x5, x6)

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

(47) PiDPToQDPProof (SOUND transformation)

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

(48) Obligation:

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

INSERTD_IN_AAG(tree(T275, T276, T278)) → PG_IN_GAAG(T275, T278)
PG_IN_GAAG(T275, T278) → U13_GAAG(T278, lessB_in_ga(T275))
U13_GAAG(T278, lessB_out_ga) → INSERTD_IN_AAG(T278)
INSERTD_IN_AAG(tree(0, T298, T300)) → INSERTD_IN_AAG(T300)
INSERTD_IN_AAG(tree(s(T316), T298, T300)) → U34_AAG(T300, lessB_in_ga(T316))
U34_AAG(T300, lessB_out_ga) → INSERTD_IN_AAG(T300)
INSERTD_IN_AAG(tree(s(T406), T388, T390)) → U41_AAG(T390, lessB_in_ga(T406))
U41_AAG(T390, lessB_out_ga) → INSERTD_IN_AAG(T390)

The TRS R consists of the following rules:

lessB_in_ga(0) → lessB_out_ga
lessB_in_ga(s(T91)) → U2_ga(lessB_in_ga(T91))
U2_ga(lessB_out_ga) → lessB_out_ga

The set Q consists of the following terms:

lessB_in_ga(x0)
U2_ga(x0)

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

(49) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• PG_IN_GAAG(T275, T278) → U13_GAAG(T278, lessB_in_ga(T275))
  The graph contains the following edges 2 >= 1

• U13_GAAG(T278, lessB_out_ga) → INSERTD_IN_AAG(T278)
  The graph contains the following edges 1 >= 1

• INSERTD_IN_AAG(tree(T275, T276, T278)) → PG_IN_GAAG(T275, T278)
  The graph contains the following edges 1 > 1, 1 > 2

• INSERTD_IN_AAG(tree(0, T298, T300)) → INSERTD_IN_AAG(T300)
  The graph contains the following edges 1 > 1

• U34_AAG(T300, lessB_out_ga) → INSERTD_IN_AAG(T300)
  The graph contains the following edges 1 >= 1

• U41_AAG(T390, lessB_out_ga) → INSERTD_IN_AAG(T390)
  The graph contains the following edges 1 >= 1

• INSERTD_IN_AAG(tree(s(T316), T298, T300)) → U34_AAG(T300, lessB_in_ga(T316))
  The graph contains the following edges 1 > 1

• INSERTD_IN_AAG(tree(s(T406), T388, T390)) → U41_AAG(T390, lessB_in_ga(T406))
  The graph contains the following edges 1 > 1

(50) YES