Left Termination of the query pattern p_in_2(a, g) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

p(d(e(t)), const(1)).
p(d(e(const(A))), const(0)).
p(d(e(+(X, Y))), +(DX, DY)) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY)).
p(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY)).
p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX)).

Queries:

p(a,g).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: p(T1, T2)\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: p(T1, T2), SCOPE: 1, CLAUSE: 0 | p(T1, T2), SCOPE: 1, CLAUSE: 1 | p(T1, T2), SCOPE: 1, CLAUSE: 2 | p(T1, T2), SCOPE: 1, CLAUSE: 3 | p(T1, T2), SCOPE: 1, CLAUSE: 4\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | p(T1, const(1)), SCOPE: 1, CLAUSE: 1 | p(T1, const(1)), SCOPE: 1, CLAUSE: 2 | p(T1, const(1)), SCOPE: 1, CLAUSE: 3 | p(T1, const(1)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: p(T1, T2), SCOPE: 1, CLAUSE: 1 | p(T1, T2), SCOPE: 1, CLAUSE: 2 | p(T1, T2), SCOPE: 1, CLAUSE: 3 | p(T1, T2), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\np(T1, T2) !=? p(d(e(t)), const(1))", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: p(T1, const(1)), SCOPE: 1, CLAUSE: 1 | p(T1, const(1)), SCOPE: 1, CLAUSE: 2 | p(T1, const(1)), SCOPE: 1, CLAUSE: 3 | p(T1, const(1)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: p(T1, const(1)), SCOPE: 1, CLAUSE: 2 | p(T1, const(1)), SCOPE: 1, CLAUSE: 3 | p(T1, const(1)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: p(T1, const(1)), SCOPE: 1, CLAUSE: 3 | p(T1, const(1)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: p(T1, const(1)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(p(d(T10), X14), p(d(e(X14)), const(1)))\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 0 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 1 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 2 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 3 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 4\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 0\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 1 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 2 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 3 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 4\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: p(d(e(const(1))), const(1))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 1\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 2 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 3 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 4\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: p(d(e(const(0))), const(1))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 2\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 3 | ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 4\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: ','(p(d(e(T26)), X77), ','(p(d(e(T27)), X78), p(d(e(+(X77, X78))), const(1))))\n\nX77 is free\nX78 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: p(d(e(T26)), X77)\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(p(d(e(T29)), X78), p(d(e(+(T28, X78))), const(1)))\n\nX78 is free", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 0 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 1 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 2 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 3 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 4\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 0\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 1 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 2 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 3 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 4\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 1\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 2 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 3 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 4\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 2\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 3 | p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 4\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: ','(p(d(e(T45)), X117), p(d(e(T46)), X118))\n\nX117 is free\nX118 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: p(d(e(T45)), X117)\n\nX117 is free", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: p(d(e(T48)), X118)\n\nX118 is free", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 3\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: p(d(e(T26)), X77), SCOPE: 3, CLAUSE: 4\n\nX77 is free", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(p(d(e(T59)), X152), p(d(e(T60)), X151))\n\nX151 is free\nX152 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: p(d(e(T29)), X78)\n\nX78 is free", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: p(d(e(+(T62, T61))), const(1))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 3\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: ','(p(d(T10), X14), p(d(e(X14)), const(1))), SCOPE: 2, CLAUSE: 4\n\nX14 is free", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: ','(p(d(e(T75)), X201), ','(p(d(e(T76)), X200), p(d(e(+(*(T75, X200), *(T76, X201)))), const(1))))\n\nX200 is free\nX201 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: p(d(e(T75)), X201)\n\nX201 is free", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(p(d(e(T78)), X200), p(d(e(+(*(T79, X200), *(T78, T77)))), const(1)))\n\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: p(d(e(T78)), X200)\n\nX200 is free", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: p(d(e(+(*(T81, T80), *(T82, T83)))), const(1))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(p(d(T91), X228), ','(p(d(e(X228)), X229), p(d(e(X229)), const(1))))\n\nX229 is free\nX228 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: p(d(T91), X228)\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: ','(p(d(e(T92)), X229), p(d(e(X229)), const(1)))\n\nX229 is free", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: p(d(T91), X228), SCOPE: 4, CLAUSE: 0 | p(d(T91), X228), SCOPE: 4, CLAUSE: 1 | p(d(T91), X228), SCOPE: 4, CLAUSE: 2 | p(d(T91), X228), SCOPE: 4, CLAUSE: 3 | p(d(T91), X228), SCOPE: 4, CLAUSE: 4\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: p(d(T91), X228), SCOPE: 4, CLAUSE: 0\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: p(d(T91), X228), SCOPE: 4, CLAUSE: 1 | p(d(T91), X228), SCOPE: 4, CLAUSE: 2 | p(d(T91), X228), SCOPE: 4, CLAUSE: 3 | p(d(T91), X228), SCOPE: 4, CLAUSE: 4\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: p(d(T91), X228), SCOPE: 4, CLAUSE: 1\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: p(d(T91), X228), SCOPE: 4, CLAUSE: 2 | p(d(T91), X228), SCOPE: 4, CLAUSE: 3 | p(d(T91), X228), SCOPE: 4, CLAUSE: 4\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: p(d(T91), X228), SCOPE: 4, CLAUSE: 2\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: p(d(T91), X228), SCOPE: 4, CLAUSE: 3 | p(d(T91), X228), SCOPE: 4, CLAUSE: 4\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(p(d(e(T108)), X266), p(d(e(T109)), X267))\n\nX266 is free\nX267 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: p(d(T91), X228), SCOPE: 4, CLAUSE: 3\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: p(d(T91), X228), SCOPE: 4, CLAUSE: 4\n\nX228 is free", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(p(d(e(T120)), X301), p(d(e(T121)), X300))\n\nX300 is free\nX301 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: ','(p(d(T125), X315), p(d(e(X315)), X316))\n\nX316 is free\nX315 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: p(d(T125), X315)\n\nX315 is free", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: p(d(e(T126)), X316)\n\nX316 is free", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: true | p(T1, const(0)), SCOPE: 1, CLAUSE: 2 | p(T1, const(0)), SCOPE: 1, CLAUSE: 3 | p(T1, const(0)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: p(T1, T2), SCOPE: 1, CLAUSE: 2 | p(T1, T2), SCOPE: 1, CLAUSE: 3 | p(T1, T2), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\np(T1, T2) !=? p(d(e(t)), const(1))\np(T1, T2) !=? p(d(e(const(X320))), const(0))", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: p(T1, const(0)), SCOPE: 1, CLAUSE: 2 | p(T1, const(0)), SCOPE: 1, CLAUSE: 3 | p(T1, const(0)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: p(T1, const(0)), SCOPE: 1, CLAUSE: 3 | p(T1, const(0)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: p(T1, const(0)), SCOPE: 1, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(p(d(T135), X334), p(d(e(X334)), const(0)))\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 0 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 1 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 2 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 3 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 4\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 0\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 1 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 2 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 3 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 4\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: p(d(e(const(1))), const(0))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 1\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 2 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 3 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 4\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: p(d(e(const(0))), const(0))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 2\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 3 | ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 4\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: ','(p(d(e(T151)), X373), ','(p(d(e(T152)), X374), p(d(e(+(X373, X374))), const(0))))\n\nX373 is free\nX374 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: p(d(e(T151)), X373)\n\nX373 is free", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(p(d(e(T154)), X374), p(d(e(+(T153, X374))), const(0)))\n\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: p(d(e(T154)), X374)\n\nX374 is free", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: p(d(e(+(T156, T155))), const(0))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 3\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ','(p(d(T135), X334), p(d(e(X334)), const(0))), SCOPE: 5, CLAUSE: 4\n\nX334 is free", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(p(d(e(T169)), X421), ','(p(d(e(T170)), X420), p(d(e(+(*(T169, X420), *(T170, X421)))), const(0))))\n\nX420 is free\nX421 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: p(d(e(T169)), X421)\n\nX421 is free", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(p(d(e(T172)), X420), p(d(e(+(*(T173, X420), *(T172, T171)))), const(0)))\n\nX420 is free", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: p(d(e(T172)), X420)\n\nX420 is free", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: p(d(e(+(*(T175, T174), *(T176, T177)))), const(0))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: ','(p(d(T185), X448), ','(p(d(e(X448)), X449), p(d(e(X449)), const(0))))\n\nX449 is free\nX448 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: p(d(T185), X448)\n\nX448 is free", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(p(d(e(T186)), X449), p(d(e(X449)), const(0)))\n\nX449 is free", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)) | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: p(T1, T2), SCOPE: 1, CLAUSE: 3 | p(T1, T2), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\np(T1, T2) !=? p(d(e(t)), const(1))\np(T1, T2) !=? p(d(e(const(X320))), const(0))\np(T1, T2) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 0 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 1 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 2 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 3 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 4 | ?_6 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 0\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 1 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 2 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 3 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 4 | ?_6 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: p(d(e(T197)), T194)\n\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 1\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 2 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 3 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 4 | ?_6 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: p(d(e(T203)), T194)\n\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 2\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 3 | ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 4 | ?_6 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: ','(p(d(e(T224)), T222), ','(p(d(e(T225)), T223), p(d(e(T226)), T194)))\n\nT194 is ground\nT222 is ground\nT223 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: p(d(e(T224)), T222)\n\nT222 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ','(p(d(e(T227)), T223), p(d(e(T228)), T194))\n\nT194 is ground\nT223 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: p(d(e(T227)), T223)\n\nT223 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: p(d(e(T229)), T194)\n\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 3\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: ','(p(d(e(T195)), T193), p(d(e(T196)), T194)), SCOPE: 6, CLAUSE: 4 | ?_6 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: ','(p(d(e(T246)), T249), ','(p(d(e(T247)), T248), p(d(e(T250)), T194)))\n\nT194 is ground\nT246 is ground\nT248 is ground\nT247 is ground\nT249 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: ?_6 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3 | p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 3\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: p(T1, +(T193, T194)), SCOPE: 1, CLAUSE: 4\n\nT193 is ground\nT194 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: ','(p(d(e(T267)), T270), p(d(e(T268)), T269))\n\nT267 is ground\nT269 is ground\nT268 is ground\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(p(d(T280), X551), p(d(e(X551)), +(T278, T279)))\n\nT278 is ground\nT279 is ground\nX551 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: p(d(T280), X551)\n\nX551 is free", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: p(d(e(T281)), +(T278, T279))\n\nT278 is ground\nT279 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)) | p(T1, +(*(T292, T294), *(T293, T295))), SCOPE: 1, CLAUSE: 4\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground\np(T1, +(*(T292, T294), *(T293, T295))) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: p(T1, T2), SCOPE: 1, CLAUSE: 4\n\nT2 is ground\np(T1, T2) !=? p(d(e(t)), const(1))\np(T1, T2) !=? p(d(e(const(X320))), const(0))\np(T1, T2) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T2) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 0 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 1 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 2 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 3 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 4 | ?_7 | p(T1, +(*(T292, T294), *(T293, T295))), SCOPE: 1, CLAUSE: 4\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground\np(T1, +(*(T292, T294), *(T293, T295))) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 0\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 1 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 2 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 3 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 4 | ?_7 | p(T1, +(*(T292, T294), *(T293, T295))), SCOPE: 1, CLAUSE: 4\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground\np(T1, +(*(T292, T294), *(T293, T295))) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: p(d(e(T293)), T294)\n\nT294 is ground\nT293 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 1\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 2 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 3 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 4 | ?_7 | p(T1, +(*(T292, T294), *(T293, T295))), SCOPE: 1, CLAUSE: 4\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground\np(T1, +(*(T292, T294), *(T293, T295))) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: p(d(e(T293)), T294)\n\nT294 is ground\nT293 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 2\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 3 | ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 4 | ?_7 | p(T1, +(*(T292, T294), *(T293, T295))), SCOPE: 1, CLAUSE: 4\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground\np(T1, +(*(T292, T294), *(T293, T295))) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: ','(p(d(e(T317)), T319), ','(p(d(e(T318)), T320), p(d(e(T293)), T294)))\n\nT294 is ground\nT293 is ground\nT317 is ground\nT318 is ground\nT319 is ground\nT320 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 3\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: ','(p(d(e(T292)), T295), p(d(e(T293)), T294)), SCOPE: 7, CLAUSE: 4 | ?_7 | p(T1, +(*(T292, T294), *(T293, T295))), SCOPE: 1, CLAUSE: 4\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground\np(T1, +(*(T292, T294), *(T293, T295))) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: ','(p(d(e(T337)), T340), ','(p(d(e(T338)), T339), p(d(e(T293)), T294)))\n\nT294 is ground\nT293 is ground\nT337 is ground\nT338 is ground\nT339 is ground\nT340 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ?_7 | p(T1, +(*(T292, T294), *(T293, T295))), SCOPE: 1, CLAUSE: 4\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground\np(T1, +(*(T292, T294), *(T293, T295))) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: p(T1, +(*(T292, T294), *(T293, T295))), SCOPE: 1, CLAUSE: 4\n\nT292 is ground\nT294 is ground\nT293 is ground\nT295 is ground\np(T1, +(*(T292, T294), *(T293, T295))) !=? p(d(e(+(X456, X457))), +(X458, X459))", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: ','(p(d(T356), X635), p(d(e(X635)), +(*(T352, T353), *(T354, T355))))\n\nT352 is ground\nT353 is ground\nT354 is ground\nT355 is ground\nX635 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: ','(p(d(T361), X642), p(d(e(X642)), T360))\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 0 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 1 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 2 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 3 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 4\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 0\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 1 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 2 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 3 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 4\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: p(d(e(const(1))), T360)\n\nT360 is ground\np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 1\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 2 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 3 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 4\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: p(d(e(const(0))), T360)\n\nT360 is ground\np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 2\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 3 | ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 4\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: ','(p(d(e(T377)), X683), ','(p(d(e(T378)), X684), p(d(e(+(X683, X684))), T360)))\n\nT360 is ground\nX683 is free; \nX684 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: p(d(e(T377)), X683)\n\nX683 is free", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: ','(p(d(e(T380)), X684), p(d(e(+(T379, X684))), T360))\n\nT360 is ground\nX684 is free; \np(T381, T360) !=? p(d(e(t)), const(1))\np(T381, T360) !=? p(d(e(const(T382))), const(0))\np(T381, T360) !=? p(d(e(+(T383, T384))), +(T385, T386))\np(T381, T360) !=? p(d(e(*(T387, T388))), +(*(T387, T389), *(T388, T390)))", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: p(d(e(T380)), X684)\n\nX684 is free", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: p(d(e(+(T392, T391))), T360)\n\nT360 is ground\np(T393, T360) !=? p(d(e(t)), const(1))\np(T393, T360) !=? p(d(e(const(T394))), const(0))\np(T393, T360) !=? p(d(e(+(T395, T396))), +(T397, T398))\np(T393, T360) !=? p(d(e(*(T399, T400))), +(*(T399, T401), *(T400, T402)))", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 3\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: ','(p(d(T361), X642), p(d(e(X642)), T360)), SCOPE: 8, CLAUSE: 4\n\nT360 is ground\nX642 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: ','(p(d(e(T417)), X724), ','(p(d(e(T418)), X723), p(d(e(+(*(T417, X723), *(T418, X724)))), T360)))\n\nT360 is ground\nX723 is free; \nX724 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: p(d(e(T417)), X724)\n\nX724 is free", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(p(d(e(T420)), X723), p(d(e(+(*(T421, X723), *(T420, T419)))), T360))\n\nT360 is ground\nX723 is free; \np(T422, T360) !=? p(d(e(t)), const(1))\np(T422, T360) !=? p(d(e(const(T423))), const(0))\np(T422, T360) !=? p(d(e(+(T424, T425))), +(T426, T427))\np(T422, T360) !=? p(d(e(*(T428, T429))), +(*(T428, T430), *(T429, T431)))", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: p(d(e(T420)), X723)\n\nX723 is free", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: p(d(e(+(*(T433, T432), *(T434, T435)))), T360)\n\nT360 is ground\np(T436, T360) !=? p(d(e(t)), const(1))\np(T436, T360) !=? p(d(e(const(T437))), const(0))\np(T436, T360) !=? p(d(e(+(T438, T439))), +(T440, T441))\np(T436, T360) !=? p(d(e(*(T442, T443))), +(*(T442, T444), *(T443, T445)))", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: ','(p(d(T455), X744), ','(p(d(e(X744)), X745), p(d(e(X745)), T360)))\n\nT360 is ground\nX745 is free; \nX744 is free; \np(T1, T360) !=? p(d(e(t)), const(1))\np(T1, T360) !=? p(d(e(const(X320))), const(0))\np(T1, T360) !=? p(d(e(+(X456, X457))), +(X458, X459))\np(T1, T360) !=? p(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567)))", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: p(d(T455), X744)\n\nX744 is free", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ','(p(d(e(T456)), X745), p(d(e(X745)), T360))\n\nT360 is ground\nX745 is free; \np(T457, T360) !=? p(d(e(t)), const(1))\np(T457, T360) !=? p(d(e(const(T458))), const(0))\np(T457, T360) !=? p(d(e(+(T459, T460))), +(T461, T462))\np(T457, T360) !=? p(d(e(*(T463, T464))), +(*(T463, T465), *(T464, T466)))", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: p(d(e(T456)), X745)\n\nX745 is free", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: p(d(e(T467)), T360)\n\nT360 is ground\np(T468, T360) !=? p(d(e(t)), const(1))\np(T468, T360) !=? p(d(e(const(T469))), const(0))\np(T468, T360) !=? p(d(e(+(T470, T471))), +(T472, T473))\np(T468, T360) !=? p(d(e(*(T474, T475))), +(*(T474, T476), *(T475, T477)))", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 210 [arrowhead = none ];
210 -> 2;

211 [label="EVAL with clause\np(d(e(t)), const(1)).\nand substitution\nT1 -> d(e(t))\nT2 -> const(1)", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 211 [arrowhead = none ];
211 -> 3;

212 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 212 [arrowhead = none ];
212 -> 4;

213 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 213 [arrowhead = none ];
213 -> 5;

214 [label="EVAL with clause\np(d(e(const(X320))), const(0)).\nand substitution\nX320 -> T128\nT1 -> d(e(const(T128)))\nT2 -> const(0)", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 214 [arrowhead = none ];
214 -> 85;

215 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 215 [arrowhead = none ];
215 -> 86;

216 [label="BACKTRACK\nfor clause: p(d(e(const(A))), const(0))because of non-unification", fontsize=14, style = filled, fillcolor = white];
5 -> 216 [arrowhead = none ];
216 -> 6;

217 [label="BACKTRACK\nfor clause: p(d(e(+(X, Y))), +(DX, DY)) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY))because of non-unification", fontsize=14, style = filled, fillcolor = white];
6 -> 217 [arrowhead = none ];
217 -> 7;

218 [label="BACKTRACK\nfor clause: p(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY))because of non-unification", fontsize=14, style = filled, fillcolor = white];
7 -> 218 [arrowhead = none ];
218 -> 8;

219 [label="EVAL with clause\np(d(d(X12)), X13) :- ','(p(d(X12), X14), p(d(e(X14)), X13)).\nand substitution\nX12 -> T10\nT1 -> d(d(T10))\nX13 -> const(1)\nT9 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 219 [arrowhead = none ];
219 -> 9;

220 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 220 [arrowhead = none ];
220 -> 10;

221 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 221 [arrowhead = none ];
221 -> 11;

222 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 222 [arrowhead = none ];
222 -> 12;

223 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 223 [arrowhead = none ];
223 -> 13;

224 [label="EVAL with clause\np(d(e(t)), const(1)).\nand substitution\nT10 -> e(t)\nX14 -> const(1)", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 224 [arrowhead = none ];
224 -> 14;

225 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 225 [arrowhead = none ];
225 -> 15;

226 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 226 [arrowhead = none ];
226 -> 16;

227 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 227 [arrowhead = none ];
227 -> 17;

228 [label="INSTANCE with matching:\nT1 -> d(e(const(1)))\nT2 -> const(1)", fontsize=14, style = filled, fillcolor = lightgrey];
14 -> 228 [arrowhead = none , style=dashed];
228 -> 1[style=dashed];

229 [label="EVAL with clause\np(d(e(const(X34))), const(0)).\nand substitution\nX34 -> T15\nT10 -> e(const(T15))\nX14 -> const(0)", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 229 [arrowhead = none ];
229 -> 18;

230 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 230 [arrowhead = none ];
230 -> 19;

231 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
17 -> 231 [arrowhead = none ];
231 -> 20;

232 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
17 -> 232 [arrowhead = none ];
232 -> 21;

233 [label="INSTANCE with matching:\nT1 -> d(e(const(0)))\nT2 -> const(1)", fontsize=14, style = filled, fillcolor = lightgrey];
18 -> 233 [arrowhead = none , style=dashed];
233 -> 1[style=dashed];

234 [label="EVAL with clause\np(d(e(+(X73, X74))), +(X75, X76)) :- ','(p(d(e(X73)), X75), p(d(e(X74)), X76)).\nand substitution\nX73 -> T26\nX74 -> T27\nT10 -> e(+(T26, T27))\nX75 -> X77\nX76 -> X78\nX14 -> +(X77, X78)\nT24 -> T26\nT25 -> T27", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 234 [arrowhead = none ];
234 -> 22;

235 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 235 [arrowhead = none ];
235 -> 23;

236 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 236 [arrowhead = none ];
236 -> 50;

237 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 237 [arrowhead = none ];
237 -> 51;

238 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
22 -> 238 [arrowhead = none ];
238 -> 24;

239 [label="SPLIT 2\nreplacements:\nX77 -> T28\nT27 -> T29", fontsize=14, style = filled, fillcolor = violet];
22 -> 239 [arrowhead = none ];
239 -> 25;

240 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
24 -> 240 [arrowhead = none ];
240 -> 26;

241 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
25 -> 241 [arrowhead = none ];
241 -> 48;

242 [label="SPLIT 2\nreplacements:\nX78 -> T61\nT28 -> T62", fontsize=14, style = filled, fillcolor = violet];
25 -> 242 [arrowhead = none ];
242 -> 49;

243 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 243 [arrowhead = none ];
243 -> 27;

244 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 244 [arrowhead = none ];
244 -> 28;

245 [label="EVAL with clause\np(d(e(t)), const(1)).\nand substitution\nT26 -> t\nX77 -> const(1)", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 245 [arrowhead = none ];
245 -> 29;

246 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
27 -> 246 [arrowhead = none ];
246 -> 30;

247 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
28 -> 247 [arrowhead = none ];
247 -> 32;

248 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
28 -> 248 [arrowhead = none ];
248 -> 33;

249 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
29 -> 249 [arrowhead = none ];
249 -> 31;

250 [label="EVAL with clause\np(d(e(const(X87))), const(0)).\nand substitution\nX87 -> T34\nT26 -> const(T34)\nX77 -> const(0)", fontsize=14, style = filled, fillcolor = lightblue];
32 -> 250 [arrowhead = none ];
250 -> 34;

251 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
32 -> 251 [arrowhead = none ];
251 -> 35;

252 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
33 -> 252 [arrowhead = none ];
252 -> 37;

253 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
33 -> 253 [arrowhead = none ];
253 -> 38;

254 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
34 -> 254 [arrowhead = none ];
254 -> 36;

255 [label="EVAL with clause\np(d(e(+(X113, X114))), +(X115, X116)) :- ','(p(d(e(X113)), X115), p(d(e(X114)), X116)).\nand substitution\nX113 -> T45\nX114 -> T46\nT26 -> +(T45, T46)\nX115 -> X117\nX116 -> X118\nX77 -> +(X117, X118)\nT43 -> T45\nT44 -> T46", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 255 [arrowhead = none ];
255 -> 39;

256 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 256 [arrowhead = none ];
256 -> 40;

257 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 257 [arrowhead = none ];
257 -> 43;

258 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 258 [arrowhead = none ];
258 -> 44;

259 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
39 -> 259 [arrowhead = none ];
259 -> 41;

260 [label="SPLIT 2\nreplacements:\nX117 -> T47\nT46 -> T48", fontsize=14, style = filled, fillcolor = violet];
39 -> 260 [arrowhead = none ];
260 -> 42;

261 [label="INSTANCE with matching:\nT26 -> T45\nX77 -> X117", fontsize=14, style = filled, fillcolor = lightgrey];
41 -> 261 [arrowhead = none , style=dashed];
261 -> 24[style=dashed];

262 [label="INSTANCE with matching:\nT26 -> T48\nX77 -> X118", fontsize=14, style = filled, fillcolor = lightgrey];
42 -> 262 [arrowhead = none , style=dashed];
262 -> 24[style=dashed];

263 [label="EVAL with clause\np(d(e(*(X147, X148))), +(*(X147, X149), *(X148, X150))) :- ','(p(d(e(X147)), X150), p(d(e(X148)), X149)).\nand substitution\nX147 -> T59\nX148 -> T60\nT26 -> *(T59, T60)\nX149 -> X151\nX150 -> X152\nX77 -> +(*(T59, X151), *(T60, X152))\nT57 -> T59\nT58 -> T60", fontsize=14, style = filled, fillcolor = lightblue];
43 -> 263 [arrowhead = none ];
263 -> 45;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
43 -> 264 [arrowhead = none ];
264 -> 46;

265 [label="BACKTRACK\nfor clause: p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX))because of non-unification", fontsize=14, style = filled, fillcolor = white];
44 -> 265 [arrowhead = none ];
265 -> 47;

266 [label="INSTANCE with matching:\nT45 -> T59\nX117 -> X152\nT46 -> T60\nX118 -> X151", fontsize=14, style = filled, fillcolor = lightgrey];
45 -> 266 [arrowhead = none , style=dashed];
266 -> 39[style=dashed];

267 [label="INSTANCE with matching:\nT26 -> T29\nX77 -> X78", fontsize=14, style = filled, fillcolor = lightgrey];
48 -> 267 [arrowhead = none , style=dashed];
267 -> 24[style=dashed];

268 [label="INSTANCE with matching:\nT1 -> d(e(+(T62, T61)))\nT2 -> const(1)", fontsize=14, style = filled, fillcolor = lightgrey];
49 -> 268 [arrowhead = none , style=dashed];
268 -> 1[style=dashed];

269 [label="EVAL with clause\np(d(e(*(X196, X197))), +(*(X196, X198), *(X197, X199))) :- ','(p(d(e(X196)), X199), p(d(e(X197)), X198)).\nand substitution\nX196 -> T75\nX197 -> T76\nT10 -> e(*(T75, T76))\nX198 -> X200\nX199 -> X201\nX14 -> +(*(T75, X200), *(T76, X201))\nT73 -> T75\nT74 -> T76", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 269 [arrowhead = none ];
269 -> 52;

270 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 270 [arrowhead = none ];
270 -> 53;

271 [label="EVAL with clause\np(d(d(X226)), X227) :- ','(p(d(X226), X228), p(d(e(X228)), X227)).\nand substitution\nX226 -> T91\nT10 -> d(T91)\nX14 -> X229\nX227 -> X229\nT90 -> T91", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 271 [arrowhead = none ];
271 -> 58;

272 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
51 -> 272 [arrowhead = none ];
272 -> 59;

273 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
52 -> 273 [arrowhead = none ];
273 -> 54;

274 [label="SPLIT 2\nreplacements:\nX201 -> T77\nT76 -> T78\nT75 -> T79", fontsize=14, style = filled, fillcolor = violet];
52 -> 274 [arrowhead = none ];
274 -> 55;

275 [label="INSTANCE with matching:\nT26 -> T75\nX77 -> X201", fontsize=14, style = filled, fillcolor = lightgrey];
54 -> 275 [arrowhead = none , style=dashed];
275 -> 24[style=dashed];

276 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
55 -> 276 [arrowhead = none ];
276 -> 56;

277 [label="SPLIT 2\nreplacements:\nX200 -> T80\nT79 -> T81\nT78 -> T82\nT77 -> T83", fontsize=14, style = filled, fillcolor = violet];
55 -> 277 [arrowhead = none ];
277 -> 57;

278 [label="INSTANCE with matching:\nT26 -> T78\nX77 -> X200", fontsize=14, style = filled, fillcolor = lightgrey];
56 -> 278 [arrowhead = none , style=dashed];
278 -> 24[style=dashed];

279 [label="INSTANCE with matching:\nT1 -> d(e(+(*(T81, T80), *(T82, T83))))\nT2 -> const(1)", fontsize=14, style = filled, fillcolor = lightgrey];
57 -> 279 [arrowhead = none , style=dashed];
279 -> 1[style=dashed];

280 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
58 -> 280 [arrowhead = none ];
280 -> 60;

281 [label="SPLIT 2\nreplacements:\nX228 -> T92", fontsize=14, style = filled, fillcolor = violet];
58 -> 281 [arrowhead = none ];
281 -> 61;

282 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
60 -> 282 [arrowhead = none ];
282 -> 62;

283 [label="INSTANCE with matching:\nT10 -> e(T92)\nX14 -> X229", fontsize=14, style = filled, fillcolor = lightgrey];
61 -> 283 [arrowhead = none , style=dashed];
283 -> 9[style=dashed];

284 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
62 -> 284 [arrowhead = none ];
284 -> 63;

285 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
62 -> 285 [arrowhead = none ];
285 -> 64;

286 [label="EVAL with clause\np(d(e(t)), const(1)).\nand substitution\nT91 -> e(t)\nX228 -> const(1)", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 286 [arrowhead = none ];
286 -> 65;

287 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 287 [arrowhead = none ];
287 -> 66;

288 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
64 -> 288 [arrowhead = none ];
288 -> 68;

289 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
64 -> 289 [arrowhead = none ];
289 -> 69;

290 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
65 -> 290 [arrowhead = none ];
290 -> 67;

291 [label="EVAL with clause\np(d(e(const(X236))), const(0)).\nand substitution\nX236 -> T97\nT91 -> e(const(T97))\nX228 -> const(0)", fontsize=14, style = filled, fillcolor = lightblue];
68 -> 291 [arrowhead = none ];
291 -> 70;

292 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
68 -> 292 [arrowhead = none ];
292 -> 71;

293 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
69 -> 293 [arrowhead = none ];
293 -> 73;

294 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
69 -> 294 [arrowhead = none ];
294 -> 74;

295 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
70 -> 295 [arrowhead = none ];
295 -> 72;

296 [label="EVAL with clause\np(d(e(+(X262, X263))), +(X264, X265)) :- ','(p(d(e(X262)), X264), p(d(e(X263)), X265)).\nand substitution\nX262 -> T108\nX263 -> T109\nT91 -> e(+(T108, T109))\nX264 -> X266\nX265 -> X267\nX228 -> +(X266, X267)\nT106 -> T108\nT107 -> T109", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 296 [arrowhead = none ];
296 -> 75;

297 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
73 -> 297 [arrowhead = none ];
297 -> 76;

298 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 298 [arrowhead = none ];
298 -> 77;

299 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 299 [arrowhead = none ];
299 -> 78;

300 [label="INSTANCE with matching:\nT45 -> T108\nX117 -> X266\nT46 -> T109\nX118 -> X267", fontsize=14, style = filled, fillcolor = lightgrey];
75 -> 300 [arrowhead = none , style=dashed];
300 -> 39[style=dashed];

301 [label="EVAL with clause\np(d(e(*(X296, X297))), +(*(X296, X298), *(X297, X299))) :- ','(p(d(e(X296)), X299), p(d(e(X297)), X298)).\nand substitution\nX296 -> T120\nX297 -> T121\nT91 -> e(*(T120, T121))\nX298 -> X300\nX299 -> X301\nX228 -> +(*(T120, X300), *(T121, X301))\nT118 -> T120\nT119 -> T121", fontsize=14, style = filled, fillcolor = lightblue];
77 -> 301 [arrowhead = none ];
301 -> 79;

302 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
77 -> 302 [arrowhead = none ];
302 -> 80;

303 [label="EVAL with clause\np(d(d(X313)), X314) :- ','(p(d(X313), X315), p(d(e(X315)), X314)).\nand substitution\nX313 -> T125\nT91 -> d(T125)\nX228 -> X316\nX314 -> X316\nT124 -> T125", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 303 [arrowhead = none ];
303 -> 81;

304 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
78 -> 304 [arrowhead = none ];
304 -> 82;

305 [label="INSTANCE with matching:\nT45 -> T120\nX117 -> X301\nT46 -> T121\nX118 -> X300", fontsize=14, style = filled, fillcolor = lightgrey];
79 -> 305 [arrowhead = none , style=dashed];
305 -> 39[style=dashed];

306 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
81 -> 306 [arrowhead = none ];
306 -> 83;

307 [label="SPLIT 2\nreplacements:\nX315 -> T126", fontsize=14, style = filled, fillcolor = violet];
81 -> 307 [arrowhead = none ];
307 -> 84;

308 [label="INSTANCE with matching:\nT91 -> T125\nX228 -> X315", fontsize=14, style = filled, fillcolor = lightgrey];
83 -> 308 [arrowhead = none , style=dashed];
308 -> 60[style=dashed];

309 [label="INSTANCE with matching:\nT26 -> T126\nX77 -> X316", fontsize=14, style = filled, fillcolor = lightgrey];
84 -> 309 [arrowhead = none , style=dashed];
309 -> 24[style=dashed];

310 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
85 -> 310 [arrowhead = none ];
310 -> 87;

311 [label="EVAL with clause\np(d(e(+(X456, X457))), +(X458, X459)) :- ','(p(d(e(X456)), X458), p(d(e(X457)), X459)).\nand substitution\nX456 -> T195\nX457 -> T196\nT1 -> d(e(+(T195, T196)))\nX458 -> T193\nX459 -> T194\nT2 -> +(T193, T194)\nT191 -> T195\nT192 -> T196", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 311 [arrowhead = none ];
311 -> 121;

312 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 312 [arrowhead = none ];
312 -> 122;

313 [label="BACKTRACK\nfor clause: p(d(e(+(X, Y))), +(DX, DY)) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY))because of non-unification", fontsize=14, style = filled, fillcolor = white];
87 -> 313 [arrowhead = none ];
313 -> 88;

314 [label="BACKTRACK\nfor clause: p(d(e(*(X, Y))), +(*(X, DY), *(Y, DX))) :- ','(p(d(e(X)), DX), p(d(e(Y)), DY))because of non-unification", fontsize=14, style = filled, fillcolor = white];
88 -> 314 [arrowhead = none ];
314 -> 89;

315 [label="EVAL with clause\np(d(d(X332)), X333) :- ','(p(d(X332), X334), p(d(e(X334)), X333)).\nand substitution\nX332 -> T135\nT1 -> d(d(T135))\nX333 -> const(0)\nT134 -> T135", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 315 [arrowhead = none ];
315 -> 90;

316 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
89 -> 316 [arrowhead = none ];
316 -> 91;

317 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
90 -> 317 [arrowhead = none ];
317 -> 92;

318 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
92 -> 318 [arrowhead = none ];
318 -> 93;

319 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
92 -> 319 [arrowhead = none ];
319 -> 94;

320 [label="EVAL with clause\np(d(e(t)), const(1)).\nand substitution\nT135 -> e(t)\nX334 -> const(1)", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 320 [arrowhead = none ];
320 -> 95;

321 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 321 [arrowhead = none ];
321 -> 96;

322 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
94 -> 322 [arrowhead = none ];
322 -> 97;

323 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
94 -> 323 [arrowhead = none ];
323 -> 98;

324 [label="INSTANCE with matching:\nT1 -> d(e(const(1)))\nT2 -> const(0)", fontsize=14, style = filled, fillcolor = lightgrey];
95 -> 324 [arrowhead = none , style=dashed];
324 -> 1[style=dashed];

325 [label="EVAL with clause\np(d(e(const(X342))), const(0)).\nand substitution\nX342 -> T140\nT135 -> e(const(T140))\nX334 -> const(0)", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 325 [arrowhead = none ];
325 -> 99;

326 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 326 [arrowhead = none ];
326 -> 100;

327 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
98 -> 327 [arrowhead = none ];
327 -> 101;

328 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
98 -> 328 [arrowhead = none ];
328 -> 102;

329 [label="INSTANCE with matching:\nT1 -> d(e(const(0)))\nT2 -> const(0)", fontsize=14, style = filled, fillcolor = lightgrey];
99 -> 329 [arrowhead = none , style=dashed];
329 -> 1[style=dashed];

330 [label="EVAL with clause\np(d(e(+(X369, X370))), +(X371, X372)) :- ','(p(d(e(X369)), X371), p(d(e(X370)), X372)).\nand substitution\nX369 -> T151\nX370 -> T152\nT135 -> e(+(T151, T152))\nX371 -> X373\nX372 -> X374\nX334 -> +(X373, X374)\nT149 -> T151\nT150 -> T152", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 330 [arrowhead = none ];
330 -> 103;

331 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
101 -> 331 [arrowhead = none ];
331 -> 104;

332 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
102 -> 332 [arrowhead = none ];
332 -> 109;

333 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
102 -> 333 [arrowhead = none ];
333 -> 110;

334 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
103 -> 334 [arrowhead = none ];
334 -> 105;

335 [label="SPLIT 2\nreplacements:\nX373 -> T153\nT152 -> T154", fontsize=14, style = filled, fillcolor = violet];
103 -> 335 [arrowhead = none ];
335 -> 106;

336 [label="INSTANCE with matching:\nT26 -> T151\nX77 -> X373", fontsize=14, style = filled, fillcolor = lightgrey];
105 -> 336 [arrowhead = none , style=dashed];
336 -> 24[style=dashed];

337 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
106 -> 337 [arrowhead = none ];
337 -> 107;

338 [label="SPLIT 2\nreplacements:\nX374 -> T155\nT153 -> T156", fontsize=14, style = filled, fillcolor = violet];
106 -> 338 [arrowhead = none ];
338 -> 108;

339 [label="INSTANCE with matching:\nT26 -> T154\nX77 -> X374", fontsize=14, style = filled, fillcolor = lightgrey];
107 -> 339 [arrowhead = none , style=dashed];
339 -> 24[style=dashed];

340 [label="INSTANCE with matching:\nT1 -> d(e(+(T156, T155)))\nT2 -> const(0)", fontsize=14, style = filled, fillcolor = lightgrey];
108 -> 340 [arrowhead = none , style=dashed];
340 -> 1[style=dashed];

341 [label="EVAL with clause\np(d(e(*(X416, X417))), +(*(X416, X418), *(X417, X419))) :- ','(p(d(e(X416)), X419), p(d(e(X417)), X418)).\nand substitution\nX416 -> T169\nX417 -> T170\nT135 -> e(*(T169, T170))\nX418 -> X420\nX419 -> X421\nX334 -> +(*(T169, X420), *(T170, X421))\nT167 -> T169\nT168 -> T170", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 341 [arrowhead = none ];
341 -> 111;

342 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 342 [arrowhead = none ];
342 -> 112;

343 [label="EVAL with clause\np(d(d(X446)), X447) :- ','(p(d(X446), X448), p(d(e(X448)), X447)).\nand substitution\nX446 -> T185\nT135 -> d(T185)\nX334 -> X449\nX447 -> X449\nT184 -> T185", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 343 [arrowhead = none ];
343 -> 117;

344 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
110 -> 344 [arrowhead = none ];
344 -> 118;

345 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
111 -> 345 [arrowhead = none ];
345 -> 113;

346 [label="SPLIT 2\nreplacements:\nX421 -> T171\nT170 -> T172\nT169 -> T173", fontsize=14, style = filled, fillcolor = violet];
111 -> 346 [arrowhead = none ];
346 -> 114;

347 [label="INSTANCE with matching:\nT26 -> T169\nX77 -> X421", fontsize=14, style = filled, fillcolor = lightgrey];
113 -> 347 [arrowhead = none , style=dashed];
347 -> 24[style=dashed];

348 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
114 -> 348 [arrowhead = none ];
348 -> 115;

349 [label="SPLIT 2\nreplacements:\nX420 -> T174\nT173 -> T175\nT172 -> T176\nT171 -> T177", fontsize=14, style = filled, fillcolor = violet];
114 -> 349 [arrowhead = none ];
349 -> 116;

350 [label="INSTANCE with matching:\nT26 -> T172\nX77 -> X420", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 350 [arrowhead = none , style=dashed];
350 -> 24[style=dashed];

351 [label="INSTANCE with matching:\nT1 -> d(e(+(*(T175, T174), *(T176, T177))))\nT2 -> const(0)", fontsize=14, style = filled, fillcolor = lightgrey];
116 -> 351 [arrowhead = none , style=dashed];
351 -> 1[style=dashed];

352 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
117 -> 352 [arrowhead = none ];
352 -> 119;

353 [label="SPLIT 2\nreplacements:\nX448 -> T186", fontsize=14, style = filled, fillcolor = violet];
117 -> 353 [arrowhead = none ];
353 -> 120;

354 [label="INSTANCE with matching:\nT91 -> T185\nX228 -> X448", fontsize=14, style = filled, fillcolor = lightgrey];
119 -> 354 [arrowhead = none , style=dashed];
354 -> 60[style=dashed];

355 [label="INSTANCE with matching:\nT135 -> e(T186)\nX334 -> X449", fontsize=14, style = filled, fillcolor = lightgrey];
120 -> 355 [arrowhead = none , style=dashed];
355 -> 90[style=dashed];

356 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
121 -> 356 [arrowhead = none ];
356 -> 123;

357 [label="EVAL with clause\np(d(e(*(X564, X565))), +(*(X564, X566), *(X565, X567))) :- ','(p(d(e(X564)), X567), p(d(e(X565)), X566)).\nand substitution\nX564 -> T292\nX565 -> T293\nT1 -> d(e(*(T292, T293)))\nX566 -> T294\nX567 -> T295\nT2 -> +(*(T292, T294), *(T293, T295))", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 357 [arrowhead = none ];
357 -> 154;

358 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 358 [arrowhead = none ];
358 -> 155;

359 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
123 -> 359 [arrowhead = none ];
359 -> 124;

360 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
123 -> 360 [arrowhead = none ];
360 -> 125;

361 [label="EVAL with clause\np(d(e(t)), const(1)).\nand substitution\nT195 -> t\nT193 -> const(1)\nT196 -> T197", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 361 [arrowhead = none ];
361 -> 126;

362 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
124 -> 362 [arrowhead = none ];
362 -> 127;

363 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
125 -> 363 [arrowhead = none ];
363 -> 128;

364 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
125 -> 364 [arrowhead = none ];
364 -> 129;

365 [label="INSTANCE with matching:\nT1 -> d(e(T197))\nT2 -> T194", fontsize=14, style = filled, fillcolor = lightgrey];
126 -> 365 [arrowhead = none , style=dashed];
365 -> 1[style=dashed];

366 [label="EVAL with clause\np(d(e(const(X468))), const(0)).\nand substitution\nX468 -> T202\nT195 -> const(T202)\nT193 -> const(0)\nT196 -> T203", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 366 [arrowhead = none ];
366 -> 130;

367 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
128 -> 367 [arrowhead = none ];
367 -> 131;

368 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 368 [arrowhead = none ];
368 -> 132;

369 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
129 -> 369 [arrowhead = none ];
369 -> 133;

370 [label="INSTANCE with matching:\nT1 -> d(e(T203))\nT2 -> T194", fontsize=14, style = filled, fillcolor = lightgrey];
130 -> 370 [arrowhead = none , style=dashed];
370 -> 1[style=dashed];

371 [label="EVAL with clause\np(d(e(+(X486, X487))), +(X488, X489)) :- ','(p(d(e(X486)), X488), p(d(e(X487)), X489)).\nand substitution\nX486 -> T224\nX487 -> T225\nT195 -> +(T224, T225)\nX488 -> T222\nX489 -> T223\nT193 -> +(T222, T223)\nT220 -> T224\nT221 -> T225\nT196 -> T226", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 371 [arrowhead = none ];
371 -> 134;

372 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 372 [arrowhead = none ];
372 -> 135;

373 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
133 -> 373 [arrowhead = none ];
373 -> 140;

374 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
133 -> 374 [arrowhead = none ];
374 -> 141;

375 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
134 -> 375 [arrowhead = none ];
375 -> 136;

376 [label="SPLIT 2\nreplacements:\nT225 -> T227\nT226 -> T228", fontsize=14, style = filled, fillcolor = violet];
134 -> 376 [arrowhead = none ];
376 -> 137;

377 [label="INSTANCE with matching:\nT1 -> d(e(T224))\nT2 -> T222", fontsize=14, style = filled, fillcolor = lightgrey];
136 -> 377 [arrowhead = none , style=dashed];
377 -> 1[style=dashed];

378 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
137 -> 378 [arrowhead = none ];
378 -> 138;

379 [label="SPLIT 2\nreplacements:\nT228 -> T229", fontsize=14, style = filled, fillcolor = violet];
137 -> 379 [arrowhead = none ];
379 -> 139;

380 [label="INSTANCE with matching:\nT1 -> d(e(T227))\nT2 -> T223", fontsize=14, style = filled, fillcolor = lightgrey];
138 -> 380 [arrowhead = none , style=dashed];
380 -> 1[style=dashed];

381 [label="INSTANCE with matching:\nT1 -> d(e(T229))\nT2 -> T194", fontsize=14, style = filled, fillcolor = lightgrey];
139 -> 381 [arrowhead = none , style=dashed];
381 -> 1[style=dashed];

382 [label="EVAL with clause\np(d(e(*(X510, X511))), +(*(X510, X512), *(X511, X513))) :- ','(p(d(e(X510)), X513), p(d(e(X511)), X512)).\nand substitution\nX510 -> T246\nX511 -> T247\nT195 -> *(T246, T247)\nX512 -> T248\nX513 -> T249\nT193 -> +(*(T246, T248), *(T247, T249))\nT196 -> T250", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 382 [arrowhead = none ];
382 -> 142;

383 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
140 -> 383 [arrowhead = none ];
383 -> 143;

384 [label="BACKTRACK\nfor clause: p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX))because of non-unification", fontsize=14, style = filled, fillcolor = white];
141 -> 384 [arrowhead = none ];
384 -> 144;

385 [label="INSTANCE with matching:\nT224 -> T246\nT222 -> T249\nT225 -> T247\nT223 -> T248\nT226 -> T250", fontsize=14, style = filled, fillcolor = lightgrey];
142 -> 385 [arrowhead = none , style=dashed];
385 -> 134[style=dashed];

386 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
144 -> 386 [arrowhead = none ];
386 -> 145;

387 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
145 -> 387 [arrowhead = none ];
387 -> 146;

388 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
145 -> 388 [arrowhead = none ];
388 -> 147;

389 [label="EVAL with clause\np(d(e(*(X536, X537))), +(*(X536, X538), *(X537, X539))) :- ','(p(d(e(X536)), X539), p(d(e(X537)), X538)).\nand substitution\nX536 -> T267\nX537 -> T268\nT1 -> d(e(*(T267, T268)))\nX538 -> T269\nT193 -> *(T267, T269)\nX539 -> T270\nT194 -> *(T268, T270)", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 389 [arrowhead = none ];
389 -> 148;

390 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
146 -> 390 [arrowhead = none ];
390 -> 149;

391 [label="EVAL with clause\np(d(d(X549)), X550) :- ','(p(d(X549), X551), p(d(e(X551)), X550)).\nand substitution\nX549 -> T280\nT1 -> d(d(T280))\nT193 -> T278\nT194 -> T279\nX550 -> +(T278, T279)\nT277 -> T280", fontsize=14, style = filled, fillcolor = lightblue];
147 -> 391 [arrowhead = none ];
391 -> 150;

392 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
147 -> 392 [arrowhead = none ];
392 -> 151;

393 [label="INSTANCE with matching:\nT227 -> T267\nT223 -> T270\nT228 -> T268\nT194 -> T269", fontsize=14, style = filled, fillcolor = lightgrey];
148 -> 393 [arrowhead = none , style=dashed];
393 -> 137[style=dashed];

394 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
150 -> 394 [arrowhead = none ];
394 -> 152;

395 [label="SPLIT 2\nreplacements:\nX551 -> T281", fontsize=14, style = filled, fillcolor = violet];
150 -> 395 [arrowhead = none ];
395 -> 153;

396 [label="INSTANCE with matching:\nT91 -> T280\nX228 -> X551", fontsize=14, style = filled, fillcolor = lightgrey];
152 -> 396 [arrowhead = none , style=dashed];
396 -> 60[style=dashed];

397 [label="INSTANCE with matching:\nT1 -> d(e(T281))\nT2 -> +(T278, T279)", fontsize=14, style = filled, fillcolor = lightgrey];
153 -> 397 [arrowhead = none , style=dashed];
397 -> 1[style=dashed];

398 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
154 -> 398 [arrowhead = none ];
398 -> 156;

399 [label="EVAL with clause\np(d(d(X640)), X641) :- ','(p(d(X640), X642), p(d(e(X642)), X641)).\nand substitution\nX640 -> T361\nT1 -> d(d(T361))\nT2 -> T360\nX641 -> T360\nT359 -> T361", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 399 [arrowhead = none ];
399 -> 177;

400 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 400 [arrowhead = none ];
400 -> 178;

401 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
156 -> 401 [arrowhead = none ];
401 -> 157;

402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
156 -> 402 [arrowhead = none ];
402 -> 158;

403 [label="EVAL with clause\np(d(e(t)), const(1)).\nand substitution\nT292 -> t\nT295 -> const(1)", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 403 [arrowhead = none ];
403 -> 159;

404 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
157 -> 404 [arrowhead = none ];
404 -> 160;

405 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
158 -> 405 [arrowhead = none ];
405 -> 161;

406 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
158 -> 406 [arrowhead = none ];
406 -> 162;

407 [label="INSTANCE with matching:\nT1 -> d(e(T293))\nT2 -> T294", fontsize=14, style = filled, fillcolor = lightgrey];
159 -> 407 [arrowhead = none , style=dashed];
407 -> 1[style=dashed];

408 [label="EVAL with clause\np(d(e(const(X576))), const(0)).\nand substitution\nX576 -> T300\nT292 -> const(T300)\nT295 -> const(0)", fontsize=14, style = filled, fillcolor = lightblue];
161 -> 408 [arrowhead = none ];
408 -> 163;

409 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
161 -> 409 [arrowhead = none ];
409 -> 164;

410 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
162 -> 410 [arrowhead = none ];
410 -> 165;

411 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
162 -> 411 [arrowhead = none ];
411 -> 166;

412 [label="INSTANCE with matching:\nT1 -> d(e(T293))\nT2 -> T294", fontsize=14, style = filled, fillcolor = lightgrey];
163 -> 412 [arrowhead = none , style=dashed];
412 -> 1[style=dashed];

413 [label="EVAL with clause\np(d(e(+(X594, X595))), +(X596, X597)) :- ','(p(d(e(X594)), X596), p(d(e(X595)), X597)).\nand substitution\nX594 -> T317\nX595 -> T318\nT292 -> +(T317, T318)\nX596 -> T319\nX597 -> T320\nT295 -> +(T319, T320)", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 413 [arrowhead = none ];
413 -> 167;

414 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 414 [arrowhead = none ];
414 -> 168;

415 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 415 [arrowhead = none ];
415 -> 169;

416 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
166 -> 416 [arrowhead = none ];
416 -> 170;

417 [label="INSTANCE with matching:\nT224 -> T317\nT222 -> T319\nT225 -> T318\nT223 -> T320\nT226 -> T293\nT194 -> T294", fontsize=14, style = filled, fillcolor = lightgrey];
167 -> 417 [arrowhead = none , style=dashed];
417 -> 134[style=dashed];

418 [label="EVAL with clause\np(d(e(*(X618, X619))), +(*(X618, X620), *(X619, X621))) :- ','(p(d(e(X618)), X621), p(d(e(X619)), X620)).\nand substitution\nX618 -> T337\nX619 -> T338\nT292 -> *(T337, T338)\nX620 -> T339\nX621 -> T340\nT295 -> +(*(T337, T339), *(T338, T340))", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 418 [arrowhead = none ];
418 -> 171;

419 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
169 -> 419 [arrowhead = none ];
419 -> 172;

420 [label="BACKTRACK\nfor clause: p(d(d(X)), DDX) :- ','(p(d(X), DX), p(d(e(DX)), DDX))because of non-unification", fontsize=14, style = filled, fillcolor = white];
170 -> 420 [arrowhead = none ];
420 -> 173;

421 [label="INSTANCE with matching:\nT224 -> T337\nT222 -> T340\nT225 -> T338\nT223 -> T339\nT226 -> T293\nT194 -> T294", fontsize=14, style = filled, fillcolor = lightgrey];
171 -> 421 [arrowhead = none , style=dashed];
421 -> 134[style=dashed];

422 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 422 [arrowhead = none ];
422 -> 174;

423 [label="EVAL with clause\np(d(d(X633)), X634) :- ','(p(d(X633), X635), p(d(e(X635)), X634)).\nand substitution\nX633 -> T356\nT1 -> d(d(T356))\nT292 -> T352\nT294 -> T353\nT293 -> T354\nT295 -> T355\nX634 -> +(*(T352, T353), *(T354, T355))\nT351 -> T356", fontsize=14, style = filled, fillcolor = lightblue];
174 -> 423 [arrowhead = none ];
423 -> 175;

424 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
174 -> 424 [arrowhead = none ];
424 -> 176;

425 [label="INSTANCE with matching:\nT280 -> T356\nX551 -> X635\nT278 -> *(T352, T353)\nT279 -> *(T354, T355)", fontsize=14, style = filled, fillcolor = lightgrey];
175 -> 425 [arrowhead = none , style=dashed];
425 -> 150[style=dashed];

426 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
177 -> 426 [arrowhead = none ];
426 -> 179;

427 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
179 -> 427 [arrowhead = none ];
427 -> 180;

428 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
179 -> 428 [arrowhead = none ];
428 -> 181;

429 [label="EVAL with clause\np(d(e(t)), const(1)).\nand substitution\nT361 -> e(t)\nX642 -> const(1)", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 429 [arrowhead = none ];
429 -> 182;

430 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 430 [arrowhead = none ];
430 -> 183;

431 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
181 -> 431 [arrowhead = none ];
431 -> 184;

432 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
181 -> 432 [arrowhead = none ];
432 -> 185;

433 [label="INSTANCE with matching:\nT1 -> d(e(const(1)))\nT2 -> T360", fontsize=14, style = filled, fillcolor = lightgrey];
182 -> 433 [arrowhead = none , style=dashed];
433 -> 1[style=dashed];

434 [label="EVAL with clause\np(d(e(const(X651))), const(0)).\nand substitution\nX651 -> T366\nT361 -> e(const(T366))\nX642 -> const(0)", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 434 [arrowhead = none ];
434 -> 186;

435 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 435 [arrowhead = none ];
435 -> 187;

436 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
185 -> 436 [arrowhead = none ];
436 -> 188;

437 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
185 -> 437 [arrowhead = none ];
437 -> 189;

438 [label="INSTANCE with matching:\nT1 -> d(e(const(0)))\nT2 -> T360", fontsize=14, style = filled, fillcolor = lightgrey];
186 -> 438 [arrowhead = none , style=dashed];
438 -> 1[style=dashed];

439 [label="EVAL with clause\np(d(e(+(X679, X680))), +(X681, X682)) :- ','(p(d(e(X679)), X681), p(d(e(X680)), X682)).\nand substitution\nX679 -> T377\nX680 -> T378\nT361 -> e(+(T377, T378))\nX681 -> X683\nX682 -> X684\nX642 -> +(X683, X684)\nT375 -> T377\nT376 -> T378", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 439 [arrowhead = none ];
439 -> 190;

440 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
188 -> 440 [arrowhead = none ];
440 -> 191;

441 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
189 -> 441 [arrowhead = none ];
441 -> 196;

442 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
189 -> 442 [arrowhead = none ];
442 -> 197;

443 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
190 -> 443 [arrowhead = none ];
443 -> 192;

444 [label="SPLIT 2\nreplacements:\nX683 -> T379\nT378 -> T380\nT1 -> T381\nX320 -> T382\nX456 -> T383\nX457 -> T384\nX458 -> T385\nX459 -> T386\nX564 -> T387\nX565 -> T388\nX566 -> T389\nX567 -> T390", fontsize=14, style = filled, fillcolor = violet];
190 -> 444 [arrowhead = none ];
444 -> 193;

445 [label="INSTANCE with matching:\nT26 -> T377\nX77 -> X683", fontsize=14, style = filled, fillcolor = lightgrey];
192 -> 445 [arrowhead = none , style=dashed];
445 -> 24[style=dashed];

446 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
193 -> 446 [arrowhead = none ];
446 -> 194;

447 [label="SPLIT 2\nreplacements:\nX684 -> T391\nT379 -> T392\nT381 -> T393\nT382 -> T394\nT383 -> T395\nT384 -> T396\nT385 -> T397\nT386 -> T398\nT387 -> T399\nT388 -> T400\nT389 -> T401\nT390 -> T402", fontsize=14, style = filled, fillcolor = violet];
193 -> 447 [arrowhead = none ];
447 -> 195;

448 [label="INSTANCE with matching:\nT377 -> T380\nX683 -> X684", fontsize=14, style = filled, fillcolor = lightgrey];
194 -> 448 [arrowhead = none , style=dashed];
448 -> 192[style=dashed];

449 [label="INSTANCE with matching:\nT1 -> d(e(+(T392, T391)))\nT2 -> T360", fontsize=14, style = filled, fillcolor = lightgrey];
195 -> 449 [arrowhead = none , style=dashed];
449 -> 1[style=dashed];

450 [label="EVAL with clause\np(d(e(*(X719, X720))), +(*(X719, X721), *(X720, X722))) :- ','(p(d(e(X719)), X722), p(d(e(X720)), X721)).\nand substitution\nX719 -> T417\nX720 -> T418\nT361 -> e(*(T417, T418))\nX721 -> X723\nX722 -> X724\nX642 -> +(*(T417, X723), *(T418, X724))\nT415 -> T417\nT416 -> T418", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 450 [arrowhead = none ];
450 -> 198;

451 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 451 [arrowhead = none ];
451 -> 199;

452 [label="EVAL with clause\np(d(d(X742)), X743) :- ','(p(d(X742), X744), p(d(e(X744)), X743)).\nand substitution\nX742 -> T455\nT361 -> d(T455)\nX642 -> X745\nX743 -> X745\nT454 -> T455", fontsize=14, style = filled, fillcolor = lightblue];
197 -> 452 [arrowhead = none ];
452 -> 204;

453 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
197 -> 453 [arrowhead = none ];
453 -> 205;

454 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
198 -> 454 [arrowhead = none ];
454 -> 200;

455 [label="SPLIT 2\nreplacements:\nX724 -> T419\nT418 -> T420\nT417 -> T421\nT1 -> T422\nX320 -> T423\nX456 -> T424\nX457 -> T425\nX458 -> T426\nX459 -> T427\nX564 -> T428\nX565 -> T429\nX566 -> T430\nX567 -> T431", fontsize=14, style = filled, fillcolor = violet];
198 -> 455 [arrowhead = none ];
455 -> 201;

456 [label="INSTANCE with matching:\nT377 -> T417\nX683 -> X724", fontsize=14, style = filled, fillcolor = lightgrey];
200 -> 456 [arrowhead = none , style=dashed];
456 -> 192[style=dashed];

457 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
201 -> 457 [arrowhead = none ];
457 -> 202;

458 [label="SPLIT 2\nreplacements:\nX723 -> T432\nT421 -> T433\nT420 -> T434\nT419 -> T435\nT422 -> T436\nT423 -> T437\nT424 -> T438\nT425 -> T439\nT426 -> T440\nT427 -> T441\nT428 -> T442\nT429 -> T443\nT430 -> T444\nT431 -> T445", fontsize=14, style = filled, fillcolor = violet];
201 -> 458 [arrowhead = none ];
458 -> 203;

459 [label="INSTANCE with matching:\nT377 -> T420\nX683 -> X723", fontsize=14, style = filled, fillcolor = lightgrey];
202 -> 459 [arrowhead = none , style=dashed];
459 -> 192[style=dashed];

460 [label="INSTANCE with matching:\nT1 -> d(e(+(*(T433, T432), *(T434, T435))))\nT2 -> T360", fontsize=14, style = filled, fillcolor = lightgrey];
203 -> 460 [arrowhead = none , style=dashed];
460 -> 1[style=dashed];

461 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
204 -> 461 [arrowhead = none ];
461 -> 206;

462 [label="SPLIT 2\nreplacements:\nX744 -> T456\nT1 -> T457\nX320 -> T458\nX456 -> T459\nX457 -> T460\nX458 -> T461\nX459 -> T462\nX564 -> T463\nX565 -> T464\nX566 -> T465\nX567 -> T466", fontsize=14, style = filled, fillcolor = violet];
204 -> 462 [arrowhead = none ];
462 -> 207;

463 [label="INSTANCE with matching:\nT91 -> T455\nX228 -> X744", fontsize=14, style = filled, fillcolor = lightgrey];
206 -> 463 [arrowhead = none , style=dashed];
463 -> 60[style=dashed];

464 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
207 -> 464 [arrowhead = none ];
464 -> 208;

465 [label="SPLIT 2\nreplacements:\nX745 -> T467\nT457 -> T468\nT458 -> T469\nT459 -> T470\nT460 -> T471\nT461 -> T472\nT462 -> T473\nT463 -> T474\nT464 -> T475\nT465 -> T476\nT466 -> T477", fontsize=14, style = filled, fillcolor = violet];
207 -> 465 [arrowhead = none ];
465 -> 209;

466 [label="INSTANCE with matching:\nT377 -> T456\nX683 -> X745", fontsize=14, style = filled, fillcolor = lightgrey];
208 -> 466 [arrowhead = none , style=dashed];
466 -> 192[style=dashed];

467 [label="INSTANCE with matching:\nT1 -> d(e(T467))\nT2 -> T360", fontsize=14, style = filled, fillcolor = lightgrey];
209 -> 467 [arrowhead = none , style=dashed];
467 -> 1[style=dashed];

}

(2) Obligation:

Clauses:

p24(t, const(1)).
p24(const(T34), const(0)).
p24(+(T45, T46), +(X117, X118)) :- p39(T45, X117, T46, X118).
p24(*(T59, T60), +(*(T59, X151), *(T60, X152))) :- p39(T59, X152, T60, X151).
p39(T45, X117, T46, X118) :- p24(T45, X117).
p39(T45, T47, T48, X118) :- ','(p24(T45, T47), p24(T48, X118)).
p9(e(t), const(1)) :- p1(d(e(const(1))), const(1)).
p9(e(const(T15)), const(0)) :- p1(d(e(const(0))), const(1)).
p9(e(+(T26, T27)), +(X77, X78)) :- p24(T26, X77).
p9(e(+(T26, T29)), +(T28, X78)) :- ','(p24(T26, T28), p24(T29, X78)).
p9(e(+(T26, T29)), +(T62, T61)) :- ','(p24(T26, T62), ','(p24(T29, T61), p1(d(e(+(T62, T61))), const(1)))).
p9(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) :- p24(T75, X201).
p9(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) :- ','(p24(T79, T77), p24(T78, X200)).
p9(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) :- ','(p24(T81, T83), ','(p24(T82, T80), p1(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))).
p9(d(T91), X229) :- p60(T91, X228).
p9(d(T91), X229) :- ','(p60(T91, T92), p9(e(T92), X229)).
p60(e(t), const(1)).
p60(e(const(T97)), const(0)).
p60(e(+(T108, T109)), +(X266, X267)) :- p39(T108, X266, T109, X267).
p60(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) :- p39(T120, X301, T121, X300).
p60(d(T125), X316) :- p60(T125, X315).
p60(d(T125), X316) :- ','(p60(T125, T126), p24(T126, X316)).
p90(e(t), const(1)) :- p1(d(e(const(1))), const(0)).
p90(e(const(T140)), const(0)) :- p1(d(e(const(0))), const(0)).
p90(e(+(T151, T152)), +(X373, X374)) :- p24(T151, X373).
p90(e(+(T151, T154)), +(T153, X374)) :- ','(p24(T151, T153), p24(T154, X374)).
p90(e(+(T151, T154)), +(T156, T155)) :- ','(p24(T151, T156), ','(p24(T154, T155), p1(d(e(+(T156, T155))), const(0)))).
p90(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) :- p24(T169, X421).
p90(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) :- ','(p24(T173, T171), p24(T172, X420)).
p90(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) :- ','(p24(T175, T177), ','(p24(T176, T174), p1(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))).
p90(d(T185), X449) :- p60(T185, X448).
p90(d(T185), X449) :- ','(p60(T185, T186), p90(e(T186), X449)).
p134(T224, T222, T225, T223, T226, T194) :- p1(d(e(T224)), T222).
p134(T224, T222, T227, T223, T228, T194) :- ','(p1(d(e(T224)), T222), p137(T227, T223, T228, T194)).
p137(T227, T223, T228, T194) :- p1(d(e(T227)), T223).
p137(T227, T223, T229, T194) :- ','(p1(d(e(T227)), T223), p1(d(e(T229)), T194)).
p150(T280, X551, T278, T279) :- p60(T280, X551).
p150(T280, T281, T278, T279) :- ','(p60(T280, T281), p1(d(e(T281)), +(T278, T279))).
p1(d(e(t)), const(1)).
p1(d(d(T10)), const(1)) :- p9(T10, X14).
p1(d(e(const(T128))), const(0)).
p1(d(d(T135)), const(0)) :- p90(T135, X334).
p1(d(e(+(t, T197))), +(const(1), T194)) :- p1(d(e(T197)), T194).
p1(d(e(+(const(T202), T203))), +(const(0), T194)) :- p1(d(e(T203)), T194).
p1(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) :- p134(T224, T222, T225, T223, T226, T194).
p1(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) :- p134(T246, T249, T247, T248, T250, T194).
p1(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) :- p137(T267, T270, T268, T269).
p1(d(d(T280)), +(T278, T279)) :- p150(T280, X551, T278, T279).
p1(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) :- p1(d(e(T293)), T294).
p1(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) :- p1(d(e(T293)), T294).
p1(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) :- p134(T317, T319, T318, T320, T293, T294).
p1(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) :- p134(T337, T340, T338, T339, T293, T294).
p1(d(d(T356)), +(*(T352, T353), *(T354, T355))) :- p150(T356, X635, *(T352, T353), *(T354, T355)).
p1(d(d(e(t))), T360) :- p1(d(e(const(1))), T360).
p1(d(d(e(const(T366)))), T360) :- p1(d(e(const(0))), T360).
p1(d(d(e(+(T377, T378)))), T360) :- p24(T377, X683).
p1(d(d(e(+(T377, T380)))), T360) :- ','(p24(T377, T379), p24(T380, X684)).
p1(d(d(e(+(T377, T380)))), T360) :- ','(p24(T377, T392), ','(p24(T380, T391), p1(d(e(+(T392, T391))), T360))).
p1(d(d(e(*(T417, T418)))), T360) :- p24(T417, X724).
p1(d(d(e(*(T421, T420)))), T360) :- ','(p24(T421, T419), p24(T420, X723)).
p1(d(d(e(*(T433, T434)))), T360) :- ','(p24(T433, T435), ','(p24(T434, T432), p1(d(e(+(*(T433, T432), *(T434, T435)))), T360))).
p1(d(d(d(T455))), T360) :- p60(T455, X744).
p1(d(d(d(T455))), T360) :- ','(p60(T455, T456), p24(T456, X745)).
p1(d(d(d(T455))), T360) :- ','(p60(T455, T456), ','(p24(T456, T467), p1(d(e(T467)), T360))).

Queries:

p1(a,g).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
p1_in: (f,b) (b,b)
p9_in: (f,f) (b,f)
p90_in: (b,f) (f,f)
p134_in: (b,b,b,b,b,b) (f,b,f,b,f,b) (b,b,b,b,f,b)
p137_in: (b,b,b,b) (b,b,f,b) (f,b,f,b)
p150_in: (b,f,b,b) (f,f,b,b)
p60_in: (b,f) (f,f)
p39_in: (b,f,b,f) (f,f,f,f)
p24_in: (b,f) (f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)

(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:

P1_IN_AG(d(d(T10)), const(1)) → U54_AG(T10, p9_in_aa(T10, X14))
P1_IN_AG(d(d(T10)), const(1)) → P9_IN_AA(T10, X14)
P9_IN_AA(e(t), const(1)) → U6_AA(p1_in_gg(d(e(const(1))), const(1)))
P9_IN_AA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(1))
P1_IN_GG(d(d(T10)), const(1)) → U54_GG(T10, p9_in_ga(T10, X14))
P1_IN_GG(d(d(T10)), const(1)) → P9_IN_GA(T10, X14)
P9_IN_GA(e(t), const(1)) → U6_GA(p1_in_gg(d(e(const(1))), const(1)))
P9_IN_GA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(1))
P1_IN_GG(d(d(T135)), const(0)) → U55_GG(T135, p90_in_ga(T135, X334))
P1_IN_GG(d(d(T135)), const(0)) → P90_IN_GA(T135, X334)
P90_IN_GA(e(t), const(1)) → U28_GA(p1_in_gg(d(e(const(1))), const(0)))
P90_IN_GA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(0))
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → U56_GG(T197, T194, p1_in_gg(d(e(T197)), T194))
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_GG(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_GG(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → U45_GGGGGG(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_GG(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_GG(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T228, T194) → U48_GGGG(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(d(T280)), +(T278, T279)) → U61_GG(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
P1_IN_GG(d(d(T280)), +(T278, T279)) → P150_IN_GAGG(T280, X551, T278, T279)
P150_IN_GAGG(T280, X551, T278, T279) → U51_GAGG(T280, X551, T278, T279, p60_in_ga(T280, X551))
P150_IN_GAGG(T280, X551, T278, T279) → P60_IN_GA(T280, X551)
P60_IN_GA(e(+(T108, T109)), +(X266, X267)) → U23_GA(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
P60_IN_GA(e(+(T108, T109)), +(X266, X267)) → P39_IN_GAGA(T108, X266, T109, X267)
P39_IN_GAGA(T45, X117, T46, X118) → U3_GAGA(T45, X117, T46, X118, p24_in_ga(T45, X117))
P39_IN_GAGA(T45, X117, T46, X118) → P24_IN_GA(T45, X117)
P24_IN_GA(+(T45, T46), +(X117, X118)) → U1_GA(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
P24_IN_GA(+(T45, T46), +(X117, X118)) → P39_IN_GAGA(T45, X117, T46, X118)
P39_IN_GAGA(T45, T47, T48, X118) → U4_GAGA(T45, T47, T48, X118, p24_in_ga(T45, T47))
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_GA(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_GAGA(T59, X152, T60, X151)
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_GAGA(T45, T47, T48, X118, p24_in_ga(T48, X118))
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → P24_IN_GA(T48, X118)
P60_IN_GA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_GA(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
P60_IN_GA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → P39_IN_GAGA(T120, X301, T121, X300)
P60_IN_GA(d(T125), X316) → U25_GA(T125, X316, p60_in_ga(T125, X315))
P60_IN_GA(d(T125), X316) → P60_IN_GA(T125, X315)
P60_IN_GA(d(T125), X316) → U26_GA(T125, X316, p60_in_ga(T125, T126))
U26_GA(T125, X316, p60_out_ga(T125, T126)) → U27_GA(T125, X316, p24_in_aa(T126, X316))
U26_GA(T125, X316, p60_out_ga(T125, T126)) → P24_IN_AA(T126, X316)
P24_IN_AA(+(T45, T46), +(X117, X118)) → U1_AA(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
P24_IN_AA(+(T45, T46), +(X117, X118)) → P39_IN_AAAA(T45, X117, T46, X118)
P39_IN_AAAA(T45, X117, T46, X118) → U3_AAAA(T45, X117, T46, X118, p24_in_aa(T45, X117))
P39_IN_AAAA(T45, X117, T46, X118) → P24_IN_AA(T45, X117)
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_AA(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_AAAA(T59, X152, T60, X151)
P39_IN_AAAA(T45, T47, T48, X118) → U4_AAAA(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_AAAA(T45, T47, T48, X118, p24_in_aa(T48, X118))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → P24_IN_AA(T48, X118)
P150_IN_GAGG(T280, T281, T278, T279) → U52_GAGG(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_GAGG(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_GAGG(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
U52_GAGG(T280, T281, T278, T279, p60_out_ga(T280, T281)) → P1_IN_AG(d(e(T281)), +(T278, T279))
P1_IN_AG(d(d(T135)), const(0)) → U55_AG(T135, p90_in_aa(T135, X334))
P1_IN_AG(d(d(T135)), const(0)) → P90_IN_AA(T135, X334)
P90_IN_AA(e(t), const(1)) → U28_AA(p1_in_gg(d(e(const(1))), const(0)))
P90_IN_AA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(0))
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_GG(T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_GG(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_GG(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_GG(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
P1_IN_GG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_GG(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
P1_IN_GG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → P150_IN_GAGG(T356, X635, *(T352, T353), *(T354, T355))
P1_IN_GG(d(d(e(t))), T360) → U67_GG(T360, p1_in_gg(d(e(const(1))), T360))
P1_IN_GG(d(d(e(t))), T360) → P1_IN_GG(d(e(const(1))), T360)
P1_IN_GG(d(d(e(const(T366)))), T360) → U68_GG(T366, T360, p1_in_gg(d(e(const(0))), T360))
P1_IN_GG(d(d(e(const(T366)))), T360) → P1_IN_GG(d(e(const(0))), T360)
P1_IN_GG(d(d(e(+(T377, T378)))), T360) → U69_GG(T377, T378, T360, p24_in_ga(T377, X683))
P1_IN_GG(d(d(e(+(T377, T378)))), T360) → P24_IN_GA(T377, X683)
P1_IN_GG(d(d(e(+(T377, T380)))), T360) → U70_GG(T377, T380, T360, p24_in_ga(T377, T379))
U70_GG(T377, T380, T360, p24_out_ga(T377, T379)) → U71_GG(T377, T380, T360, p24_in_ga(T380, X684))
U70_GG(T377, T380, T360, p24_out_ga(T377, T379)) → P24_IN_GA(T380, X684)
P1_IN_GG(d(d(e(+(T377, T380)))), T360) → U72_GG(T377, T380, T360, p24_in_ga(T377, T392))
U72_GG(T377, T380, T360, p24_out_ga(T377, T392)) → U73_GG(T377, T380, T360, T392, p24_in_ga(T380, T391))
U72_GG(T377, T380, T360, p24_out_ga(T377, T392)) → P24_IN_GA(T380, T391)
U73_GG(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_GG(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
U73_GG(T377, T380, T360, T392, p24_out_ga(T380, T391)) → P1_IN_AG(d(e(+(T392, T391))), T360)
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → U56_AG(T197, T194, p1_in_ag(d(e(T197)), T194))
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_AG(d(e(T197)), T194)
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_AG(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_AG(d(e(T203)), T194)
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_AG(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194)
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → U45_AGAGAG(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → P1_IN_AG(d(e(T224)), T222)
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_AG(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGAG(T224, T222, T225, T223, T226, T194) → U45_GGGGAG(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
P134_IN_GGGGAG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(d(e(*(T417, T418)))), T360) → U75_GG(T417, T418, T360, p24_in_ga(T417, X724))
P1_IN_GG(d(d(e(*(T417, T418)))), T360) → P24_IN_GA(T417, X724)
P1_IN_GG(d(d(e(*(T421, T420)))), T360) → U76_GG(T421, T420, T360, p24_in_ga(T421, T419))
U76_GG(T421, T420, T360, p24_out_ga(T421, T419)) → U77_GG(T421, T420, T360, p24_in_ga(T420, X723))
U76_GG(T421, T420, T360, p24_out_ga(T421, T419)) → P24_IN_GA(T420, X723)
P1_IN_GG(d(d(e(*(T433, T434)))), T360) → U78_GG(T433, T434, T360, p24_in_ga(T433, T435))
U78_GG(T433, T434, T360, p24_out_ga(T433, T435)) → U79_GG(T433, T434, T360, T435, p24_in_ga(T434, T432))
U78_GG(T433, T434, T360, p24_out_ga(T433, T435)) → P24_IN_GA(T434, T432)
U79_GG(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_GG(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
U79_GG(T433, T434, T360, T435, p24_out_ga(T434, T432)) → P1_IN_AG(d(e(+(*(T433, T432), *(T434, T435)))), T360)
P1_IN_AG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_AG(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
P1_IN_AG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
P1_IN_GG(d(d(d(T455))), T360) → U81_GG(T455, T360, p60_in_ga(T455, X744))
P1_IN_GG(d(d(d(T455))), T360) → P60_IN_GA(T455, X744)
P1_IN_GG(d(d(d(T455))), T360) → U82_GG(T455, T360, p60_in_ga(T455, T456))
U82_GG(T455, T360, p60_out_ga(T455, T456)) → U83_GG(T455, T360, p24_in_aa(T456, X745))
U82_GG(T455, T360, p60_out_ga(T455, T456)) → P24_IN_AA(T456, X745)
U82_GG(T455, T360, p60_out_ga(T455, T456)) → U84_GG(T455, T360, p24_in_aa(T456, T467))
U84_GG(T455, T360, p24_out_aa(T456, T467)) → U85_GG(T455, T360, p1_in_ag(d(e(T467)), T360))
U84_GG(T455, T360, p24_out_aa(T456, T467)) → P1_IN_AG(d(e(T467)), T360)
P1_IN_AG(d(d(T280)), +(T278, T279)) → U61_AG(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
P1_IN_AG(d(d(T280)), +(T278, T279)) → P150_IN_AAGG(T280, X551, T278, T279)
P150_IN_AAGG(T280, X551, T278, T279) → U51_AAGG(T280, X551, T278, T279, p60_in_aa(T280, X551))
P150_IN_AAGG(T280, X551, T278, T279) → P60_IN_AA(T280, X551)
P60_IN_AA(e(+(T108, T109)), +(X266, X267)) → U23_AA(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
P60_IN_AA(e(+(T108, T109)), +(X266, X267)) → P39_IN_AAAA(T108, X266, T109, X267)
P60_IN_AA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_AA(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
P60_IN_AA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → P39_IN_AAAA(T120, X301, T121, X300)
P60_IN_AA(d(T125), X316) → U25_AA(T125, X316, p60_in_aa(T125, X315))
P60_IN_AA(d(T125), X316) → P60_IN_AA(T125, X315)
P60_IN_AA(d(T125), X316) → U26_AA(T125, X316, p60_in_aa(T125, T126))
U26_AA(T125, X316, p60_out_aa(T125, T126)) → U27_AA(T125, X316, p24_in_aa(T126, X316))
U26_AA(T125, X316, p60_out_aa(T125, T126)) → P24_IN_AA(T126, X316)
P150_IN_AAGG(T280, T281, T278, T279) → U52_AAGG(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_AAGG(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_AAGG(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
U52_AAGG(T280, T281, T278, T279, p60_out_aa(T280, T281)) → P1_IN_AG(d(e(T281)), +(T278, T279))
P1_IN_AG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_AG(T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_AG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_AG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_AG(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_AG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_AG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_AG(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
P1_IN_AG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_AG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_AG(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
P1_IN_AG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
P1_IN_AG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_AG(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
P1_IN_AG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → P150_IN_AAGG(T356, X635, *(T352, T353), *(T354, T355))
P1_IN_AG(d(d(e(t))), T360) → U67_AG(T360, p1_in_gg(d(e(const(1))), T360))
P1_IN_AG(d(d(e(t))), T360) → P1_IN_GG(d(e(const(1))), T360)
P1_IN_AG(d(d(e(const(T366)))), T360) → U68_AG(T366, T360, p1_in_gg(d(e(const(0))), T360))
P1_IN_AG(d(d(e(const(T366)))), T360) → P1_IN_GG(d(e(const(0))), T360)
P1_IN_AG(d(d(e(+(T377, T378)))), T360) → U69_AG(T377, T378, T360, p24_in_aa(T377, X683))
P1_IN_AG(d(d(e(+(T377, T378)))), T360) → P24_IN_AA(T377, X683)
P1_IN_AG(d(d(e(+(T377, T380)))), T360) → U70_AG(T377, T380, T360, p24_in_aa(T377, T379))
U70_AG(T377, T380, T360, p24_out_aa(T377, T379)) → U71_AG(T377, T380, T360, p24_in_aa(T380, X684))
U70_AG(T377, T380, T360, p24_out_aa(T377, T379)) → P24_IN_AA(T380, X684)
P1_IN_AG(d(d(e(+(T377, T380)))), T360) → U72_AG(T377, T380, T360, p24_in_aa(T377, T392))
U72_AG(T377, T380, T360, p24_out_aa(T377, T392)) → U73_AG(T377, T380, T360, T392, p24_in_aa(T380, T391))
U72_AG(T377, T380, T360, p24_out_aa(T377, T392)) → P24_IN_AA(T380, T391)
U73_AG(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_AG(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
U73_AG(T377, T380, T360, T392, p24_out_aa(T380, T391)) → P1_IN_AG(d(e(+(T392, T391))), T360)
P1_IN_AG(d(d(e(*(T417, T418)))), T360) → U75_AG(T417, T418, T360, p24_in_aa(T417, X724))
P1_IN_AG(d(d(e(*(T417, T418)))), T360) → P24_IN_AA(T417, X724)
P1_IN_AG(d(d(e(*(T421, T420)))), T360) → U76_AG(T421, T420, T360, p24_in_aa(T421, T419))
U76_AG(T421, T420, T360, p24_out_aa(T421, T419)) → U77_AG(T421, T420, T360, p24_in_aa(T420, X723))
U76_AG(T421, T420, T360, p24_out_aa(T421, T419)) → P24_IN_AA(T420, X723)
P1_IN_AG(d(d(e(*(T433, T434)))), T360) → U78_AG(T433, T434, T360, p24_in_aa(T433, T435))
U78_AG(T433, T434, T360, p24_out_aa(T433, T435)) → U79_AG(T433, T434, T360, T435, p24_in_aa(T434, T432))
U78_AG(T433, T434, T360, p24_out_aa(T433, T435)) → P24_IN_AA(T434, T432)
U79_AG(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_AG(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
U79_AG(T433, T434, T360, T435, p24_out_aa(T434, T432)) → P1_IN_AG(d(e(+(*(T433, T432), *(T434, T435)))), T360)
P1_IN_AG(d(d(d(T455))), T360) → U81_AG(T455, T360, p60_in_aa(T455, X744))
P1_IN_AG(d(d(d(T455))), T360) → P60_IN_AA(T455, X744)
P1_IN_AG(d(d(d(T455))), T360) → U82_AG(T455, T360, p60_in_aa(T455, T456))
U82_AG(T455, T360, p60_out_aa(T455, T456)) → U83_AG(T455, T360, p24_in_aa(T456, X745))
U82_AG(T455, T360, p60_out_aa(T455, T456)) → P24_IN_AA(T456, X745)
U82_AG(T455, T360, p60_out_aa(T455, T456)) → U84_AG(T455, T360, p24_in_aa(T456, T467))
U84_AG(T455, T360, p24_out_aa(T456, T467)) → U85_AG(T455, T360, p1_in_ag(d(e(T467)), T360))
U84_AG(T455, T360, p24_out_aa(T456, T467)) → P1_IN_AG(d(e(T467)), T360)
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P134_IN_GGGGAG(T224, T222, T227, T223, T228, T194) → U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_GGGGAG(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T228, T194)
P137_IN_GGAG(T227, T223, T228, T194) → U48_GGAG(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
P137_IN_GGAG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P137_IN_GGAG(T227, T223, T229, T194) → U49_GGAG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_GGAG(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P134_IN_AGAGAG(T224, T222, T227, T223, T228, T194) → U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_AGAGAG(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → P137_IN_AGAG(T227, T223, T228, T194)
P137_IN_AGAG(T227, T223, T228, T194) → U48_AGAG(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
P137_IN_AGAG(T227, T223, T228, T194) → P1_IN_AG(d(e(T227)), T223)
P137_IN_AGAG(T227, T223, T229, T194) → U49_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P90_IN_AA(e(const(T140)), const(0)) → U29_AA(T140, p1_in_gg(d(e(const(0))), const(0)))
P90_IN_AA(e(const(T140)), const(0)) → P1_IN_GG(d(e(const(0))), const(0))
P90_IN_AA(e(+(T151, T152)), +(X373, X374)) → U30_AA(T151, T152, X373, X374, p24_in_aa(T151, X373))
P90_IN_AA(e(+(T151, T152)), +(X373, X374)) → P24_IN_AA(T151, X373)
P90_IN_AA(e(+(T151, T154)), +(T153, X374)) → U31_AA(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_AA(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_AA(T151, T154, T153, X374, p24_in_aa(T154, X374))
U31_AA(T151, T154, T153, X374, p24_out_aa(T151, T153)) → P24_IN_AA(T154, X374)
P90_IN_AA(e(+(T151, T154)), +(T156, T155)) → U33_AA(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_AA(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_AA(T151, T154, T156, T155, p24_in_aa(T154, T155))
U33_AA(T151, T154, T156, T155, p24_out_aa(T151, T156)) → P24_IN_AA(T154, T155)
U34_AA(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_AA(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U34_AA(T151, T154, T156, T155, p24_out_aa(T154, T155)) → P1_IN_AG(d(e(+(T156, T155))), const(0))
P90_IN_AA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_AA(T169, T170, X420, X421, p24_in_aa(T169, X421))
P90_IN_AA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → P24_IN_AA(T169, X421)
P90_IN_AA(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_AA(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_AA(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_AA(T173, T172, X420, T171, p24_in_aa(T172, X420))
U37_AA(T173, T172, X420, T171, p24_out_aa(T173, T171)) → P24_IN_AA(T172, X420)
P90_IN_AA(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_AA(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_AA(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_AA(T175, T176, T174, T177, p24_in_aa(T176, T174))
U39_AA(T175, T176, T174, T177, p24_out_aa(T175, T177)) → P24_IN_AA(T176, T174)
U40_AA(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_AA(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U40_AA(T175, T176, T174, T177, p24_out_aa(T176, T174)) → P1_IN_AG(d(e(+(*(T175, T174), *(T176, T177)))), const(0))
P90_IN_AA(d(T185), X449) → U42_AA(T185, X449, p60_in_aa(T185, X448))
P90_IN_AA(d(T185), X449) → P60_IN_AA(T185, X448)
P90_IN_AA(d(T185), X449) → U43_AA(T185, X449, p60_in_aa(T185, T186))
U43_AA(T185, X449, p60_out_aa(T185, T186)) → U44_AA(T185, X449, p90_in_aa(e(T186), X449))
U43_AA(T185, X449, p60_out_aa(T185, T186)) → P90_IN_AA(e(T186), X449)
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_GGGGGG(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P90_IN_GA(e(const(T140)), const(0)) → U29_GA(T140, p1_in_gg(d(e(const(0))), const(0)))
P90_IN_GA(e(const(T140)), const(0)) → P1_IN_GG(d(e(const(0))), const(0))
P90_IN_GA(e(+(T151, T152)), +(X373, X374)) → U30_GA(T151, T152, X373, X374, p24_in_ga(T151, X373))
P90_IN_GA(e(+(T151, T152)), +(X373, X374)) → P24_IN_GA(T151, X373)
P90_IN_GA(e(+(T151, T154)), +(T153, X374)) → U31_GA(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_GA(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_GA(T151, T154, T153, X374, p24_in_ga(T154, X374))
U31_GA(T151, T154, T153, X374, p24_out_ga(T151, T153)) → P24_IN_GA(T154, X374)
P90_IN_GA(e(+(T151, T154)), +(T156, T155)) → U33_GA(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_GA(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_GA(T151, T154, T156, T155, p24_in_ga(T154, T155))
U33_GA(T151, T154, T156, T155, p24_out_ga(T151, T156)) → P24_IN_GA(T154, T155)
U34_GA(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_GA(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U34_GA(T151, T154, T156, T155, p24_out_ga(T154, T155)) → P1_IN_AG(d(e(+(T156, T155))), const(0))
P90_IN_GA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_GA(T169, T170, X420, X421, p24_in_ga(T169, X421))
P90_IN_GA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → P24_IN_GA(T169, X421)
P90_IN_GA(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_GA(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_GA(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_GA(T173, T172, X420, T171, p24_in_ga(T172, X420))
U37_GA(T173, T172, X420, T171, p24_out_ga(T173, T171)) → P24_IN_GA(T172, X420)
P90_IN_GA(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_GA(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_GA(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_GA(T175, T176, T174, T177, p24_in_ga(T176, T174))
U39_GA(T175, T176, T174, T177, p24_out_ga(T175, T177)) → P24_IN_GA(T176, T174)
U40_GA(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_GA(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U40_GA(T175, T176, T174, T177, p24_out_ga(T176, T174)) → P1_IN_AG(d(e(+(*(T175, T174), *(T176, T177)))), const(0))
P90_IN_GA(d(T185), X449) → U42_GA(T185, X449, p60_in_ga(T185, X448))
P90_IN_GA(d(T185), X449) → P60_IN_GA(T185, X448)
P90_IN_GA(d(T185), X449) → U43_GA(T185, X449, p60_in_ga(T185, T186))
U43_GA(T185, X449, p60_out_ga(T185, T186)) → U44_GA(T185, X449, p90_in_aa(e(T186), X449))
U43_GA(T185, X449, p60_out_ga(T185, T186)) → P90_IN_AA(e(T186), X449)
P9_IN_GA(e(const(T15)), const(0)) → U7_GA(T15, p1_in_gg(d(e(const(0))), const(1)))
P9_IN_GA(e(const(T15)), const(0)) → P1_IN_GG(d(e(const(0))), const(1))
P9_IN_GA(e(+(T26, T27)), +(X77, X78)) → U8_GA(T26, T27, X77, X78, p24_in_ga(T26, X77))
P9_IN_GA(e(+(T26, T27)), +(X77, X78)) → P24_IN_GA(T26, X77)
P9_IN_GA(e(+(T26, T29)), +(T28, X78)) → U9_GA(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_GA(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_GA(T26, T29, T28, X78, p24_in_ga(T29, X78))
U9_GA(T26, T29, T28, X78, p24_out_ga(T26, T28)) → P24_IN_GA(T29, X78)
P9_IN_GA(e(+(T26, T29)), +(T62, T61)) → U11_GA(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_GA(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_GA(T26, T29, T62, T61, p24_in_ga(T29, T61))
U11_GA(T26, T29, T62, T61, p24_out_ga(T26, T62)) → P24_IN_GA(T29, T61)
U12_GA(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_GA(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U12_GA(T26, T29, T62, T61, p24_out_ga(T29, T61)) → P1_IN_AG(d(e(+(T62, T61))), const(1))
P9_IN_GA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_GA(T75, T76, X200, X201, p24_in_ga(T75, X201))
P9_IN_GA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → P24_IN_GA(T75, X201)
P9_IN_GA(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_GA(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_GA(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_GA(T79, T78, X200, T77, p24_in_ga(T78, X200))
U15_GA(T79, T78, X200, T77, p24_out_ga(T79, T77)) → P24_IN_GA(T78, X200)
P9_IN_GA(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_GA(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_GA(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_GA(T81, T82, T80, T83, p24_in_ga(T82, T80))
U17_GA(T81, T82, T80, T83, p24_out_ga(T81, T83)) → P24_IN_GA(T82, T80)
U18_GA(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_GA(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U18_GA(T81, T82, T80, T83, p24_out_ga(T82, T80)) → P1_IN_AG(d(e(+(*(T81, T80), *(T82, T83)))), const(1))
P9_IN_GA(d(T91), X229) → U20_GA(T91, X229, p60_in_ga(T91, X228))
P9_IN_GA(d(T91), X229) → P60_IN_GA(T91, X228)
P9_IN_GA(d(T91), X229) → U21_GA(T91, X229, p60_in_ga(T91, T92))
U21_GA(T91, X229, p60_out_ga(T91, T92)) → U22_GA(T91, X229, p9_in_aa(e(T92), X229))
U21_GA(T91, X229, p60_out_ga(T91, T92)) → P9_IN_AA(e(T92), X229)
P9_IN_AA(e(const(T15)), const(0)) → U7_AA(T15, p1_in_gg(d(e(const(0))), const(1)))
P9_IN_AA(e(const(T15)), const(0)) → P1_IN_GG(d(e(const(0))), const(1))
P9_IN_AA(e(+(T26, T27)), +(X77, X78)) → U8_AA(T26, T27, X77, X78, p24_in_aa(T26, X77))
P9_IN_AA(e(+(T26, T27)), +(X77, X78)) → P24_IN_AA(T26, X77)
P9_IN_AA(e(+(T26, T29)), +(T28, X78)) → U9_AA(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_AA(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_AA(T26, T29, T28, X78, p24_in_aa(T29, X78))
U9_AA(T26, T29, T28, X78, p24_out_aa(T26, T28)) → P24_IN_AA(T29, X78)
P9_IN_AA(e(+(T26, T29)), +(T62, T61)) → U11_AA(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_AA(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_AA(T26, T29, T62, T61, p24_in_aa(T29, T61))
U11_AA(T26, T29, T62, T61, p24_out_aa(T26, T62)) → P24_IN_AA(T29, T61)
U12_AA(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_AA(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U12_AA(T26, T29, T62, T61, p24_out_aa(T29, T61)) → P1_IN_AG(d(e(+(T62, T61))), const(1))
P9_IN_AA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_AA(T75, T76, X200, X201, p24_in_aa(T75, X201))
P9_IN_AA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → P24_IN_AA(T75, X201)
P9_IN_AA(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_AA(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_AA(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_AA(T79, T78, X200, T77, p24_in_aa(T78, X200))
U15_AA(T79, T78, X200, T77, p24_out_aa(T79, T77)) → P24_IN_AA(T78, X200)
P9_IN_AA(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_AA(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_AA(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_AA(T81, T82, T80, T83, p24_in_aa(T82, T80))
U17_AA(T81, T82, T80, T83, p24_out_aa(T81, T83)) → P24_IN_AA(T82, T80)
U18_AA(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_AA(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U18_AA(T81, T82, T80, T83, p24_out_aa(T82, T80)) → P1_IN_AG(d(e(+(*(T81, T80), *(T82, T83)))), const(1))
P9_IN_AA(d(T91), X229) → U20_AA(T91, X229, p60_in_aa(T91, X228))
P9_IN_AA(d(T91), X229) → P60_IN_AA(T91, X228)
P9_IN_AA(d(T91), X229) → U21_AA(T91, X229, p60_in_aa(T91, T92))
U21_AA(T91, X229, p60_out_aa(T91, T92)) → U22_AA(T91, X229, p9_in_aa(e(T92), X229))
U21_AA(T91, X229, p60_out_aa(T91, T92)) → P9_IN_AA(e(T92), X229)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P1_IN_AG(x1, x2)  =  P1_IN_AG(x2)
U54_AG(x1, x2)  =  U54_AG(x2)
P9_IN_AA(x1, x2)  =  P9_IN_AA
U6_AA(x1)  =  U6_AA(x1)
P1_IN_GG(x1, x2)  =  P1_IN_GG(x1, x2)
U54_GG(x1, x2)  =  U54_GG(x1, x2)
P9_IN_GA(x1, x2)  =  P9_IN_GA(x1)
U6_GA(x1)  =  U6_GA(x1)
U55_GG(x1, x2)  =  U55_GG(x1, x2)
P90_IN_GA(x1, x2)  =  P90_IN_GA(x1)
U28_GA(x1)  =  U28_GA(x1)
U56_GG(x1, x2, x3)  =  U56_GG(x1, x2, x3)
U57_GG(x1, x2, x3, x4)  =  U57_GG(x2, x3, x4)
U58_GG(x1, x2, x3, x4, x5, x6, x7)  =  U58_GG(x1, x2, x3, x4, x5, x6, x7)
P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)
U45_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U45_GGGGGG(x1, x2, x3, x4, x5, x6, x7)
U59_GG(x1, x2, x3, x4, x5, x6, x7)  =  U59_GG(x1, x2, x3, x4, x5, x6, x7)
U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)
U60_GG(x1, x2, x3, x4, x5)  =  U60_GG(x1, x2, x3, x4, x5)
P137_IN_GGGG(x1, x2, x3, x4)  =  P137_IN_GGGG(x1, x2, x3, x4)
U48_GGGG(x1, x2, x3, x4, x5)  =  U48_GGGG(x1, x2, x3, x4, x5)
U61_GG(x1, x2, x3, x4)  =  U61_GG(x1, x2, x3, x4)
P150_IN_GAGG(x1, x2, x3, x4)  =  P150_IN_GAGG(x1, x3, x4)
U51_GAGG(x1, x2, x3, x4, x5)  =  U51_GAGG(x1, x3, x4, x5)
P60_IN_GA(x1, x2)  =  P60_IN_GA(x1)
U23_GA(x1, x2, x3, x4, x5)  =  U23_GA(x1, x2, x5)
P39_IN_GAGA(x1, x2, x3, x4)  =  P39_IN_GAGA(x1, x3)
U3_GAGA(x1, x2, x3, x4, x5)  =  U3_GAGA(x1, x3, x5)
P24_IN_GA(x1, x2)  =  P24_IN_GA(x1)
U1_GA(x1, x2, x3, x4, x5)  =  U1_GA(x1, x2, x5)
U4_GAGA(x1, x2, x3, x4, x5)  =  U4_GAGA(x1, x3, x5)
U2_GA(x1, x2, x3, x4, x5)  =  U2_GA(x1, x2, x5)
U5_GAGA(x1, x2, x3, x4, x5)  =  U5_GAGA(x1, x3, x5)
U24_GA(x1, x2, x3, x4, x5)  =  U24_GA(x1, x2, x5)
U25_GA(x1, x2, x3)  =  U25_GA(x1, x3)
U26_GA(x1, x2, x3)  =  U26_GA(x1, x3)
U27_GA(x1, x2, x3)  =  U27_GA(x1, x3)
P24_IN_AA(x1, x2)  =  P24_IN_AA
U1_AA(x1, x2, x3, x4, x5)  =  U1_AA(x5)
P39_IN_AAAA(x1, x2, x3, x4)  =  P39_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5)  =  U3_AAAA(x5)
U2_AA(x1, x2, x3, x4, x5)  =  U2_AA(x5)
U4_AAAA(x1, x2, x3, x4, x5)  =  U4_AAAA(x5)
U5_AAAA(x1, x2, x3, x4, x5)  =  U5_AAAA(x5)
U52_GAGG(x1, x2, x3, x4, x5)  =  U52_GAGG(x1, x3, x4, x5)
U53_GAGG(x1, x2, x3, x4, x5)  =  U53_GAGG(x1, x3, x4, x5)
U55_AG(x1, x2)  =  U55_AG(x2)
P90_IN_AA(x1, x2)  =  P90_IN_AA
U28_AA(x1)  =  U28_AA(x1)
U62_GG(x1, x2, x3)  =  U62_GG(x1, x2, x3)
U63_GG(x1, x2, x3, x4)  =  U63_GG(x2, x3, x4)
U64_GG(x1, x2, x3, x4, x5, x6, x7)  =  U64_GG(x1, x2, x3, x4, x5, x6, x7)
U65_GG(x1, x2, x3, x4, x5, x6, x7)  =  U65_GG(x1, x2, x3, x4, x5, x6, x7)
U66_GG(x1, x2, x3, x4, x5, x6)  =  U66_GG(x1, x2, x3, x4, x5, x6)
U67_GG(x1, x2)  =  U67_GG(x1, x2)
U68_GG(x1, x2, x3)  =  U68_GG(x2, x3)
U69_GG(x1, x2, x3, x4)  =  U69_GG(x1, x2, x3, x4)
U70_GG(x1, x2, x3, x4)  =  U70_GG(x1, x2, x3, x4)
U71_GG(x1, x2, x3, x4)  =  U71_GG(x1, x2, x3, x4)
U72_GG(x1, x2, x3, x4)  =  U72_GG(x1, x2, x3, x4)
U73_GG(x1, x2, x3, x4, x5)  =  U73_GG(x1, x2, x3, x5)
U74_GG(x1, x2, x3, x4)  =  U74_GG(x1, x2, x3, x4)
U56_AG(x1, x2, x3)  =  U56_AG(x2, x3)
U57_AG(x1, x2, x3, x4)  =  U57_AG(x3, x4)
U58_AG(x1, x2, x3, x4, x5, x6, x7)  =  U58_AG(x4, x5, x6, x7)
P134_IN_AGAGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_AGAGAG(x2, x4, x6)
U45_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U45_AGAGAG(x2, x4, x6, x7)
U59_AG(x1, x2, x3, x4, x5, x6, x7)  =  U59_AG(x1, x2, x4, x5, x6, x7)
P134_IN_GGGGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGAG(x1, x2, x3, x4, x6)
U45_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U45_GGGGAG(x1, x2, x3, x4, x6, x7)
U75_GG(x1, x2, x3, x4)  =  U75_GG(x1, x2, x3, x4)
U76_GG(x1, x2, x3, x4)  =  U76_GG(x1, x2, x3, x4)
U77_GG(x1, x2, x3, x4)  =  U77_GG(x1, x2, x3, x4)
U78_GG(x1, x2, x3, x4)  =  U78_GG(x1, x2, x3, x4)
U79_GG(x1, x2, x3, x4, x5)  =  U79_GG(x1, x2, x3, x5)
U80_GG(x1, x2, x3, x4)  =  U80_GG(x1, x2, x3, x4)
U60_AG(x1, x2, x3, x4, x5)  =  U60_AG(x1, x2, x3, x4, x5)
U49_GGGG(x1, x2, x3, x4, x5)  =  U49_GGGG(x1, x2, x3, x4, x5)
U81_GG(x1, x2, x3)  =  U81_GG(x1, x2, x3)
U82_GG(x1, x2, x3)  =  U82_GG(x1, x2, x3)
U83_GG(x1, x2, x3)  =  U83_GG(x1, x2, x3)
U84_GG(x1, x2, x3)  =  U84_GG(x1, x2, x3)
U85_GG(x1, x2, x3)  =  U85_GG(x1, x2, x3)
U61_AG(x1, x2, x3, x4)  =  U61_AG(x2, x3, x4)
P150_IN_AAGG(x1, x2, x3, x4)  =  P150_IN_AAGG(x3, x4)
U51_AAGG(x1, x2, x3, x4, x5)  =  U51_AAGG(x3, x4, x5)
P60_IN_AA(x1, x2)  =  P60_IN_AA
U23_AA(x1, x2, x3, x4, x5)  =  U23_AA(x5)
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
U25_AA(x1, x2, x3)  =  U25_AA(x3)
U26_AA(x1, x2, x3)  =  U26_AA(x3)
U27_AA(x1, x2, x3)  =  U27_AA(x3)
U52_AAGG(x1, x2, x3, x4, x5)  =  U52_AAGG(x3, x4, x5)
U53_AAGG(x1, x2, x3, x4, x5)  =  U53_AAGG(x3, x4, x5)
U62_AG(x1, x2, x3)  =  U62_AG(x1, x2, x3)
U63_AG(x1, x2, x3, x4)  =  U63_AG(x2, x3, x4)
U64_AG(x1, x2, x3, x4, x5, x6, x7)  =  U64_AG(x1, x2, x3, x4, x5, x6, x7)
U65_AG(x1, x2, x3, x4, x5, x6, x7)  =  U65_AG(x1, x2, x3, x4, x5, x6, x7)
U66_AG(x1, x2, x3, x4, x5, x6)  =  U66_AG(x2, x3, x4, x5, x6)
U67_AG(x1, x2)  =  U67_AG(x1, x2)
U68_AG(x1, x2, x3)  =  U68_AG(x2, x3)
U69_AG(x1, x2, x3, x4)  =  U69_AG(x3, x4)
U70_AG(x1, x2, x3, x4)  =  U70_AG(x3, x4)
U71_AG(x1, x2, x3, x4)  =  U71_AG(x3, x4)
U72_AG(x1, x2, x3, x4)  =  U72_AG(x3, x4)
U73_AG(x1, x2, x3, x4, x5)  =  U73_AG(x3, x5)
U74_AG(x1, x2, x3, x4)  =  U74_AG(x3, x4)
U75_AG(x1, x2, x3, x4)  =  U75_AG(x3, x4)
U76_AG(x1, x2, x3, x4)  =  U76_AG(x3, x4)
U77_AG(x1, x2, x3, x4)  =  U77_AG(x3, x4)
U78_AG(x1, x2, x3, x4)  =  U78_AG(x3, x4)
U79_AG(x1, x2, x3, x4, x5)  =  U79_AG(x3, x5)
U80_AG(x1, x2, x3, x4)  =  U80_AG(x3, x4)
U81_AG(x1, x2, x3)  =  U81_AG(x2, x3)
U82_AG(x1, x2, x3)  =  U82_AG(x2, x3)
U83_AG(x1, x2, x3)  =  U83_AG(x2, x3)
U84_AG(x1, x2, x3)  =  U84_AG(x2, x3)
U85_AG(x1, x2, x3)  =  U85_AG(x2, x3)
U50_GGGG(x1, x2, x3, x4, x5)  =  U50_GGGG(x1, x2, x3, x4, x5)
U46_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGAG(x1, x2, x3, x4, x6, x7)
U47_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U47_GGGGAG(x1, x2, x3, x4, x6, x7)
P137_IN_GGAG(x1, x2, x3, x4)  =  P137_IN_GGAG(x1, x2, x4)
U48_GGAG(x1, x2, x3, x4, x5)  =  U48_GGAG(x1, x2, x4, x5)
U49_GGAG(x1, x2, x3, x4, x5)  =  U49_GGAG(x1, x2, x4, x5)
U50_GGAG(x1, x2, x3, x4, x5)  =  U50_GGAG(x1, x2, x4, x5)
U46_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_AGAGAG(x2, x4, x6, x7)
U47_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U47_AGAGAG(x2, x4, x6, x7)
P137_IN_AGAG(x1, x2, x3, x4)  =  P137_IN_AGAG(x2, x4)
U48_AGAG(x1, x2, x3, x4, x5)  =  U48_AGAG(x2, x4, x5)
U49_AGAG(x1, x2, x3, x4, x5)  =  U49_AGAG(x2, x4, x5)
U50_AGAG(x1, x2, x3, x4, x5)  =  U50_AGAG(x2, x4, x5)
U29_AA(x1, x2)  =  U29_AA(x2)
U30_AA(x1, x2, x3, x4, x5)  =  U30_AA(x5)
U31_AA(x1, x2, x3, x4, x5)  =  U31_AA(x5)
U32_AA(x1, x2, x3, x4, x5)  =  U32_AA(x5)
U33_AA(x1, x2, x3, x4, x5)  =  U33_AA(x5)
U34_AA(x1, x2, x3, x4, x5)  =  U34_AA(x5)
U35_AA(x1, x2, x3, x4, x5)  =  U35_AA(x5)
U36_AA(x1, x2, x3, x4, x5)  =  U36_AA(x5)
U37_AA(x1, x2, x3, x4, x5)  =  U37_AA(x5)
U38_AA(x1, x2, x3, x4, x5)  =  U38_AA(x5)
U39_AA(x1, x2, x3, x4, x5)  =  U39_AA(x5)
U40_AA(x1, x2, x3, x4, x5)  =  U40_AA(x5)
U41_AA(x1, x2, x3, x4, x5)  =  U41_AA(x5)
U42_AA(x1, x2, x3)  =  U42_AA(x3)
U43_AA(x1, x2, x3)  =  U43_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U47_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U47_GGGGGG(x1, x2, x3, x4, x5, x6, x7)
U29_GA(x1, x2)  =  U29_GA(x2)
U30_GA(x1, x2, x3, x4, x5)  =  U30_GA(x1, x2, x5)
U31_GA(x1, x2, x3, x4, x5)  =  U31_GA(x1, x2, x5)
U32_GA(x1, x2, x3, x4, x5)  =  U32_GA(x1, x2, x5)
U33_GA(x1, x2, x3, x4, x5)  =  U33_GA(x1, x2, x5)
U34_GA(x1, x2, x3, x4, x5)  =  U34_GA(x1, x2, x5)
U35_GA(x1, x2, x3, x4, x5)  =  U35_GA(x1, x2, x5)
U36_GA(x1, x2, x3, x4, x5)  =  U36_GA(x1, x2, x5)
U37_GA(x1, x2, x3, x4, x5)  =  U37_GA(x1, x2, x5)
U38_GA(x1, x2, x3, x4, x5)  =  U38_GA(x1, x2, x5)
U39_GA(x1, x2, x3, x4, x5)  =  U39_GA(x1, x2, x5)
U40_GA(x1, x2, x3, x4, x5)  =  U40_GA(x1, x2, x5)
U41_GA(x1, x2, x3, x4, x5)  =  U41_GA(x1, x2, x5)
U42_GA(x1, x2, x3)  =  U42_GA(x1, x3)
U43_GA(x1, x2, x3)  =  U43_GA(x1, x3)
U44_GA(x1, x2, x3)  =  U44_GA(x1, x3)
U7_GA(x1, x2)  =  U7_GA(x2)
U8_GA(x1, x2, x3, x4, x5)  =  U8_GA(x1, x2, x5)
U9_GA(x1, x2, x3, x4, x5)  =  U9_GA(x1, x2, x5)
U10_GA(x1, x2, x3, x4, x5)  =  U10_GA(x1, x2, x5)
U11_GA(x1, x2, x3, x4, x5)  =  U11_GA(x1, x2, x5)
U12_GA(x1, x2, x3, x4, x5)  =  U12_GA(x1, x2, x5)
U13_GA(x1, x2, x3, x4, x5)  =  U13_GA(x1, x2, x5)
U14_GA(x1, x2, x3, x4, x5)  =  U14_GA(x1, x2, x5)
U15_GA(x1, x2, x3, x4, x5)  =  U15_GA(x1, x2, x5)
U16_GA(x1, x2, x3, x4, x5)  =  U16_GA(x1, x2, x5)
U17_GA(x1, x2, x3, x4, x5)  =  U17_GA(x1, x2, x5)
U18_GA(x1, x2, x3, x4, x5)  =  U18_GA(x1, x2, x5)
U19_GA(x1, x2, x3, x4, x5)  =  U19_GA(x1, x2, x5)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x3)
U22_GA(x1, x2, x3)  =  U22_GA(x1, x3)
U7_AA(x1, x2)  =  U7_AA(x2)
U8_AA(x1, x2, x3, x4, x5)  =  U8_AA(x5)
U9_AA(x1, x2, x3, x4, x5)  =  U9_AA(x5)
U10_AA(x1, x2, x3, x4, x5)  =  U10_AA(x5)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)
U12_AA(x1, x2, x3, x4, x5)  =  U12_AA(x5)
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U14_AA(x1, x2, x3, x4, x5)  =  U14_AA(x5)
U15_AA(x1, x2, x3, x4, x5)  =  U15_AA(x5)
U16_AA(x1, x2, x3, x4, x5)  =  U16_AA(x5)
U17_AA(x1, x2, x3, x4, x5)  =  U17_AA(x5)
U18_AA(x1, x2, x3, x4, x5)  =  U18_AA(x5)
U19_AA(x1, x2, x3, x4, x5)  =  U19_AA(x5)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U22_AA(x1, x2, x3)  =  U22_AA(x3)

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

(6) Obligation:

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

P1_IN_AG(d(d(T10)), const(1)) → U54_AG(T10, p9_in_aa(T10, X14))
P1_IN_AG(d(d(T10)), const(1)) → P9_IN_AA(T10, X14)
P9_IN_AA(e(t), const(1)) → U6_AA(p1_in_gg(d(e(const(1))), const(1)))
P9_IN_AA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(1))
P1_IN_GG(d(d(T10)), const(1)) → U54_GG(T10, p9_in_ga(T10, X14))
P1_IN_GG(d(d(T10)), const(1)) → P9_IN_GA(T10, X14)
P9_IN_GA(e(t), const(1)) → U6_GA(p1_in_gg(d(e(const(1))), const(1)))
P9_IN_GA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(1))
P1_IN_GG(d(d(T135)), const(0)) → U55_GG(T135, p90_in_ga(T135, X334))
P1_IN_GG(d(d(T135)), const(0)) → P90_IN_GA(T135, X334)
P90_IN_GA(e(t), const(1)) → U28_GA(p1_in_gg(d(e(const(1))), const(0)))
P90_IN_GA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(0))
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → U56_GG(T197, T194, p1_in_gg(d(e(T197)), T194))
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_GG(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_GG(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → U45_GGGGGG(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_GG(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_GG(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T228, T194) → U48_GGGG(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(d(T280)), +(T278, T279)) → U61_GG(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
P1_IN_GG(d(d(T280)), +(T278, T279)) → P150_IN_GAGG(T280, X551, T278, T279)
P150_IN_GAGG(T280, X551, T278, T279) → U51_GAGG(T280, X551, T278, T279, p60_in_ga(T280, X551))
P150_IN_GAGG(T280, X551, T278, T279) → P60_IN_GA(T280, X551)
P60_IN_GA(e(+(T108, T109)), +(X266, X267)) → U23_GA(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
P60_IN_GA(e(+(T108, T109)), +(X266, X267)) → P39_IN_GAGA(T108, X266, T109, X267)
P39_IN_GAGA(T45, X117, T46, X118) → U3_GAGA(T45, X117, T46, X118, p24_in_ga(T45, X117))
P39_IN_GAGA(T45, X117, T46, X118) → P24_IN_GA(T45, X117)
P24_IN_GA(+(T45, T46), +(X117, X118)) → U1_GA(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
P24_IN_GA(+(T45, T46), +(X117, X118)) → P39_IN_GAGA(T45, X117, T46, X118)
P39_IN_GAGA(T45, T47, T48, X118) → U4_GAGA(T45, T47, T48, X118, p24_in_ga(T45, T47))
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_GA(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_GAGA(T59, X152, T60, X151)
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_GAGA(T45, T47, T48, X118, p24_in_ga(T48, X118))
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → P24_IN_GA(T48, X118)
P60_IN_GA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_GA(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
P60_IN_GA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → P39_IN_GAGA(T120, X301, T121, X300)
P60_IN_GA(d(T125), X316) → U25_GA(T125, X316, p60_in_ga(T125, X315))
P60_IN_GA(d(T125), X316) → P60_IN_GA(T125, X315)
P60_IN_GA(d(T125), X316) → U26_GA(T125, X316, p60_in_ga(T125, T126))
U26_GA(T125, X316, p60_out_ga(T125, T126)) → U27_GA(T125, X316, p24_in_aa(T126, X316))
U26_GA(T125, X316, p60_out_ga(T125, T126)) → P24_IN_AA(T126, X316)
P24_IN_AA(+(T45, T46), +(X117, X118)) → U1_AA(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
P24_IN_AA(+(T45, T46), +(X117, X118)) → P39_IN_AAAA(T45, X117, T46, X118)
P39_IN_AAAA(T45, X117, T46, X118) → U3_AAAA(T45, X117, T46, X118, p24_in_aa(T45, X117))
P39_IN_AAAA(T45, X117, T46, X118) → P24_IN_AA(T45, X117)
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_AA(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_AAAA(T59, X152, T60, X151)
P39_IN_AAAA(T45, T47, T48, X118) → U4_AAAA(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_AAAA(T45, T47, T48, X118, p24_in_aa(T48, X118))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → P24_IN_AA(T48, X118)
P150_IN_GAGG(T280, T281, T278, T279) → U52_GAGG(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_GAGG(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_GAGG(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
U52_GAGG(T280, T281, T278, T279, p60_out_ga(T280, T281)) → P1_IN_AG(d(e(T281)), +(T278, T279))
P1_IN_AG(d(d(T135)), const(0)) → U55_AG(T135, p90_in_aa(T135, X334))
P1_IN_AG(d(d(T135)), const(0)) → P90_IN_AA(T135, X334)
P90_IN_AA(e(t), const(1)) → U28_AA(p1_in_gg(d(e(const(1))), const(0)))
P90_IN_AA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(0))
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_GG(T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_GG(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_GG(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_GG(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
P1_IN_GG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_GG(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
P1_IN_GG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → P150_IN_GAGG(T356, X635, *(T352, T353), *(T354, T355))
P1_IN_GG(d(d(e(t))), T360) → U67_GG(T360, p1_in_gg(d(e(const(1))), T360))
P1_IN_GG(d(d(e(t))), T360) → P1_IN_GG(d(e(const(1))), T360)
P1_IN_GG(d(d(e(const(T366)))), T360) → U68_GG(T366, T360, p1_in_gg(d(e(const(0))), T360))
P1_IN_GG(d(d(e(const(T366)))), T360) → P1_IN_GG(d(e(const(0))), T360)
P1_IN_GG(d(d(e(+(T377, T378)))), T360) → U69_GG(T377, T378, T360, p24_in_ga(T377, X683))
P1_IN_GG(d(d(e(+(T377, T378)))), T360) → P24_IN_GA(T377, X683)
P1_IN_GG(d(d(e(+(T377, T380)))), T360) → U70_GG(T377, T380, T360, p24_in_ga(T377, T379))
U70_GG(T377, T380, T360, p24_out_ga(T377, T379)) → U71_GG(T377, T380, T360, p24_in_ga(T380, X684))
U70_GG(T377, T380, T360, p24_out_ga(T377, T379)) → P24_IN_GA(T380, X684)
P1_IN_GG(d(d(e(+(T377, T380)))), T360) → U72_GG(T377, T380, T360, p24_in_ga(T377, T392))
U72_GG(T377, T380, T360, p24_out_ga(T377, T392)) → U73_GG(T377, T380, T360, T392, p24_in_ga(T380, T391))
U72_GG(T377, T380, T360, p24_out_ga(T377, T392)) → P24_IN_GA(T380, T391)
U73_GG(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_GG(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
U73_GG(T377, T380, T360, T392, p24_out_ga(T380, T391)) → P1_IN_AG(d(e(+(T392, T391))), T360)
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → U56_AG(T197, T194, p1_in_ag(d(e(T197)), T194))
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_AG(d(e(T197)), T194)
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_AG(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_AG(d(e(T203)), T194)
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_AG(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194)
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → U45_AGAGAG(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → P1_IN_AG(d(e(T224)), T222)
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_AG(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGAG(T224, T222, T225, T223, T226, T194) → U45_GGGGAG(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
P134_IN_GGGGAG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(d(e(*(T417, T418)))), T360) → U75_GG(T417, T418, T360, p24_in_ga(T417, X724))
P1_IN_GG(d(d(e(*(T417, T418)))), T360) → P24_IN_GA(T417, X724)
P1_IN_GG(d(d(e(*(T421, T420)))), T360) → U76_GG(T421, T420, T360, p24_in_ga(T421, T419))
U76_GG(T421, T420, T360, p24_out_ga(T421, T419)) → U77_GG(T421, T420, T360, p24_in_ga(T420, X723))
U76_GG(T421, T420, T360, p24_out_ga(T421, T419)) → P24_IN_GA(T420, X723)
P1_IN_GG(d(d(e(*(T433, T434)))), T360) → U78_GG(T433, T434, T360, p24_in_ga(T433, T435))
U78_GG(T433, T434, T360, p24_out_ga(T433, T435)) → U79_GG(T433, T434, T360, T435, p24_in_ga(T434, T432))
U78_GG(T433, T434, T360, p24_out_ga(T433, T435)) → P24_IN_GA(T434, T432)
U79_GG(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_GG(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
U79_GG(T433, T434, T360, T435, p24_out_ga(T434, T432)) → P1_IN_AG(d(e(+(*(T433, T432), *(T434, T435)))), T360)
P1_IN_AG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_AG(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
P1_IN_AG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
P1_IN_GG(d(d(d(T455))), T360) → U81_GG(T455, T360, p60_in_ga(T455, X744))
P1_IN_GG(d(d(d(T455))), T360) → P60_IN_GA(T455, X744)
P1_IN_GG(d(d(d(T455))), T360) → U82_GG(T455, T360, p60_in_ga(T455, T456))
U82_GG(T455, T360, p60_out_ga(T455, T456)) → U83_GG(T455, T360, p24_in_aa(T456, X745))
U82_GG(T455, T360, p60_out_ga(T455, T456)) → P24_IN_AA(T456, X745)
U82_GG(T455, T360, p60_out_ga(T455, T456)) → U84_GG(T455, T360, p24_in_aa(T456, T467))
U84_GG(T455, T360, p24_out_aa(T456, T467)) → U85_GG(T455, T360, p1_in_ag(d(e(T467)), T360))
U84_GG(T455, T360, p24_out_aa(T456, T467)) → P1_IN_AG(d(e(T467)), T360)
P1_IN_AG(d(d(T280)), +(T278, T279)) → U61_AG(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
P1_IN_AG(d(d(T280)), +(T278, T279)) → P150_IN_AAGG(T280, X551, T278, T279)
P150_IN_AAGG(T280, X551, T278, T279) → U51_AAGG(T280, X551, T278, T279, p60_in_aa(T280, X551))
P150_IN_AAGG(T280, X551, T278, T279) → P60_IN_AA(T280, X551)
P60_IN_AA(e(+(T108, T109)), +(X266, X267)) → U23_AA(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
P60_IN_AA(e(+(T108, T109)), +(X266, X267)) → P39_IN_AAAA(T108, X266, T109, X267)
P60_IN_AA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_AA(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
P60_IN_AA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → P39_IN_AAAA(T120, X301, T121, X300)
P60_IN_AA(d(T125), X316) → U25_AA(T125, X316, p60_in_aa(T125, X315))
P60_IN_AA(d(T125), X316) → P60_IN_AA(T125, X315)
P60_IN_AA(d(T125), X316) → U26_AA(T125, X316, p60_in_aa(T125, T126))
U26_AA(T125, X316, p60_out_aa(T125, T126)) → U27_AA(T125, X316, p24_in_aa(T126, X316))
U26_AA(T125, X316, p60_out_aa(T125, T126)) → P24_IN_AA(T126, X316)
P150_IN_AAGG(T280, T281, T278, T279) → U52_AAGG(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_AAGG(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_AAGG(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
U52_AAGG(T280, T281, T278, T279, p60_out_aa(T280, T281)) → P1_IN_AG(d(e(T281)), +(T278, T279))
P1_IN_AG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_AG(T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_AG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_AG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_AG(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_AG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_AG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_AG(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
P1_IN_AG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_AG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_AG(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
P1_IN_AG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
P1_IN_AG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_AG(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
P1_IN_AG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → P150_IN_AAGG(T356, X635, *(T352, T353), *(T354, T355))
P1_IN_AG(d(d(e(t))), T360) → U67_AG(T360, p1_in_gg(d(e(const(1))), T360))
P1_IN_AG(d(d(e(t))), T360) → P1_IN_GG(d(e(const(1))), T360)
P1_IN_AG(d(d(e(const(T366)))), T360) → U68_AG(T366, T360, p1_in_gg(d(e(const(0))), T360))
P1_IN_AG(d(d(e(const(T366)))), T360) → P1_IN_GG(d(e(const(0))), T360)
P1_IN_AG(d(d(e(+(T377, T378)))), T360) → U69_AG(T377, T378, T360, p24_in_aa(T377, X683))
P1_IN_AG(d(d(e(+(T377, T378)))), T360) → P24_IN_AA(T377, X683)
P1_IN_AG(d(d(e(+(T377, T380)))), T360) → U70_AG(T377, T380, T360, p24_in_aa(T377, T379))
U70_AG(T377, T380, T360, p24_out_aa(T377, T379)) → U71_AG(T377, T380, T360, p24_in_aa(T380, X684))
U70_AG(T377, T380, T360, p24_out_aa(T377, T379)) → P24_IN_AA(T380, X684)
P1_IN_AG(d(d(e(+(T377, T380)))), T360) → U72_AG(T377, T380, T360, p24_in_aa(T377, T392))
U72_AG(T377, T380, T360, p24_out_aa(T377, T392)) → U73_AG(T377, T380, T360, T392, p24_in_aa(T380, T391))
U72_AG(T377, T380, T360, p24_out_aa(T377, T392)) → P24_IN_AA(T380, T391)
U73_AG(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_AG(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
U73_AG(T377, T380, T360, T392, p24_out_aa(T380, T391)) → P1_IN_AG(d(e(+(T392, T391))), T360)
P1_IN_AG(d(d(e(*(T417, T418)))), T360) → U75_AG(T417, T418, T360, p24_in_aa(T417, X724))
P1_IN_AG(d(d(e(*(T417, T418)))), T360) → P24_IN_AA(T417, X724)
P1_IN_AG(d(d(e(*(T421, T420)))), T360) → U76_AG(T421, T420, T360, p24_in_aa(T421, T419))
U76_AG(T421, T420, T360, p24_out_aa(T421, T419)) → U77_AG(T421, T420, T360, p24_in_aa(T420, X723))
U76_AG(T421, T420, T360, p24_out_aa(T421, T419)) → P24_IN_AA(T420, X723)
P1_IN_AG(d(d(e(*(T433, T434)))), T360) → U78_AG(T433, T434, T360, p24_in_aa(T433, T435))
U78_AG(T433, T434, T360, p24_out_aa(T433, T435)) → U79_AG(T433, T434, T360, T435, p24_in_aa(T434, T432))
U78_AG(T433, T434, T360, p24_out_aa(T433, T435)) → P24_IN_AA(T434, T432)
U79_AG(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_AG(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
U79_AG(T433, T434, T360, T435, p24_out_aa(T434, T432)) → P1_IN_AG(d(e(+(*(T433, T432), *(T434, T435)))), T360)
P1_IN_AG(d(d(d(T455))), T360) → U81_AG(T455, T360, p60_in_aa(T455, X744))
P1_IN_AG(d(d(d(T455))), T360) → P60_IN_AA(T455, X744)
P1_IN_AG(d(d(d(T455))), T360) → U82_AG(T455, T360, p60_in_aa(T455, T456))
U82_AG(T455, T360, p60_out_aa(T455, T456)) → U83_AG(T455, T360, p24_in_aa(T456, X745))
U82_AG(T455, T360, p60_out_aa(T455, T456)) → P24_IN_AA(T456, X745)
U82_AG(T455, T360, p60_out_aa(T455, T456)) → U84_AG(T455, T360, p24_in_aa(T456, T467))
U84_AG(T455, T360, p24_out_aa(T456, T467)) → U85_AG(T455, T360, p1_in_ag(d(e(T467)), T360))
U84_AG(T455, T360, p24_out_aa(T456, T467)) → P1_IN_AG(d(e(T467)), T360)
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P134_IN_GGGGAG(T224, T222, T227, T223, T228, T194) → U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_GGGGAG(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T228, T194)
P137_IN_GGAG(T227, T223, T228, T194) → U48_GGAG(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
P137_IN_GGAG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P137_IN_GGAG(T227, T223, T229, T194) → U49_GGAG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_GGAG(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P134_IN_AGAGAG(T224, T222, T227, T223, T228, T194) → U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_AGAGAG(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → P137_IN_AGAG(T227, T223, T228, T194)
P137_IN_AGAG(T227, T223, T228, T194) → U48_AGAG(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
P137_IN_AGAG(T227, T223, T228, T194) → P1_IN_AG(d(e(T227)), T223)
P137_IN_AGAG(T227, T223, T229, T194) → U49_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P90_IN_AA(e(const(T140)), const(0)) → U29_AA(T140, p1_in_gg(d(e(const(0))), const(0)))
P90_IN_AA(e(const(T140)), const(0)) → P1_IN_GG(d(e(const(0))), const(0))
P90_IN_AA(e(+(T151, T152)), +(X373, X374)) → U30_AA(T151, T152, X373, X374, p24_in_aa(T151, X373))
P90_IN_AA(e(+(T151, T152)), +(X373, X374)) → P24_IN_AA(T151, X373)
P90_IN_AA(e(+(T151, T154)), +(T153, X374)) → U31_AA(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_AA(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_AA(T151, T154, T153, X374, p24_in_aa(T154, X374))
U31_AA(T151, T154, T153, X374, p24_out_aa(T151, T153)) → P24_IN_AA(T154, X374)
P90_IN_AA(e(+(T151, T154)), +(T156, T155)) → U33_AA(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_AA(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_AA(T151, T154, T156, T155, p24_in_aa(T154, T155))
U33_AA(T151, T154, T156, T155, p24_out_aa(T151, T156)) → P24_IN_AA(T154, T155)
U34_AA(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_AA(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U34_AA(T151, T154, T156, T155, p24_out_aa(T154, T155)) → P1_IN_AG(d(e(+(T156, T155))), const(0))
P90_IN_AA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_AA(T169, T170, X420, X421, p24_in_aa(T169, X421))
P90_IN_AA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → P24_IN_AA(T169, X421)
P90_IN_AA(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_AA(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_AA(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_AA(T173, T172, X420, T171, p24_in_aa(T172, X420))
U37_AA(T173, T172, X420, T171, p24_out_aa(T173, T171)) → P24_IN_AA(T172, X420)
P90_IN_AA(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_AA(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_AA(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_AA(T175, T176, T174, T177, p24_in_aa(T176, T174))
U39_AA(T175, T176, T174, T177, p24_out_aa(T175, T177)) → P24_IN_AA(T176, T174)
U40_AA(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_AA(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U40_AA(T175, T176, T174, T177, p24_out_aa(T176, T174)) → P1_IN_AG(d(e(+(*(T175, T174), *(T176, T177)))), const(0))
P90_IN_AA(d(T185), X449) → U42_AA(T185, X449, p60_in_aa(T185, X448))
P90_IN_AA(d(T185), X449) → P60_IN_AA(T185, X448)
P90_IN_AA(d(T185), X449) → U43_AA(T185, X449, p60_in_aa(T185, T186))
U43_AA(T185, X449, p60_out_aa(T185, T186)) → U44_AA(T185, X449, p90_in_aa(e(T186), X449))
U43_AA(T185, X449, p60_out_aa(T185, T186)) → P90_IN_AA(e(T186), X449)
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_GGGGGG(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P90_IN_GA(e(const(T140)), const(0)) → U29_GA(T140, p1_in_gg(d(e(const(0))), const(0)))
P90_IN_GA(e(const(T140)), const(0)) → P1_IN_GG(d(e(const(0))), const(0))
P90_IN_GA(e(+(T151, T152)), +(X373, X374)) → U30_GA(T151, T152, X373, X374, p24_in_ga(T151, X373))
P90_IN_GA(e(+(T151, T152)), +(X373, X374)) → P24_IN_GA(T151, X373)
P90_IN_GA(e(+(T151, T154)), +(T153, X374)) → U31_GA(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_GA(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_GA(T151, T154, T153, X374, p24_in_ga(T154, X374))
U31_GA(T151, T154, T153, X374, p24_out_ga(T151, T153)) → P24_IN_GA(T154, X374)
P90_IN_GA(e(+(T151, T154)), +(T156, T155)) → U33_GA(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_GA(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_GA(T151, T154, T156, T155, p24_in_ga(T154, T155))
U33_GA(T151, T154, T156, T155, p24_out_ga(T151, T156)) → P24_IN_GA(T154, T155)
U34_GA(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_GA(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U34_GA(T151, T154, T156, T155, p24_out_ga(T154, T155)) → P1_IN_AG(d(e(+(T156, T155))), const(0))
P90_IN_GA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_GA(T169, T170, X420, X421, p24_in_ga(T169, X421))
P90_IN_GA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → P24_IN_GA(T169, X421)
P90_IN_GA(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_GA(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_GA(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_GA(T173, T172, X420, T171, p24_in_ga(T172, X420))
U37_GA(T173, T172, X420, T171, p24_out_ga(T173, T171)) → P24_IN_GA(T172, X420)
P90_IN_GA(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_GA(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_GA(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_GA(T175, T176, T174, T177, p24_in_ga(T176, T174))
U39_GA(T175, T176, T174, T177, p24_out_ga(T175, T177)) → P24_IN_GA(T176, T174)
U40_GA(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_GA(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U40_GA(T175, T176, T174, T177, p24_out_ga(T176, T174)) → P1_IN_AG(d(e(+(*(T175, T174), *(T176, T177)))), const(0))
P90_IN_GA(d(T185), X449) → U42_GA(T185, X449, p60_in_ga(T185, X448))
P90_IN_GA(d(T185), X449) → P60_IN_GA(T185, X448)
P90_IN_GA(d(T185), X449) → U43_GA(T185, X449, p60_in_ga(T185, T186))
U43_GA(T185, X449, p60_out_ga(T185, T186)) → U44_GA(T185, X449, p90_in_aa(e(T186), X449))
U43_GA(T185, X449, p60_out_ga(T185, T186)) → P90_IN_AA(e(T186), X449)
P9_IN_GA(e(const(T15)), const(0)) → U7_GA(T15, p1_in_gg(d(e(const(0))), const(1)))
P9_IN_GA(e(const(T15)), const(0)) → P1_IN_GG(d(e(const(0))), const(1))
P9_IN_GA(e(+(T26, T27)), +(X77, X78)) → U8_GA(T26, T27, X77, X78, p24_in_ga(T26, X77))
P9_IN_GA(e(+(T26, T27)), +(X77, X78)) → P24_IN_GA(T26, X77)
P9_IN_GA(e(+(T26, T29)), +(T28, X78)) → U9_GA(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_GA(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_GA(T26, T29, T28, X78, p24_in_ga(T29, X78))
U9_GA(T26, T29, T28, X78, p24_out_ga(T26, T28)) → P24_IN_GA(T29, X78)
P9_IN_GA(e(+(T26, T29)), +(T62, T61)) → U11_GA(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_GA(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_GA(T26, T29, T62, T61, p24_in_ga(T29, T61))
U11_GA(T26, T29, T62, T61, p24_out_ga(T26, T62)) → P24_IN_GA(T29, T61)
U12_GA(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_GA(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U12_GA(T26, T29, T62, T61, p24_out_ga(T29, T61)) → P1_IN_AG(d(e(+(T62, T61))), const(1))
P9_IN_GA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_GA(T75, T76, X200, X201, p24_in_ga(T75, X201))
P9_IN_GA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → P24_IN_GA(T75, X201)
P9_IN_GA(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_GA(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_GA(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_GA(T79, T78, X200, T77, p24_in_ga(T78, X200))
U15_GA(T79, T78, X200, T77, p24_out_ga(T79, T77)) → P24_IN_GA(T78, X200)
P9_IN_GA(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_GA(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_GA(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_GA(T81, T82, T80, T83, p24_in_ga(T82, T80))
U17_GA(T81, T82, T80, T83, p24_out_ga(T81, T83)) → P24_IN_GA(T82, T80)
U18_GA(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_GA(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U18_GA(T81, T82, T80, T83, p24_out_ga(T82, T80)) → P1_IN_AG(d(e(+(*(T81, T80), *(T82, T83)))), const(1))
P9_IN_GA(d(T91), X229) → U20_GA(T91, X229, p60_in_ga(T91, X228))
P9_IN_GA(d(T91), X229) → P60_IN_GA(T91, X228)
P9_IN_GA(d(T91), X229) → U21_GA(T91, X229, p60_in_ga(T91, T92))
U21_GA(T91, X229, p60_out_ga(T91, T92)) → U22_GA(T91, X229, p9_in_aa(e(T92), X229))
U21_GA(T91, X229, p60_out_ga(T91, T92)) → P9_IN_AA(e(T92), X229)
P9_IN_AA(e(const(T15)), const(0)) → U7_AA(T15, p1_in_gg(d(e(const(0))), const(1)))
P9_IN_AA(e(const(T15)), const(0)) → P1_IN_GG(d(e(const(0))), const(1))
P9_IN_AA(e(+(T26, T27)), +(X77, X78)) → U8_AA(T26, T27, X77, X78, p24_in_aa(T26, X77))
P9_IN_AA(e(+(T26, T27)), +(X77, X78)) → P24_IN_AA(T26, X77)
P9_IN_AA(e(+(T26, T29)), +(T28, X78)) → U9_AA(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_AA(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_AA(T26, T29, T28, X78, p24_in_aa(T29, X78))
U9_AA(T26, T29, T28, X78, p24_out_aa(T26, T28)) → P24_IN_AA(T29, X78)
P9_IN_AA(e(+(T26, T29)), +(T62, T61)) → U11_AA(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_AA(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_AA(T26, T29, T62, T61, p24_in_aa(T29, T61))
U11_AA(T26, T29, T62, T61, p24_out_aa(T26, T62)) → P24_IN_AA(T29, T61)
U12_AA(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_AA(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U12_AA(T26, T29, T62, T61, p24_out_aa(T29, T61)) → P1_IN_AG(d(e(+(T62, T61))), const(1))
P9_IN_AA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_AA(T75, T76, X200, X201, p24_in_aa(T75, X201))
P9_IN_AA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → P24_IN_AA(T75, X201)
P9_IN_AA(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_AA(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_AA(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_AA(T79, T78, X200, T77, p24_in_aa(T78, X200))
U15_AA(T79, T78, X200, T77, p24_out_aa(T79, T77)) → P24_IN_AA(T78, X200)
P9_IN_AA(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_AA(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_AA(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_AA(T81, T82, T80, T83, p24_in_aa(T82, T80))
U17_AA(T81, T82, T80, T83, p24_out_aa(T81, T83)) → P24_IN_AA(T82, T80)
U18_AA(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_AA(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U18_AA(T81, T82, T80, T83, p24_out_aa(T82, T80)) → P1_IN_AG(d(e(+(*(T81, T80), *(T82, T83)))), const(1))
P9_IN_AA(d(T91), X229) → U20_AA(T91, X229, p60_in_aa(T91, X228))
P9_IN_AA(d(T91), X229) → P60_IN_AA(T91, X228)
P9_IN_AA(d(T91), X229) → U21_AA(T91, X229, p60_in_aa(T91, T92))
U21_AA(T91, X229, p60_out_aa(T91, T92)) → U22_AA(T91, X229, p9_in_aa(e(T92), X229))
U21_AA(T91, X229, p60_out_aa(T91, T92)) → P9_IN_AA(e(T92), X229)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P1_IN_AG(x1, x2)  =  P1_IN_AG(x2)
U54_AG(x1, x2)  =  U54_AG(x2)
P9_IN_AA(x1, x2)  =  P9_IN_AA
U6_AA(x1)  =  U6_AA(x1)
P1_IN_GG(x1, x2)  =  P1_IN_GG(x1, x2)
U54_GG(x1, x2)  =  U54_GG(x1, x2)
P9_IN_GA(x1, x2)  =  P9_IN_GA(x1)
U6_GA(x1)  =  U6_GA(x1)
U55_GG(x1, x2)  =  U55_GG(x1, x2)
P90_IN_GA(x1, x2)  =  P90_IN_GA(x1)
U28_GA(x1)  =  U28_GA(x1)
U56_GG(x1, x2, x3)  =  U56_GG(x1, x2, x3)
U57_GG(x1, x2, x3, x4)  =  U57_GG(x2, x3, x4)
U58_GG(x1, x2, x3, x4, x5, x6, x7)  =  U58_GG(x1, x2, x3, x4, x5, x6, x7)
P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)
U45_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U45_GGGGGG(x1, x2, x3, x4, x5, x6, x7)
U59_GG(x1, x2, x3, x4, x5, x6, x7)  =  U59_GG(x1, x2, x3, x4, x5, x6, x7)
U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)
U60_GG(x1, x2, x3, x4, x5)  =  U60_GG(x1, x2, x3, x4, x5)
P137_IN_GGGG(x1, x2, x3, x4)  =  P137_IN_GGGG(x1, x2, x3, x4)
U48_GGGG(x1, x2, x3, x4, x5)  =  U48_GGGG(x1, x2, x3, x4, x5)
U61_GG(x1, x2, x3, x4)  =  U61_GG(x1, x2, x3, x4)
P150_IN_GAGG(x1, x2, x3, x4)  =  P150_IN_GAGG(x1, x3, x4)
U51_GAGG(x1, x2, x3, x4, x5)  =  U51_GAGG(x1, x3, x4, x5)
P60_IN_GA(x1, x2)  =  P60_IN_GA(x1)
U23_GA(x1, x2, x3, x4, x5)  =  U23_GA(x1, x2, x5)
P39_IN_GAGA(x1, x2, x3, x4)  =  P39_IN_GAGA(x1, x3)
U3_GAGA(x1, x2, x3, x4, x5)  =  U3_GAGA(x1, x3, x5)
P24_IN_GA(x1, x2)  =  P24_IN_GA(x1)
U1_GA(x1, x2, x3, x4, x5)  =  U1_GA(x1, x2, x5)
U4_GAGA(x1, x2, x3, x4, x5)  =  U4_GAGA(x1, x3, x5)
U2_GA(x1, x2, x3, x4, x5)  =  U2_GA(x1, x2, x5)
U5_GAGA(x1, x2, x3, x4, x5)  =  U5_GAGA(x1, x3, x5)
U24_GA(x1, x2, x3, x4, x5)  =  U24_GA(x1, x2, x5)
U25_GA(x1, x2, x3)  =  U25_GA(x1, x3)
U26_GA(x1, x2, x3)  =  U26_GA(x1, x3)
U27_GA(x1, x2, x3)  =  U27_GA(x1, x3)
P24_IN_AA(x1, x2)  =  P24_IN_AA
U1_AA(x1, x2, x3, x4, x5)  =  U1_AA(x5)
P39_IN_AAAA(x1, x2, x3, x4)  =  P39_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5)  =  U3_AAAA(x5)
U2_AA(x1, x2, x3, x4, x5)  =  U2_AA(x5)
U4_AAAA(x1, x2, x3, x4, x5)  =  U4_AAAA(x5)
U5_AAAA(x1, x2, x3, x4, x5)  =  U5_AAAA(x5)
U52_GAGG(x1, x2, x3, x4, x5)  =  U52_GAGG(x1, x3, x4, x5)
U53_GAGG(x1, x2, x3, x4, x5)  =  U53_GAGG(x1, x3, x4, x5)
U55_AG(x1, x2)  =  U55_AG(x2)
P90_IN_AA(x1, x2)  =  P90_IN_AA
U28_AA(x1)  =  U28_AA(x1)
U62_GG(x1, x2, x3)  =  U62_GG(x1, x2, x3)
U63_GG(x1, x2, x3, x4)  =  U63_GG(x2, x3, x4)
U64_GG(x1, x2, x3, x4, x5, x6, x7)  =  U64_GG(x1, x2, x3, x4, x5, x6, x7)
U65_GG(x1, x2, x3, x4, x5, x6, x7)  =  U65_GG(x1, x2, x3, x4, x5, x6, x7)
U66_GG(x1, x2, x3, x4, x5, x6)  =  U66_GG(x1, x2, x3, x4, x5, x6)
U67_GG(x1, x2)  =  U67_GG(x1, x2)
U68_GG(x1, x2, x3)  =  U68_GG(x2, x3)
U69_GG(x1, x2, x3, x4)  =  U69_GG(x1, x2, x3, x4)
U70_GG(x1, x2, x3, x4)  =  U70_GG(x1, x2, x3, x4)
U71_GG(x1, x2, x3, x4)  =  U71_GG(x1, x2, x3, x4)
U72_GG(x1, x2, x3, x4)  =  U72_GG(x1, x2, x3, x4)
U73_GG(x1, x2, x3, x4, x5)  =  U73_GG(x1, x2, x3, x5)
U74_GG(x1, x2, x3, x4)  =  U74_GG(x1, x2, x3, x4)
U56_AG(x1, x2, x3)  =  U56_AG(x2, x3)
U57_AG(x1, x2, x3, x4)  =  U57_AG(x3, x4)
U58_AG(x1, x2, x3, x4, x5, x6, x7)  =  U58_AG(x4, x5, x6, x7)
P134_IN_AGAGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_AGAGAG(x2, x4, x6)
U45_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U45_AGAGAG(x2, x4, x6, x7)
U59_AG(x1, x2, x3, x4, x5, x6, x7)  =  U59_AG(x1, x2, x4, x5, x6, x7)
P134_IN_GGGGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGAG(x1, x2, x3, x4, x6)
U45_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U45_GGGGAG(x1, x2, x3, x4, x6, x7)
U75_GG(x1, x2, x3, x4)  =  U75_GG(x1, x2, x3, x4)
U76_GG(x1, x2, x3, x4)  =  U76_GG(x1, x2, x3, x4)
U77_GG(x1, x2, x3, x4)  =  U77_GG(x1, x2, x3, x4)
U78_GG(x1, x2, x3, x4)  =  U78_GG(x1, x2, x3, x4)
U79_GG(x1, x2, x3, x4, x5)  =  U79_GG(x1, x2, x3, x5)
U80_GG(x1, x2, x3, x4)  =  U80_GG(x1, x2, x3, x4)
U60_AG(x1, x2, x3, x4, x5)  =  U60_AG(x1, x2, x3, x4, x5)
U49_GGGG(x1, x2, x3, x4, x5)  =  U49_GGGG(x1, x2, x3, x4, x5)
U81_GG(x1, x2, x3)  =  U81_GG(x1, x2, x3)
U82_GG(x1, x2, x3)  =  U82_GG(x1, x2, x3)
U83_GG(x1, x2, x3)  =  U83_GG(x1, x2, x3)
U84_GG(x1, x2, x3)  =  U84_GG(x1, x2, x3)
U85_GG(x1, x2, x3)  =  U85_GG(x1, x2, x3)
U61_AG(x1, x2, x3, x4)  =  U61_AG(x2, x3, x4)
P150_IN_AAGG(x1, x2, x3, x4)  =  P150_IN_AAGG(x3, x4)
U51_AAGG(x1, x2, x3, x4, x5)  =  U51_AAGG(x3, x4, x5)
P60_IN_AA(x1, x2)  =  P60_IN_AA
U23_AA(x1, x2, x3, x4, x5)  =  U23_AA(x5)
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
U25_AA(x1, x2, x3)  =  U25_AA(x3)
U26_AA(x1, x2, x3)  =  U26_AA(x3)
U27_AA(x1, x2, x3)  =  U27_AA(x3)
U52_AAGG(x1, x2, x3, x4, x5)  =  U52_AAGG(x3, x4, x5)
U53_AAGG(x1, x2, x3, x4, x5)  =  U53_AAGG(x3, x4, x5)
U62_AG(x1, x2, x3)  =  U62_AG(x1, x2, x3)
U63_AG(x1, x2, x3, x4)  =  U63_AG(x2, x3, x4)
U64_AG(x1, x2, x3, x4, x5, x6, x7)  =  U64_AG(x1, x2, x3, x4, x5, x6, x7)
U65_AG(x1, x2, x3, x4, x5, x6, x7)  =  U65_AG(x1, x2, x3, x4, x5, x6, x7)
U66_AG(x1, x2, x3, x4, x5, x6)  =  U66_AG(x2, x3, x4, x5, x6)
U67_AG(x1, x2)  =  U67_AG(x1, x2)
U68_AG(x1, x2, x3)  =  U68_AG(x2, x3)
U69_AG(x1, x2, x3, x4)  =  U69_AG(x3, x4)
U70_AG(x1, x2, x3, x4)  =  U70_AG(x3, x4)
U71_AG(x1, x2, x3, x4)  =  U71_AG(x3, x4)
U72_AG(x1, x2, x3, x4)  =  U72_AG(x3, x4)
U73_AG(x1, x2, x3, x4, x5)  =  U73_AG(x3, x5)
U74_AG(x1, x2, x3, x4)  =  U74_AG(x3, x4)
U75_AG(x1, x2, x3, x4)  =  U75_AG(x3, x4)
U76_AG(x1, x2, x3, x4)  =  U76_AG(x3, x4)
U77_AG(x1, x2, x3, x4)  =  U77_AG(x3, x4)
U78_AG(x1, x2, x3, x4)  =  U78_AG(x3, x4)
U79_AG(x1, x2, x3, x4, x5)  =  U79_AG(x3, x5)
U80_AG(x1, x2, x3, x4)  =  U80_AG(x3, x4)
U81_AG(x1, x2, x3)  =  U81_AG(x2, x3)
U82_AG(x1, x2, x3)  =  U82_AG(x2, x3)
U83_AG(x1, x2, x3)  =  U83_AG(x2, x3)
U84_AG(x1, x2, x3)  =  U84_AG(x2, x3)
U85_AG(x1, x2, x3)  =  U85_AG(x2, x3)
U50_GGGG(x1, x2, x3, x4, x5)  =  U50_GGGG(x1, x2, x3, x4, x5)
U46_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGAG(x1, x2, x3, x4, x6, x7)
U47_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U47_GGGGAG(x1, x2, x3, x4, x6, x7)
P137_IN_GGAG(x1, x2, x3, x4)  =  P137_IN_GGAG(x1, x2, x4)
U48_GGAG(x1, x2, x3, x4, x5)  =  U48_GGAG(x1, x2, x4, x5)
U49_GGAG(x1, x2, x3, x4, x5)  =  U49_GGAG(x1, x2, x4, x5)
U50_GGAG(x1, x2, x3, x4, x5)  =  U50_GGAG(x1, x2, x4, x5)
U46_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_AGAGAG(x2, x4, x6, x7)
U47_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U47_AGAGAG(x2, x4, x6, x7)
P137_IN_AGAG(x1, x2, x3, x4)  =  P137_IN_AGAG(x2, x4)
U48_AGAG(x1, x2, x3, x4, x5)  =  U48_AGAG(x2, x4, x5)
U49_AGAG(x1, x2, x3, x4, x5)  =  U49_AGAG(x2, x4, x5)
U50_AGAG(x1, x2, x3, x4, x5)  =  U50_AGAG(x2, x4, x5)
U29_AA(x1, x2)  =  U29_AA(x2)
U30_AA(x1, x2, x3, x4, x5)  =  U30_AA(x5)
U31_AA(x1, x2, x3, x4, x5)  =  U31_AA(x5)
U32_AA(x1, x2, x3, x4, x5)  =  U32_AA(x5)
U33_AA(x1, x2, x3, x4, x5)  =  U33_AA(x5)
U34_AA(x1, x2, x3, x4, x5)  =  U34_AA(x5)
U35_AA(x1, x2, x3, x4, x5)  =  U35_AA(x5)
U36_AA(x1, x2, x3, x4, x5)  =  U36_AA(x5)
U37_AA(x1, x2, x3, x4, x5)  =  U37_AA(x5)
U38_AA(x1, x2, x3, x4, x5)  =  U38_AA(x5)
U39_AA(x1, x2, x3, x4, x5)  =  U39_AA(x5)
U40_AA(x1, x2, x3, x4, x5)  =  U40_AA(x5)
U41_AA(x1, x2, x3, x4, x5)  =  U41_AA(x5)
U42_AA(x1, x2, x3)  =  U42_AA(x3)
U43_AA(x1, x2, x3)  =  U43_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U47_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U47_GGGGGG(x1, x2, x3, x4, x5, x6, x7)
U29_GA(x1, x2)  =  U29_GA(x2)
U30_GA(x1, x2, x3, x4, x5)  =  U30_GA(x1, x2, x5)
U31_GA(x1, x2, x3, x4, x5)  =  U31_GA(x1, x2, x5)
U32_GA(x1, x2, x3, x4, x5)  =  U32_GA(x1, x2, x5)
U33_GA(x1, x2, x3, x4, x5)  =  U33_GA(x1, x2, x5)
U34_GA(x1, x2, x3, x4, x5)  =  U34_GA(x1, x2, x5)
U35_GA(x1, x2, x3, x4, x5)  =  U35_GA(x1, x2, x5)
U36_GA(x1, x2, x3, x4, x5)  =  U36_GA(x1, x2, x5)
U37_GA(x1, x2, x3, x4, x5)  =  U37_GA(x1, x2, x5)
U38_GA(x1, x2, x3, x4, x5)  =  U38_GA(x1, x2, x5)
U39_GA(x1, x2, x3, x4, x5)  =  U39_GA(x1, x2, x5)
U40_GA(x1, x2, x3, x4, x5)  =  U40_GA(x1, x2, x5)
U41_GA(x1, x2, x3, x4, x5)  =  U41_GA(x1, x2, x5)
U42_GA(x1, x2, x3)  =  U42_GA(x1, x3)
U43_GA(x1, x2, x3)  =  U43_GA(x1, x3)
U44_GA(x1, x2, x3)  =  U44_GA(x1, x3)
U7_GA(x1, x2)  =  U7_GA(x2)
U8_GA(x1, x2, x3, x4, x5)  =  U8_GA(x1, x2, x5)
U9_GA(x1, x2, x3, x4, x5)  =  U9_GA(x1, x2, x5)
U10_GA(x1, x2, x3, x4, x5)  =  U10_GA(x1, x2, x5)
U11_GA(x1, x2, x3, x4, x5)  =  U11_GA(x1, x2, x5)
U12_GA(x1, x2, x3, x4, x5)  =  U12_GA(x1, x2, x5)
U13_GA(x1, x2, x3, x4, x5)  =  U13_GA(x1, x2, x5)
U14_GA(x1, x2, x3, x4, x5)  =  U14_GA(x1, x2, x5)
U15_GA(x1, x2, x3, x4, x5)  =  U15_GA(x1, x2, x5)
U16_GA(x1, x2, x3, x4, x5)  =  U16_GA(x1, x2, x5)
U17_GA(x1, x2, x3, x4, x5)  =  U17_GA(x1, x2, x5)
U18_GA(x1, x2, x3, x4, x5)  =  U18_GA(x1, x2, x5)
U19_GA(x1, x2, x3, x4, x5)  =  U19_GA(x1, x2, x5)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x3)
U22_GA(x1, x2, x3)  =  U22_GA(x1, x3)
U7_AA(x1, x2)  =  U7_AA(x2)
U8_AA(x1, x2, x3, x4, x5)  =  U8_AA(x5)
U9_AA(x1, x2, x3, x4, x5)  =  U9_AA(x5)
U10_AA(x1, x2, x3, x4, x5)  =  U10_AA(x5)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)
U12_AA(x1, x2, x3, x4, x5)  =  U12_AA(x5)
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U14_AA(x1, x2, x3, x4, x5)  =  U14_AA(x5)
U15_AA(x1, x2, x3, x4, x5)  =  U15_AA(x5)
U16_AA(x1, x2, x3, x4, x5)  =  U16_AA(x5)
U17_AA(x1, x2, x3, x4, x5)  =  U17_AA(x5)
U18_AA(x1, x2, x3, x4, x5)  =  U18_AA(x5)
U19_AA(x1, x2, x3, x4, x5)  =  U19_AA(x5)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U22_AA(x1, x2, x3)  =  U22_AA(x3)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 267 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

P24_IN_AA(+(T45, T46), +(X117, X118)) → P39_IN_AAAA(T45, X117, T46, X118)
P39_IN_AAAA(T45, X117, T46, X118) → P24_IN_AA(T45, X117)
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_AAAA(T59, X152, T60, X151)
P39_IN_AAAA(T45, T47, T48, X118) → U4_AAAA(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → P24_IN_AA(T48, X118)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P24_IN_AA(x1, x2)  =  P24_IN_AA
P39_IN_AAAA(x1, x2, x3, x4)  =  P39_IN_AAAA
U4_AAAA(x1, x2, x3, x4, x5)  =  U4_AAAA(x5)

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:

P24_IN_AA(+(T45, T46), +(X117, X118)) → P39_IN_AAAA(T45, X117, T46, X118)
P39_IN_AAAA(T45, X117, T46, X118) → P24_IN_AA(T45, X117)
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_AAAA(T59, X152, T60, X151)
P39_IN_AAAA(T45, T47, T48, X118) → U4_AAAA(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → P24_IN_AA(T48, X118)

The TRS R consists of the following rules:

p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)

The argument filtering Pi contains the following mapping:
const(x1)  =  const
1  =  1
t  =  t
0  =  0
+(x1, x2)  =  +(x1, x2)
*(x1, x2)  =  *(x1, x2)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
P24_IN_AA(x1, x2)  =  P24_IN_AA
P39_IN_AAAA(x1, x2, x3, x4)  =  P39_IN_AAAA
U4_AAAA(x1, x2, x3, x4, x5)  =  U4_AAAA(x5)

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:

P24_IN_AA → P39_IN_AAAA
P39_IN_AAAA → P24_IN_AA
P39_IN_AAAA → U4_AAAA(p24_in_aa)
U4_AAAA(p24_out_aa) → P24_IN_AA

The TRS R consists of the following rules:

p24_in_aa → p24_out_aa
p24_in_aa → U1_aa(p39_in_aaaa)
p24_in_aa → U2_aa(p39_in_aaaa)
U1_aa(p39_out_aaaa) → p24_out_aa
U2_aa(p39_out_aaaa) → p24_out_aa
p39_in_aaaa → U3_aaaa(p24_in_aa)
p39_in_aaaa → U4_aaaa(p24_in_aa)
U3_aaaa(p24_out_aa) → p39_out_aaaa
U4_aaaa(p24_out_aa) → U5_aaaa(p24_in_aa)
U5_aaaa(p24_out_aa) → p39_out_aaaa

The set Q consists of the following terms:

p24_in_aa
U1_aa(x0)
U2_aa(x0)
p39_in_aaaa
U3_aaaa(x0)
U4_aaaa(x0)
U5_aaaa(x0)

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

(14) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P39_IN_AAAA → U4_AAAA(p24_in_aa) at position [0] we obtained the following new rules [LPAR04]:

P39_IN_AAAA → U4_AAAA(p24_out_aa)
P39_IN_AAAA → U4_AAAA(U1_aa(p39_in_aaaa))
P39_IN_AAAA → U4_AAAA(U2_aa(p39_in_aaaa))

(15) Obligation:

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

P24_IN_AA → P39_IN_AAAA
P39_IN_AAAA → P24_IN_AA
U4_AAAA(p24_out_aa) → P24_IN_AA
P39_IN_AAAA → U4_AAAA(p24_out_aa)
P39_IN_AAAA → U4_AAAA(U1_aa(p39_in_aaaa))
P39_IN_AAAA → U4_AAAA(U2_aa(p39_in_aaaa))

The TRS R consists of the following rules:

p24_in_aa → p24_out_aa
p24_in_aa → U1_aa(p39_in_aaaa)
p24_in_aa → U2_aa(p39_in_aaaa)
U1_aa(p39_out_aaaa) → p24_out_aa
U2_aa(p39_out_aaaa) → p24_out_aa
p39_in_aaaa → U3_aaaa(p24_in_aa)
p39_in_aaaa → U4_aaaa(p24_in_aa)
U3_aaaa(p24_out_aa) → p39_out_aaaa
U4_aaaa(p24_out_aa) → U5_aaaa(p24_in_aa)
U5_aaaa(p24_out_aa) → p39_out_aaaa

The set Q consists of the following terms:

p24_in_aa
U1_aa(x0)
U2_aa(x0)
p39_in_aaaa
U3_aaaa(x0)
U4_aaaa(x0)
U5_aaaa(x0)

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

(16) NonTerminationProof (EQUIVALENT transformation)

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

s = P39_IN_AAAA evaluates to t =P39_IN_AAAA

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

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

P39_IN_AAAA → P24_IN_AA
with rule P39_IN_AAAA → P24_IN_AA at position [] and matcher [ ]

P24_IN_AA → P39_IN_AAAA
with rule P24_IN_AA → P39_IN_AAAA

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


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

(17) NO

(18) Obligation:

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

P60_IN_AA(d(T125), X316) → P60_IN_AA(T125, X315)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P60_IN_AA(x1, x2)  =  P60_IN_AA

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

(19) UsableRulesProof (EQUIVALENT transformation)

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

(20) Obligation:

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

P60_IN_AA(d(T125), X316) → P60_IN_AA(T125, X315)

R is empty.
The argument filtering Pi contains the following mapping:
d(x1)  =  d(x1)
P60_IN_AA(x1, x2)  =  P60_IN_AA

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

(21) PiDPToQDPProof (SOUND transformation)

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

(22) Obligation:

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

P60_IN_AA → P60_IN_AA

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

(23) NonTerminationProof (EQUIVALENT transformation)

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

s = P60_IN_AA evaluates to t =P60_IN_AA

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

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from P60_IN_AA to P60_IN_AA.

(24) NO

(25) Obligation:

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

P39_IN_GAGA(T45, X117, T46, X118) → P24_IN_GA(T45, X117)
P24_IN_GA(+(T45, T46), +(X117, X118)) → P39_IN_GAGA(T45, X117, T46, X118)
P39_IN_GAGA(T45, T47, T48, X118) → U4_GAGA(T45, T47, T48, X118, p24_in_ga(T45, T47))
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → P24_IN_GA(T48, X118)
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_GAGA(T59, X152, T60, X151)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P39_IN_GAGA(x1, x2, x3, x4)  =  P39_IN_GAGA(x1, x3)
P24_IN_GA(x1, x2)  =  P24_IN_GA(x1)
U4_GAGA(x1, x2, x3, x4, x5)  =  U4_GAGA(x1, x3, x5)

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

(26) UsableRulesProof (EQUIVALENT transformation)

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

(27) Obligation:

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

P39_IN_GAGA(T45, X117, T46, X118) → P24_IN_GA(T45, X117)
P24_IN_GA(+(T45, T46), +(X117, X118)) → P39_IN_GAGA(T45, X117, T46, X118)
P39_IN_GAGA(T45, T47, T48, X118) → U4_GAGA(T45, T47, T48, X118, p24_in_ga(T45, T47))
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → P24_IN_GA(T48, X118)
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_GAGA(T59, X152, T60, X151)

The TRS R consists of the following rules:

p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)

The argument filtering Pi contains the following mapping:
const(x1)  =  const
1  =  1
t  =  t
0  =  0
+(x1, x2)  =  +(x1, x2)
*(x1, x2)  =  *(x1, x2)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
P39_IN_GAGA(x1, x2, x3, x4)  =  P39_IN_GAGA(x1, x3)
P24_IN_GA(x1, x2)  =  P24_IN_GA(x1)
U4_GAGA(x1, x2, x3, x4, x5)  =  U4_GAGA(x1, x3, x5)

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

(28) PiDPToQDPProof (SOUND transformation)

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

(29) Obligation:

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

P39_IN_GAGA(T45, T46) → P24_IN_GA(T45)
P24_IN_GA(+(T45, T46)) → P39_IN_GAGA(T45, T46)
P39_IN_GAGA(T45, T48) → U4_GAGA(T45, T48, p24_in_ga(T45))
U4_GAGA(T45, T48, p24_out_ga(T45)) → P24_IN_GA(T48)
P24_IN_GA(*(T59, T60)) → P39_IN_GAGA(T59, T60)

The TRS R consists of the following rules:

p24_in_ga(t) → p24_out_ga(t)
p24_in_ga(const) → p24_out_ga(const)
p24_in_ga(+(T45, T46)) → U1_ga(T45, T46, p39_in_gaga(T45, T46))
p24_in_ga(*(T59, T60)) → U2_ga(T59, T60, p39_in_gaga(T59, T60))
U1_ga(T45, T46, p39_out_gaga(T45, T46)) → p24_out_ga(+(T45, T46))
U2_ga(T59, T60, p39_out_gaga(T59, T60)) → p24_out_ga(*(T59, T60))
p39_in_gaga(T45, T46) → U3_gaga(T45, T46, p24_in_ga(T45))
p39_in_gaga(T45, T48) → U4_gaga(T45, T48, p24_in_ga(T45))
U3_gaga(T45, T46, p24_out_ga(T45)) → p39_out_gaga(T45, T46)
U4_gaga(T45, T48, p24_out_ga(T45)) → U5_gaga(T45, T48, p24_in_ga(T48))
U5_gaga(T45, T48, p24_out_ga(T48)) → p39_out_gaga(T45, T48)

The set Q consists of the following terms:

p24_in_ga(x0)
U1_ga(x0, x1, x2)
U2_ga(x0, x1, x2)
p39_in_gaga(x0, x1)
U3_gaga(x0, x1, x2)
U4_gaga(x0, x1, x2)
U5_gaga(x0, x1, x2)

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

(30) 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:

• P39_IN_GAGA(T45, T46) → P24_IN_GA(T45)
  The graph contains the following edges 1 >= 1

• P39_IN_GAGA(T45, T48) → U4_GAGA(T45, T48, p24_in_ga(T45))
  The graph contains the following edges 1 >= 1, 2 >= 2

• U4_GAGA(T45, T48, p24_out_ga(T45)) → P24_IN_GA(T48)
  The graph contains the following edges 2 >= 1

• P24_IN_GA(+(T45, T46)) → P39_IN_GAGA(T45, T46)
  The graph contains the following edges 1 > 1, 1 > 2

• P24_IN_GA(*(T59, T60)) → P39_IN_GAGA(T59, T60)
  The graph contains the following edges 1 > 1, 1 > 2

(31) YES

(32) Obligation:

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

P60_IN_GA(d(T125), X316) → P60_IN_GA(T125, X315)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P60_IN_GA(x1, x2)  =  P60_IN_GA(x1)

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

(33) UsableRulesProof (EQUIVALENT transformation)

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

(34) Obligation:

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

P60_IN_GA(d(T125), X316) → P60_IN_GA(T125, X315)

R is empty.
The argument filtering Pi contains the following mapping:
d(x1)  =  d(x1)
P60_IN_GA(x1, x2)  =  P60_IN_GA(x1)

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

(35) PiDPToQDPProof (SOUND transformation)

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

(36) Obligation:

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

P60_IN_GA(d(T125)) → P60_IN_GA(T125)

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

(37) 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:

• P60_IN_GA(d(T125)) → P60_IN_GA(T125)
  The graph contains the following edges 1 > 1

(38) YES

(39) Obligation:

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

P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P1_IN_GG(x1, x2)  =  P1_IN_GG(x1, x2)
P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)
U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)
P137_IN_GGGG(x1, x2, x3, x4)  =  P137_IN_GGGG(x1, x2, x3, x4)
U49_GGGG(x1, x2, x3, x4, x5)  =  U49_GGGG(x1, x2, x3, x4, x5)

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

(40) UsableRulesProof (EQUIVALENT transformation)

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

(41) Obligation:

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

P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)

The TRS R consists of the following rules:

p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)

The argument filtering Pi contains the following mapping:
const(x1)  =  const
1  =  1
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
0  =  0
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
P1_IN_GG(x1, x2)  =  P1_IN_GG(x1, x2)
P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)
U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)
P137_IN_GGGG(x1, x2, x3, x4)  =  P137_IN_GGGG(x1, x2, x3, x4)
U49_GGGG(x1, x2, x3, x4, x5)  =  U49_GGGG(x1, x2, x3, x4, x5)

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

(42) PiDPToQDPProof (SOUND transformation)

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

(43) Obligation:

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

P1_IN_GG(d(e(+(const, T203))), +(const, T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(t, T197))), +(const, T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const, T293))), +(*(const, T294), *(T293, const))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)

The TRS R consists of the following rules:

p1_in_gg(d(e(t)), const) → p1_out_gg(d(e(t)), const)
p1_in_gg(d(e(const)), const) → p1_out_gg(d(e(const)), const)
p1_in_gg(d(e(+(t, T197))), +(const, T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const, T203))), +(const, T194)) → U57_gg(T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const, T293))), +(*(const, T294), *(T293, const))) → U63_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const, T194))
U57_gg(T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const, T203))), +(const, T194))
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const)))
U63_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const, T293))), +(*(const, T294), *(T293, const)))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)

The set Q consists of the following terms:

p1_in_gg(x0, x1)
U56_gg(x0, x1, x2)
U57_gg(x0, x1, x2)
U58_gg(x0, x1, x2, x3, x4, x5, x6)
U59_gg(x0, x1, x2, x3, x4, x5, x6)
U60_gg(x0, x1, x2, x3, x4)
U62_gg(x0, x1, x2)
U63_gg(x0, x1, x2)
U64_gg(x0, x1, x2, x3, x4, x5, x6)
U65_gg(x0, x1, x2, x3, x4, x5, x6)
p134_in_gggggg(x0, x1, x2, x3, x4, x5)
p137_in_gggg(x0, x1, x2, x3)
U45_gggggg(x0, x1, x2, x3, x4, x5, x6)
U46_gggggg(x0, x1, x2, x3, x4, x5, x6)
U48_gggg(x0, x1, x2, x3, x4)
U49_gggg(x0, x1, x2, x3, x4)
U47_gggggg(x0, x1, x2, x3, x4, x5, x6)
U50_gggg(x0, x1, x2, x3, x4)

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

(44) 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:

• P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
  The graph contains the following edges 2 >= 2

• P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 >= 6

• P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
  The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4

• U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
  The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 4

• P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4

• P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
  The graph contains the following edges 2 >= 2

• U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
  The graph contains the following edges 4 >= 2

• P1_IN_GG(d(e(+(const, T203))), +(const, T194)) → P1_IN_GG(d(e(T203)), T194)
  The graph contains the following edges 2 > 2

• P1_IN_GG(d(e(+(t, T197))), +(const, T194)) → P1_IN_GG(d(e(T197)), T194)
  The graph contains the following edges 2 > 2

• P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const))) → P1_IN_GG(d(e(T293)), T294)
  The graph contains the following edges 2 > 2

• P1_IN_GG(d(e(*(const, T293))), +(*(const, T294), *(T293, const))) → P1_IN_GG(d(e(T293)), T294)
  The graph contains the following edges 2 > 2

• P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
  The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4, 1 > 5, 2 > 6

• P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
  The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4, 1 > 5, 2 > 6

• P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
  The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4, 1 > 5, 2 > 5, 2 > 6

• P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
  The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4, 1 > 5, 2 > 5, 2 > 6

(45) YES

(46) Obligation:

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

P134_IN_GGGGAG(T224, T222, T227, T223, T228, T194) → U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T228, T194)
P137_IN_GGAG(T227, T223, T229, T194) → U49_GGAG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_AG(d(e(T197)), T194)
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_AG(d(e(T203)), T194)
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194)
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → P1_IN_AG(d(e(T224)), T222)
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T250, T194)
P134_IN_AGAGAG(T224, T222, T227, T223, T228, T194) → U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → P137_IN_AGAG(T227, T223, T228, T194)
P137_IN_AGAG(T227, T223, T228, T194) → P1_IN_AG(d(e(T227)), T223)
P137_IN_AGAG(T227, T223, T229, T194) → U49_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
U54_gg(x1, x2)  =  U54_gg(x1, x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x1, x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x1, x2, x3, x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x1, x3, x4, x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga(x1)
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x1, x2, x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x1, x3, x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga(x1)
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x1, x2, x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x1, x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x1, x2, x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga(x1, x3)
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x1, x3, x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x1, x2, x5)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg(x1, x3, x4)
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x1, x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x1, x3, x4, x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x1, x2, x3, x4, x5, x6)
U67_gg(x1, x2)  =  U67_gg(x1, x2)
U68_gg(x1, x2, x3)  =  U68_gg(x2, x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x1, x2, x3, x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x1, x2, x3, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x1, x2, x3, x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x1, x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x1, x2, x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x1, x2, x3, x4)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x1, x2, x3, x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x1, x2, x3, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x1, x2, x3, x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x1, x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x1, x2, x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x1, x2, x3, x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x1, x2, x3)
U82_gg(x1, x2, x3)  =  U82_gg(x1, x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x1, x2, x3)
U84_gg(x1, x2, x3)  =  U84_gg(x1, x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x1, x2, x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x2, x3, x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x3, x4, x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg(x3, x4)
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x2, x3, x4, x5, x6)
U67_ag(x1, x2)  =  U67_ag(x1, x2)
U68_ag(x1, x2, x3)  =  U68_ag(x2, x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x3, x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x3, x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x3, x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x3, x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x3, x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x3, x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x3, x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x3, x4)
U81_ag(x1, x2, x3)  =  U81_ag(x2, x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x2, x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x2, x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
p90_out_ga(x1, x2)  =  p90_out_ga(x1)
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x1, x2, x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x1, x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x1, x2, x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x1, x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x1, x2, x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x1, x2, x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x1, x2, x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x1, x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x1, x2, x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x1, x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x1, x2, x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x1, x2, x5)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
p9_out_ga(x1, x2)  =  p9_out_ga(x1)
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x1, x2, x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x1, x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x1, x2, x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x1, x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x1, x2, x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x1, x2, x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x1, x2, x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x1, x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x1, x2, x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x1, x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x1, x2, x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x1, x2, x5)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P1_IN_AG(x1, x2)  =  P1_IN_AG(x2)
P134_IN_AGAGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_AGAGAG(x2, x4, x6)
P134_IN_GGGGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGAG(x1, x2, x3, x4, x6)
U46_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGAG(x1, x2, x3, x4, x6, x7)
P137_IN_GGAG(x1, x2, x3, x4)  =  P137_IN_GGAG(x1, x2, x4)
U49_GGAG(x1, x2, x3, x4, x5)  =  U49_GGAG(x1, x2, x4, x5)
U46_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_AGAGAG(x2, x4, x6, x7)
P137_IN_AGAG(x1, x2, x3, x4)  =  P137_IN_AGAG(x2, x4)
U49_AGAG(x1, x2, x3, x4, x5)  =  U49_AGAG(x2, x4, x5)

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

(47) UsableRulesProof (EQUIVALENT transformation)

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

(48) Obligation:

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

P134_IN_GGGGAG(T224, T222, T227, T223, T228, T194) → U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T228, T194)
P137_IN_GGAG(T227, T223, T229, T194) → U49_GGAG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_AG(d(e(T197)), T194)
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_AG(d(e(T203)), T194)
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194)
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → P1_IN_AG(d(e(T224)), T222)
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T250, T194)
P134_IN_AGAGAG(T224, T222, T227, T223, T228, T194) → U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → P137_IN_AGAG(T227, T223, T228, T194)
P137_IN_AGAG(T227, T223, T228, T194) → P1_IN_AG(d(e(T227)), T223)
P137_IN_AGAG(T227, T223, T229, T194) → U49_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)

The TRS R consists of the following rules:

p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag(x2)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg(x1, x2)
0  =  0
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x1, x2, x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x2, x3, x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x1, x2, x3, x4, x5, x6, x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x1, x2, x3, x4, x5, x6, x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x1, x2, x3, x4, x5, x6, x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x1, x2, x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x1, x2, x3, x4, x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x1, x2, x3, x4, x5)
U62_gg(x1, x2, x3)  =  U62_gg(x1, x2, x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x2, x3, x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x1, x2, x3, x4, x5, x6, x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg(x1, x2, x3, x4, x5, x6)
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x1, x2, x3, x4, x5, x6, x7)
U56_ag(x1, x2, x3)  =  U56_ag(x2, x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x3, x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x4, x5, x6, x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x2, x4, x6, x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x1, x2, x4, x5, x6, x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x1, x2, x3, x4, x6, x7)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x1, x2, x3, x4, x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x1, x2, x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x1, x2, x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x2, x3, x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x1, x2, x3, x4, x5, x6, x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x1, x2, x3, x4, x5, x6, x7)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x1, x2, x3, x4, x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg(x1, x2, x3, x4)
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag(x1, x2, x3, x4, x6)
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x1, x2, x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x1, x2, x3, x4, x6, x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x1, x2, x4, x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag(x1, x2, x4)
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x1, x2, x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x1, x2, x4, x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag(x2, x4, x6)
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x2, x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x2, x4, x6, x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x2, x4, x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag(x2, x4)
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x2, x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x2, x4, x5)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x1, x2, x3, x4, x5, x6, x7)
P1_IN_AG(x1, x2)  =  P1_IN_AG(x2)
P134_IN_AGAGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_AGAGAG(x2, x4, x6)
P134_IN_GGGGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGAG(x1, x2, x3, x4, x6)
U46_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGAG(x1, x2, x3, x4, x6, x7)
P137_IN_GGAG(x1, x2, x3, x4)  =  P137_IN_GGAG(x1, x2, x4)
U49_GGAG(x1, x2, x3, x4, x5)  =  U49_GGAG(x1, x2, x4, x5)
U46_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_AGAGAG(x2, x4, x6, x7)
P137_IN_AGAG(x1, x2, x3, x4)  =  P137_IN_AGAG(x2, x4)
U49_AGAG(x1, x2, x3, x4, x5)  =  U49_AGAG(x2, x4, x5)

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

(49) PiDPToQDPProof (SOUND transformation)

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

(50) Obligation:

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

P134_IN_GGGGAG(T224, T222, T227, T223, T194) → U46_GGGGAG(T224, T222, T227, T223, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T194)
P137_IN_GGAG(T227, T223, T194) → U49_GGAG(T227, T223, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(T194)
P1_IN_AG(+(const, T194)) → P1_IN_AG(T194)
P1_IN_AG(+(+(T222, T223), T194)) → P134_IN_AGAGAG(T222, T223, T194)
P134_IN_AGAGAG(T222, T223, T194) → P1_IN_AG(T222)
P1_IN_AG(+(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T194)
P134_IN_AGAGAG(T222, T223, T194) → U46_AGAGAG(T222, T223, T194, p1_in_ag(T222))
U46_AGAGAG(T222, T223, T194, p1_out_ag(T222)) → P137_IN_AGAG(T223, T194)
P137_IN_AGAG(T223, T194) → P1_IN_AG(T223)
P137_IN_AGAG(T223, T194) → U49_AGAG(T223, T194, p1_in_ag(T223))
U49_AGAG(T223, T194, p1_out_ag(T223)) → P1_IN_AG(T194)

The TRS R consists of the following rules:

p1_in_gg(d(e(t)), const) → p1_out_gg(d(e(t)), const)
p1_in_gg(d(e(const)), const) → p1_out_gg(d(e(const)), const)
p1_in_gg(d(e(+(t, T197))), +(const, T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const, T203))), +(const, T194)) → U57_gg(T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const, T293))), +(*(const, T294), *(T293, const))) → U63_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
p1_in_ag(const) → p1_out_ag(const)
p1_in_ag(+(const, T194)) → U56_ag(T194, p1_in_ag(T194))
p1_in_ag(+(const, T194)) → U57_ag(T194, p1_in_ag(T194))
p1_in_ag(+(+(T222, T223), T194)) → U58_ag(T222, T223, T194, p134_in_agagag(T222, T223, T194))
p1_in_ag(+(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T194))
p1_in_ag(+(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_ag(+(*(t, T294), *(T293, const))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_ag(+(*(const, T294), *(T293, const))) → U63_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_ag(+(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_ag(+(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const, T194))
U57_gg(T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const, T203))), +(const, T194))
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const)))
U63_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const, T293))), +(*(const, T294), *(T293, const)))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
U56_ag(T194, p1_out_ag(T194)) → p1_out_ag(+(const, T194))
U57_ag(T194, p1_out_ag(T194)) → p1_out_ag(+(const, T194))
U58_ag(T222, T223, T194, p134_out_agagag(T222, T223, T194)) → p1_out_ag(+(+(T222, T223), T194))
U59_ag(T246, T247, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T194)) → p1_out_ag(+(+(*(T246, T248), *(T247, T249)), T194))
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(+(*(T267, T269), *(T268, T270)))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(+(*(t, T294), *(T293, const)))
U63_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(+(*(const, T294), *(T293, const)))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(+(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(+(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p134_in_agagag(T222, T223, T194) → U45_agagag(T222, T223, T194, p1_in_ag(T222))
p134_in_agagag(T222, T223, T194) → U46_agagag(T222, T223, T194, p1_in_ag(T222))
p134_in_ggggag(T224, T222, T225, T223, T194) → U45_ggggag(T224, T222, T225, T223, T194, p1_in_gg(d(e(T224)), T222))
p134_in_ggggag(T224, T222, T227, T223, T194) → U46_ggggag(T224, T222, T227, T223, T194, p1_in_gg(d(e(T224)), T222))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U45_agagag(T222, T223, T194, p1_out_ag(T222)) → p134_out_agagag(T222, T223, T194)
U46_agagag(T222, T223, T194, p1_out_ag(T222)) → U47_agagag(T222, T223, T194, p137_in_agag(T223, T194))
U45_ggggag(T224, T222, T225, T223, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T194)
U46_ggggag(T224, T222, T227, T223, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T194, p137_in_ggag(T227, T223, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U47_agagag(T222, T223, T194, p137_out_agag(T223, T194)) → p134_out_agagag(T222, T223, T194)
U47_ggggag(T224, T222, T227, T223, T194, p137_out_ggag(T227, T223, T194)) → p134_out_ggggag(T224, T222, T227, T223, T194)
p137_in_agag(T223, T194) → U48_agag(T223, T194, p1_in_ag(T223))
p137_in_agag(T223, T194) → U49_agag(T223, T194, p1_in_ag(T223))
p137_in_ggag(T227, T223, T194) → U48_ggag(T227, T223, T194, p1_in_gg(d(e(T227)), T223))
p137_in_ggag(T227, T223, T194) → U49_ggag(T227, T223, T194, p1_in_gg(d(e(T227)), T223))
U48_agag(T223, T194, p1_out_ag(T223)) → p137_out_agag(T223, T194)
U49_agag(T223, T194, p1_out_ag(T223)) → U50_agag(T223, T194, p1_in_ag(T194))
U48_ggag(T227, T223, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T194)
U49_ggag(T227, T223, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T194, p1_in_ag(T194))
U50_agag(T223, T194, p1_out_ag(T194)) → p137_out_agag(T223, T194)
U50_ggag(T227, T223, T194, p1_out_ag(T194)) → p137_out_ggag(T227, T223, T194)

The set Q consists of the following terms:

p1_in_gg(x0, x1)
p1_in_ag(x0)
U56_gg(x0, x1, x2)
U57_gg(x0, x1, x2)
U58_gg(x0, x1, x2, x3, x4, x5, x6)
U59_gg(x0, x1, x2, x3, x4, x5, x6)
U60_gg(x0, x1, x2, x3, x4)
U62_gg(x0, x1, x2)
U63_gg(x0, x1, x2)
U64_gg(x0, x1, x2, x3, x4, x5, x6)
U65_gg(x0, x1, x2, x3, x4, x5, x6)
U56_ag(x0, x1)
U57_ag(x0, x1)
U58_ag(x0, x1, x2, x3)
U59_ag(x0, x1, x2, x3, x4, x5)
U60_ag(x0, x1, x2, x3, x4)
U62_ag(x0, x1, x2)
U63_ag(x0, x1, x2)
U64_ag(x0, x1, x2, x3, x4, x5, x6)
U65_ag(x0, x1, x2, x3, x4, x5, x6)
p134_in_gggggg(x0, x1, x2, x3, x4, x5)
p137_in_gggg(x0, x1, x2, x3)
p134_in_agagag(x0, x1, x2)
p134_in_ggggag(x0, x1, x2, x3, x4)
U45_gggggg(x0, x1, x2, x3, x4, x5, x6)
U46_gggggg(x0, x1, x2, x3, x4, x5, x6)
U48_gggg(x0, x1, x2, x3, x4)
U49_gggg(x0, x1, x2, x3, x4)
U45_agagag(x0, x1, x2, x3)
U46_agagag(x0, x1, x2, x3)
U45_ggggag(x0, x1, x2, x3, x4, x5)
U46_ggggag(x0, x1, x2, x3, x4, x5)
U47_gggggg(x0, x1, x2, x3, x4, x5, x6)
U50_gggg(x0, x1, x2, x3, x4)
U47_agagag(x0, x1, x2, x3)
U47_ggggag(x0, x1, x2, x3, x4, x5)
p137_in_agag(x0, x1)
p137_in_ggag(x0, x1, x2)
U48_agag(x0, x1, x2)
U49_agag(x0, x1, x2)
U48_ggag(x0, x1, x2, x3)
U49_ggag(x0, x1, x2, x3)
U50_agag(x0, x1, x2)
U50_ggag(x0, x1, x2, x3)

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

(51) 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:

• U46_GGGGAG(T224, T222, T227, T223, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T194)
  The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3

• P1_IN_AG(+(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T194)
  The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5

• P137_IN_GGAG(T227, T223, T194) → U49_GGAG(T227, T223, T194, p1_in_gg(d(e(T227)), T223))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3

• P134_IN_GGGGAG(T224, T222, T227, T223, T194) → U46_GGGGAG(T224, T222, T227, T223, T194, p1_in_gg(d(e(T224)), T222))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5

• U49_GGAG(T227, T223, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(T194)
  The graph contains the following edges 3 >= 1

• P1_IN_AG(+(const, T194)) → P1_IN_AG(T194)
  The graph contains the following edges 1 > 1

• P1_IN_AG(+(+(T222, T223), T194)) → P134_IN_AGAGAG(T222, T223, T194)
  The graph contains the following edges 1 > 1, 1 > 2, 1 > 3

• P134_IN_AGAGAG(T222, T223, T194) → P1_IN_AG(T222)
  The graph contains the following edges 1 >= 1

• P134_IN_AGAGAG(T222, T223, T194) → U46_AGAGAG(T222, T223, T194, p1_in_ag(T222))
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3

• U46_AGAGAG(T222, T223, T194, p1_out_ag(T222)) → P137_IN_AGAG(T223, T194)
  The graph contains the following edges 2 >= 1, 3 >= 2

• P137_IN_AGAG(T223, T194) → U49_AGAG(T223, T194, p1_in_ag(T223))
  The graph contains the following edges 1 >= 1, 2 >= 2

• P137_IN_AGAG(T223, T194) → P1_IN_AG(T223)
  The graph contains the following edges 1 >= 1

• U49_AGAG(T223, T194, p1_out_ag(T223)) → P1_IN_AG(T194)
  The graph contains the following edges 2 >= 1

(52) YES

(53) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
p1_in: (f,b) (b,b)
p9_in: (f,f) (b,f)
p90_in: (b,f) (f,f)
p134_in: (b,b,b,b,b,b) (f,b,f,b,f,b) (b,b,b,b,f,b)
p137_in: (b,b,b,b) (b,b,f,b) (f,b,f,b)
p150_in: (b,f,b,b) (f,f,b,b)
p60_in: (b,f) (f,f)
p39_in: (b,f,b,f) (f,f,f,f)
p24_in: (b,f) (f,f)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(54) Obligation:

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

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)

(55) 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:

P1_IN_AG(d(d(T10)), const(1)) → U54_AG(T10, p9_in_aa(T10, X14))
P1_IN_AG(d(d(T10)), const(1)) → P9_IN_AA(T10, X14)
P9_IN_AA(e(t), const(1)) → U6_AA(p1_in_gg(d(e(const(1))), const(1)))
P9_IN_AA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(1))
P1_IN_GG(d(d(T10)), const(1)) → U54_GG(T10, p9_in_ga(T10, X14))
P1_IN_GG(d(d(T10)), const(1)) → P9_IN_GA(T10, X14)
P9_IN_GA(e(t), const(1)) → U6_GA(p1_in_gg(d(e(const(1))), const(1)))
P9_IN_GA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(1))
P1_IN_GG(d(d(T135)), const(0)) → U55_GG(T135, p90_in_ga(T135, X334))
P1_IN_GG(d(d(T135)), const(0)) → P90_IN_GA(T135, X334)
P90_IN_GA(e(t), const(1)) → U28_GA(p1_in_gg(d(e(const(1))), const(0)))
P90_IN_GA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(0))
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → U56_GG(T197, T194, p1_in_gg(d(e(T197)), T194))
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_GG(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_GG(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → U45_GGGGGG(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_GG(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_GG(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T228, T194) → U48_GGGG(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(d(T280)), +(T278, T279)) → U61_GG(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
P1_IN_GG(d(d(T280)), +(T278, T279)) → P150_IN_GAGG(T280, X551, T278, T279)
P150_IN_GAGG(T280, X551, T278, T279) → U51_GAGG(T280, X551, T278, T279, p60_in_ga(T280, X551))
P150_IN_GAGG(T280, X551, T278, T279) → P60_IN_GA(T280, X551)
P60_IN_GA(e(+(T108, T109)), +(X266, X267)) → U23_GA(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
P60_IN_GA(e(+(T108, T109)), +(X266, X267)) → P39_IN_GAGA(T108, X266, T109, X267)
P39_IN_GAGA(T45, X117, T46, X118) → U3_GAGA(T45, X117, T46, X118, p24_in_ga(T45, X117))
P39_IN_GAGA(T45, X117, T46, X118) → P24_IN_GA(T45, X117)
P24_IN_GA(+(T45, T46), +(X117, X118)) → U1_GA(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
P24_IN_GA(+(T45, T46), +(X117, X118)) → P39_IN_GAGA(T45, X117, T46, X118)
P39_IN_GAGA(T45, T47, T48, X118) → U4_GAGA(T45, T47, T48, X118, p24_in_ga(T45, T47))
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_GA(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_GAGA(T59, X152, T60, X151)
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_GAGA(T45, T47, T48, X118, p24_in_ga(T48, X118))
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → P24_IN_GA(T48, X118)
P60_IN_GA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_GA(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
P60_IN_GA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → P39_IN_GAGA(T120, X301, T121, X300)
P60_IN_GA(d(T125), X316) → U25_GA(T125, X316, p60_in_ga(T125, X315))
P60_IN_GA(d(T125), X316) → P60_IN_GA(T125, X315)
P60_IN_GA(d(T125), X316) → U26_GA(T125, X316, p60_in_ga(T125, T126))
U26_GA(T125, X316, p60_out_ga(T125, T126)) → U27_GA(T125, X316, p24_in_aa(T126, X316))
U26_GA(T125, X316, p60_out_ga(T125, T126)) → P24_IN_AA(T126, X316)
P24_IN_AA(+(T45, T46), +(X117, X118)) → U1_AA(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
P24_IN_AA(+(T45, T46), +(X117, X118)) → P39_IN_AAAA(T45, X117, T46, X118)
P39_IN_AAAA(T45, X117, T46, X118) → U3_AAAA(T45, X117, T46, X118, p24_in_aa(T45, X117))
P39_IN_AAAA(T45, X117, T46, X118) → P24_IN_AA(T45, X117)
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_AA(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_AAAA(T59, X152, T60, X151)
P39_IN_AAAA(T45, T47, T48, X118) → U4_AAAA(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_AAAA(T45, T47, T48, X118, p24_in_aa(T48, X118))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → P24_IN_AA(T48, X118)
P150_IN_GAGG(T280, T281, T278, T279) → U52_GAGG(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_GAGG(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_GAGG(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
U52_GAGG(T280, T281, T278, T279, p60_out_ga(T280, T281)) → P1_IN_AG(d(e(T281)), +(T278, T279))
P1_IN_AG(d(d(T135)), const(0)) → U55_AG(T135, p90_in_aa(T135, X334))
P1_IN_AG(d(d(T135)), const(0)) → P90_IN_AA(T135, X334)
P90_IN_AA(e(t), const(1)) → U28_AA(p1_in_gg(d(e(const(1))), const(0)))
P90_IN_AA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(0))
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_GG(T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_GG(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_GG(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_GG(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
P1_IN_GG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_GG(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
P1_IN_GG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → P150_IN_GAGG(T356, X635, *(T352, T353), *(T354, T355))
P1_IN_GG(d(d(e(t))), T360) → U67_GG(T360, p1_in_gg(d(e(const(1))), T360))
P1_IN_GG(d(d(e(t))), T360) → P1_IN_GG(d(e(const(1))), T360)
P1_IN_GG(d(d(e(const(T366)))), T360) → U68_GG(T366, T360, p1_in_gg(d(e(const(0))), T360))
P1_IN_GG(d(d(e(const(T366)))), T360) → P1_IN_GG(d(e(const(0))), T360)
P1_IN_GG(d(d(e(+(T377, T378)))), T360) → U69_GG(T377, T378, T360, p24_in_ga(T377, X683))
P1_IN_GG(d(d(e(+(T377, T378)))), T360) → P24_IN_GA(T377, X683)
P1_IN_GG(d(d(e(+(T377, T380)))), T360) → U70_GG(T377, T380, T360, p24_in_ga(T377, T379))
U70_GG(T377, T380, T360, p24_out_ga(T377, T379)) → U71_GG(T377, T380, T360, p24_in_ga(T380, X684))
U70_GG(T377, T380, T360, p24_out_ga(T377, T379)) → P24_IN_GA(T380, X684)
P1_IN_GG(d(d(e(+(T377, T380)))), T360) → U72_GG(T377, T380, T360, p24_in_ga(T377, T392))
U72_GG(T377, T380, T360, p24_out_ga(T377, T392)) → U73_GG(T377, T380, T360, T392, p24_in_ga(T380, T391))
U72_GG(T377, T380, T360, p24_out_ga(T377, T392)) → P24_IN_GA(T380, T391)
U73_GG(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_GG(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
U73_GG(T377, T380, T360, T392, p24_out_ga(T380, T391)) → P1_IN_AG(d(e(+(T392, T391))), T360)
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → U56_AG(T197, T194, p1_in_ag(d(e(T197)), T194))
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_AG(d(e(T197)), T194)
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_AG(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_AG(d(e(T203)), T194)
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_AG(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194)
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → U45_AGAGAG(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → P1_IN_AG(d(e(T224)), T222)
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_AG(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGAG(T224, T222, T225, T223, T226, T194) → U45_GGGGAG(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
P134_IN_GGGGAG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(d(e(*(T417, T418)))), T360) → U75_GG(T417, T418, T360, p24_in_ga(T417, X724))
P1_IN_GG(d(d(e(*(T417, T418)))), T360) → P24_IN_GA(T417, X724)
P1_IN_GG(d(d(e(*(T421, T420)))), T360) → U76_GG(T421, T420, T360, p24_in_ga(T421, T419))
U76_GG(T421, T420, T360, p24_out_ga(T421, T419)) → U77_GG(T421, T420, T360, p24_in_ga(T420, X723))
U76_GG(T421, T420, T360, p24_out_ga(T421, T419)) → P24_IN_GA(T420, X723)
P1_IN_GG(d(d(e(*(T433, T434)))), T360) → U78_GG(T433, T434, T360, p24_in_ga(T433, T435))
U78_GG(T433, T434, T360, p24_out_ga(T433, T435)) → U79_GG(T433, T434, T360, T435, p24_in_ga(T434, T432))
U78_GG(T433, T434, T360, p24_out_ga(T433, T435)) → P24_IN_GA(T434, T432)
U79_GG(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_GG(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
U79_GG(T433, T434, T360, T435, p24_out_ga(T434, T432)) → P1_IN_AG(d(e(+(*(T433, T432), *(T434, T435)))), T360)
P1_IN_AG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_AG(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
P1_IN_AG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
P1_IN_GG(d(d(d(T455))), T360) → U81_GG(T455, T360, p60_in_ga(T455, X744))
P1_IN_GG(d(d(d(T455))), T360) → P60_IN_GA(T455, X744)
P1_IN_GG(d(d(d(T455))), T360) → U82_GG(T455, T360, p60_in_ga(T455, T456))
U82_GG(T455, T360, p60_out_ga(T455, T456)) → U83_GG(T455, T360, p24_in_aa(T456, X745))
U82_GG(T455, T360, p60_out_ga(T455, T456)) → P24_IN_AA(T456, X745)
U82_GG(T455, T360, p60_out_ga(T455, T456)) → U84_GG(T455, T360, p24_in_aa(T456, T467))
U84_GG(T455, T360, p24_out_aa(T456, T467)) → U85_GG(T455, T360, p1_in_ag(d(e(T467)), T360))
U84_GG(T455, T360, p24_out_aa(T456, T467)) → P1_IN_AG(d(e(T467)), T360)
P1_IN_AG(d(d(T280)), +(T278, T279)) → U61_AG(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
P1_IN_AG(d(d(T280)), +(T278, T279)) → P150_IN_AAGG(T280, X551, T278, T279)
P150_IN_AAGG(T280, X551, T278, T279) → U51_AAGG(T280, X551, T278, T279, p60_in_aa(T280, X551))
P150_IN_AAGG(T280, X551, T278, T279) → P60_IN_AA(T280, X551)
P60_IN_AA(e(+(T108, T109)), +(X266, X267)) → U23_AA(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
P60_IN_AA(e(+(T108, T109)), +(X266, X267)) → P39_IN_AAAA(T108, X266, T109, X267)
P60_IN_AA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_AA(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
P60_IN_AA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → P39_IN_AAAA(T120, X301, T121, X300)
P60_IN_AA(d(T125), X316) → U25_AA(T125, X316, p60_in_aa(T125, X315))
P60_IN_AA(d(T125), X316) → P60_IN_AA(T125, X315)
P60_IN_AA(d(T125), X316) → U26_AA(T125, X316, p60_in_aa(T125, T126))
U26_AA(T125, X316, p60_out_aa(T125, T126)) → U27_AA(T125, X316, p24_in_aa(T126, X316))
U26_AA(T125, X316, p60_out_aa(T125, T126)) → P24_IN_AA(T126, X316)
P150_IN_AAGG(T280, T281, T278, T279) → U52_AAGG(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_AAGG(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_AAGG(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
U52_AAGG(T280, T281, T278, T279, p60_out_aa(T280, T281)) → P1_IN_AG(d(e(T281)), +(T278, T279))
P1_IN_AG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_AG(T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_AG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_AG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_AG(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_AG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_AG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_AG(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
P1_IN_AG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_AG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_AG(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
P1_IN_AG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
P1_IN_AG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_AG(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
P1_IN_AG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → P150_IN_AAGG(T356, X635, *(T352, T353), *(T354, T355))
P1_IN_AG(d(d(e(t))), T360) → U67_AG(T360, p1_in_gg(d(e(const(1))), T360))
P1_IN_AG(d(d(e(t))), T360) → P1_IN_GG(d(e(const(1))), T360)
P1_IN_AG(d(d(e(const(T366)))), T360) → U68_AG(T366, T360, p1_in_gg(d(e(const(0))), T360))
P1_IN_AG(d(d(e(const(T366)))), T360) → P1_IN_GG(d(e(const(0))), T360)
P1_IN_AG(d(d(e(+(T377, T378)))), T360) → U69_AG(T377, T378, T360, p24_in_aa(T377, X683))
P1_IN_AG(d(d(e(+(T377, T378)))), T360) → P24_IN_AA(T377, X683)
P1_IN_AG(d(d(e(+(T377, T380)))), T360) → U70_AG(T377, T380, T360, p24_in_aa(T377, T379))
U70_AG(T377, T380, T360, p24_out_aa(T377, T379)) → U71_AG(T377, T380, T360, p24_in_aa(T380, X684))
U70_AG(T377, T380, T360, p24_out_aa(T377, T379)) → P24_IN_AA(T380, X684)
P1_IN_AG(d(d(e(+(T377, T380)))), T360) → U72_AG(T377, T380, T360, p24_in_aa(T377, T392))
U72_AG(T377, T380, T360, p24_out_aa(T377, T392)) → U73_AG(T377, T380, T360, T392, p24_in_aa(T380, T391))
U72_AG(T377, T380, T360, p24_out_aa(T377, T392)) → P24_IN_AA(T380, T391)
U73_AG(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_AG(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
U73_AG(T377, T380, T360, T392, p24_out_aa(T380, T391)) → P1_IN_AG(d(e(+(T392, T391))), T360)
P1_IN_AG(d(d(e(*(T417, T418)))), T360) → U75_AG(T417, T418, T360, p24_in_aa(T417, X724))
P1_IN_AG(d(d(e(*(T417, T418)))), T360) → P24_IN_AA(T417, X724)
P1_IN_AG(d(d(e(*(T421, T420)))), T360) → U76_AG(T421, T420, T360, p24_in_aa(T421, T419))
U76_AG(T421, T420, T360, p24_out_aa(T421, T419)) → U77_AG(T421, T420, T360, p24_in_aa(T420, X723))
U76_AG(T421, T420, T360, p24_out_aa(T421, T419)) → P24_IN_AA(T420, X723)
P1_IN_AG(d(d(e(*(T433, T434)))), T360) → U78_AG(T433, T434, T360, p24_in_aa(T433, T435))
U78_AG(T433, T434, T360, p24_out_aa(T433, T435)) → U79_AG(T433, T434, T360, T435, p24_in_aa(T434, T432))
U78_AG(T433, T434, T360, p24_out_aa(T433, T435)) → P24_IN_AA(T434, T432)
U79_AG(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_AG(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
U79_AG(T433, T434, T360, T435, p24_out_aa(T434, T432)) → P1_IN_AG(d(e(+(*(T433, T432), *(T434, T435)))), T360)
P1_IN_AG(d(d(d(T455))), T360) → U81_AG(T455, T360, p60_in_aa(T455, X744))
P1_IN_AG(d(d(d(T455))), T360) → P60_IN_AA(T455, X744)
P1_IN_AG(d(d(d(T455))), T360) → U82_AG(T455, T360, p60_in_aa(T455, T456))
U82_AG(T455, T360, p60_out_aa(T455, T456)) → U83_AG(T455, T360, p24_in_aa(T456, X745))
U82_AG(T455, T360, p60_out_aa(T455, T456)) → P24_IN_AA(T456, X745)
U82_AG(T455, T360, p60_out_aa(T455, T456)) → U84_AG(T455, T360, p24_in_aa(T456, T467))
U84_AG(T455, T360, p24_out_aa(T456, T467)) → U85_AG(T455, T360, p1_in_ag(d(e(T467)), T360))
U84_AG(T455, T360, p24_out_aa(T456, T467)) → P1_IN_AG(d(e(T467)), T360)
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P134_IN_GGGGAG(T224, T222, T227, T223, T228, T194) → U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_GGGGAG(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T228, T194)
P137_IN_GGAG(T227, T223, T228, T194) → U48_GGAG(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
P137_IN_GGAG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P137_IN_GGAG(T227, T223, T229, T194) → U49_GGAG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_GGAG(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P134_IN_AGAGAG(T224, T222, T227, T223, T228, T194) → U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_AGAGAG(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → P137_IN_AGAG(T227, T223, T228, T194)
P137_IN_AGAG(T227, T223, T228, T194) → U48_AGAG(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
P137_IN_AGAG(T227, T223, T228, T194) → P1_IN_AG(d(e(T227)), T223)
P137_IN_AGAG(T227, T223, T229, T194) → U49_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P90_IN_AA(e(const(T140)), const(0)) → U29_AA(T140, p1_in_gg(d(e(const(0))), const(0)))
P90_IN_AA(e(const(T140)), const(0)) → P1_IN_GG(d(e(const(0))), const(0))
P90_IN_AA(e(+(T151, T152)), +(X373, X374)) → U30_AA(T151, T152, X373, X374, p24_in_aa(T151, X373))
P90_IN_AA(e(+(T151, T152)), +(X373, X374)) → P24_IN_AA(T151, X373)
P90_IN_AA(e(+(T151, T154)), +(T153, X374)) → U31_AA(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_AA(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_AA(T151, T154, T153, X374, p24_in_aa(T154, X374))
U31_AA(T151, T154, T153, X374, p24_out_aa(T151, T153)) → P24_IN_AA(T154, X374)
P90_IN_AA(e(+(T151, T154)), +(T156, T155)) → U33_AA(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_AA(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_AA(T151, T154, T156, T155, p24_in_aa(T154, T155))
U33_AA(T151, T154, T156, T155, p24_out_aa(T151, T156)) → P24_IN_AA(T154, T155)
U34_AA(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_AA(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U34_AA(T151, T154, T156, T155, p24_out_aa(T154, T155)) → P1_IN_AG(d(e(+(T156, T155))), const(0))
P90_IN_AA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_AA(T169, T170, X420, X421, p24_in_aa(T169, X421))
P90_IN_AA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → P24_IN_AA(T169, X421)
P90_IN_AA(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_AA(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_AA(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_AA(T173, T172, X420, T171, p24_in_aa(T172, X420))
U37_AA(T173, T172, X420, T171, p24_out_aa(T173, T171)) → P24_IN_AA(T172, X420)
P90_IN_AA(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_AA(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_AA(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_AA(T175, T176, T174, T177, p24_in_aa(T176, T174))
U39_AA(T175, T176, T174, T177, p24_out_aa(T175, T177)) → P24_IN_AA(T176, T174)
U40_AA(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_AA(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U40_AA(T175, T176, T174, T177, p24_out_aa(T176, T174)) → P1_IN_AG(d(e(+(*(T175, T174), *(T176, T177)))), const(0))
P90_IN_AA(d(T185), X449) → U42_AA(T185, X449, p60_in_aa(T185, X448))
P90_IN_AA(d(T185), X449) → P60_IN_AA(T185, X448)
P90_IN_AA(d(T185), X449) → U43_AA(T185, X449, p60_in_aa(T185, T186))
U43_AA(T185, X449, p60_out_aa(T185, T186)) → U44_AA(T185, X449, p90_in_aa(e(T186), X449))
U43_AA(T185, X449, p60_out_aa(T185, T186)) → P90_IN_AA(e(T186), X449)
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_GGGGGG(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P90_IN_GA(e(const(T140)), const(0)) → U29_GA(T140, p1_in_gg(d(e(const(0))), const(0)))
P90_IN_GA(e(const(T140)), const(0)) → P1_IN_GG(d(e(const(0))), const(0))
P90_IN_GA(e(+(T151, T152)), +(X373, X374)) → U30_GA(T151, T152, X373, X374, p24_in_ga(T151, X373))
P90_IN_GA(e(+(T151, T152)), +(X373, X374)) → P24_IN_GA(T151, X373)
P90_IN_GA(e(+(T151, T154)), +(T153, X374)) → U31_GA(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_GA(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_GA(T151, T154, T153, X374, p24_in_ga(T154, X374))
U31_GA(T151, T154, T153, X374, p24_out_ga(T151, T153)) → P24_IN_GA(T154, X374)
P90_IN_GA(e(+(T151, T154)), +(T156, T155)) → U33_GA(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_GA(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_GA(T151, T154, T156, T155, p24_in_ga(T154, T155))
U33_GA(T151, T154, T156, T155, p24_out_ga(T151, T156)) → P24_IN_GA(T154, T155)
U34_GA(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_GA(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U34_GA(T151, T154, T156, T155, p24_out_ga(T154, T155)) → P1_IN_AG(d(e(+(T156, T155))), const(0))
P90_IN_GA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_GA(T169, T170, X420, X421, p24_in_ga(T169, X421))
P90_IN_GA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → P24_IN_GA(T169, X421)
P90_IN_GA(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_GA(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_GA(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_GA(T173, T172, X420, T171, p24_in_ga(T172, X420))
U37_GA(T173, T172, X420, T171, p24_out_ga(T173, T171)) → P24_IN_GA(T172, X420)
P90_IN_GA(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_GA(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_GA(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_GA(T175, T176, T174, T177, p24_in_ga(T176, T174))
U39_GA(T175, T176, T174, T177, p24_out_ga(T175, T177)) → P24_IN_GA(T176, T174)
U40_GA(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_GA(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U40_GA(T175, T176, T174, T177, p24_out_ga(T176, T174)) → P1_IN_AG(d(e(+(*(T175, T174), *(T176, T177)))), const(0))
P90_IN_GA(d(T185), X449) → U42_GA(T185, X449, p60_in_ga(T185, X448))
P90_IN_GA(d(T185), X449) → P60_IN_GA(T185, X448)
P90_IN_GA(d(T185), X449) → U43_GA(T185, X449, p60_in_ga(T185, T186))
U43_GA(T185, X449, p60_out_ga(T185, T186)) → U44_GA(T185, X449, p90_in_aa(e(T186), X449))
U43_GA(T185, X449, p60_out_ga(T185, T186)) → P90_IN_AA(e(T186), X449)
P9_IN_GA(e(const(T15)), const(0)) → U7_GA(T15, p1_in_gg(d(e(const(0))), const(1)))
P9_IN_GA(e(const(T15)), const(0)) → P1_IN_GG(d(e(const(0))), const(1))
P9_IN_GA(e(+(T26, T27)), +(X77, X78)) → U8_GA(T26, T27, X77, X78, p24_in_ga(T26, X77))
P9_IN_GA(e(+(T26, T27)), +(X77, X78)) → P24_IN_GA(T26, X77)
P9_IN_GA(e(+(T26, T29)), +(T28, X78)) → U9_GA(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_GA(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_GA(T26, T29, T28, X78, p24_in_ga(T29, X78))
U9_GA(T26, T29, T28, X78, p24_out_ga(T26, T28)) → P24_IN_GA(T29, X78)
P9_IN_GA(e(+(T26, T29)), +(T62, T61)) → U11_GA(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_GA(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_GA(T26, T29, T62, T61, p24_in_ga(T29, T61))
U11_GA(T26, T29, T62, T61, p24_out_ga(T26, T62)) → P24_IN_GA(T29, T61)
U12_GA(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_GA(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U12_GA(T26, T29, T62, T61, p24_out_ga(T29, T61)) → P1_IN_AG(d(e(+(T62, T61))), const(1))
P9_IN_GA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_GA(T75, T76, X200, X201, p24_in_ga(T75, X201))
P9_IN_GA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → P24_IN_GA(T75, X201)
P9_IN_GA(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_GA(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_GA(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_GA(T79, T78, X200, T77, p24_in_ga(T78, X200))
U15_GA(T79, T78, X200, T77, p24_out_ga(T79, T77)) → P24_IN_GA(T78, X200)
P9_IN_GA(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_GA(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_GA(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_GA(T81, T82, T80, T83, p24_in_ga(T82, T80))
U17_GA(T81, T82, T80, T83, p24_out_ga(T81, T83)) → P24_IN_GA(T82, T80)
U18_GA(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_GA(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U18_GA(T81, T82, T80, T83, p24_out_ga(T82, T80)) → P1_IN_AG(d(e(+(*(T81, T80), *(T82, T83)))), const(1))
P9_IN_GA(d(T91), X229) → U20_GA(T91, X229, p60_in_ga(T91, X228))
P9_IN_GA(d(T91), X229) → P60_IN_GA(T91, X228)
P9_IN_GA(d(T91), X229) → U21_GA(T91, X229, p60_in_ga(T91, T92))
U21_GA(T91, X229, p60_out_ga(T91, T92)) → U22_GA(T91, X229, p9_in_aa(e(T92), X229))
U21_GA(T91, X229, p60_out_ga(T91, T92)) → P9_IN_AA(e(T92), X229)
P9_IN_AA(e(const(T15)), const(0)) → U7_AA(T15, p1_in_gg(d(e(const(0))), const(1)))
P9_IN_AA(e(const(T15)), const(0)) → P1_IN_GG(d(e(const(0))), const(1))
P9_IN_AA(e(+(T26, T27)), +(X77, X78)) → U8_AA(T26, T27, X77, X78, p24_in_aa(T26, X77))
P9_IN_AA(e(+(T26, T27)), +(X77, X78)) → P24_IN_AA(T26, X77)
P9_IN_AA(e(+(T26, T29)), +(T28, X78)) → U9_AA(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_AA(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_AA(T26, T29, T28, X78, p24_in_aa(T29, X78))
U9_AA(T26, T29, T28, X78, p24_out_aa(T26, T28)) → P24_IN_AA(T29, X78)
P9_IN_AA(e(+(T26, T29)), +(T62, T61)) → U11_AA(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_AA(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_AA(T26, T29, T62, T61, p24_in_aa(T29, T61))
U11_AA(T26, T29, T62, T61, p24_out_aa(T26, T62)) → P24_IN_AA(T29, T61)
U12_AA(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_AA(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U12_AA(T26, T29, T62, T61, p24_out_aa(T29, T61)) → P1_IN_AG(d(e(+(T62, T61))), const(1))
P9_IN_AA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_AA(T75, T76, X200, X201, p24_in_aa(T75, X201))
P9_IN_AA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → P24_IN_AA(T75, X201)
P9_IN_AA(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_AA(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_AA(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_AA(T79, T78, X200, T77, p24_in_aa(T78, X200))
U15_AA(T79, T78, X200, T77, p24_out_aa(T79, T77)) → P24_IN_AA(T78, X200)
P9_IN_AA(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_AA(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_AA(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_AA(T81, T82, T80, T83, p24_in_aa(T82, T80))
U17_AA(T81, T82, T80, T83, p24_out_aa(T81, T83)) → P24_IN_AA(T82, T80)
U18_AA(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_AA(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U18_AA(T81, T82, T80, T83, p24_out_aa(T82, T80)) → P1_IN_AG(d(e(+(*(T81, T80), *(T82, T83)))), const(1))
P9_IN_AA(d(T91), X229) → U20_AA(T91, X229, p60_in_aa(T91, X228))
P9_IN_AA(d(T91), X229) → P60_IN_AA(T91, X228)
P9_IN_AA(d(T91), X229) → U21_AA(T91, X229, p60_in_aa(T91, T92))
U21_AA(T91, X229, p60_out_aa(T91, T92)) → U22_AA(T91, X229, p9_in_aa(e(T92), X229))
U21_AA(T91, X229, p60_out_aa(T91, T92)) → P9_IN_AA(e(T92), X229)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P1_IN_AG(x1, x2)  =  P1_IN_AG(x2)
U54_AG(x1, x2)  =  U54_AG(x2)
P9_IN_AA(x1, x2)  =  P9_IN_AA
U6_AA(x1)  =  U6_AA(x1)
P1_IN_GG(x1, x2)  =  P1_IN_GG(x1, x2)
U54_GG(x1, x2)  =  U54_GG(x2)
P9_IN_GA(x1, x2)  =  P9_IN_GA(x1)
U6_GA(x1)  =  U6_GA(x1)
U55_GG(x1, x2)  =  U55_GG(x2)
P90_IN_GA(x1, x2)  =  P90_IN_GA(x1)
U28_GA(x1)  =  U28_GA(x1)
U56_GG(x1, x2, x3)  =  U56_GG(x3)
U57_GG(x1, x2, x3, x4)  =  U57_GG(x4)
U58_GG(x1, x2, x3, x4, x5, x6, x7)  =  U58_GG(x7)
P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)
U45_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U45_GGGGGG(x7)
U59_GG(x1, x2, x3, x4, x5, x6, x7)  =  U59_GG(x7)
U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGGG(x3, x4, x5, x6, x7)
U60_GG(x1, x2, x3, x4, x5)  =  U60_GG(x5)
P137_IN_GGGG(x1, x2, x3, x4)  =  P137_IN_GGGG(x1, x2, x3, x4)
U48_GGGG(x1, x2, x3, x4, x5)  =  U48_GGGG(x5)
U61_GG(x1, x2, x3, x4)  =  U61_GG(x4)
P150_IN_GAGG(x1, x2, x3, x4)  =  P150_IN_GAGG(x1, x3, x4)
U51_GAGG(x1, x2, x3, x4, x5)  =  U51_GAGG(x5)
P60_IN_GA(x1, x2)  =  P60_IN_GA(x1)
U23_GA(x1, x2, x3, x4, x5)  =  U23_GA(x5)
P39_IN_GAGA(x1, x2, x3, x4)  =  P39_IN_GAGA(x1, x3)
U3_GAGA(x1, x2, x3, x4, x5)  =  U3_GAGA(x5)
P24_IN_GA(x1, x2)  =  P24_IN_GA(x1)
U1_GA(x1, x2, x3, x4, x5)  =  U1_GA(x5)
U4_GAGA(x1, x2, x3, x4, x5)  =  U4_GAGA(x3, x5)
U2_GA(x1, x2, x3, x4, x5)  =  U2_GA(x5)
U5_GAGA(x1, x2, x3, x4, x5)  =  U5_GAGA(x5)
U24_GA(x1, x2, x3, x4, x5)  =  U24_GA(x5)
U25_GA(x1, x2, x3)  =  U25_GA(x3)
U26_GA(x1, x2, x3)  =  U26_GA(x3)
U27_GA(x1, x2, x3)  =  U27_GA(x3)
P24_IN_AA(x1, x2)  =  P24_IN_AA
U1_AA(x1, x2, x3, x4, x5)  =  U1_AA(x5)
P39_IN_AAAA(x1, x2, x3, x4)  =  P39_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5)  =  U3_AAAA(x5)
U2_AA(x1, x2, x3, x4, x5)  =  U2_AA(x5)
U4_AAAA(x1, x2, x3, x4, x5)  =  U4_AAAA(x5)
U5_AAAA(x1, x2, x3, x4, x5)  =  U5_AAAA(x5)
U52_GAGG(x1, x2, x3, x4, x5)  =  U52_GAGG(x3, x4, x5)
U53_GAGG(x1, x2, x3, x4, x5)  =  U53_GAGG(x5)
U55_AG(x1, x2)  =  U55_AG(x2)
P90_IN_AA(x1, x2)  =  P90_IN_AA
U28_AA(x1)  =  U28_AA(x1)
U62_GG(x1, x2, x3)  =  U62_GG(x3)
U63_GG(x1, x2, x3, x4)  =  U63_GG(x4)
U64_GG(x1, x2, x3, x4, x5, x6, x7)  =  U64_GG(x7)
U65_GG(x1, x2, x3, x4, x5, x6, x7)  =  U65_GG(x7)
U66_GG(x1, x2, x3, x4, x5, x6)  =  U66_GG(x6)
U67_GG(x1, x2)  =  U67_GG(x2)
U68_GG(x1, x2, x3)  =  U68_GG(x3)
U69_GG(x1, x2, x3, x4)  =  U69_GG(x4)
U70_GG(x1, x2, x3, x4)  =  U70_GG(x2, x4)
U71_GG(x1, x2, x3, x4)  =  U71_GG(x4)
U72_GG(x1, x2, x3, x4)  =  U72_GG(x2, x3, x4)
U73_GG(x1, x2, x3, x4, x5)  =  U73_GG(x3, x5)
U74_GG(x1, x2, x3, x4)  =  U74_GG(x4)
U56_AG(x1, x2, x3)  =  U56_AG(x3)
U57_AG(x1, x2, x3, x4)  =  U57_AG(x4)
U58_AG(x1, x2, x3, x4, x5, x6, x7)  =  U58_AG(x7)
P134_IN_AGAGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_AGAGAG(x2, x4, x6)
U45_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U45_AGAGAG(x7)
U59_AG(x1, x2, x3, x4, x5, x6, x7)  =  U59_AG(x7)
P134_IN_GGGGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGAG(x1, x2, x3, x4, x6)
U45_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U45_GGGGAG(x7)
U75_GG(x1, x2, x3, x4)  =  U75_GG(x4)
U76_GG(x1, x2, x3, x4)  =  U76_GG(x2, x4)
U77_GG(x1, x2, x3, x4)  =  U77_GG(x4)
U78_GG(x1, x2, x3, x4)  =  U78_GG(x2, x3, x4)
U79_GG(x1, x2, x3, x4, x5)  =  U79_GG(x3, x5)
U80_GG(x1, x2, x3, x4)  =  U80_GG(x4)
U60_AG(x1, x2, x3, x4, x5)  =  U60_AG(x5)
U49_GGGG(x1, x2, x3, x4, x5)  =  U49_GGGG(x3, x4, x5)
U81_GG(x1, x2, x3)  =  U81_GG(x3)
U82_GG(x1, x2, x3)  =  U82_GG(x2, x3)
U83_GG(x1, x2, x3)  =  U83_GG(x3)
U84_GG(x1, x2, x3)  =  U84_GG(x2, x3)
U85_GG(x1, x2, x3)  =  U85_GG(x3)
U61_AG(x1, x2, x3, x4)  =  U61_AG(x4)
P150_IN_AAGG(x1, x2, x3, x4)  =  P150_IN_AAGG(x3, x4)
U51_AAGG(x1, x2, x3, x4, x5)  =  U51_AAGG(x5)
P60_IN_AA(x1, x2)  =  P60_IN_AA
U23_AA(x1, x2, x3, x4, x5)  =  U23_AA(x5)
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
U25_AA(x1, x2, x3)  =  U25_AA(x3)
U26_AA(x1, x2, x3)  =  U26_AA(x3)
U27_AA(x1, x2, x3)  =  U27_AA(x3)
U52_AAGG(x1, x2, x3, x4, x5)  =  U52_AAGG(x3, x4, x5)
U53_AAGG(x1, x2, x3, x4, x5)  =  U53_AAGG(x5)
U62_AG(x1, x2, x3)  =  U62_AG(x3)
U63_AG(x1, x2, x3, x4)  =  U63_AG(x4)
U64_AG(x1, x2, x3, x4, x5, x6, x7)  =  U64_AG(x7)
U65_AG(x1, x2, x3, x4, x5, x6, x7)  =  U65_AG(x7)
U66_AG(x1, x2, x3, x4, x5, x6)  =  U66_AG(x6)
U67_AG(x1, x2)  =  U67_AG(x2)
U68_AG(x1, x2, x3)  =  U68_AG(x3)
U69_AG(x1, x2, x3, x4)  =  U69_AG(x4)
U70_AG(x1, x2, x3, x4)  =  U70_AG(x4)
U71_AG(x1, x2, x3, x4)  =  U71_AG(x4)
U72_AG(x1, x2, x3, x4)  =  U72_AG(x3, x4)
U73_AG(x1, x2, x3, x4, x5)  =  U73_AG(x3, x5)
U74_AG(x1, x2, x3, x4)  =  U74_AG(x4)
U75_AG(x1, x2, x3, x4)  =  U75_AG(x4)
U76_AG(x1, x2, x3, x4)  =  U76_AG(x4)
U77_AG(x1, x2, x3, x4)  =  U77_AG(x4)
U78_AG(x1, x2, x3, x4)  =  U78_AG(x3, x4)
U79_AG(x1, x2, x3, x4, x5)  =  U79_AG(x3, x5)
U80_AG(x1, x2, x3, x4)  =  U80_AG(x4)
U81_AG(x1, x2, x3)  =  U81_AG(x3)
U82_AG(x1, x2, x3)  =  U82_AG(x2, x3)
U83_AG(x1, x2, x3)  =  U83_AG(x3)
U84_AG(x1, x2, x3)  =  U84_AG(x2, x3)
U85_AG(x1, x2, x3)  =  U85_AG(x3)
U50_GGGG(x1, x2, x3, x4, x5)  =  U50_GGGG(x5)
U46_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGAG(x3, x4, x6, x7)
U47_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U47_GGGGAG(x7)
P137_IN_GGAG(x1, x2, x3, x4)  =  P137_IN_GGAG(x1, x2, x4)
U48_GGAG(x1, x2, x3, x4, x5)  =  U48_GGAG(x5)
U49_GGAG(x1, x2, x3, x4, x5)  =  U49_GGAG(x4, x5)
U50_GGAG(x1, x2, x3, x4, x5)  =  U50_GGAG(x5)
U46_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_AGAGAG(x4, x6, x7)
U47_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U47_AGAGAG(x7)
P137_IN_AGAG(x1, x2, x3, x4)  =  P137_IN_AGAG(x2, x4)
U48_AGAG(x1, x2, x3, x4, x5)  =  U48_AGAG(x5)
U49_AGAG(x1, x2, x3, x4, x5)  =  U49_AGAG(x4, x5)
U50_AGAG(x1, x2, x3, x4, x5)  =  U50_AGAG(x5)
U29_AA(x1, x2)  =  U29_AA(x2)
U30_AA(x1, x2, x3, x4, x5)  =  U30_AA(x5)
U31_AA(x1, x2, x3, x4, x5)  =  U31_AA(x5)
U32_AA(x1, x2, x3, x4, x5)  =  U32_AA(x5)
U33_AA(x1, x2, x3, x4, x5)  =  U33_AA(x5)
U34_AA(x1, x2, x3, x4, x5)  =  U34_AA(x5)
U35_AA(x1, x2, x3, x4, x5)  =  U35_AA(x5)
U36_AA(x1, x2, x3, x4, x5)  =  U36_AA(x5)
U37_AA(x1, x2, x3, x4, x5)  =  U37_AA(x5)
U38_AA(x1, x2, x3, x4, x5)  =  U38_AA(x5)
U39_AA(x1, x2, x3, x4, x5)  =  U39_AA(x5)
U40_AA(x1, x2, x3, x4, x5)  =  U40_AA(x5)
U41_AA(x1, x2, x3, x4, x5)  =  U41_AA(x5)
U42_AA(x1, x2, x3)  =  U42_AA(x3)
U43_AA(x1, x2, x3)  =  U43_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U47_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U47_GGGGGG(x7)
U29_GA(x1, x2)  =  U29_GA(x2)
U30_GA(x1, x2, x3, x4, x5)  =  U30_GA(x5)
U31_GA(x1, x2, x3, x4, x5)  =  U31_GA(x2, x5)
U32_GA(x1, x2, x3, x4, x5)  =  U32_GA(x5)
U33_GA(x1, x2, x3, x4, x5)  =  U33_GA(x2, x5)
U34_GA(x1, x2, x3, x4, x5)  =  U34_GA(x5)
U35_GA(x1, x2, x3, x4, x5)  =  U35_GA(x5)
U36_GA(x1, x2, x3, x4, x5)  =  U36_GA(x5)
U37_GA(x1, x2, x3, x4, x5)  =  U37_GA(x2, x5)
U38_GA(x1, x2, x3, x4, x5)  =  U38_GA(x5)
U39_GA(x1, x2, x3, x4, x5)  =  U39_GA(x2, x5)
U40_GA(x1, x2, x3, x4, x5)  =  U40_GA(x5)
U41_GA(x1, x2, x3, x4, x5)  =  U41_GA(x5)
U42_GA(x1, x2, x3)  =  U42_GA(x3)
U43_GA(x1, x2, x3)  =  U43_GA(x3)
U44_GA(x1, x2, x3)  =  U44_GA(x3)
U7_GA(x1, x2)  =  U7_GA(x2)
U8_GA(x1, x2, x3, x4, x5)  =  U8_GA(x5)
U9_GA(x1, x2, x3, x4, x5)  =  U9_GA(x2, x5)
U10_GA(x1, x2, x3, x4, x5)  =  U10_GA(x5)
U11_GA(x1, x2, x3, x4, x5)  =  U11_GA(x2, x5)
U12_GA(x1, x2, x3, x4, x5)  =  U12_GA(x5)
U13_GA(x1, x2, x3, x4, x5)  =  U13_GA(x5)
U14_GA(x1, x2, x3, x4, x5)  =  U14_GA(x5)
U15_GA(x1, x2, x3, x4, x5)  =  U15_GA(x2, x5)
U16_GA(x1, x2, x3, x4, x5)  =  U16_GA(x5)
U17_GA(x1, x2, x3, x4, x5)  =  U17_GA(x2, x5)
U18_GA(x1, x2, x3, x4, x5)  =  U18_GA(x5)
U19_GA(x1, x2, x3, x4, x5)  =  U19_GA(x5)
U20_GA(x1, x2, x3)  =  U20_GA(x3)
U21_GA(x1, x2, x3)  =  U21_GA(x3)
U22_GA(x1, x2, x3)  =  U22_GA(x3)
U7_AA(x1, x2)  =  U7_AA(x2)
U8_AA(x1, x2, x3, x4, x5)  =  U8_AA(x5)
U9_AA(x1, x2, x3, x4, x5)  =  U9_AA(x5)
U10_AA(x1, x2, x3, x4, x5)  =  U10_AA(x5)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)
U12_AA(x1, x2, x3, x4, x5)  =  U12_AA(x5)
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U14_AA(x1, x2, x3, x4, x5)  =  U14_AA(x5)
U15_AA(x1, x2, x3, x4, x5)  =  U15_AA(x5)
U16_AA(x1, x2, x3, x4, x5)  =  U16_AA(x5)
U17_AA(x1, x2, x3, x4, x5)  =  U17_AA(x5)
U18_AA(x1, x2, x3, x4, x5)  =  U18_AA(x5)
U19_AA(x1, x2, x3, x4, x5)  =  U19_AA(x5)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U22_AA(x1, x2, x3)  =  U22_AA(x3)

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

(56) Obligation:

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

P1_IN_AG(d(d(T10)), const(1)) → U54_AG(T10, p9_in_aa(T10, X14))
P1_IN_AG(d(d(T10)), const(1)) → P9_IN_AA(T10, X14)
P9_IN_AA(e(t), const(1)) → U6_AA(p1_in_gg(d(e(const(1))), const(1)))
P9_IN_AA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(1))
P1_IN_GG(d(d(T10)), const(1)) → U54_GG(T10, p9_in_ga(T10, X14))
P1_IN_GG(d(d(T10)), const(1)) → P9_IN_GA(T10, X14)
P9_IN_GA(e(t), const(1)) → U6_GA(p1_in_gg(d(e(const(1))), const(1)))
P9_IN_GA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(1))
P1_IN_GG(d(d(T135)), const(0)) → U55_GG(T135, p90_in_ga(T135, X334))
P1_IN_GG(d(d(T135)), const(0)) → P90_IN_GA(T135, X334)
P90_IN_GA(e(t), const(1)) → U28_GA(p1_in_gg(d(e(const(1))), const(0)))
P90_IN_GA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(0))
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → U56_GG(T197, T194, p1_in_gg(d(e(T197)), T194))
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_GG(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_GG(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → U45_GGGGGG(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_GG(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_GG(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T228, T194) → U48_GGGG(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(d(T280)), +(T278, T279)) → U61_GG(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
P1_IN_GG(d(d(T280)), +(T278, T279)) → P150_IN_GAGG(T280, X551, T278, T279)
P150_IN_GAGG(T280, X551, T278, T279) → U51_GAGG(T280, X551, T278, T279, p60_in_ga(T280, X551))
P150_IN_GAGG(T280, X551, T278, T279) → P60_IN_GA(T280, X551)
P60_IN_GA(e(+(T108, T109)), +(X266, X267)) → U23_GA(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
P60_IN_GA(e(+(T108, T109)), +(X266, X267)) → P39_IN_GAGA(T108, X266, T109, X267)
P39_IN_GAGA(T45, X117, T46, X118) → U3_GAGA(T45, X117, T46, X118, p24_in_ga(T45, X117))
P39_IN_GAGA(T45, X117, T46, X118) → P24_IN_GA(T45, X117)
P24_IN_GA(+(T45, T46), +(X117, X118)) → U1_GA(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
P24_IN_GA(+(T45, T46), +(X117, X118)) → P39_IN_GAGA(T45, X117, T46, X118)
P39_IN_GAGA(T45, T47, T48, X118) → U4_GAGA(T45, T47, T48, X118, p24_in_ga(T45, T47))
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_GA(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_GAGA(T59, X152, T60, X151)
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_GAGA(T45, T47, T48, X118, p24_in_ga(T48, X118))
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → P24_IN_GA(T48, X118)
P60_IN_GA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_GA(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
P60_IN_GA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → P39_IN_GAGA(T120, X301, T121, X300)
P60_IN_GA(d(T125), X316) → U25_GA(T125, X316, p60_in_ga(T125, X315))
P60_IN_GA(d(T125), X316) → P60_IN_GA(T125, X315)
P60_IN_GA(d(T125), X316) → U26_GA(T125, X316, p60_in_ga(T125, T126))
U26_GA(T125, X316, p60_out_ga(T125, T126)) → U27_GA(T125, X316, p24_in_aa(T126, X316))
U26_GA(T125, X316, p60_out_ga(T125, T126)) → P24_IN_AA(T126, X316)
P24_IN_AA(+(T45, T46), +(X117, X118)) → U1_AA(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
P24_IN_AA(+(T45, T46), +(X117, X118)) → P39_IN_AAAA(T45, X117, T46, X118)
P39_IN_AAAA(T45, X117, T46, X118) → U3_AAAA(T45, X117, T46, X118, p24_in_aa(T45, X117))
P39_IN_AAAA(T45, X117, T46, X118) → P24_IN_AA(T45, X117)
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_AA(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_AAAA(T59, X152, T60, X151)
P39_IN_AAAA(T45, T47, T48, X118) → U4_AAAA(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_AAAA(T45, T47, T48, X118, p24_in_aa(T48, X118))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → P24_IN_AA(T48, X118)
P150_IN_GAGG(T280, T281, T278, T279) → U52_GAGG(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_GAGG(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_GAGG(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
U52_GAGG(T280, T281, T278, T279, p60_out_ga(T280, T281)) → P1_IN_AG(d(e(T281)), +(T278, T279))
P1_IN_AG(d(d(T135)), const(0)) → U55_AG(T135, p90_in_aa(T135, X334))
P1_IN_AG(d(d(T135)), const(0)) → P90_IN_AA(T135, X334)
P90_IN_AA(e(t), const(1)) → U28_AA(p1_in_gg(d(e(const(1))), const(0)))
P90_IN_AA(e(t), const(1)) → P1_IN_GG(d(e(const(1))), const(0))
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_GG(T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_GG(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_GG(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_GG(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
P1_IN_GG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_GG(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
P1_IN_GG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → P150_IN_GAGG(T356, X635, *(T352, T353), *(T354, T355))
P1_IN_GG(d(d(e(t))), T360) → U67_GG(T360, p1_in_gg(d(e(const(1))), T360))
P1_IN_GG(d(d(e(t))), T360) → P1_IN_GG(d(e(const(1))), T360)
P1_IN_GG(d(d(e(const(T366)))), T360) → U68_GG(T366, T360, p1_in_gg(d(e(const(0))), T360))
P1_IN_GG(d(d(e(const(T366)))), T360) → P1_IN_GG(d(e(const(0))), T360)
P1_IN_GG(d(d(e(+(T377, T378)))), T360) → U69_GG(T377, T378, T360, p24_in_ga(T377, X683))
P1_IN_GG(d(d(e(+(T377, T378)))), T360) → P24_IN_GA(T377, X683)
P1_IN_GG(d(d(e(+(T377, T380)))), T360) → U70_GG(T377, T380, T360, p24_in_ga(T377, T379))
U70_GG(T377, T380, T360, p24_out_ga(T377, T379)) → U71_GG(T377, T380, T360, p24_in_ga(T380, X684))
U70_GG(T377, T380, T360, p24_out_ga(T377, T379)) → P24_IN_GA(T380, X684)
P1_IN_GG(d(d(e(+(T377, T380)))), T360) → U72_GG(T377, T380, T360, p24_in_ga(T377, T392))
U72_GG(T377, T380, T360, p24_out_ga(T377, T392)) → U73_GG(T377, T380, T360, T392, p24_in_ga(T380, T391))
U72_GG(T377, T380, T360, p24_out_ga(T377, T392)) → P24_IN_GA(T380, T391)
U73_GG(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_GG(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
U73_GG(T377, T380, T360, T392, p24_out_ga(T380, T391)) → P1_IN_AG(d(e(+(T392, T391))), T360)
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → U56_AG(T197, T194, p1_in_ag(d(e(T197)), T194))
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_AG(d(e(T197)), T194)
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_AG(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_AG(d(e(T203)), T194)
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_AG(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194)
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → U45_AGAGAG(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → P1_IN_AG(d(e(T224)), T222)
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_AG(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGAG(T224, T222, T225, T223, T226, T194) → U45_GGGGAG(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
P134_IN_GGGGAG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(d(e(*(T417, T418)))), T360) → U75_GG(T417, T418, T360, p24_in_ga(T417, X724))
P1_IN_GG(d(d(e(*(T417, T418)))), T360) → P24_IN_GA(T417, X724)
P1_IN_GG(d(d(e(*(T421, T420)))), T360) → U76_GG(T421, T420, T360, p24_in_ga(T421, T419))
U76_GG(T421, T420, T360, p24_out_ga(T421, T419)) → U77_GG(T421, T420, T360, p24_in_ga(T420, X723))
U76_GG(T421, T420, T360, p24_out_ga(T421, T419)) → P24_IN_GA(T420, X723)
P1_IN_GG(d(d(e(*(T433, T434)))), T360) → U78_GG(T433, T434, T360, p24_in_ga(T433, T435))
U78_GG(T433, T434, T360, p24_out_ga(T433, T435)) → U79_GG(T433, T434, T360, T435, p24_in_ga(T434, T432))
U78_GG(T433, T434, T360, p24_out_ga(T433, T435)) → P24_IN_GA(T434, T432)
U79_GG(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_GG(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
U79_GG(T433, T434, T360, T435, p24_out_ga(T434, T432)) → P1_IN_AG(d(e(+(*(T433, T432), *(T434, T435)))), T360)
P1_IN_AG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_AG(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
P1_IN_AG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
P1_IN_GG(d(d(d(T455))), T360) → U81_GG(T455, T360, p60_in_ga(T455, X744))
P1_IN_GG(d(d(d(T455))), T360) → P60_IN_GA(T455, X744)
P1_IN_GG(d(d(d(T455))), T360) → U82_GG(T455, T360, p60_in_ga(T455, T456))
U82_GG(T455, T360, p60_out_ga(T455, T456)) → U83_GG(T455, T360, p24_in_aa(T456, X745))
U82_GG(T455, T360, p60_out_ga(T455, T456)) → P24_IN_AA(T456, X745)
U82_GG(T455, T360, p60_out_ga(T455, T456)) → U84_GG(T455, T360, p24_in_aa(T456, T467))
U84_GG(T455, T360, p24_out_aa(T456, T467)) → U85_GG(T455, T360, p1_in_ag(d(e(T467)), T360))
U84_GG(T455, T360, p24_out_aa(T456, T467)) → P1_IN_AG(d(e(T467)), T360)
P1_IN_AG(d(d(T280)), +(T278, T279)) → U61_AG(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
P1_IN_AG(d(d(T280)), +(T278, T279)) → P150_IN_AAGG(T280, X551, T278, T279)
P150_IN_AAGG(T280, X551, T278, T279) → U51_AAGG(T280, X551, T278, T279, p60_in_aa(T280, X551))
P150_IN_AAGG(T280, X551, T278, T279) → P60_IN_AA(T280, X551)
P60_IN_AA(e(+(T108, T109)), +(X266, X267)) → U23_AA(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
P60_IN_AA(e(+(T108, T109)), +(X266, X267)) → P39_IN_AAAA(T108, X266, T109, X267)
P60_IN_AA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_AA(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
P60_IN_AA(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → P39_IN_AAAA(T120, X301, T121, X300)
P60_IN_AA(d(T125), X316) → U25_AA(T125, X316, p60_in_aa(T125, X315))
P60_IN_AA(d(T125), X316) → P60_IN_AA(T125, X315)
P60_IN_AA(d(T125), X316) → U26_AA(T125, X316, p60_in_aa(T125, T126))
U26_AA(T125, X316, p60_out_aa(T125, T126)) → U27_AA(T125, X316, p24_in_aa(T126, X316))
U26_AA(T125, X316, p60_out_aa(T125, T126)) → P24_IN_AA(T126, X316)
P150_IN_AAGG(T280, T281, T278, T279) → U52_AAGG(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_AAGG(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_AAGG(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
U52_AAGG(T280, T281, T278, T279, p60_out_aa(T280, T281)) → P1_IN_AG(d(e(T281)), +(T278, T279))
P1_IN_AG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_AG(T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_AG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_AG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_AG(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
P1_IN_AG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_AG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_AG(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
P1_IN_AG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_AG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_AG(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
P1_IN_AG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
P1_IN_AG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_AG(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
P1_IN_AG(d(d(T356)), +(*(T352, T353), *(T354, T355))) → P150_IN_AAGG(T356, X635, *(T352, T353), *(T354, T355))
P1_IN_AG(d(d(e(t))), T360) → U67_AG(T360, p1_in_gg(d(e(const(1))), T360))
P1_IN_AG(d(d(e(t))), T360) → P1_IN_GG(d(e(const(1))), T360)
P1_IN_AG(d(d(e(const(T366)))), T360) → U68_AG(T366, T360, p1_in_gg(d(e(const(0))), T360))
P1_IN_AG(d(d(e(const(T366)))), T360) → P1_IN_GG(d(e(const(0))), T360)
P1_IN_AG(d(d(e(+(T377, T378)))), T360) → U69_AG(T377, T378, T360, p24_in_aa(T377, X683))
P1_IN_AG(d(d(e(+(T377, T378)))), T360) → P24_IN_AA(T377, X683)
P1_IN_AG(d(d(e(+(T377, T380)))), T360) → U70_AG(T377, T380, T360, p24_in_aa(T377, T379))
U70_AG(T377, T380, T360, p24_out_aa(T377, T379)) → U71_AG(T377, T380, T360, p24_in_aa(T380, X684))
U70_AG(T377, T380, T360, p24_out_aa(T377, T379)) → P24_IN_AA(T380, X684)
P1_IN_AG(d(d(e(+(T377, T380)))), T360) → U72_AG(T377, T380, T360, p24_in_aa(T377, T392))
U72_AG(T377, T380, T360, p24_out_aa(T377, T392)) → U73_AG(T377, T380, T360, T392, p24_in_aa(T380, T391))
U72_AG(T377, T380, T360, p24_out_aa(T377, T392)) → P24_IN_AA(T380, T391)
U73_AG(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_AG(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
U73_AG(T377, T380, T360, T392, p24_out_aa(T380, T391)) → P1_IN_AG(d(e(+(T392, T391))), T360)
P1_IN_AG(d(d(e(*(T417, T418)))), T360) → U75_AG(T417, T418, T360, p24_in_aa(T417, X724))
P1_IN_AG(d(d(e(*(T417, T418)))), T360) → P24_IN_AA(T417, X724)
P1_IN_AG(d(d(e(*(T421, T420)))), T360) → U76_AG(T421, T420, T360, p24_in_aa(T421, T419))
U76_AG(T421, T420, T360, p24_out_aa(T421, T419)) → U77_AG(T421, T420, T360, p24_in_aa(T420, X723))
U76_AG(T421, T420, T360, p24_out_aa(T421, T419)) → P24_IN_AA(T420, X723)
P1_IN_AG(d(d(e(*(T433, T434)))), T360) → U78_AG(T433, T434, T360, p24_in_aa(T433, T435))
U78_AG(T433, T434, T360, p24_out_aa(T433, T435)) → U79_AG(T433, T434, T360, T435, p24_in_aa(T434, T432))
U78_AG(T433, T434, T360, p24_out_aa(T433, T435)) → P24_IN_AA(T434, T432)
U79_AG(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_AG(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
U79_AG(T433, T434, T360, T435, p24_out_aa(T434, T432)) → P1_IN_AG(d(e(+(*(T433, T432), *(T434, T435)))), T360)
P1_IN_AG(d(d(d(T455))), T360) → U81_AG(T455, T360, p60_in_aa(T455, X744))
P1_IN_AG(d(d(d(T455))), T360) → P60_IN_AA(T455, X744)
P1_IN_AG(d(d(d(T455))), T360) → U82_AG(T455, T360, p60_in_aa(T455, T456))
U82_AG(T455, T360, p60_out_aa(T455, T456)) → U83_AG(T455, T360, p24_in_aa(T456, X745))
U82_AG(T455, T360, p60_out_aa(T455, T456)) → P24_IN_AA(T456, X745)
U82_AG(T455, T360, p60_out_aa(T455, T456)) → U84_AG(T455, T360, p24_in_aa(T456, T467))
U84_AG(T455, T360, p24_out_aa(T456, T467)) → U85_AG(T455, T360, p1_in_ag(d(e(T467)), T360))
U84_AG(T455, T360, p24_out_aa(T456, T467)) → P1_IN_AG(d(e(T467)), T360)
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P134_IN_GGGGAG(T224, T222, T227, T223, T228, T194) → U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_GGGGAG(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T228, T194)
P137_IN_GGAG(T227, T223, T228, T194) → U48_GGAG(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
P137_IN_GGAG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P137_IN_GGAG(T227, T223, T229, T194) → U49_GGAG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_GGAG(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P134_IN_AGAGAG(T224, T222, T227, T223, T228, T194) → U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_AGAGAG(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → P137_IN_AGAG(T227, T223, T228, T194)
P137_IN_AGAG(T227, T223, T228, T194) → U48_AGAG(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
P137_IN_AGAG(T227, T223, T228, T194) → P1_IN_AG(d(e(T227)), T223)
P137_IN_AGAG(T227, T223, T229, T194) → U49_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P90_IN_AA(e(const(T140)), const(0)) → U29_AA(T140, p1_in_gg(d(e(const(0))), const(0)))
P90_IN_AA(e(const(T140)), const(0)) → P1_IN_GG(d(e(const(0))), const(0))
P90_IN_AA(e(+(T151, T152)), +(X373, X374)) → U30_AA(T151, T152, X373, X374, p24_in_aa(T151, X373))
P90_IN_AA(e(+(T151, T152)), +(X373, X374)) → P24_IN_AA(T151, X373)
P90_IN_AA(e(+(T151, T154)), +(T153, X374)) → U31_AA(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_AA(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_AA(T151, T154, T153, X374, p24_in_aa(T154, X374))
U31_AA(T151, T154, T153, X374, p24_out_aa(T151, T153)) → P24_IN_AA(T154, X374)
P90_IN_AA(e(+(T151, T154)), +(T156, T155)) → U33_AA(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_AA(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_AA(T151, T154, T156, T155, p24_in_aa(T154, T155))
U33_AA(T151, T154, T156, T155, p24_out_aa(T151, T156)) → P24_IN_AA(T154, T155)
U34_AA(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_AA(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U34_AA(T151, T154, T156, T155, p24_out_aa(T154, T155)) → P1_IN_AG(d(e(+(T156, T155))), const(0))
P90_IN_AA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_AA(T169, T170, X420, X421, p24_in_aa(T169, X421))
P90_IN_AA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → P24_IN_AA(T169, X421)
P90_IN_AA(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_AA(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_AA(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_AA(T173, T172, X420, T171, p24_in_aa(T172, X420))
U37_AA(T173, T172, X420, T171, p24_out_aa(T173, T171)) → P24_IN_AA(T172, X420)
P90_IN_AA(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_AA(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_AA(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_AA(T175, T176, T174, T177, p24_in_aa(T176, T174))
U39_AA(T175, T176, T174, T177, p24_out_aa(T175, T177)) → P24_IN_AA(T176, T174)
U40_AA(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_AA(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U40_AA(T175, T176, T174, T177, p24_out_aa(T176, T174)) → P1_IN_AG(d(e(+(*(T175, T174), *(T176, T177)))), const(0))
P90_IN_AA(d(T185), X449) → U42_AA(T185, X449, p60_in_aa(T185, X448))
P90_IN_AA(d(T185), X449) → P60_IN_AA(T185, X448)
P90_IN_AA(d(T185), X449) → U43_AA(T185, X449, p60_in_aa(T185, T186))
U43_AA(T185, X449, p60_out_aa(T185, T186)) → U44_AA(T185, X449, p90_in_aa(e(T186), X449))
U43_AA(T185, X449, p60_out_aa(T185, T186)) → P90_IN_AA(e(T186), X449)
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_GGGGGG(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P90_IN_GA(e(const(T140)), const(0)) → U29_GA(T140, p1_in_gg(d(e(const(0))), const(0)))
P90_IN_GA(e(const(T140)), const(0)) → P1_IN_GG(d(e(const(0))), const(0))
P90_IN_GA(e(+(T151, T152)), +(X373, X374)) → U30_GA(T151, T152, X373, X374, p24_in_ga(T151, X373))
P90_IN_GA(e(+(T151, T152)), +(X373, X374)) → P24_IN_GA(T151, X373)
P90_IN_GA(e(+(T151, T154)), +(T153, X374)) → U31_GA(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_GA(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_GA(T151, T154, T153, X374, p24_in_ga(T154, X374))
U31_GA(T151, T154, T153, X374, p24_out_ga(T151, T153)) → P24_IN_GA(T154, X374)
P90_IN_GA(e(+(T151, T154)), +(T156, T155)) → U33_GA(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_GA(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_GA(T151, T154, T156, T155, p24_in_ga(T154, T155))
U33_GA(T151, T154, T156, T155, p24_out_ga(T151, T156)) → P24_IN_GA(T154, T155)
U34_GA(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_GA(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U34_GA(T151, T154, T156, T155, p24_out_ga(T154, T155)) → P1_IN_AG(d(e(+(T156, T155))), const(0))
P90_IN_GA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_GA(T169, T170, X420, X421, p24_in_ga(T169, X421))
P90_IN_GA(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → P24_IN_GA(T169, X421)
P90_IN_GA(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_GA(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_GA(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_GA(T173, T172, X420, T171, p24_in_ga(T172, X420))
U37_GA(T173, T172, X420, T171, p24_out_ga(T173, T171)) → P24_IN_GA(T172, X420)
P90_IN_GA(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_GA(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_GA(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_GA(T175, T176, T174, T177, p24_in_ga(T176, T174))
U39_GA(T175, T176, T174, T177, p24_out_ga(T175, T177)) → P24_IN_GA(T176, T174)
U40_GA(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_GA(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U40_GA(T175, T176, T174, T177, p24_out_ga(T176, T174)) → P1_IN_AG(d(e(+(*(T175, T174), *(T176, T177)))), const(0))
P90_IN_GA(d(T185), X449) → U42_GA(T185, X449, p60_in_ga(T185, X448))
P90_IN_GA(d(T185), X449) → P60_IN_GA(T185, X448)
P90_IN_GA(d(T185), X449) → U43_GA(T185, X449, p60_in_ga(T185, T186))
U43_GA(T185, X449, p60_out_ga(T185, T186)) → U44_GA(T185, X449, p90_in_aa(e(T186), X449))
U43_GA(T185, X449, p60_out_ga(T185, T186)) → P90_IN_AA(e(T186), X449)
P9_IN_GA(e(const(T15)), const(0)) → U7_GA(T15, p1_in_gg(d(e(const(0))), const(1)))
P9_IN_GA(e(const(T15)), const(0)) → P1_IN_GG(d(e(const(0))), const(1))
P9_IN_GA(e(+(T26, T27)), +(X77, X78)) → U8_GA(T26, T27, X77, X78, p24_in_ga(T26, X77))
P9_IN_GA(e(+(T26, T27)), +(X77, X78)) → P24_IN_GA(T26, X77)
P9_IN_GA(e(+(T26, T29)), +(T28, X78)) → U9_GA(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_GA(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_GA(T26, T29, T28, X78, p24_in_ga(T29, X78))
U9_GA(T26, T29, T28, X78, p24_out_ga(T26, T28)) → P24_IN_GA(T29, X78)
P9_IN_GA(e(+(T26, T29)), +(T62, T61)) → U11_GA(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_GA(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_GA(T26, T29, T62, T61, p24_in_ga(T29, T61))
U11_GA(T26, T29, T62, T61, p24_out_ga(T26, T62)) → P24_IN_GA(T29, T61)
U12_GA(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_GA(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U12_GA(T26, T29, T62, T61, p24_out_ga(T29, T61)) → P1_IN_AG(d(e(+(T62, T61))), const(1))
P9_IN_GA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_GA(T75, T76, X200, X201, p24_in_ga(T75, X201))
P9_IN_GA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → P24_IN_GA(T75, X201)
P9_IN_GA(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_GA(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_GA(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_GA(T79, T78, X200, T77, p24_in_ga(T78, X200))
U15_GA(T79, T78, X200, T77, p24_out_ga(T79, T77)) → P24_IN_GA(T78, X200)
P9_IN_GA(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_GA(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_GA(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_GA(T81, T82, T80, T83, p24_in_ga(T82, T80))
U17_GA(T81, T82, T80, T83, p24_out_ga(T81, T83)) → P24_IN_GA(T82, T80)
U18_GA(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_GA(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U18_GA(T81, T82, T80, T83, p24_out_ga(T82, T80)) → P1_IN_AG(d(e(+(*(T81, T80), *(T82, T83)))), const(1))
P9_IN_GA(d(T91), X229) → U20_GA(T91, X229, p60_in_ga(T91, X228))
P9_IN_GA(d(T91), X229) → P60_IN_GA(T91, X228)
P9_IN_GA(d(T91), X229) → U21_GA(T91, X229, p60_in_ga(T91, T92))
U21_GA(T91, X229, p60_out_ga(T91, T92)) → U22_GA(T91, X229, p9_in_aa(e(T92), X229))
U21_GA(T91, X229, p60_out_ga(T91, T92)) → P9_IN_AA(e(T92), X229)
P9_IN_AA(e(const(T15)), const(0)) → U7_AA(T15, p1_in_gg(d(e(const(0))), const(1)))
P9_IN_AA(e(const(T15)), const(0)) → P1_IN_GG(d(e(const(0))), const(1))
P9_IN_AA(e(+(T26, T27)), +(X77, X78)) → U8_AA(T26, T27, X77, X78, p24_in_aa(T26, X77))
P9_IN_AA(e(+(T26, T27)), +(X77, X78)) → P24_IN_AA(T26, X77)
P9_IN_AA(e(+(T26, T29)), +(T28, X78)) → U9_AA(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_AA(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_AA(T26, T29, T28, X78, p24_in_aa(T29, X78))
U9_AA(T26, T29, T28, X78, p24_out_aa(T26, T28)) → P24_IN_AA(T29, X78)
P9_IN_AA(e(+(T26, T29)), +(T62, T61)) → U11_AA(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_AA(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_AA(T26, T29, T62, T61, p24_in_aa(T29, T61))
U11_AA(T26, T29, T62, T61, p24_out_aa(T26, T62)) → P24_IN_AA(T29, T61)
U12_AA(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_AA(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U12_AA(T26, T29, T62, T61, p24_out_aa(T29, T61)) → P1_IN_AG(d(e(+(T62, T61))), const(1))
P9_IN_AA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_AA(T75, T76, X200, X201, p24_in_aa(T75, X201))
P9_IN_AA(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → P24_IN_AA(T75, X201)
P9_IN_AA(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_AA(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_AA(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_AA(T79, T78, X200, T77, p24_in_aa(T78, X200))
U15_AA(T79, T78, X200, T77, p24_out_aa(T79, T77)) → P24_IN_AA(T78, X200)
P9_IN_AA(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_AA(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_AA(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_AA(T81, T82, T80, T83, p24_in_aa(T82, T80))
U17_AA(T81, T82, T80, T83, p24_out_aa(T81, T83)) → P24_IN_AA(T82, T80)
U18_AA(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_AA(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U18_AA(T81, T82, T80, T83, p24_out_aa(T82, T80)) → P1_IN_AG(d(e(+(*(T81, T80), *(T82, T83)))), const(1))
P9_IN_AA(d(T91), X229) → U20_AA(T91, X229, p60_in_aa(T91, X228))
P9_IN_AA(d(T91), X229) → P60_IN_AA(T91, X228)
P9_IN_AA(d(T91), X229) → U21_AA(T91, X229, p60_in_aa(T91, T92))
U21_AA(T91, X229, p60_out_aa(T91, T92)) → U22_AA(T91, X229, p9_in_aa(e(T92), X229))
U21_AA(T91, X229, p60_out_aa(T91, T92)) → P9_IN_AA(e(T92), X229)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P1_IN_AG(x1, x2)  =  P1_IN_AG(x2)
U54_AG(x1, x2)  =  U54_AG(x2)
P9_IN_AA(x1, x2)  =  P9_IN_AA
U6_AA(x1)  =  U6_AA(x1)
P1_IN_GG(x1, x2)  =  P1_IN_GG(x1, x2)
U54_GG(x1, x2)  =  U54_GG(x2)
P9_IN_GA(x1, x2)  =  P9_IN_GA(x1)
U6_GA(x1)  =  U6_GA(x1)
U55_GG(x1, x2)  =  U55_GG(x2)
P90_IN_GA(x1, x2)  =  P90_IN_GA(x1)
U28_GA(x1)  =  U28_GA(x1)
U56_GG(x1, x2, x3)  =  U56_GG(x3)
U57_GG(x1, x2, x3, x4)  =  U57_GG(x4)
U58_GG(x1, x2, x3, x4, x5, x6, x7)  =  U58_GG(x7)
P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)
U45_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U45_GGGGGG(x7)
U59_GG(x1, x2, x3, x4, x5, x6, x7)  =  U59_GG(x7)
U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGGG(x3, x4, x5, x6, x7)
U60_GG(x1, x2, x3, x4, x5)  =  U60_GG(x5)
P137_IN_GGGG(x1, x2, x3, x4)  =  P137_IN_GGGG(x1, x2, x3, x4)
U48_GGGG(x1, x2, x3, x4, x5)  =  U48_GGGG(x5)
U61_GG(x1, x2, x3, x4)  =  U61_GG(x4)
P150_IN_GAGG(x1, x2, x3, x4)  =  P150_IN_GAGG(x1, x3, x4)
U51_GAGG(x1, x2, x3, x4, x5)  =  U51_GAGG(x5)
P60_IN_GA(x1, x2)  =  P60_IN_GA(x1)
U23_GA(x1, x2, x3, x4, x5)  =  U23_GA(x5)
P39_IN_GAGA(x1, x2, x3, x4)  =  P39_IN_GAGA(x1, x3)
U3_GAGA(x1, x2, x3, x4, x5)  =  U3_GAGA(x5)
P24_IN_GA(x1, x2)  =  P24_IN_GA(x1)
U1_GA(x1, x2, x3, x4, x5)  =  U1_GA(x5)
U4_GAGA(x1, x2, x3, x4, x5)  =  U4_GAGA(x3, x5)
U2_GA(x1, x2, x3, x4, x5)  =  U2_GA(x5)
U5_GAGA(x1, x2, x3, x4, x5)  =  U5_GAGA(x5)
U24_GA(x1, x2, x3, x4, x5)  =  U24_GA(x5)
U25_GA(x1, x2, x3)  =  U25_GA(x3)
U26_GA(x1, x2, x3)  =  U26_GA(x3)
U27_GA(x1, x2, x3)  =  U27_GA(x3)
P24_IN_AA(x1, x2)  =  P24_IN_AA
U1_AA(x1, x2, x3, x4, x5)  =  U1_AA(x5)
P39_IN_AAAA(x1, x2, x3, x4)  =  P39_IN_AAAA
U3_AAAA(x1, x2, x3, x4, x5)  =  U3_AAAA(x5)
U2_AA(x1, x2, x3, x4, x5)  =  U2_AA(x5)
U4_AAAA(x1, x2, x3, x4, x5)  =  U4_AAAA(x5)
U5_AAAA(x1, x2, x3, x4, x5)  =  U5_AAAA(x5)
U52_GAGG(x1, x2, x3, x4, x5)  =  U52_GAGG(x3, x4, x5)
U53_GAGG(x1, x2, x3, x4, x5)  =  U53_GAGG(x5)
U55_AG(x1, x2)  =  U55_AG(x2)
P90_IN_AA(x1, x2)  =  P90_IN_AA
U28_AA(x1)  =  U28_AA(x1)
U62_GG(x1, x2, x3)  =  U62_GG(x3)
U63_GG(x1, x2, x3, x4)  =  U63_GG(x4)
U64_GG(x1, x2, x3, x4, x5, x6, x7)  =  U64_GG(x7)
U65_GG(x1, x2, x3, x4, x5, x6, x7)  =  U65_GG(x7)
U66_GG(x1, x2, x3, x4, x5, x6)  =  U66_GG(x6)
U67_GG(x1, x2)  =  U67_GG(x2)
U68_GG(x1, x2, x3)  =  U68_GG(x3)
U69_GG(x1, x2, x3, x4)  =  U69_GG(x4)
U70_GG(x1, x2, x3, x4)  =  U70_GG(x2, x4)
U71_GG(x1, x2, x3, x4)  =  U71_GG(x4)
U72_GG(x1, x2, x3, x4)  =  U72_GG(x2, x3, x4)
U73_GG(x1, x2, x3, x4, x5)  =  U73_GG(x3, x5)
U74_GG(x1, x2, x3, x4)  =  U74_GG(x4)
U56_AG(x1, x2, x3)  =  U56_AG(x3)
U57_AG(x1, x2, x3, x4)  =  U57_AG(x4)
U58_AG(x1, x2, x3, x4, x5, x6, x7)  =  U58_AG(x7)
P134_IN_AGAGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_AGAGAG(x2, x4, x6)
U45_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U45_AGAGAG(x7)
U59_AG(x1, x2, x3, x4, x5, x6, x7)  =  U59_AG(x7)
P134_IN_GGGGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGAG(x1, x2, x3, x4, x6)
U45_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U45_GGGGAG(x7)
U75_GG(x1, x2, x3, x4)  =  U75_GG(x4)
U76_GG(x1, x2, x3, x4)  =  U76_GG(x2, x4)
U77_GG(x1, x2, x3, x4)  =  U77_GG(x4)
U78_GG(x1, x2, x3, x4)  =  U78_GG(x2, x3, x4)
U79_GG(x1, x2, x3, x4, x5)  =  U79_GG(x3, x5)
U80_GG(x1, x2, x3, x4)  =  U80_GG(x4)
U60_AG(x1, x2, x3, x4, x5)  =  U60_AG(x5)
U49_GGGG(x1, x2, x3, x4, x5)  =  U49_GGGG(x3, x4, x5)
U81_GG(x1, x2, x3)  =  U81_GG(x3)
U82_GG(x1, x2, x3)  =  U82_GG(x2, x3)
U83_GG(x1, x2, x3)  =  U83_GG(x3)
U84_GG(x1, x2, x3)  =  U84_GG(x2, x3)
U85_GG(x1, x2, x3)  =  U85_GG(x3)
U61_AG(x1, x2, x3, x4)  =  U61_AG(x4)
P150_IN_AAGG(x1, x2, x3, x4)  =  P150_IN_AAGG(x3, x4)
U51_AAGG(x1, x2, x3, x4, x5)  =  U51_AAGG(x5)
P60_IN_AA(x1, x2)  =  P60_IN_AA
U23_AA(x1, x2, x3, x4, x5)  =  U23_AA(x5)
U24_AA(x1, x2, x3, x4, x5)  =  U24_AA(x5)
U25_AA(x1, x2, x3)  =  U25_AA(x3)
U26_AA(x1, x2, x3)  =  U26_AA(x3)
U27_AA(x1, x2, x3)  =  U27_AA(x3)
U52_AAGG(x1, x2, x3, x4, x5)  =  U52_AAGG(x3, x4, x5)
U53_AAGG(x1, x2, x3, x4, x5)  =  U53_AAGG(x5)
U62_AG(x1, x2, x3)  =  U62_AG(x3)
U63_AG(x1, x2, x3, x4)  =  U63_AG(x4)
U64_AG(x1, x2, x3, x4, x5, x6, x7)  =  U64_AG(x7)
U65_AG(x1, x2, x3, x4, x5, x6, x7)  =  U65_AG(x7)
U66_AG(x1, x2, x3, x4, x5, x6)  =  U66_AG(x6)
U67_AG(x1, x2)  =  U67_AG(x2)
U68_AG(x1, x2, x3)  =  U68_AG(x3)
U69_AG(x1, x2, x3, x4)  =  U69_AG(x4)
U70_AG(x1, x2, x3, x4)  =  U70_AG(x4)
U71_AG(x1, x2, x3, x4)  =  U71_AG(x4)
U72_AG(x1, x2, x3, x4)  =  U72_AG(x3, x4)
U73_AG(x1, x2, x3, x4, x5)  =  U73_AG(x3, x5)
U74_AG(x1, x2, x3, x4)  =  U74_AG(x4)
U75_AG(x1, x2, x3, x4)  =  U75_AG(x4)
U76_AG(x1, x2, x3, x4)  =  U76_AG(x4)
U77_AG(x1, x2, x3, x4)  =  U77_AG(x4)
U78_AG(x1, x2, x3, x4)  =  U78_AG(x3, x4)
U79_AG(x1, x2, x3, x4, x5)  =  U79_AG(x3, x5)
U80_AG(x1, x2, x3, x4)  =  U80_AG(x4)
U81_AG(x1, x2, x3)  =  U81_AG(x3)
U82_AG(x1, x2, x3)  =  U82_AG(x2, x3)
U83_AG(x1, x2, x3)  =  U83_AG(x3)
U84_AG(x1, x2, x3)  =  U84_AG(x2, x3)
U85_AG(x1, x2, x3)  =  U85_AG(x3)
U50_GGGG(x1, x2, x3, x4, x5)  =  U50_GGGG(x5)
U46_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGAG(x3, x4, x6, x7)
U47_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U47_GGGGAG(x7)
P137_IN_GGAG(x1, x2, x3, x4)  =  P137_IN_GGAG(x1, x2, x4)
U48_GGAG(x1, x2, x3, x4, x5)  =  U48_GGAG(x5)
U49_GGAG(x1, x2, x3, x4, x5)  =  U49_GGAG(x4, x5)
U50_GGAG(x1, x2, x3, x4, x5)  =  U50_GGAG(x5)
U46_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_AGAGAG(x4, x6, x7)
U47_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U47_AGAGAG(x7)
P137_IN_AGAG(x1, x2, x3, x4)  =  P137_IN_AGAG(x2, x4)
U48_AGAG(x1, x2, x3, x4, x5)  =  U48_AGAG(x5)
U49_AGAG(x1, x2, x3, x4, x5)  =  U49_AGAG(x4, x5)
U50_AGAG(x1, x2, x3, x4, x5)  =  U50_AGAG(x5)
U29_AA(x1, x2)  =  U29_AA(x2)
U30_AA(x1, x2, x3, x4, x5)  =  U30_AA(x5)
U31_AA(x1, x2, x3, x4, x5)  =  U31_AA(x5)
U32_AA(x1, x2, x3, x4, x5)  =  U32_AA(x5)
U33_AA(x1, x2, x3, x4, x5)  =  U33_AA(x5)
U34_AA(x1, x2, x3, x4, x5)  =  U34_AA(x5)
U35_AA(x1, x2, x3, x4, x5)  =  U35_AA(x5)
U36_AA(x1, x2, x3, x4, x5)  =  U36_AA(x5)
U37_AA(x1, x2, x3, x4, x5)  =  U37_AA(x5)
U38_AA(x1, x2, x3, x4, x5)  =  U38_AA(x5)
U39_AA(x1, x2, x3, x4, x5)  =  U39_AA(x5)
U40_AA(x1, x2, x3, x4, x5)  =  U40_AA(x5)
U41_AA(x1, x2, x3, x4, x5)  =  U41_AA(x5)
U42_AA(x1, x2, x3)  =  U42_AA(x3)
U43_AA(x1, x2, x3)  =  U43_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U47_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U47_GGGGGG(x7)
U29_GA(x1, x2)  =  U29_GA(x2)
U30_GA(x1, x2, x3, x4, x5)  =  U30_GA(x5)
U31_GA(x1, x2, x3, x4, x5)  =  U31_GA(x2, x5)
U32_GA(x1, x2, x3, x4, x5)  =  U32_GA(x5)
U33_GA(x1, x2, x3, x4, x5)  =  U33_GA(x2, x5)
U34_GA(x1, x2, x3, x4, x5)  =  U34_GA(x5)
U35_GA(x1, x2, x3, x4, x5)  =  U35_GA(x5)
U36_GA(x1, x2, x3, x4, x5)  =  U36_GA(x5)
U37_GA(x1, x2, x3, x4, x5)  =  U37_GA(x2, x5)
U38_GA(x1, x2, x3, x4, x5)  =  U38_GA(x5)
U39_GA(x1, x2, x3, x4, x5)  =  U39_GA(x2, x5)
U40_GA(x1, x2, x3, x4, x5)  =  U40_GA(x5)
U41_GA(x1, x2, x3, x4, x5)  =  U41_GA(x5)
U42_GA(x1, x2, x3)  =  U42_GA(x3)
U43_GA(x1, x2, x3)  =  U43_GA(x3)
U44_GA(x1, x2, x3)  =  U44_GA(x3)
U7_GA(x1, x2)  =  U7_GA(x2)
U8_GA(x1, x2, x3, x4, x5)  =  U8_GA(x5)
U9_GA(x1, x2, x3, x4, x5)  =  U9_GA(x2, x5)
U10_GA(x1, x2, x3, x4, x5)  =  U10_GA(x5)
U11_GA(x1, x2, x3, x4, x5)  =  U11_GA(x2, x5)
U12_GA(x1, x2, x3, x4, x5)  =  U12_GA(x5)
U13_GA(x1, x2, x3, x4, x5)  =  U13_GA(x5)
U14_GA(x1, x2, x3, x4, x5)  =  U14_GA(x5)
U15_GA(x1, x2, x3, x4, x5)  =  U15_GA(x2, x5)
U16_GA(x1, x2, x3, x4, x5)  =  U16_GA(x5)
U17_GA(x1, x2, x3, x4, x5)  =  U17_GA(x2, x5)
U18_GA(x1, x2, x3, x4, x5)  =  U18_GA(x5)
U19_GA(x1, x2, x3, x4, x5)  =  U19_GA(x5)
U20_GA(x1, x2, x3)  =  U20_GA(x3)
U21_GA(x1, x2, x3)  =  U21_GA(x3)
U22_GA(x1, x2, x3)  =  U22_GA(x3)
U7_AA(x1, x2)  =  U7_AA(x2)
U8_AA(x1, x2, x3, x4, x5)  =  U8_AA(x5)
U9_AA(x1, x2, x3, x4, x5)  =  U9_AA(x5)
U10_AA(x1, x2, x3, x4, x5)  =  U10_AA(x5)
U11_AA(x1, x2, x3, x4, x5)  =  U11_AA(x5)
U12_AA(x1, x2, x3, x4, x5)  =  U12_AA(x5)
U13_AA(x1, x2, x3, x4, x5)  =  U13_AA(x5)
U14_AA(x1, x2, x3, x4, x5)  =  U14_AA(x5)
U15_AA(x1, x2, x3, x4, x5)  =  U15_AA(x5)
U16_AA(x1, x2, x3, x4, x5)  =  U16_AA(x5)
U17_AA(x1, x2, x3, x4, x5)  =  U17_AA(x5)
U18_AA(x1, x2, x3, x4, x5)  =  U18_AA(x5)
U19_AA(x1, x2, x3, x4, x5)  =  U19_AA(x5)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U22_AA(x1, x2, x3)  =  U22_AA(x3)

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

(57) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 6 SCCs with 267 less nodes.

(58) Complex Obligation (AND)

(59) Obligation:

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

P24_IN_AA(+(T45, T46), +(X117, X118)) → P39_IN_AAAA(T45, X117, T46, X118)
P39_IN_AAAA(T45, X117, T46, X118) → P24_IN_AA(T45, X117)
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_AAAA(T59, X152, T60, X151)
P39_IN_AAAA(T45, T47, T48, X118) → U4_AAAA(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → P24_IN_AA(T48, X118)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P24_IN_AA(x1, x2)  =  P24_IN_AA
P39_IN_AAAA(x1, x2, x3, x4)  =  P39_IN_AAAA
U4_AAAA(x1, x2, x3, x4, x5)  =  U4_AAAA(x5)

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

(60) UsableRulesProof (EQUIVALENT transformation)

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

(61) Obligation:

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

P24_IN_AA(+(T45, T46), +(X117, X118)) → P39_IN_AAAA(T45, X117, T46, X118)
P39_IN_AAAA(T45, X117, T46, X118) → P24_IN_AA(T45, X117)
P24_IN_AA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_AAAA(T59, X152, T60, X151)
P39_IN_AAAA(T45, T47, T48, X118) → U4_AAAA(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_AAAA(T45, T47, T48, X118, p24_out_aa(T45, T47)) → P24_IN_AA(T48, X118)

The TRS R consists of the following rules:

p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)

The argument filtering Pi contains the following mapping:
const(x1)  =  const
1  =  1
t  =  t
0  =  0
+(x1, x2)  =  +(x1, x2)
*(x1, x2)  =  *(x1, x2)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
P24_IN_AA(x1, x2)  =  P24_IN_AA
P39_IN_AAAA(x1, x2, x3, x4)  =  P39_IN_AAAA
U4_AAAA(x1, x2, x3, x4, x5)  =  U4_AAAA(x5)

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

(62) PiDPToQDPProof (SOUND transformation)

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

(63) Obligation:

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

P24_IN_AA → P39_IN_AAAA
P39_IN_AAAA → P24_IN_AA
P39_IN_AAAA → U4_AAAA(p24_in_aa)
U4_AAAA(p24_out_aa) → P24_IN_AA

The TRS R consists of the following rules:

p24_in_aa → p24_out_aa
p24_in_aa → U1_aa(p39_in_aaaa)
p24_in_aa → U2_aa(p39_in_aaaa)
U1_aa(p39_out_aaaa) → p24_out_aa
U2_aa(p39_out_aaaa) → p24_out_aa
p39_in_aaaa → U3_aaaa(p24_in_aa)
p39_in_aaaa → U4_aaaa(p24_in_aa)
U3_aaaa(p24_out_aa) → p39_out_aaaa
U4_aaaa(p24_out_aa) → U5_aaaa(p24_in_aa)
U5_aaaa(p24_out_aa) → p39_out_aaaa

The set Q consists of the following terms:

p24_in_aa
U1_aa(x0)
U2_aa(x0)
p39_in_aaaa
U3_aaaa(x0)
U4_aaaa(x0)
U5_aaaa(x0)

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

(64) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P39_IN_AAAA → U4_AAAA(p24_in_aa) at position [0] we obtained the following new rules [LPAR04]:

P39_IN_AAAA → U4_AAAA(p24_out_aa)
P39_IN_AAAA → U4_AAAA(U1_aa(p39_in_aaaa))
P39_IN_AAAA → U4_AAAA(U2_aa(p39_in_aaaa))

(65) Obligation:

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

P24_IN_AA → P39_IN_AAAA
P39_IN_AAAA → P24_IN_AA
U4_AAAA(p24_out_aa) → P24_IN_AA
P39_IN_AAAA → U4_AAAA(p24_out_aa)
P39_IN_AAAA → U4_AAAA(U1_aa(p39_in_aaaa))
P39_IN_AAAA → U4_AAAA(U2_aa(p39_in_aaaa))

The TRS R consists of the following rules:

p24_in_aa → p24_out_aa
p24_in_aa → U1_aa(p39_in_aaaa)
p24_in_aa → U2_aa(p39_in_aaaa)
U1_aa(p39_out_aaaa) → p24_out_aa
U2_aa(p39_out_aaaa) → p24_out_aa
p39_in_aaaa → U3_aaaa(p24_in_aa)
p39_in_aaaa → U4_aaaa(p24_in_aa)
U3_aaaa(p24_out_aa) → p39_out_aaaa
U4_aaaa(p24_out_aa) → U5_aaaa(p24_in_aa)
U5_aaaa(p24_out_aa) → p39_out_aaaa

The set Q consists of the following terms:

p24_in_aa
U1_aa(x0)
U2_aa(x0)
p39_in_aaaa
U3_aaaa(x0)
U4_aaaa(x0)
U5_aaaa(x0)

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

(66) NonTerminationProof (EQUIVALENT transformation)

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

s = P39_IN_AAAA evaluates to t =P39_IN_AAAA

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

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

P39_IN_AAAA → P24_IN_AA
with rule P39_IN_AAAA → P24_IN_AA at position [] and matcher [ ]

P24_IN_AA → P39_IN_AAAA
with rule P24_IN_AA → P39_IN_AAAA

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


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

(67) NO

(68) Obligation:

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

P60_IN_AA(d(T125), X316) → P60_IN_AA(T125, X315)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P60_IN_AA(x1, x2)  =  P60_IN_AA

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

(69) UsableRulesProof (EQUIVALENT transformation)

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

(70) Obligation:

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

P60_IN_AA(d(T125), X316) → P60_IN_AA(T125, X315)

R is empty.
The argument filtering Pi contains the following mapping:
d(x1)  =  d(x1)
P60_IN_AA(x1, x2)  =  P60_IN_AA

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

(71) PiDPToQDPProof (SOUND transformation)

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

(72) Obligation:

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

P60_IN_AA → P60_IN_AA

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

(73) NonTerminationProof (EQUIVALENT transformation)

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

s = P60_IN_AA evaluates to t =P60_IN_AA

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

• Semiunifier: [ ]
• Matcher: [ ]

---

Rewriting sequence

The DP semiunifies directly so there is only one rewrite step from P60_IN_AA to P60_IN_AA.

(74) NO

(75) Obligation:

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

P39_IN_GAGA(T45, X117, T46, X118) → P24_IN_GA(T45, X117)
P24_IN_GA(+(T45, T46), +(X117, X118)) → P39_IN_GAGA(T45, X117, T46, X118)
P39_IN_GAGA(T45, T47, T48, X118) → U4_GAGA(T45, T47, T48, X118, p24_in_ga(T45, T47))
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → P24_IN_GA(T48, X118)
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_GAGA(T59, X152, T60, X151)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P39_IN_GAGA(x1, x2, x3, x4)  =  P39_IN_GAGA(x1, x3)
P24_IN_GA(x1, x2)  =  P24_IN_GA(x1)
U4_GAGA(x1, x2, x3, x4, x5)  =  U4_GAGA(x3, x5)

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

(76) UsableRulesProof (EQUIVALENT transformation)

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

(77) Obligation:

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

P39_IN_GAGA(T45, X117, T46, X118) → P24_IN_GA(T45, X117)
P24_IN_GA(+(T45, T46), +(X117, X118)) → P39_IN_GAGA(T45, X117, T46, X118)
P39_IN_GAGA(T45, T47, T48, X118) → U4_GAGA(T45, T47, T48, X118, p24_in_ga(T45, T47))
U4_GAGA(T45, T47, T48, X118, p24_out_ga(T45, T47)) → P24_IN_GA(T48, X118)
P24_IN_GA(*(T59, T60), +(*(T59, X151), *(T60, X152))) → P39_IN_GAGA(T59, X152, T60, X151)

The TRS R consists of the following rules:

p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)

The argument filtering Pi contains the following mapping:
const(x1)  =  const
1  =  1
t  =  t
0  =  0
+(x1, x2)  =  +(x1, x2)
*(x1, x2)  =  *(x1, x2)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
P39_IN_GAGA(x1, x2, x3, x4)  =  P39_IN_GAGA(x1, x3)
P24_IN_GA(x1, x2)  =  P24_IN_GA(x1)
U4_GAGA(x1, x2, x3, x4, x5)  =  U4_GAGA(x3, x5)

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

(78) PiDPToQDPProof (SOUND transformation)

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

(79) Obligation:

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

P39_IN_GAGA(T45, T46) → P24_IN_GA(T45)
P24_IN_GA(+(T45, T46)) → P39_IN_GAGA(T45, T46)
P39_IN_GAGA(T45, T48) → U4_GAGA(T48, p24_in_ga(T45))
U4_GAGA(T48, p24_out_ga) → P24_IN_GA(T48)
P24_IN_GA(*(T59, T60)) → P39_IN_GAGA(T59, T60)

The TRS R consists of the following rules:

p24_in_ga(t) → p24_out_ga
p24_in_ga(const) → p24_out_ga
p24_in_ga(+(T45, T46)) → U1_ga(p39_in_gaga(T45, T46))
p24_in_ga(*(T59, T60)) → U2_ga(p39_in_gaga(T59, T60))
U1_ga(p39_out_gaga) → p24_out_ga
U2_ga(p39_out_gaga) → p24_out_ga
p39_in_gaga(T45, T46) → U3_gaga(p24_in_ga(T45))
p39_in_gaga(T45, T48) → U4_gaga(T48, p24_in_ga(T45))
U3_gaga(p24_out_ga) → p39_out_gaga
U4_gaga(T48, p24_out_ga) → U5_gaga(p24_in_ga(T48))
U5_gaga(p24_out_ga) → p39_out_gaga

The set Q consists of the following terms:

p24_in_ga(x0)
U1_ga(x0)
U2_ga(x0)
p39_in_gaga(x0, x1)
U3_gaga(x0)
U4_gaga(x0, x1)
U5_gaga(x0)

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

(80) 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:

• P39_IN_GAGA(T45, T46) → P24_IN_GA(T45)
  The graph contains the following edges 1 >= 1

• P39_IN_GAGA(T45, T48) → U4_GAGA(T48, p24_in_ga(T45))
  The graph contains the following edges 2 >= 1

• U4_GAGA(T48, p24_out_ga) → P24_IN_GA(T48)
  The graph contains the following edges 1 >= 1

• P24_IN_GA(+(T45, T46)) → P39_IN_GAGA(T45, T46)
  The graph contains the following edges 1 > 1, 1 > 2

• P24_IN_GA(*(T59, T60)) → P39_IN_GAGA(T59, T60)
  The graph contains the following edges 1 > 1, 1 > 2

(81) YES

(82) Obligation:

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

P60_IN_GA(d(T125), X316) → P60_IN_GA(T125, X315)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P60_IN_GA(x1, x2)  =  P60_IN_GA(x1)

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

(83) UsableRulesProof (EQUIVALENT transformation)

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

(84) Obligation:

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

P60_IN_GA(d(T125), X316) → P60_IN_GA(T125, X315)

R is empty.
The argument filtering Pi contains the following mapping:
d(x1)  =  d(x1)
P60_IN_GA(x1, x2)  =  P60_IN_GA(x1)

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

(85) PiDPToQDPProof (SOUND transformation)

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

(86) Obligation:

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

P60_IN_GA(d(T125)) → P60_IN_GA(T125)

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

(87) 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:

• P60_IN_GA(d(T125)) → P60_IN_GA(T125)
  The graph contains the following edges 1 > 1

(88) YES

(89) Obligation:

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

P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P1_IN_GG(x1, x2)  =  P1_IN_GG(x1, x2)
P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)
U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGGG(x3, x4, x5, x6, x7)
P137_IN_GGGG(x1, x2, x3, x4)  =  P137_IN_GGGG(x1, x2, x3, x4)
U49_GGGG(x1, x2, x3, x4, x5)  =  U49_GGGG(x3, x4, x5)

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

(90) UsableRulesProof (EQUIVALENT transformation)

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

(91) Obligation:

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

P1_IN_GG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGGG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGGG(T227, T223, T228, T194)
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGGG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_GG(d(e(T229)), T194)
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)

The TRS R consists of the following rules:

p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)

The argument filtering Pi contains the following mapping:
const(x1)  =  const
1  =  1
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
0  =  0
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
P1_IN_GG(x1, x2)  =  P1_IN_GG(x1, x2)
P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGGG(x1, x2, x3, x4, x5, x6)
U46_GGGGGG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGGG(x3, x4, x5, x6, x7)
P137_IN_GGGG(x1, x2, x3, x4)  =  P137_IN_GGGG(x1, x2, x3, x4)
U49_GGGG(x1, x2, x3, x4, x5)  =  U49_GGGG(x3, x4, x5)

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

(92) PiDPToQDPProof (SOUND transformation)

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

(93) Obligation:

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

P1_IN_GG(d(e(+(const, T203))), +(const, T194)) → P1_IN_GG(d(e(T203)), T194)
P1_IN_GG(d(e(+(t, T197))), +(const, T194)) → P1_IN_GG(d(e(T197)), T194)
P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGGG(T227, T223, T228, T194, p1_out_gg) → P137_IN_GGGG(T227, T223, T228, T194)
P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGGG(T229, T194, p1_out_gg) → P1_IN_GG(d(e(T229)), T194)
P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(const, T293))), +(*(const, T294), *(T293, const))) → P1_IN_GG(d(e(T293)), T294)
P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)

The TRS R consists of the following rules:

p1_in_gg(d(e(t)), const) → p1_out_gg
p1_in_gg(d(e(const)), const) → p1_out_gg
p1_in_gg(d(e(+(t, T197))), +(const, T194)) → U56_gg(p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const, T203))), +(const, T194)) → U57_gg(p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(p137_in_gggg(T267, T270, T268, T269))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const))) → U62_gg(p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const, T293))), +(*(const, T294), *(T293, const))) → U63_gg(p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U56_gg(p1_out_gg) → p1_out_gg
U57_gg(p1_out_gg) → p1_out_gg
U58_gg(p134_out_gggggg) → p1_out_gg
U59_gg(p134_out_gggggg) → p1_out_gg
U60_gg(p137_out_gggg) → p1_out_gg
U62_gg(p1_out_gg) → p1_out_gg
U63_gg(p1_out_gg) → p1_out_gg
U64_gg(p134_out_gggggg) → p1_out_gg
U65_gg(p134_out_gggggg) → p1_out_gg
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(p1_in_gg(d(e(T224)), T222))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(p1_in_gg(d(e(T227)), T223))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T229, T194, p1_in_gg(d(e(T227)), T223))
U45_gggggg(p1_out_gg) → p134_out_gggggg
U46_gggggg(T227, T223, T228, T194, p1_out_gg) → U47_gggggg(p137_in_gggg(T227, T223, T228, T194))
U48_gggg(p1_out_gg) → p137_out_gggg
U49_gggg(T229, T194, p1_out_gg) → U50_gggg(p1_in_gg(d(e(T229)), T194))
U47_gggggg(p137_out_gggg) → p134_out_gggggg
U50_gggg(p1_out_gg) → p137_out_gggg

The set Q consists of the following terms:

p1_in_gg(x0, x1)
U56_gg(x0)
U57_gg(x0)
U58_gg(x0)
U59_gg(x0)
U60_gg(x0)
U62_gg(x0)
U63_gg(x0)
U64_gg(x0)
U65_gg(x0)
p134_in_gggggg(x0, x1, x2, x3, x4, x5)
p137_in_gggg(x0, x1, x2, x3)
U45_gggggg(x0)
U46_gggggg(x0, x1, x2, x3, x4)
U48_gggg(x0)
U49_gggg(x0, x1, x2)
U47_gggggg(x0)
U50_gggg(x0)

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

(94) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194) → P1_IN_GG(d(e(T224)), T222)
  The graph contains the following edges 2 >= 2

• P134_IN_GGGGGG(T224, T222, T227, T223, T228, T194) → U46_GGGGGG(T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
  The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 4

• P1_IN_GG(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → P137_IN_GGGG(T267, T270, T268, T269)
  The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4

• U46_GGGGGG(T227, T223, T228, T194, p1_out_gg) → P137_IN_GGGG(T227, T223, T228, T194)
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4

• P137_IN_GGGG(T227, T223, T229, T194) → U49_GGGG(T229, T194, p1_in_gg(d(e(T227)), T223))
  The graph contains the following edges 3 >= 1, 4 >= 2

• P137_IN_GGGG(T227, T223, T228, T194) → P1_IN_GG(d(e(T227)), T223)
  The graph contains the following edges 2 >= 2

• U49_GGGG(T229, T194, p1_out_gg) → P1_IN_GG(d(e(T229)), T194)
  The graph contains the following edges 2 >= 2

• P1_IN_GG(d(e(+(const, T203))), +(const, T194)) → P1_IN_GG(d(e(T203)), T194)
  The graph contains the following edges 2 > 2

• P1_IN_GG(d(e(+(t, T197))), +(const, T194)) → P1_IN_GG(d(e(T197)), T194)
  The graph contains the following edges 2 > 2

• P1_IN_GG(d(e(*(t, T293))), +(*(t, T294), *(T293, const))) → P1_IN_GG(d(e(T293)), T294)
  The graph contains the following edges 2 > 2

• P1_IN_GG(d(e(*(const, T293))), +(*(const, T294), *(T293, const))) → P1_IN_GG(d(e(T293)), T294)
  The graph contains the following edges 2 > 2

• P1_IN_GG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_GGGGGG(T224, T222, T225, T223, T226, T194)
  The graph contains the following edges 1 > 1, 2 > 2, 1 > 3, 2 > 4, 1 > 5, 2 > 6

• P1_IN_GG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGGG(T246, T249, T247, T248, T250, T194)
  The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4, 1 > 5, 2 > 6

• P1_IN_GG(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → P134_IN_GGGGGG(T317, T319, T318, T320, T293, T294)
  The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4, 1 > 5, 2 > 5, 2 > 6

• P1_IN_GG(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → P134_IN_GGGGGG(T337, T340, T338, T339, T293, T294)
  The graph contains the following edges 1 > 1, 2 > 1, 2 > 2, 1 > 3, 2 > 3, 2 > 4, 1 > 5, 2 > 5, 2 > 6

(95) YES

(96) Obligation:

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

P134_IN_GGGGAG(T224, T222, T227, T223, T228, T194) → U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T228, T194)
P137_IN_GGAG(T227, T223, T229, T194) → U49_GGAG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_AG(d(e(T197)), T194)
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_AG(d(e(T203)), T194)
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194)
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → P1_IN_AG(d(e(T224)), T222)
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T250, T194)
P134_IN_AGAGAG(T224, T222, T227, T223, T228, T194) → U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → P137_IN_AGAG(T227, T223, T228, T194)
P137_IN_AGAG(T227, T223, T228, T194) → P1_IN_AG(d(e(T227)), T223)
P137_IN_AGAG(T227, T223, T229, T194) → U49_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)

The TRS R consists of the following rules:

p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(d(T10)), const(1)) → U54_ag(T10, p9_in_aa(T10, X14))
p9_in_aa(e(t), const(1)) → U6_aa(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(d(T10)), const(1)) → U54_gg(T10, p9_in_ga(T10, X14))
p9_in_ga(e(t), const(1)) → U6_ga(p1_in_gg(d(e(const(1))), const(1)))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(d(T135)), const(0)) → U55_gg(T135, p90_in_ga(T135, X334))
p90_in_ga(e(t), const(1)) → U28_ga(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(T280)), +(T278, T279)) → U61_gg(T280, T278, T279, p150_in_gagg(T280, X551, T278, T279))
p150_in_gagg(T280, X551, T278, T279) → U51_gagg(T280, X551, T278, T279, p60_in_ga(T280, X551))
p60_in_ga(e(t), const(1)) → p60_out_ga(e(t), const(1))
p60_in_ga(e(const(T97)), const(0)) → p60_out_ga(e(const(T97)), const(0))
p60_in_ga(e(+(T108, T109)), +(X266, X267)) → U23_ga(T108, T109, X266, X267, p39_in_gaga(T108, X266, T109, X267))
p39_in_gaga(T45, X117, T46, X118) → U3_gaga(T45, X117, T46, X118, p24_in_ga(T45, X117))
p24_in_ga(t, const(1)) → p24_out_ga(t, const(1))
p24_in_ga(const(T34), const(0)) → p24_out_ga(const(T34), const(0))
p24_in_ga(+(T45, T46), +(X117, X118)) → U1_ga(T45, T46, X117, X118, p39_in_gaga(T45, X117, T46, X118))
p39_in_gaga(T45, T47, T48, X118) → U4_gaga(T45, T47, T48, X118, p24_in_ga(T45, T47))
p24_in_ga(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_ga(T59, T60, X151, X152, p39_in_gaga(T59, X152, T60, X151))
U2_ga(T59, T60, X151, X152, p39_out_gaga(T59, X152, T60, X151)) → p24_out_ga(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U4_gaga(T45, T47, T48, X118, p24_out_ga(T45, T47)) → U5_gaga(T45, T47, T48, X118, p24_in_ga(T48, X118))
U5_gaga(T45, T47, T48, X118, p24_out_ga(T48, X118)) → p39_out_gaga(T45, T47, T48, X118)
U1_ga(T45, T46, X117, X118, p39_out_gaga(T45, X117, T46, X118)) → p24_out_ga(+(T45, T46), +(X117, X118))
U3_gaga(T45, X117, T46, X118, p24_out_ga(T45, X117)) → p39_out_gaga(T45, X117, T46, X118)
U23_ga(T108, T109, X266, X267, p39_out_gaga(T108, X266, T109, X267)) → p60_out_ga(e(+(T108, T109)), +(X266, X267))
p60_in_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_ga(T120, T121, X300, X301, p39_in_gaga(T120, X301, T121, X300))
U24_ga(T120, T121, X300, X301, p39_out_gaga(T120, X301, T121, X300)) → p60_out_ga(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_ga(d(T125), X316) → U25_ga(T125, X316, p60_in_ga(T125, X315))
p60_in_ga(d(T125), X316) → U26_ga(T125, X316, p60_in_ga(T125, T126))
U26_ga(T125, X316, p60_out_ga(T125, T126)) → U27_ga(T125, X316, p24_in_aa(T126, X316))
p24_in_aa(t, const(1)) → p24_out_aa(t, const(1))
p24_in_aa(const(T34), const(0)) → p24_out_aa(const(T34), const(0))
p24_in_aa(+(T45, T46), +(X117, X118)) → U1_aa(T45, T46, X117, X118, p39_in_aaaa(T45, X117, T46, X118))
p39_in_aaaa(T45, X117, T46, X118) → U3_aaaa(T45, X117, T46, X118, p24_in_aa(T45, X117))
p24_in_aa(*(T59, T60), +(*(T59, X151), *(T60, X152))) → U2_aa(T59, T60, X151, X152, p39_in_aaaa(T59, X152, T60, X151))
p39_in_aaaa(T45, T47, T48, X118) → U4_aaaa(T45, T47, T48, X118, p24_in_aa(T45, T47))
U4_aaaa(T45, T47, T48, X118, p24_out_aa(T45, T47)) → U5_aaaa(T45, T47, T48, X118, p24_in_aa(T48, X118))
U5_aaaa(T45, T47, T48, X118, p24_out_aa(T48, X118)) → p39_out_aaaa(T45, T47, T48, X118)
U2_aa(T59, T60, X151, X152, p39_out_aaaa(T59, X152, T60, X151)) → p24_out_aa(*(T59, T60), +(*(T59, X151), *(T60, X152)))
U3_aaaa(T45, X117, T46, X118, p24_out_aa(T45, X117)) → p39_out_aaaa(T45, X117, T46, X118)
U1_aa(T45, T46, X117, X118, p39_out_aaaa(T45, X117, T46, X118)) → p24_out_aa(+(T45, T46), +(X117, X118))
U27_ga(T125, X316, p24_out_aa(T126, X316)) → p60_out_ga(d(T125), X316)
U25_ga(T125, X316, p60_out_ga(T125, X315)) → p60_out_ga(d(T125), X316)
U51_gagg(T280, X551, T278, T279, p60_out_ga(T280, X551)) → p150_out_gagg(T280, X551, T278, T279)
p150_in_gagg(T280, T281, T278, T279) → U52_gagg(T280, T281, T278, T279, p60_in_ga(T280, T281))
U52_gagg(T280, T281, T278, T279, p60_out_ga(T280, T281)) → U53_gagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(d(T135)), const(0)) → U55_ag(T135, p90_in_aa(T135, X334))
p90_in_aa(e(t), const(1)) → U28_aa(p1_in_gg(d(e(const(1))), const(0)))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_gg(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_gg(T356, T352, T353, T354, T355, p150_in_gagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_gg(T356, T352, T353, T354, T355, p150_out_gagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_gg(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_gg(d(d(e(t))), T360) → U67_gg(T360, p1_in_gg(d(e(const(1))), T360))
p1_in_gg(d(d(e(const(T366)))), T360) → U68_gg(T366, T360, p1_in_gg(d(e(const(0))), T360))
p1_in_gg(d(d(e(+(T377, T378)))), T360) → U69_gg(T377, T378, T360, p24_in_ga(T377, X683))
U69_gg(T377, T378, T360, p24_out_ga(T377, X683)) → p1_out_gg(d(d(e(+(T377, T378)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U70_gg(T377, T380, T360, p24_in_ga(T377, T379))
U70_gg(T377, T380, T360, p24_out_ga(T377, T379)) → U71_gg(T377, T380, T360, p24_in_ga(T380, X684))
U71_gg(T377, T380, T360, p24_out_ga(T380, X684)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
p1_in_gg(d(d(e(+(T377, T380)))), T360) → U72_gg(T377, T380, T360, p24_in_ga(T377, T392))
U72_gg(T377, T380, T360, p24_out_ga(T377, T392)) → U73_gg(T377, T380, T360, T392, p24_in_ga(T380, T391))
U73_gg(T377, T380, T360, T392, p24_out_ga(T380, T391)) → U74_gg(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p1_in_gg(d(d(e(*(T417, T418)))), T360) → U75_gg(T417, T418, T360, p24_in_ga(T417, X724))
U75_gg(T417, T418, T360, p24_out_ga(T417, X724)) → p1_out_gg(d(d(e(*(T417, T418)))), T360)
p1_in_gg(d(d(e(*(T421, T420)))), T360) → U76_gg(T421, T420, T360, p24_in_ga(T421, T419))
U76_gg(T421, T420, T360, p24_out_ga(T421, T419)) → U77_gg(T421, T420, T360, p24_in_ga(T420, X723))
U77_gg(T421, T420, T360, p24_out_ga(T420, X723)) → p1_out_gg(d(d(e(*(T421, T420)))), T360)
p1_in_gg(d(d(e(*(T433, T434)))), T360) → U78_gg(T433, T434, T360, p24_in_ga(T433, T435))
U78_gg(T433, T434, T360, p24_out_ga(T433, T435)) → U79_gg(T433, T434, T360, T435, p24_in_ga(T434, T432))
U79_gg(T433, T434, T360, T435, p24_out_ga(T434, T432)) → U80_gg(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p1_in_gg(d(d(d(T455))), T360) → U81_gg(T455, T360, p60_in_ga(T455, X744))
U81_gg(T455, T360, p60_out_ga(T455, X744)) → p1_out_gg(d(d(d(T455))), T360)
p1_in_gg(d(d(d(T455))), T360) → U82_gg(T455, T360, p60_in_ga(T455, T456))
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U83_gg(T455, T360, p24_in_aa(T456, X745))
U83_gg(T455, T360, p24_out_aa(T456, X745)) → p1_out_gg(d(d(d(T455))), T360)
U82_gg(T455, T360, p60_out_ga(T455, T456)) → U84_gg(T455, T360, p24_in_aa(T456, T467))
U84_gg(T455, T360, p24_out_aa(T456, T467)) → U85_gg(T455, T360, p1_in_ag(d(e(T467)), T360))
p1_in_ag(d(d(T280)), +(T278, T279)) → U61_ag(T280, T278, T279, p150_in_aagg(T280, X551, T278, T279))
p150_in_aagg(T280, X551, T278, T279) → U51_aagg(T280, X551, T278, T279, p60_in_aa(T280, X551))
p60_in_aa(e(t), const(1)) → p60_out_aa(e(t), const(1))
p60_in_aa(e(const(T97)), const(0)) → p60_out_aa(e(const(T97)), const(0))
p60_in_aa(e(+(T108, T109)), +(X266, X267)) → U23_aa(T108, T109, X266, X267, p39_in_aaaa(T108, X266, T109, X267))
U23_aa(T108, T109, X266, X267, p39_out_aaaa(T108, X266, T109, X267)) → p60_out_aa(e(+(T108, T109)), +(X266, X267))
p60_in_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301))) → U24_aa(T120, T121, X300, X301, p39_in_aaaa(T120, X301, T121, X300))
U24_aa(T120, T121, X300, X301, p39_out_aaaa(T120, X301, T121, X300)) → p60_out_aa(e(*(T120, T121)), +(*(T120, X300), *(T121, X301)))
p60_in_aa(d(T125), X316) → U25_aa(T125, X316, p60_in_aa(T125, X315))
p60_in_aa(d(T125), X316) → U26_aa(T125, X316, p60_in_aa(T125, T126))
U26_aa(T125, X316, p60_out_aa(T125, T126)) → U27_aa(T125, X316, p24_in_aa(T126, X316))
U27_aa(T125, X316, p24_out_aa(T126, X316)) → p60_out_aa(d(T125), X316)
U25_aa(T125, X316, p60_out_aa(T125, X315)) → p60_out_aa(d(T125), X316)
U51_aagg(T280, X551, T278, T279, p60_out_aa(T280, X551)) → p150_out_aagg(T280, X551, T278, T279)
p150_in_aagg(T280, T281, T278, T279) → U52_aagg(T280, T281, T278, T279, p60_in_aa(T280, T281))
U52_aagg(T280, T281, T278, T279, p60_out_aa(T280, T281)) → U53_aagg(T280, T281, T278, T279, p1_in_ag(d(e(T281)), +(T278, T279)))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p1_in_ag(d(d(T356)), +(*(T352, T353), *(T354, T355))) → U66_ag(T356, T352, T353, T354, T355, p150_in_aagg(T356, X635, *(T352, T353), *(T354, T355)))
U66_ag(T356, T352, T353, T354, T355, p150_out_aagg(T356, X635, *(T352, T353), *(T354, T355))) → p1_out_ag(d(d(T356)), +(*(T352, T353), *(T354, T355)))
p1_in_ag(d(d(e(t))), T360) → U67_ag(T360, p1_in_gg(d(e(const(1))), T360))
U67_ag(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_ag(d(d(e(t))), T360)
p1_in_ag(d(d(e(const(T366)))), T360) → U68_ag(T366, T360, p1_in_gg(d(e(const(0))), T360))
U68_ag(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_ag(d(d(e(const(T366)))), T360)
p1_in_ag(d(d(e(+(T377, T378)))), T360) → U69_ag(T377, T378, T360, p24_in_aa(T377, X683))
U69_ag(T377, T378, T360, p24_out_aa(T377, X683)) → p1_out_ag(d(d(e(+(T377, T378)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U70_ag(T377, T380, T360, p24_in_aa(T377, T379))
U70_ag(T377, T380, T360, p24_out_aa(T377, T379)) → U71_ag(T377, T380, T360, p24_in_aa(T380, X684))
U71_ag(T377, T380, T360, p24_out_aa(T380, X684)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
p1_in_ag(d(d(e(+(T377, T380)))), T360) → U72_ag(T377, T380, T360, p24_in_aa(T377, T392))
U72_ag(T377, T380, T360, p24_out_aa(T377, T392)) → U73_ag(T377, T380, T360, T392, p24_in_aa(T380, T391))
U73_ag(T377, T380, T360, T392, p24_out_aa(T380, T391)) → U74_ag(T377, T380, T360, p1_in_ag(d(e(+(T392, T391))), T360))
p1_in_ag(d(d(e(*(T417, T418)))), T360) → U75_ag(T417, T418, T360, p24_in_aa(T417, X724))
U75_ag(T417, T418, T360, p24_out_aa(T417, X724)) → p1_out_ag(d(d(e(*(T417, T418)))), T360)
p1_in_ag(d(d(e(*(T421, T420)))), T360) → U76_ag(T421, T420, T360, p24_in_aa(T421, T419))
U76_ag(T421, T420, T360, p24_out_aa(T421, T419)) → U77_ag(T421, T420, T360, p24_in_aa(T420, X723))
U77_ag(T421, T420, T360, p24_out_aa(T420, X723)) → p1_out_ag(d(d(e(*(T421, T420)))), T360)
p1_in_ag(d(d(e(*(T433, T434)))), T360) → U78_ag(T433, T434, T360, p24_in_aa(T433, T435))
U78_ag(T433, T434, T360, p24_out_aa(T433, T435)) → U79_ag(T433, T434, T360, T435, p24_in_aa(T434, T432))
U79_ag(T433, T434, T360, T435, p24_out_aa(T434, T432)) → U80_ag(T433, T434, T360, p1_in_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360))
p1_in_ag(d(d(d(T455))), T360) → U81_ag(T455, T360, p60_in_aa(T455, X744))
U81_ag(T455, T360, p60_out_aa(T455, X744)) → p1_out_ag(d(d(d(T455))), T360)
p1_in_ag(d(d(d(T455))), T360) → U82_ag(T455, T360, p60_in_aa(T455, T456))
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U83_ag(T455, T360, p24_in_aa(T456, X745))
U83_ag(T455, T360, p24_out_aa(T456, X745)) → p1_out_ag(d(d(d(T455))), T360)
U82_ag(T455, T360, p60_out_aa(T455, T456)) → U84_ag(T455, T360, p24_in_aa(T456, T467))
U84_ag(T455, T360, p24_out_aa(T456, T467)) → U85_ag(T455, T360, p1_in_ag(d(e(T467)), T360))
U85_ag(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_ag(d(d(d(T455))), T360)
U80_ag(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_ag(d(d(e(*(T433, T434)))), T360)
U74_ag(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_ag(d(d(e(+(T377, T380)))), T360)
U53_aagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_aagg(T280, T281, T278, T279)
U61_ag(T280, T278, T279, p150_out_aagg(T280, X551, T278, T279)) → p1_out_ag(d(d(T280)), +(T278, T279))
U85_gg(T455, T360, p1_out_ag(d(e(T467)), T360)) → p1_out_gg(d(d(d(T455))), T360)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U80_gg(T433, T434, T360, p1_out_ag(d(e(+(*(T433, T432), *(T434, T435)))), T360)) → p1_out_gg(d(d(e(*(T433, T434)))), T360)
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U74_gg(T377, T380, T360, p1_out_ag(d(e(+(T392, T391))), T360)) → p1_out_gg(d(d(e(+(T377, T380)))), T360)
U68_gg(T366, T360, p1_out_gg(d(e(const(0))), T360)) → p1_out_gg(d(d(e(const(T366)))), T360)
U67_gg(T360, p1_out_gg(d(e(const(1))), T360)) → p1_out_gg(d(d(e(t))), T360)
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U28_aa(p1_out_gg(d(e(const(1))), const(0))) → p90_out_aa(e(t), const(1))
p90_in_aa(e(const(T140)), const(0)) → U29_aa(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_aa(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_aa(e(const(T140)), const(0))
p90_in_aa(e(+(T151, T152)), +(X373, X374)) → U30_aa(T151, T152, X373, X374, p24_in_aa(T151, X373))
U30_aa(T151, T152, X373, X374, p24_out_aa(T151, X373)) → p90_out_aa(e(+(T151, T152)), +(X373, X374))
p90_in_aa(e(+(T151, T154)), +(T153, X374)) → U31_aa(T151, T154, T153, X374, p24_in_aa(T151, T153))
U31_aa(T151, T154, T153, X374, p24_out_aa(T151, T153)) → U32_aa(T151, T154, T153, X374, p24_in_aa(T154, X374))
U32_aa(T151, T154, T153, X374, p24_out_aa(T154, X374)) → p90_out_aa(e(+(T151, T154)), +(T153, X374))
p90_in_aa(e(+(T151, T154)), +(T156, T155)) → U33_aa(T151, T154, T156, T155, p24_in_aa(T151, T156))
U33_aa(T151, T154, T156, T155, p24_out_aa(T151, T156)) → U34_aa(T151, T154, T156, T155, p24_in_aa(T154, T155))
U34_aa(T151, T154, T156, T155, p24_out_aa(T154, T155)) → U35_aa(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_aa(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_aa(e(+(T151, T154)), +(T156, T155))
p90_in_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_aa(T169, T170, X420, X421, p24_in_aa(T169, X421))
U36_aa(T169, T170, X420, X421, p24_out_aa(T169, X421)) → p90_out_aa(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_aa(T173, T172, X420, T171, p24_in_aa(T173, T171))
U37_aa(T173, T172, X420, T171, p24_out_aa(T173, T171)) → U38_aa(T173, T172, X420, T171, p24_in_aa(T172, X420))
U38_aa(T173, T172, X420, T171, p24_out_aa(T172, X420)) → p90_out_aa(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_aa(T175, T176, T174, T177, p24_in_aa(T175, T177))
U39_aa(T175, T176, T174, T177, p24_out_aa(T175, T177)) → U40_aa(T175, T176, T174, T177, p24_in_aa(T176, T174))
U40_aa(T175, T176, T174, T177, p24_out_aa(T176, T174)) → U41_aa(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_aa(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_aa(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_aa(d(T185), X449) → U42_aa(T185, X449, p60_in_aa(T185, X448))
U42_aa(T185, X449, p60_out_aa(T185, X448)) → p90_out_aa(d(T185), X449)
p90_in_aa(d(T185), X449) → U43_aa(T185, X449, p60_in_aa(T185, T186))
U43_aa(T185, X449, p60_out_aa(T185, T186)) → U44_aa(T185, X449, p90_in_aa(e(T186), X449))
U44_aa(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_aa(d(T185), X449)
U55_ag(T135, p90_out_aa(T135, X334)) → p1_out_ag(d(d(T135)), const(0))
U53_gagg(T280, T281, T278, T279, p1_out_ag(d(e(T281)), +(T278, T279))) → p150_out_gagg(T280, T281, T278, T279)
U61_gg(T280, T278, T279, p150_out_gagg(T280, X551, T278, T279)) → p1_out_gg(d(d(T280)), +(T278, T279))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U28_ga(p1_out_gg(d(e(const(1))), const(0))) → p90_out_ga(e(t), const(1))
p90_in_ga(e(const(T140)), const(0)) → U29_ga(T140, p1_in_gg(d(e(const(0))), const(0)))
U29_ga(T140, p1_out_gg(d(e(const(0))), const(0))) → p90_out_ga(e(const(T140)), const(0))
p90_in_ga(e(+(T151, T152)), +(X373, X374)) → U30_ga(T151, T152, X373, X374, p24_in_ga(T151, X373))
U30_ga(T151, T152, X373, X374, p24_out_ga(T151, X373)) → p90_out_ga(e(+(T151, T152)), +(X373, X374))
p90_in_ga(e(+(T151, T154)), +(T153, X374)) → U31_ga(T151, T154, T153, X374, p24_in_ga(T151, T153))
U31_ga(T151, T154, T153, X374, p24_out_ga(T151, T153)) → U32_ga(T151, T154, T153, X374, p24_in_ga(T154, X374))
U32_ga(T151, T154, T153, X374, p24_out_ga(T154, X374)) → p90_out_ga(e(+(T151, T154)), +(T153, X374))
p90_in_ga(e(+(T151, T154)), +(T156, T155)) → U33_ga(T151, T154, T156, T155, p24_in_ga(T151, T156))
U33_ga(T151, T154, T156, T155, p24_out_ga(T151, T156)) → U34_ga(T151, T154, T156, T155, p24_in_ga(T154, T155))
U34_ga(T151, T154, T156, T155, p24_out_ga(T154, T155)) → U35_ga(T151, T154, T156, T155, p1_in_ag(d(e(+(T156, T155))), const(0)))
U35_ga(T151, T154, T156, T155, p1_out_ag(d(e(+(T156, T155))), const(0))) → p90_out_ga(e(+(T151, T154)), +(T156, T155))
p90_in_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421))) → U36_ga(T169, T170, X420, X421, p24_in_ga(T169, X421))
U36_ga(T169, T170, X420, X421, p24_out_ga(T169, X421)) → p90_out_ga(e(*(T169, T170)), +(*(T169, X420), *(T170, X421)))
p90_in_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171))) → U37_ga(T173, T172, X420, T171, p24_in_ga(T173, T171))
U37_ga(T173, T172, X420, T171, p24_out_ga(T173, T171)) → U38_ga(T173, T172, X420, T171, p24_in_ga(T172, X420))
U38_ga(T173, T172, X420, T171, p24_out_ga(T172, X420)) → p90_out_ga(e(*(T173, T172)), +(*(T173, X420), *(T172, T171)))
p90_in_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177))) → U39_ga(T175, T176, T174, T177, p24_in_ga(T175, T177))
U39_ga(T175, T176, T174, T177, p24_out_ga(T175, T177)) → U40_ga(T175, T176, T174, T177, p24_in_ga(T176, T174))
U40_ga(T175, T176, T174, T177, p24_out_ga(T176, T174)) → U41_ga(T175, T176, T174, T177, p1_in_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0)))
U41_ga(T175, T176, T174, T177, p1_out_ag(d(e(+(*(T175, T174), *(T176, T177)))), const(0))) → p90_out_ga(e(*(T175, T176)), +(*(T175, T174), *(T176, T177)))
p90_in_ga(d(T185), X449) → U42_ga(T185, X449, p60_in_ga(T185, X448))
U42_ga(T185, X449, p60_out_ga(T185, X448)) → p90_out_ga(d(T185), X449)
p90_in_ga(d(T185), X449) → U43_ga(T185, X449, p60_in_ga(T185, T186))
U43_ga(T185, X449, p60_out_ga(T185, T186)) → U44_ga(T185, X449, p90_in_aa(e(T186), X449))
U44_ga(T185, X449, p90_out_aa(e(T186), X449)) → p90_out_ga(d(T185), X449)
U55_gg(T135, p90_out_ga(T135, X334)) → p1_out_gg(d(d(T135)), const(0))
U6_ga(p1_out_gg(d(e(const(1))), const(1))) → p9_out_ga(e(t), const(1))
p9_in_ga(e(const(T15)), const(0)) → U7_ga(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_ga(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_ga(e(const(T15)), const(0))
p9_in_ga(e(+(T26, T27)), +(X77, X78)) → U8_ga(T26, T27, X77, X78, p24_in_ga(T26, X77))
U8_ga(T26, T27, X77, X78, p24_out_ga(T26, X77)) → p9_out_ga(e(+(T26, T27)), +(X77, X78))
p9_in_ga(e(+(T26, T29)), +(T28, X78)) → U9_ga(T26, T29, T28, X78, p24_in_ga(T26, T28))
U9_ga(T26, T29, T28, X78, p24_out_ga(T26, T28)) → U10_ga(T26, T29, T28, X78, p24_in_ga(T29, X78))
U10_ga(T26, T29, T28, X78, p24_out_ga(T29, X78)) → p9_out_ga(e(+(T26, T29)), +(T28, X78))
p9_in_ga(e(+(T26, T29)), +(T62, T61)) → U11_ga(T26, T29, T62, T61, p24_in_ga(T26, T62))
U11_ga(T26, T29, T62, T61, p24_out_ga(T26, T62)) → U12_ga(T26, T29, T62, T61, p24_in_ga(T29, T61))
U12_ga(T26, T29, T62, T61, p24_out_ga(T29, T61)) → U13_ga(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_ga(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_ga(e(+(T26, T29)), +(T62, T61))
p9_in_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_ga(T75, T76, X200, X201, p24_in_ga(T75, X201))
U14_ga(T75, T76, X200, X201, p24_out_ga(T75, X201)) → p9_out_ga(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_ga(T79, T78, X200, T77, p24_in_ga(T79, T77))
U15_ga(T79, T78, X200, T77, p24_out_ga(T79, T77)) → U16_ga(T79, T78, X200, T77, p24_in_ga(T78, X200))
U16_ga(T79, T78, X200, T77, p24_out_ga(T78, X200)) → p9_out_ga(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_ga(T81, T82, T80, T83, p24_in_ga(T81, T83))
U17_ga(T81, T82, T80, T83, p24_out_ga(T81, T83)) → U18_ga(T81, T82, T80, T83, p24_in_ga(T82, T80))
U18_ga(T81, T82, T80, T83, p24_out_ga(T82, T80)) → U19_ga(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_ga(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_ga(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_ga(d(T91), X229) → U20_ga(T91, X229, p60_in_ga(T91, X228))
U20_ga(T91, X229, p60_out_ga(T91, X228)) → p9_out_ga(d(T91), X229)
p9_in_ga(d(T91), X229) → U21_ga(T91, X229, p60_in_ga(T91, T92))
U21_ga(T91, X229, p60_out_ga(T91, T92)) → U22_ga(T91, X229, p9_in_aa(e(T92), X229))
p9_in_aa(e(const(T15)), const(0)) → U7_aa(T15, p1_in_gg(d(e(const(0))), const(1)))
U7_aa(T15, p1_out_gg(d(e(const(0))), const(1))) → p9_out_aa(e(const(T15)), const(0))
p9_in_aa(e(+(T26, T27)), +(X77, X78)) → U8_aa(T26, T27, X77, X78, p24_in_aa(T26, X77))
U8_aa(T26, T27, X77, X78, p24_out_aa(T26, X77)) → p9_out_aa(e(+(T26, T27)), +(X77, X78))
p9_in_aa(e(+(T26, T29)), +(T28, X78)) → U9_aa(T26, T29, T28, X78, p24_in_aa(T26, T28))
U9_aa(T26, T29, T28, X78, p24_out_aa(T26, T28)) → U10_aa(T26, T29, T28, X78, p24_in_aa(T29, X78))
U10_aa(T26, T29, T28, X78, p24_out_aa(T29, X78)) → p9_out_aa(e(+(T26, T29)), +(T28, X78))
p9_in_aa(e(+(T26, T29)), +(T62, T61)) → U11_aa(T26, T29, T62, T61, p24_in_aa(T26, T62))
U11_aa(T26, T29, T62, T61, p24_out_aa(T26, T62)) → U12_aa(T26, T29, T62, T61, p24_in_aa(T29, T61))
U12_aa(T26, T29, T62, T61, p24_out_aa(T29, T61)) → U13_aa(T26, T29, T62, T61, p1_in_ag(d(e(+(T62, T61))), const(1)))
U13_aa(T26, T29, T62, T61, p1_out_ag(d(e(+(T62, T61))), const(1))) → p9_out_aa(e(+(T26, T29)), +(T62, T61))
p9_in_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201))) → U14_aa(T75, T76, X200, X201, p24_in_aa(T75, X201))
U14_aa(T75, T76, X200, X201, p24_out_aa(T75, X201)) → p9_out_aa(e(*(T75, T76)), +(*(T75, X200), *(T76, X201)))
p9_in_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77))) → U15_aa(T79, T78, X200, T77, p24_in_aa(T79, T77))
U15_aa(T79, T78, X200, T77, p24_out_aa(T79, T77)) → U16_aa(T79, T78, X200, T77, p24_in_aa(T78, X200))
U16_aa(T79, T78, X200, T77, p24_out_aa(T78, X200)) → p9_out_aa(e(*(T79, T78)), +(*(T79, X200), *(T78, T77)))
p9_in_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83))) → U17_aa(T81, T82, T80, T83, p24_in_aa(T81, T83))
U17_aa(T81, T82, T80, T83, p24_out_aa(T81, T83)) → U18_aa(T81, T82, T80, T83, p24_in_aa(T82, T80))
U18_aa(T81, T82, T80, T83, p24_out_aa(T82, T80)) → U19_aa(T81, T82, T80, T83, p1_in_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1)))
U19_aa(T81, T82, T80, T83, p1_out_ag(d(e(+(*(T81, T80), *(T82, T83)))), const(1))) → p9_out_aa(e(*(T81, T82)), +(*(T81, T80), *(T82, T83)))
p9_in_aa(d(T91), X229) → U20_aa(T91, X229, p60_in_aa(T91, X228))
U20_aa(T91, X229, p60_out_aa(T91, X228)) → p9_out_aa(d(T91), X229)
p9_in_aa(d(T91), X229) → U21_aa(T91, X229, p60_in_aa(T91, T92))
U21_aa(T91, X229, p60_out_aa(T91, T92)) → U22_aa(T91, X229, p9_in_aa(e(T92), X229))
U22_aa(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_aa(d(T91), X229)
U22_ga(T91, X229, p9_out_aa(e(T92), X229)) → p9_out_ga(d(T91), X229)
U54_gg(T10, p9_out_ga(T10, X14)) → p1_out_gg(d(d(T10)), const(1))
U6_aa(p1_out_gg(d(e(const(1))), const(1))) → p9_out_aa(e(t), const(1))
U54_ag(T10, p9_out_aa(T10, X14)) → p1_out_ag(d(d(T10)), const(1))

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
U54_ag(x1, x2)  =  U54_ag(x2)
p9_in_aa(x1, x2)  =  p9_in_aa
U6_aa(x1)  =  U6_aa(x1)
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
U54_gg(x1, x2)  =  U54_gg(x2)
p9_in_ga(x1, x2)  =  p9_in_ga(x1)
U6_ga(x1)  =  U6_ga(x1)
0  =  0
U55_gg(x1, x2)  =  U55_gg(x2)
p90_in_ga(x1, x2)  =  p90_in_ga(x1)
U28_ga(x1)  =  U28_ga(x1)
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U61_gg(x1, x2, x3, x4)  =  U61_gg(x4)
p150_in_gagg(x1, x2, x3, x4)  =  p150_in_gagg(x1, x3, x4)
U51_gagg(x1, x2, x3, x4, x5)  =  U51_gagg(x5)
p60_in_ga(x1, x2)  =  p60_in_ga(x1)
p60_out_ga(x1, x2)  =  p60_out_ga
U23_ga(x1, x2, x3, x4, x5)  =  U23_ga(x5)
p39_in_gaga(x1, x2, x3, x4)  =  p39_in_gaga(x1, x3)
U3_gaga(x1, x2, x3, x4, x5)  =  U3_gaga(x5)
p24_in_ga(x1, x2)  =  p24_in_ga(x1)
p24_out_ga(x1, x2)  =  p24_out_ga
U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)
U4_gaga(x1, x2, x3, x4, x5)  =  U4_gaga(x3, x5)
U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x5)
p39_out_gaga(x1, x2, x3, x4)  =  p39_out_gaga
U5_gaga(x1, x2, x3, x4, x5)  =  U5_gaga(x5)
U24_ga(x1, x2, x3, x4, x5)  =  U24_ga(x5)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
U27_ga(x1, x2, x3)  =  U27_ga(x3)
p24_in_aa(x1, x2)  =  p24_in_aa
p24_out_aa(x1, x2)  =  p24_out_aa
U1_aa(x1, x2, x3, x4, x5)  =  U1_aa(x5)
p39_in_aaaa(x1, x2, x3, x4)  =  p39_in_aaaa
U3_aaaa(x1, x2, x3, x4, x5)  =  U3_aaaa(x5)
U2_aa(x1, x2, x3, x4, x5)  =  U2_aa(x5)
U4_aaaa(x1, x2, x3, x4, x5)  =  U4_aaaa(x5)
U5_aaaa(x1, x2, x3, x4, x5)  =  U5_aaaa(x5)
p39_out_aaaa(x1, x2, x3, x4)  =  p39_out_aaaa
p150_out_gagg(x1, x2, x3, x4)  =  p150_out_gagg
U52_gagg(x1, x2, x3, x4, x5)  =  U52_gagg(x3, x4, x5)
U53_gagg(x1, x2, x3, x4, x5)  =  U53_gagg(x5)
U55_ag(x1, x2)  =  U55_ag(x2)
p90_in_aa(x1, x2)  =  p90_in_aa
U28_aa(x1)  =  U28_aa(x1)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U66_gg(x1, x2, x3, x4, x5, x6)  =  U66_gg(x6)
U67_gg(x1, x2)  =  U67_gg(x2)
U68_gg(x1, x2, x3)  =  U68_gg(x3)
U69_gg(x1, x2, x3, x4)  =  U69_gg(x4)
U70_gg(x1, x2, x3, x4)  =  U70_gg(x2, x4)
U71_gg(x1, x2, x3, x4)  =  U71_gg(x4)
U72_gg(x1, x2, x3, x4)  =  U72_gg(x2, x3, x4)
U73_gg(x1, x2, x3, x4, x5)  =  U73_gg(x3, x5)
U74_gg(x1, x2, x3, x4)  =  U74_gg(x4)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U75_gg(x1, x2, x3, x4)  =  U75_gg(x4)
U76_gg(x1, x2, x3, x4)  =  U76_gg(x2, x4)
U77_gg(x1, x2, x3, x4)  =  U77_gg(x4)
U78_gg(x1, x2, x3, x4)  =  U78_gg(x2, x3, x4)
U79_gg(x1, x2, x3, x4, x5)  =  U79_gg(x3, x5)
U80_gg(x1, x2, x3, x4)  =  U80_gg(x4)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U81_gg(x1, x2, x3)  =  U81_gg(x3)
U82_gg(x1, x2, x3)  =  U82_gg(x2, x3)
U83_gg(x1, x2, x3)  =  U83_gg(x3)
U84_gg(x1, x2, x3)  =  U84_gg(x2, x3)
U85_gg(x1, x2, x3)  =  U85_gg(x3)
U61_ag(x1, x2, x3, x4)  =  U61_ag(x4)
p150_in_aagg(x1, x2, x3, x4)  =  p150_in_aagg(x3, x4)
U51_aagg(x1, x2, x3, x4, x5)  =  U51_aagg(x5)
p60_in_aa(x1, x2)  =  p60_in_aa
p60_out_aa(x1, x2)  =  p60_out_aa
U23_aa(x1, x2, x3, x4, x5)  =  U23_aa(x5)
U24_aa(x1, x2, x3, x4, x5)  =  U24_aa(x5)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
U26_aa(x1, x2, x3)  =  U26_aa(x3)
U27_aa(x1, x2, x3)  =  U27_aa(x3)
p150_out_aagg(x1, x2, x3, x4)  =  p150_out_aagg
U52_aagg(x1, x2, x3, x4, x5)  =  U52_aagg(x3, x4, x5)
U53_aagg(x1, x2, x3, x4, x5)  =  U53_aagg(x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U66_ag(x1, x2, x3, x4, x5, x6)  =  U66_ag(x6)
U67_ag(x1, x2)  =  U67_ag(x2)
U68_ag(x1, x2, x3)  =  U68_ag(x3)
U69_ag(x1, x2, x3, x4)  =  U69_ag(x4)
U70_ag(x1, x2, x3, x4)  =  U70_ag(x4)
U71_ag(x1, x2, x3, x4)  =  U71_ag(x4)
U72_ag(x1, x2, x3, x4)  =  U72_ag(x3, x4)
U73_ag(x1, x2, x3, x4, x5)  =  U73_ag(x3, x5)
U74_ag(x1, x2, x3, x4)  =  U74_ag(x4)
U75_ag(x1, x2, x3, x4)  =  U75_ag(x4)
U76_ag(x1, x2, x3, x4)  =  U76_ag(x4)
U77_ag(x1, x2, x3, x4)  =  U77_ag(x4)
U78_ag(x1, x2, x3, x4)  =  U78_ag(x3, x4)
U79_ag(x1, x2, x3, x4, x5)  =  U79_ag(x3, x5)
U80_ag(x1, x2, x3, x4)  =  U80_ag(x4)
U81_ag(x1, x2, x3)  =  U81_ag(x3)
U82_ag(x1, x2, x3)  =  U82_ag(x2, x3)
U83_ag(x1, x2, x3)  =  U83_ag(x3)
U84_ag(x1, x2, x3)  =  U84_ag(x2, x3)
U85_ag(x1, x2, x3)  =  U85_ag(x3)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
p90_out_aa(x1, x2)  =  p90_out_aa
U29_aa(x1, x2)  =  U29_aa(x2)
U30_aa(x1, x2, x3, x4, x5)  =  U30_aa(x5)
U31_aa(x1, x2, x3, x4, x5)  =  U31_aa(x5)
U32_aa(x1, x2, x3, x4, x5)  =  U32_aa(x5)
U33_aa(x1, x2, x3, x4, x5)  =  U33_aa(x5)
U34_aa(x1, x2, x3, x4, x5)  =  U34_aa(x5)
U35_aa(x1, x2, x3, x4, x5)  =  U35_aa(x5)
U36_aa(x1, x2, x3, x4, x5)  =  U36_aa(x5)
U37_aa(x1, x2, x3, x4, x5)  =  U37_aa(x5)
U38_aa(x1, x2, x3, x4, x5)  =  U38_aa(x5)
U39_aa(x1, x2, x3, x4, x5)  =  U39_aa(x5)
U40_aa(x1, x2, x3, x4, x5)  =  U40_aa(x5)
U41_aa(x1, x2, x3, x4, x5)  =  U41_aa(x5)
U42_aa(x1, x2, x3)  =  U42_aa(x3)
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
p90_out_ga(x1, x2)  =  p90_out_ga
U29_ga(x1, x2)  =  U29_ga(x2)
U30_ga(x1, x2, x3, x4, x5)  =  U30_ga(x5)
U31_ga(x1, x2, x3, x4, x5)  =  U31_ga(x2, x5)
U32_ga(x1, x2, x3, x4, x5)  =  U32_ga(x5)
U33_ga(x1, x2, x3, x4, x5)  =  U33_ga(x2, x5)
U34_ga(x1, x2, x3, x4, x5)  =  U34_ga(x5)
U35_ga(x1, x2, x3, x4, x5)  =  U35_ga(x5)
U36_ga(x1, x2, x3, x4, x5)  =  U36_ga(x5)
U37_ga(x1, x2, x3, x4, x5)  =  U37_ga(x2, x5)
U38_ga(x1, x2, x3, x4, x5)  =  U38_ga(x5)
U39_ga(x1, x2, x3, x4, x5)  =  U39_ga(x2, x5)
U40_ga(x1, x2, x3, x4, x5)  =  U40_ga(x5)
U41_ga(x1, x2, x3, x4, x5)  =  U41_ga(x5)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
p9_out_ga(x1, x2)  =  p9_out_ga
U7_ga(x1, x2)  =  U7_ga(x2)
U8_ga(x1, x2, x3, x4, x5)  =  U8_ga(x5)
U9_ga(x1, x2, x3, x4, x5)  =  U9_ga(x2, x5)
U10_ga(x1, x2, x3, x4, x5)  =  U10_ga(x5)
U11_ga(x1, x2, x3, x4, x5)  =  U11_ga(x2, x5)
U12_ga(x1, x2, x3, x4, x5)  =  U12_ga(x5)
U13_ga(x1, x2, x3, x4, x5)  =  U13_ga(x5)
U14_ga(x1, x2, x3, x4, x5)  =  U14_ga(x5)
U15_ga(x1, x2, x3, x4, x5)  =  U15_ga(x2, x5)
U16_ga(x1, x2, x3, x4, x5)  =  U16_ga(x5)
U17_ga(x1, x2, x3, x4, x5)  =  U17_ga(x2, x5)
U18_ga(x1, x2, x3, x4, x5)  =  U18_ga(x5)
U19_ga(x1, x2, x3, x4, x5)  =  U19_ga(x5)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U22_ga(x1, x2, x3)  =  U22_ga(x3)
U7_aa(x1, x2)  =  U7_aa(x2)
p9_out_aa(x1, x2)  =  p9_out_aa
U8_aa(x1, x2, x3, x4, x5)  =  U8_aa(x5)
U9_aa(x1, x2, x3, x4, x5)  =  U9_aa(x5)
U10_aa(x1, x2, x3, x4, x5)  =  U10_aa(x5)
U11_aa(x1, x2, x3, x4, x5)  =  U11_aa(x5)
U12_aa(x1, x2, x3, x4, x5)  =  U12_aa(x5)
U13_aa(x1, x2, x3, x4, x5)  =  U13_aa(x5)
U14_aa(x1, x2, x3, x4, x5)  =  U14_aa(x5)
U15_aa(x1, x2, x3, x4, x5)  =  U15_aa(x5)
U16_aa(x1, x2, x3, x4, x5)  =  U16_aa(x5)
U17_aa(x1, x2, x3, x4, x5)  =  U17_aa(x5)
U18_aa(x1, x2, x3, x4, x5)  =  U18_aa(x5)
U19_aa(x1, x2, x3, x4, x5)  =  U19_aa(x5)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U22_aa(x1, x2, x3)  =  U22_aa(x3)
P1_IN_AG(x1, x2)  =  P1_IN_AG(x2)
P134_IN_AGAGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_AGAGAG(x2, x4, x6)
P134_IN_GGGGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGAG(x1, x2, x3, x4, x6)
U46_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGAG(x3, x4, x6, x7)
P137_IN_GGAG(x1, x2, x3, x4)  =  P137_IN_GGAG(x1, x2, x4)
U49_GGAG(x1, x2, x3, x4, x5)  =  U49_GGAG(x4, x5)
U46_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_AGAGAG(x4, x6, x7)
P137_IN_AGAG(x1, x2, x3, x4)  =  P137_IN_AGAG(x2, x4)
U49_AGAG(x1, x2, x3, x4, x5)  =  U49_AGAG(x4, x5)

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

(97) UsableRulesProof (EQUIVALENT transformation)

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

(98) Obligation:

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

P134_IN_GGGGAG(T224, T222, T227, T223, T228, T194) → U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → P137_IN_GGAG(T227, T223, T228, T194)
P137_IN_GGAG(T227, T223, T229, T194) → U49_GGAG(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)
P1_IN_AG(d(e(+(t, T197))), +(const(1), T194)) → P1_IN_AG(d(e(T197)), T194)
P1_IN_AG(d(e(+(const(T202), T203))), +(const(0), T194)) → P1_IN_AG(d(e(T203)), T194)
P1_IN_AG(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194)
P134_IN_AGAGAG(T224, T222, T225, T223, T226, T194) → P1_IN_AG(d(e(T224)), T222)
P1_IN_AG(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T250, T194)
P134_IN_AGAGAG(T224, T222, T227, T223, T228, T194) → U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
U46_AGAGAG(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → P137_IN_AGAG(T227, T223, T228, T194)
P137_IN_AGAG(T227, T223, T228, T194) → P1_IN_AG(d(e(T227)), T223)
P137_IN_AGAG(T227, T223, T229, T194) → U49_AGAG(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
U49_AGAG(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → P1_IN_AG(d(e(T229)), T194)

The TRS R consists of the following rules:

p1_in_gg(d(e(t)), const(1)) → p1_out_gg(d(e(t)), const(1))
p1_in_gg(d(e(const(T128))), const(0)) → p1_out_gg(d(e(const(T128))), const(0))
p1_in_gg(d(e(+(t, T197))), +(const(1), T194)) → U56_gg(T197, T194, p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_gg(T202, T203, T194, p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(T224, T225, T226, T222, T223, T194, p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(T246, T247, T250, T248, T249, T194, p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_gg(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_gg(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
p1_in_ag(d(e(t)), const(1)) → p1_out_ag(d(e(t)), const(1))
p1_in_ag(d(e(const(T128))), const(0)) → p1_out_ag(d(e(const(T128))), const(0))
p1_in_ag(d(e(+(t, T197))), +(const(1), T194)) → U56_ag(T197, T194, p1_in_ag(d(e(T197)), T194))
p1_in_ag(d(e(+(const(T202), T203))), +(const(0), T194)) → U57_ag(T202, T203, T194, p1_in_ag(d(e(T203)), T194))
p1_in_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_ag(T224, T225, T226, T222, T223, T194, p134_in_agagag(T224, T222, T225, T223, T226, T194))
p1_in_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(T246, T247, T250, T248, T249, T194, p134_in_ggggag(T246, T249, T247, T248, T250, T194))
p1_in_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_ag(T267, T268, T269, T270, p137_in_gggg(T267, T270, T268, T269))
p1_in_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1)))) → U62_ag(T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0)))) → U63_ag(T300, T293, T294, p1_in_gg(d(e(T293)), T294))
p1_in_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(T317, T318, T293, T294, T319, T320, p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(T337, T338, T293, T294, T339, T340, p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U56_gg(T197, T194, p1_out_gg(d(e(T197)), T194)) → p1_out_gg(d(e(+(t, T197))), +(const(1), T194))
U57_gg(T202, T203, T194, p1_out_gg(d(e(T203)), T194)) → p1_out_gg(d(e(+(const(T202), T203))), +(const(0), T194))
U58_gg(T224, T225, T226, T222, T223, T194, p134_out_gggggg(T224, T222, T225, T223, T226, T194)) → p1_out_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U59_gg(T246, T247, T250, T248, T249, T194, p134_out_gggggg(T246, T249, T247, T248, T250, T194)) → p1_out_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U60_gg(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U62_gg(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U63_gg(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_gg(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U64_gg(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_gg(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
U56_ag(T197, T194, p1_out_ag(d(e(T197)), T194)) → p1_out_ag(d(e(+(t, T197))), +(const(1), T194))
U57_ag(T202, T203, T194, p1_out_ag(d(e(T203)), T194)) → p1_out_ag(d(e(+(const(T202), T203))), +(const(0), T194))
U58_ag(T224, T225, T226, T222, T223, T194, p134_out_agagag(T224, T222, T225, T223, T226, T194)) → p1_out_ag(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194))
U59_ag(T246, T247, T250, T248, T249, T194, p134_out_ggggag(T246, T249, T247, T248, T250, T194)) → p1_out_ag(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194))
U60_ag(T267, T268, T269, T270, p137_out_gggg(T267, T270, T268, T269)) → p1_out_ag(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270)))
U62_ag(T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(t, T293))), +(*(t, T294), *(T293, const(1))))
U63_ag(T300, T293, T294, p1_out_gg(d(e(T293)), T294)) → p1_out_ag(d(e(*(const(T300), T293))), +(*(const(T300), T294), *(T293, const(0))))
U64_ag(T317, T318, T293, T294, T319, T320, p134_out_gggggg(T317, T319, T318, T320, T293, T294)) → p1_out_ag(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320))))
U65_ag(T337, T338, T293, T294, T339, T340, p134_out_gggggg(T337, T340, T338, T339, T293, T294)) → p1_out_ag(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340)))))
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
p134_in_agagag(T224, T222, T225, T223, T226, T194) → U45_agagag(T224, T222, T225, T223, T226, T194, p1_in_ag(d(e(T224)), T222))
p134_in_agagag(T224, T222, T227, T223, T228, T194) → U46_agagag(T224, T222, T227, T223, T228, T194, p1_in_ag(d(e(T224)), T222))
p134_in_ggggag(T224, T222, T225, T223, T226, T194) → U45_ggggag(T224, T222, T225, T223, T226, T194, p1_in_gg(d(e(T224)), T222))
p134_in_ggggag(T224, T222, T227, T223, T228, T194) → U46_ggggag(T224, T222, T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
U45_gggggg(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_gggggg(T224, T222, T225, T223, T226, T194)
U46_gggggg(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_gggggg(T224, T222, T227, T223, T228, T194, p137_in_gggg(T227, T223, T228, T194))
U48_gggg(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_gggg(T227, T223, T228, T194)
U49_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_gggg(T227, T223, T229, T194, p1_in_gg(d(e(T229)), T194))
U45_agagag(T224, T222, T225, T223, T226, T194, p1_out_ag(d(e(T224)), T222)) → p134_out_agagag(T224, T222, T225, T223, T226, T194)
U46_agagag(T224, T222, T227, T223, T228, T194, p1_out_ag(d(e(T224)), T222)) → U47_agagag(T224, T222, T227, T223, T228, T194, p137_in_agag(T227, T223, T228, T194))
U45_ggggag(T224, T222, T225, T223, T226, T194, p1_out_gg(d(e(T224)), T222)) → p134_out_ggggag(T224, T222, T225, T223, T226, T194)
U46_ggggag(T224, T222, T227, T223, T228, T194, p1_out_gg(d(e(T224)), T222)) → U47_ggggag(T224, T222, T227, T223, T228, T194, p137_in_ggag(T227, T223, T228, T194))
U47_gggggg(T224, T222, T227, T223, T228, T194, p137_out_gggg(T227, T223, T228, T194)) → p134_out_gggggg(T224, T222, T227, T223, T228, T194)
U50_gggg(T227, T223, T229, T194, p1_out_gg(d(e(T229)), T194)) → p137_out_gggg(T227, T223, T229, T194)
U47_agagag(T224, T222, T227, T223, T228, T194, p137_out_agag(T227, T223, T228, T194)) → p134_out_agagag(T224, T222, T227, T223, T228, T194)
U47_ggggag(T224, T222, T227, T223, T228, T194, p137_out_ggag(T227, T223, T228, T194)) → p134_out_ggggag(T224, T222, T227, T223, T228, T194)
p137_in_agag(T227, T223, T228, T194) → U48_agag(T227, T223, T228, T194, p1_in_ag(d(e(T227)), T223))
p137_in_agag(T227, T223, T229, T194) → U49_agag(T227, T223, T229, T194, p1_in_ag(d(e(T227)), T223))
p137_in_ggag(T227, T223, T228, T194) → U48_ggag(T227, T223, T228, T194, p1_in_gg(d(e(T227)), T223))
p137_in_ggag(T227, T223, T229, T194) → U49_ggag(T227, T223, T229, T194, p1_in_gg(d(e(T227)), T223))
U48_agag(T227, T223, T228, T194, p1_out_ag(d(e(T227)), T223)) → p137_out_agag(T227, T223, T228, T194)
U49_agag(T227, T223, T229, T194, p1_out_ag(d(e(T227)), T223)) → U50_agag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U48_ggag(T227, T223, T228, T194, p1_out_gg(d(e(T227)), T223)) → p137_out_ggag(T227, T223, T228, T194)
U49_ggag(T227, T223, T229, T194, p1_out_gg(d(e(T227)), T223)) → U50_ggag(T227, T223, T229, T194, p1_in_ag(d(e(T229)), T194))
U50_agag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_agag(T227, T223, T229, T194)
U50_ggag(T227, T223, T229, T194, p1_out_ag(d(e(T229)), T194)) → p137_out_ggag(T227, T223, T229, T194)

The argument filtering Pi contains the following mapping:
p1_in_ag(x1, x2)  =  p1_in_ag(x2)
const(x1)  =  const
1  =  1
p1_out_ag(x1, x2)  =  p1_out_ag
p1_in_gg(x1, x2)  =  p1_in_gg(x1, x2)
d(x1)  =  d(x1)
e(x1)  =  e(x1)
t  =  t
p1_out_gg(x1, x2)  =  p1_out_gg
0  =  0
+(x1, x2)  =  +(x1, x2)
U56_gg(x1, x2, x3)  =  U56_gg(x3)
U57_gg(x1, x2, x3, x4)  =  U57_gg(x4)
U58_gg(x1, x2, x3, x4, x5, x6, x7)  =  U58_gg(x7)
p134_in_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_in_gggggg(x1, x2, x3, x4, x5, x6)
U45_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U45_gggggg(x7)
*(x1, x2)  =  *(x1, x2)
U59_gg(x1, x2, x3, x4, x5, x6, x7)  =  U59_gg(x7)
U46_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U46_gggggg(x3, x4, x5, x6, x7)
U60_gg(x1, x2, x3, x4, x5)  =  U60_gg(x5)
p137_in_gggg(x1, x2, x3, x4)  =  p137_in_gggg(x1, x2, x3, x4)
U48_gggg(x1, x2, x3, x4, x5)  =  U48_gggg(x5)
U62_gg(x1, x2, x3)  =  U62_gg(x3)
U63_gg(x1, x2, x3, x4)  =  U63_gg(x4)
U64_gg(x1, x2, x3, x4, x5, x6, x7)  =  U64_gg(x7)
p134_out_gggggg(x1, x2, x3, x4, x5, x6)  =  p134_out_gggggg
U65_gg(x1, x2, x3, x4, x5, x6, x7)  =  U65_gg(x7)
U56_ag(x1, x2, x3)  =  U56_ag(x3)
U57_ag(x1, x2, x3, x4)  =  U57_ag(x4)
U58_ag(x1, x2, x3, x4, x5, x6, x7)  =  U58_ag(x7)
p134_in_agagag(x1, x2, x3, x4, x5, x6)  =  p134_in_agagag(x2, x4, x6)
U45_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U45_agagag(x7)
U59_ag(x1, x2, x3, x4, x5, x6, x7)  =  U59_ag(x7)
p134_in_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_in_ggggag(x1, x2, x3, x4, x6)
U45_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U45_ggggag(x7)
U60_ag(x1, x2, x3, x4, x5)  =  U60_ag(x5)
U49_gggg(x1, x2, x3, x4, x5)  =  U49_gggg(x3, x4, x5)
U62_ag(x1, x2, x3)  =  U62_ag(x3)
U63_ag(x1, x2, x3, x4)  =  U63_ag(x4)
U64_ag(x1, x2, x3, x4, x5, x6, x7)  =  U64_ag(x7)
U65_ag(x1, x2, x3, x4, x5, x6, x7)  =  U65_ag(x7)
U50_gggg(x1, x2, x3, x4, x5)  =  U50_gggg(x5)
p137_out_gggg(x1, x2, x3, x4)  =  p137_out_gggg
p134_out_ggggag(x1, x2, x3, x4, x5, x6)  =  p134_out_ggggag
U46_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U46_ggggag(x3, x4, x6, x7)
U47_ggggag(x1, x2, x3, x4, x5, x6, x7)  =  U47_ggggag(x7)
p137_in_ggag(x1, x2, x3, x4)  =  p137_in_ggag(x1, x2, x4)
U48_ggag(x1, x2, x3, x4, x5)  =  U48_ggag(x5)
p137_out_ggag(x1, x2, x3, x4)  =  p137_out_ggag
U49_ggag(x1, x2, x3, x4, x5)  =  U49_ggag(x4, x5)
U50_ggag(x1, x2, x3, x4, x5)  =  U50_ggag(x5)
p134_out_agagag(x1, x2, x3, x4, x5, x6)  =  p134_out_agagag
U46_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U46_agagag(x4, x6, x7)
U47_agagag(x1, x2, x3, x4, x5, x6, x7)  =  U47_agagag(x7)
p137_in_agag(x1, x2, x3, x4)  =  p137_in_agag(x2, x4)
U48_agag(x1, x2, x3, x4, x5)  =  U48_agag(x5)
p137_out_agag(x1, x2, x3, x4)  =  p137_out_agag
U49_agag(x1, x2, x3, x4, x5)  =  U49_agag(x4, x5)
U50_agag(x1, x2, x3, x4, x5)  =  U50_agag(x5)
U47_gggggg(x1, x2, x3, x4, x5, x6, x7)  =  U47_gggggg(x7)
P1_IN_AG(x1, x2)  =  P1_IN_AG(x2)
P134_IN_AGAGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_AGAGAG(x2, x4, x6)
P134_IN_GGGGAG(x1, x2, x3, x4, x5, x6)  =  P134_IN_GGGGAG(x1, x2, x3, x4, x6)
U46_GGGGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_GGGGAG(x3, x4, x6, x7)
P137_IN_GGAG(x1, x2, x3, x4)  =  P137_IN_GGAG(x1, x2, x4)
U49_GGAG(x1, x2, x3, x4, x5)  =  U49_GGAG(x4, x5)
U46_AGAGAG(x1, x2, x3, x4, x5, x6, x7)  =  U46_AGAGAG(x4, x6, x7)
P137_IN_AGAG(x1, x2, x3, x4)  =  P137_IN_AGAG(x2, x4)
U49_AGAG(x1, x2, x3, x4, x5)  =  U49_AGAG(x4, x5)

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

(99) PiDPToQDPProof (SOUND transformation)

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

(100) Obligation:

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

P134_IN_GGGGAG(T224, T222, T227, T223, T194) → U46_GGGGAG(T227, T223, T194, p1_in_gg(d(e(T224)), T222))
U46_GGGGAG(T227, T223, T194, p1_out_gg) → P137_IN_GGAG(T227, T223, T194)
P137_IN_GGAG(T227, T223, T194) → U49_GGAG(T194, p1_in_gg(d(e(T227)), T223))
U49_GGAG(T194, p1_out_gg) → P1_IN_AG(T194)
P1_IN_AG(+(const, T194)) → P1_IN_AG(T194)
P1_IN_AG(+(+(T222, T223), T194)) → P134_IN_AGAGAG(T222, T223, T194)
P134_IN_AGAGAG(T222, T223, T194) → P1_IN_AG(T222)
P1_IN_AG(+(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T194)
P134_IN_AGAGAG(T222, T223, T194) → U46_AGAGAG(T223, T194, p1_in_ag(T222))
U46_AGAGAG(T223, T194, p1_out_ag) → P137_IN_AGAG(T223, T194)
P137_IN_AGAG(T223, T194) → P1_IN_AG(T223)
P137_IN_AGAG(T223, T194) → U49_AGAG(T194, p1_in_ag(T223))
U49_AGAG(T194, p1_out_ag) → P1_IN_AG(T194)

The TRS R consists of the following rules:

p1_in_gg(d(e(t)), const) → p1_out_gg
p1_in_gg(d(e(const)), const) → p1_out_gg
p1_in_gg(d(e(+(t, T197))), +(const, T194)) → U56_gg(p1_in_gg(d(e(T197)), T194))
p1_in_gg(d(e(+(const, T203))), +(const, T194)) → U57_gg(p1_in_gg(d(e(T203)), T194))
p1_in_gg(d(e(+(+(T224, T225), T226))), +(+(T222, T223), T194)) → U58_gg(p134_in_gggggg(T224, T222, T225, T223, T226, T194))
p1_in_gg(d(e(+(*(T246, T247), T250))), +(+(*(T246, T248), *(T247, T249)), T194)) → U59_gg(p134_in_gggggg(T246, T249, T247, T248, T250, T194))
p1_in_gg(d(e(*(T267, T268))), +(*(T267, T269), *(T268, T270))) → U60_gg(p137_in_gggg(T267, T270, T268, T269))
p1_in_gg(d(e(*(t, T293))), +(*(t, T294), *(T293, const))) → U62_gg(p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(const, T293))), +(*(const, T294), *(T293, const))) → U63_gg(p1_in_gg(d(e(T293)), T294))
p1_in_gg(d(e(*(+(T317, T318), T293))), +(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_gg(p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_gg(d(e(*(*(T337, T338), T293))), +(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_gg(p134_in_gggggg(T337, T340, T338, T339, T293, T294))
p1_in_ag(const) → p1_out_ag
p1_in_ag(+(const, T194)) → U56_ag(p1_in_ag(T194))
p1_in_ag(+(const, T194)) → U57_ag(p1_in_ag(T194))
p1_in_ag(+(+(T222, T223), T194)) → U58_ag(p134_in_agagag(T222, T223, T194))
p1_in_ag(+(+(*(T246, T248), *(T247, T249)), T194)) → U59_ag(p134_in_ggggag(T246, T249, T247, T248, T194))
p1_in_ag(+(*(T267, T269), *(T268, T270))) → U60_ag(p137_in_gggg(T267, T270, T268, T269))
p1_in_ag(+(*(t, T294), *(T293, const))) → U62_ag(p1_in_gg(d(e(T293)), T294))
p1_in_ag(+(*(const, T294), *(T293, const))) → U63_ag(p1_in_gg(d(e(T293)), T294))
p1_in_ag(+(*(+(T317, T318), T294), *(T293, +(T319, T320)))) → U64_ag(p134_in_gggggg(T317, T319, T318, T320, T293, T294))
p1_in_ag(+(*(*(T337, T338), T294), *(T293, +(*(T337, T339), *(T338, T340))))) → U65_ag(p134_in_gggggg(T337, T340, T338, T339, T293, T294))
U56_gg(p1_out_gg) → p1_out_gg
U57_gg(p1_out_gg) → p1_out_gg
U58_gg(p134_out_gggggg) → p1_out_gg
U59_gg(p134_out_gggggg) → p1_out_gg
U60_gg(p137_out_gggg) → p1_out_gg
U62_gg(p1_out_gg) → p1_out_gg
U63_gg(p1_out_gg) → p1_out_gg
U64_gg(p134_out_gggggg) → p1_out_gg
U65_gg(p134_out_gggggg) → p1_out_gg
U56_ag(p1_out_ag) → p1_out_ag
U57_ag(p1_out_ag) → p1_out_ag
U58_ag(p134_out_agagag) → p1_out_ag
U59_ag(p134_out_ggggag) → p1_out_ag
U60_ag(p137_out_gggg) → p1_out_ag
U62_ag(p1_out_gg) → p1_out_ag
U63_ag(p1_out_gg) → p1_out_ag
U64_ag(p134_out_gggggg) → p1_out_ag
U65_ag(p134_out_gggggg) → p1_out_ag
p134_in_gggggg(T224, T222, T225, T223, T226, T194) → U45_gggggg(p1_in_gg(d(e(T224)), T222))
p134_in_gggggg(T224, T222, T227, T223, T228, T194) → U46_gggggg(T227, T223, T228, T194, p1_in_gg(d(e(T224)), T222))
p137_in_gggg(T227, T223, T228, T194) → U48_gggg(p1_in_gg(d(e(T227)), T223))
p137_in_gggg(T227, T223, T229, T194) → U49_gggg(T229, T194, p1_in_gg(d(e(T227)), T223))
p134_in_agagag(T222, T223, T194) → U45_agagag(p1_in_ag(T222))
p134_in_agagag(T222, T223, T194) → U46_agagag(T223, T194, p1_in_ag(T222))
p134_in_ggggag(T224, T222, T225, T223, T194) → U45_ggggag(p1_in_gg(d(e(T224)), T222))
p134_in_ggggag(T224, T222, T227, T223, T194) → U46_ggggag(T227, T223, T194, p1_in_gg(d(e(T224)), T222))
U45_gggggg(p1_out_gg) → p134_out_gggggg
U46_gggggg(T227, T223, T228, T194, p1_out_gg) → U47_gggggg(p137_in_gggg(T227, T223, T228, T194))
U48_gggg(p1_out_gg) → p137_out_gggg
U49_gggg(T229, T194, p1_out_gg) → U50_gggg(p1_in_gg(d(e(T229)), T194))
U45_agagag(p1_out_ag) → p134_out_agagag
U46_agagag(T223, T194, p1_out_ag) → U47_agagag(p137_in_agag(T223, T194))
U45_ggggag(p1_out_gg) → p134_out_ggggag
U46_ggggag(T227, T223, T194, p1_out_gg) → U47_ggggag(p137_in_ggag(T227, T223, T194))
U47_gggggg(p137_out_gggg) → p134_out_gggggg
U50_gggg(p1_out_gg) → p137_out_gggg
U47_agagag(p137_out_agag) → p134_out_agagag
U47_ggggag(p137_out_ggag) → p134_out_ggggag
p137_in_agag(T223, T194) → U48_agag(p1_in_ag(T223))
p137_in_agag(T223, T194) → U49_agag(T194, p1_in_ag(T223))
p137_in_ggag(T227, T223, T194) → U48_ggag(p1_in_gg(d(e(T227)), T223))
p137_in_ggag(T227, T223, T194) → U49_ggag(T194, p1_in_gg(d(e(T227)), T223))
U48_agag(p1_out_ag) → p137_out_agag
U49_agag(T194, p1_out_ag) → U50_agag(p1_in_ag(T194))
U48_ggag(p1_out_gg) → p137_out_ggag
U49_ggag(T194, p1_out_gg) → U50_ggag(p1_in_ag(T194))
U50_agag(p1_out_ag) → p137_out_agag
U50_ggag(p1_out_ag) → p137_out_ggag

The set Q consists of the following terms:

p1_in_gg(x0, x1)
p1_in_ag(x0)
U56_gg(x0)
U57_gg(x0)
U58_gg(x0)
U59_gg(x0)
U60_gg(x0)
U62_gg(x0)
U63_gg(x0)
U64_gg(x0)
U65_gg(x0)
U56_ag(x0)
U57_ag(x0)
U58_ag(x0)
U59_ag(x0)
U60_ag(x0)
U62_ag(x0)
U63_ag(x0)
U64_ag(x0)
U65_ag(x0)
p134_in_gggggg(x0, x1, x2, x3, x4, x5)
p137_in_gggg(x0, x1, x2, x3)
p134_in_agagag(x0, x1, x2)
p134_in_ggggag(x0, x1, x2, x3, x4)
U45_gggggg(x0)
U46_gggggg(x0, x1, x2, x3, x4)
U48_gggg(x0)
U49_gggg(x0, x1, x2)
U45_agagag(x0)
U46_agagag(x0, x1, x2)
U45_ggggag(x0)
U46_ggggag(x0, x1, x2, x3)
U47_gggggg(x0)
U50_gggg(x0)
U47_agagag(x0)
U47_ggggag(x0)
p137_in_agag(x0, x1)
p137_in_ggag(x0, x1, x2)
U48_agag(x0)
U49_agag(x0, x1)
U48_ggag(x0)
U49_ggag(x0, x1)
U50_agag(x0)
U50_ggag(x0)

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

(101) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

• U46_GGGGAG(T227, T223, T194, p1_out_gg) → P137_IN_GGAG(T227, T223, T194)
  The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3

• P1_IN_AG(+(+(*(T246, T248), *(T247, T249)), T194)) → P134_IN_GGGGAG(T246, T249, T247, T248, T194)
  The graph contains the following edges 1 > 1, 1 > 2, 1 > 3, 1 > 4, 1 > 5

• P137_IN_GGAG(T227, T223, T194) → U49_GGAG(T194, p1_in_gg(d(e(T227)), T223))
  The graph contains the following edges 3 >= 1

• P134_IN_GGGGAG(T224, T222, T227, T223, T194) → U46_GGGGAG(T227, T223, T194, p1_in_gg(d(e(T224)), T222))
  The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3

• U49_GGAG(T194, p1_out_gg) → P1_IN_AG(T194)
  The graph contains the following edges 1 >= 1

• P1_IN_AG(+(const, T194)) → P1_IN_AG(T194)
  The graph contains the following edges 1 > 1

• P1_IN_AG(+(+(T222, T223), T194)) → P134_IN_AGAGAG(T222, T223, T194)
  The graph contains the following edges 1 > 1, 1 > 2, 1 > 3

• P134_IN_AGAGAG(T222, T223, T194) → P1_IN_AG(T222)
  The graph contains the following edges 1 >= 1

• P134_IN_AGAGAG(T222, T223, T194) → U46_AGAGAG(T223, T194, p1_in_ag(T222))
  The graph contains the following edges 2 >= 1, 3 >= 2

• U46_AGAGAG(T223, T194, p1_out_ag) → P137_IN_AGAG(T223, T194)
  The graph contains the following edges 1 >= 1, 2 >= 2

• P137_IN_AGAG(T223, T194) → U49_AGAG(T194, p1_in_ag(T223))
  The graph contains the following edges 2 >= 1

• P137_IN_AGAG(T223, T194) → P1_IN_AG(T223)
  The graph contains the following edges 1 >= 1

• U49_AGAG(T194, p1_out_ag) → P1_IN_AG(T194)
  The graph contains the following edges 1 >= 1

(102) YES