Left Termination of the query pattern e_in_2(g, a) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

e(L, T) :- t(L, T).
e(L, T) :- ','(t(L, .(plus, C)), e(C, T)).
t(L, T) :- n(L, T).
t(L, T) :- ','(n(L, .(star, C)), t(C, T)).
n(.(L, T), T) :- z(L).
n(.(lbrace, A), B) :- e(A, .(rbrace, B)).
z(a).
z(b).
z(c).

Queries:

e(g,a).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: e(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: e(T1, T2), SCOPE: 1, CLAUSE: 0 | e(T1, T2), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: t(T5, T7) | e(T5, T2), SCOPE: 1, CLAUSE: 1\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: t(T5, T7), SCOPE: 2, CLAUSE: 2 | t(T5, T7), SCOPE: 2, CLAUSE: 3 | ?_2 | e(T5, T2), SCOPE: 1, CLAUSE: 1\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: t(T5, T7), SCOPE: 2, CLAUSE: 2\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: t(T5, T7), SCOPE: 2, CLAUSE: 3 | ?_2 | e(T5, T2), SCOPE: 1, CLAUSE: 1\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: n(T22, T24)\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: n(T22, T24), SCOPE: 3, CLAUSE: 4 | n(T22, T24), SCOPE: 3, CLAUSE: 5\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: n(T22, T24), SCOPE: 3, CLAUSE: 4\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: n(T22, T24), SCOPE: 3, CLAUSE: 5\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: z(T35)\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: z(T35), SCOPE: 4, CLAUSE: 6 | z(T35), SCOPE: 4, CLAUSE: 7 | z(T35), SCOPE: 4, CLAUSE: 8\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: z(T35), SCOPE: 4, CLAUSE: 6\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: z(T35), SCOPE: 4, CLAUSE: 7 | z(T35), SCOPE: 4, CLAUSE: 8\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: z(T35), SCOPE: 4, CLAUSE: 7\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: z(T35), SCOPE: 4, CLAUSE: 8\n\nT35 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: e(T41, .(rbrace, T43))\n\nT41 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: t(T5, T7), SCOPE: 2, CLAUSE: 3\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: ?_2 | e(T5, T2), SCOPE: 1, CLAUSE: 1\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(n(T62, .(star, X59)), t(X59, T64))\n\nT62 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: n(T62, .(star, X59))\n\nT62 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: t(T68, T64)\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: n(T62, .(star, X59)), SCOPE: 5, CLAUSE: 4 | n(T62, .(star, X59)), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: n(T62, .(star, X59)), SCOPE: 5, CLAUSE: 4\n\nT62 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: n(T62, .(star, X59)), SCOPE: 5, CLAUSE: 5\n\nT62 is ground\nX59 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: z(T84)\n\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: z(T84), SCOPE: 6, CLAUSE: 6 | z(T84), SCOPE: 6, CLAUSE: 7 | z(T84), SCOPE: 6, CLAUSE: 8\n\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: z(T84), SCOPE: 6, CLAUSE: 6\n\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: z(T84), SCOPE: 6, CLAUSE: 7 | z(T84), SCOPE: 6, CLAUSE: 8\n\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: z(T84), SCOPE: 6, CLAUSE: 7\n\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: z(T84), SCOPE: 6, CLAUSE: 8\n\nT84 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: e(T89, .(rbrace, .(star, X84)))\n\nT89 is ground\nX84 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: e(T89, .(rbrace, .(star, X84))), SCOPE: 7, CLAUSE: 0 | e(T89, .(rbrace, .(star, X84))), SCOPE: 7, CLAUSE: 1\n\nT89 is ground\nX84 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: e(T89, .(rbrace, .(star, X84))), SCOPE: 7, CLAUSE: 0\n\nT89 is ground\nX84 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: e(T89, .(rbrace, .(star, X84))), SCOPE: 7, CLAUSE: 1\n\nT89 is ground\nX84 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: t(T97, .(rbrace, .(star, X110)))\n\nT97 is ground\nX110 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: t(T97, .(rbrace, .(star, X110))), SCOPE: 8, CLAUSE: 2 | t(T97, .(rbrace, .(star, X110))), SCOPE: 8, CLAUSE: 3\n\nT97 is ground\nX110 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: t(T97, .(rbrace, .(star, X110))), SCOPE: 8, CLAUSE: 2\n\nT97 is ground\nX110 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: t(T97, .(rbrace, .(star, X110))), SCOPE: 8, CLAUSE: 3\n\nT97 is ground\nX110 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: n(T109, .(rbrace, .(star, X132)))\n\nT109 is ground\nX132 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: n(T109, .(rbrace, .(star, X132))), SCOPE: 9, CLAUSE: 4 | n(T109, .(rbrace, .(star, X132))), SCOPE: 9, CLAUSE: 5\n\nT109 is ground\nX132 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: n(T109, .(rbrace, .(star, X132))), SCOPE: 9, CLAUSE: 4\n\nT109 is ground\nX132 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: n(T109, .(rbrace, .(star, X132))), SCOPE: 9, CLAUSE: 5\n\nT109 is ground\nX132 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: z(T125)\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: z(T125), SCOPE: 10, CLAUSE: 6 | z(T125), SCOPE: 10, CLAUSE: 7 | z(T125), SCOPE: 10, CLAUSE: 8\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: z(T125), SCOPE: 10, CLAUSE: 6\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: z(T125), SCOPE: 10, CLAUSE: 7 | z(T125), SCOPE: 10, CLAUSE: 8\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: z(T125), SCOPE: 10, CLAUSE: 7\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: z(T125), SCOPE: 10, CLAUSE: 8\n\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: e(T130, .(rbrace, .(rbrace, .(star, X155))))\n\nT130 is ground\nX155 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: e(T130, .(rbrace, .(rbrace, .(star, X155)))), SCOPE: 11, CLAUSE: 0 | e(T130, .(rbrace, .(rbrace, .(star, X155)))), SCOPE: 11, CLAUSE: 1\n\nT130 is ground\nX155 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: e(T130, .(rbrace, .(rbrace, .(star, X155)))), SCOPE: 11, CLAUSE: 0\n\nT130 is ground\nX155 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: e(T130, .(rbrace, .(rbrace, .(star, X155)))), SCOPE: 11, CLAUSE: 1\n\nT130 is ground\nX155 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: t(T138, .(rbrace, .(rbrace, .(star, X181))))\n\nT138 is ground\nX181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: t(T138, .(rbrace, .(rbrace, .(star, X181)))), SCOPE: 12, CLAUSE: 2 | t(T138, .(rbrace, .(rbrace, .(star, X181)))), SCOPE: 12, CLAUSE: 3\n\nT138 is ground\nX181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: t(T138, .(rbrace, .(rbrace, .(star, X181)))), SCOPE: 12, CLAUSE: 2\n\nT138 is ground\nX181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: t(T138, .(rbrace, .(rbrace, .(star, X181)))), SCOPE: 12, CLAUSE: 3\n\nT138 is ground\nX181 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: n(T150, .(rbrace, .(rbrace, .(star, X203))))\n\nT150 is ground\nX203 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: n(T150, .(rbrace, .(rbrace, .(star, X203)))), SCOPE: 13, CLAUSE: 4 | n(T150, .(rbrace, .(rbrace, .(star, X203)))), SCOPE: 13, CLAUSE: 5\n\nT150 is ground\nX203 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: n(T150, .(rbrace, .(rbrace, .(star, X203)))), SCOPE: 13, CLAUSE: 4\n\nT150 is ground\nX203 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: n(T150, .(rbrace, .(rbrace, .(star, X203)))), SCOPE: 13, CLAUSE: 5\n\nT150 is ground\nX203 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: z(T166)\n\nT166 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: z(T166), SCOPE: 14, CLAUSE: 6 | z(T166), SCOPE: 14, CLAUSE: 7 | z(T166), SCOPE: 14, CLAUSE: 8\n\nT166 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: z(T166), SCOPE: 14, CLAUSE: 6\n\nT166 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: z(T166), SCOPE: 14, CLAUSE: 7 | z(T166), SCOPE: 14, CLAUSE: 8\n\nT166 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: z(T166), SCOPE: 14, CLAUSE: 7\n\nT166 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: z(T166), SCOPE: 14, CLAUSE: 8\n\nT166 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: e(T171, .(rbrace, .(rbrace, .(rbrace, .(star, X226)))))\n\nT171 is ground\nX226 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: e(T171, .(rbrace, .(rbrace, .(rbrace, .(star, X226))))), SCOPE: 15, CLAUSE: 0 | e(T171, .(rbrace, .(rbrace, .(rbrace, .(star, X226))))), SCOPE: 15, CLAUSE: 1\n\nT171 is ground\nX226 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: e(T171, .(rbrace, .(rbrace, .(rbrace, .(star, X226))))), SCOPE: 15, CLAUSE: 0\n\nT171 is ground\nX226 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: e(T171, .(rbrace, .(rbrace, .(rbrace, .(star, X226))))), SCOPE: 15, CLAUSE: 1\n\nT171 is ground\nX226 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: t(T179, .(rbrace, .(rbrace, .(rbrace, .(star, X252)))))\n\nT179 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: t(T179, .(rbrace, .(rbrace, .(rbrace, .(star, X252))))), SCOPE: 16, CLAUSE: 2 | t(T179, .(rbrace, .(rbrace, .(rbrace, .(star, X252))))), SCOPE: 16, CLAUSE: 3\n\nT179 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: t(T179, .(rbrace, .(rbrace, .(rbrace, .(star, X252))))), SCOPE: 16, CLAUSE: 2\n\nT179 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: t(T179, .(rbrace, .(rbrace, .(rbrace, .(star, X252))))), SCOPE: 16, CLAUSE: 3\n\nT179 is ground\nX252 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: n(T191, .(rbrace, .(rbrace, .(rbrace, .(star, X274)))))\n\nT191 is ground\nX274 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: n(T191, .(rbrace, .(rbrace, .(rbrace, .(star, X274))))), SCOPE: 17, CLAUSE: 4 | n(T191, .(rbrace, .(rbrace, .(rbrace, .(star, X274))))), SCOPE: 17, CLAUSE: 5\n\nT191 is ground\nX274 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: n(T191, .(rbrace, .(rbrace, .(rbrace, .(star, X274))))), SCOPE: 17, CLAUSE: 4\n\nT191 is ground\nX274 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: n(T191, .(rbrace, .(rbrace, .(rbrace, .(star, X274))))), SCOPE: 17, CLAUSE: 5\n\nT191 is ground\nX274 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: z(T207)\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: z(T207), SCOPE: 18, CLAUSE: 6 | z(T207), SCOPE: 18, CLAUSE: 7 | z(T207), SCOPE: 18, CLAUSE: 8\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: z(T207), SCOPE: 18, CLAUSE: 6\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: z(T207), SCOPE: 18, CLAUSE: 7 | z(T207), SCOPE: 18, CLAUSE: 8\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: z(T207), SCOPE: 18, CLAUSE: 7\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: z(T207), SCOPE: 18, CLAUSE: 8\n\nT207 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: e(T212, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X297))))))\n\nT212 is ground\nX297 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: e(T212, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X297)))))), SCOPE: 19, CLAUSE: 0 | e(T212, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X297)))))), SCOPE: 19, CLAUSE: 1\n\nT212 is ground\nX297 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: e(T212, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X297)))))), SCOPE: 19, CLAUSE: 0\n\nT212 is ground\nX297 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: e(T212, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X297)))))), SCOPE: 19, CLAUSE: 1\n\nT212 is ground\nX297 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: t(T220, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X323))))))\n\nT220 is ground\nX323 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: t(T220, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X323)))))), SCOPE: 20, CLAUSE: 2 | t(T220, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X323)))))), SCOPE: 20, CLAUSE: 3\n\nT220 is ground\nX323 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: t(T220, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X323)))))), SCOPE: 20, CLAUSE: 2\n\nT220 is ground\nX323 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: t(T220, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X323)))))), SCOPE: 20, CLAUSE: 3\n\nT220 is ground\nX323 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: n(T232, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X345))))))\n\nT232 is ground\nX345 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: n(T232, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X345)))))), SCOPE: 21, CLAUSE: 4 | n(T232, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X345)))))), SCOPE: 21, CLAUSE: 5\n\nT232 is ground\nX345 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: n(T232, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X345)))))), SCOPE: 21, CLAUSE: 4\n\nT232 is ground\nX345 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: n(T232, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X345)))))), SCOPE: 21, CLAUSE: 5\n\nT232 is ground\nX345 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: z(T248)\n\nT248 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: z(T248), SCOPE: 22, CLAUSE: 6 | z(T248), SCOPE: 22, CLAUSE: 7 | z(T248), SCOPE: 22, CLAUSE: 8\n\nT248 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: z(T248), SCOPE: 22, CLAUSE: 6\n\nT248 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: z(T248), SCOPE: 22, CLAUSE: 7 | z(T248), SCOPE: 22, CLAUSE: 8\n\nT248 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: z(T248), SCOPE: 22, CLAUSE: 7\n\nT248 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: z(T248), SCOPE: 22, CLAUSE: 8\n\nT248 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: e(T253, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X368)))))))\n\nT253 is ground\nX368 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: e(T253, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X368))))))), SCOPE: 23, CLAUSE: 0 | e(T253, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X368))))))), SCOPE: 23, CLAUSE: 1\n\nT253 is ground\nX368 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: e(T253, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X368))))))), SCOPE: 23, CLAUSE: 0\n\nT253 is ground\nX368 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: e(T253, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X368))))))), SCOPE: 23, CLAUSE: 1\n\nT253 is ground\nX368 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: t(T261, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X394)))))))\n\nT261 is ground\nX394 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: t(T261, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X394))))))), SCOPE: 24, CLAUSE: 2 | t(T261, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X394))))))), SCOPE: 24, CLAUSE: 3\n\nT261 is ground\nX394 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: t(T261, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X394))))))), SCOPE: 24, CLAUSE: 2\n\nT261 is ground\nX394 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: t(T261, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X394))))))), SCOPE: 24, CLAUSE: 3\n\nT261 is ground\nX394 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: n(T273, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X416)))))))\n\nT273 is ground\nX416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: n(T273, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X416))))))), SCOPE: 25, CLAUSE: 4 | n(T273, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X416))))))), SCOPE: 25, CLAUSE: 5\n\nT273 is ground\nX416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: n(T273, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X416))))))), SCOPE: 25, CLAUSE: 4\n\nT273 is ground\nX416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: n(T273, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X416))))))), SCOPE: 25, CLAUSE: 5\n\nT273 is ground\nX416 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: z(T289)\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: z(T289), SCOPE: 26, CLAUSE: 6 | z(T289), SCOPE: 26, CLAUSE: 7 | z(T289), SCOPE: 26, CLAUSE: 8\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: z(T289), SCOPE: 26, CLAUSE: 6\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: z(T289), SCOPE: 26, CLAUSE: 7 | z(T289), SCOPE: 26, CLAUSE: 8\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: z(T289), SCOPE: 26, CLAUSE: 7\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: z(T289), SCOPE: 26, CLAUSE: 8\n\nT289 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: e(T294, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X439))))))))\n\nT294 is ground\nX439 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: e(T294, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X439)))))))), SCOPE: 27, CLAUSE: 0 | e(T294, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X439)))))))), SCOPE: 27, CLAUSE: 1\n\nT294 is ground\nX439 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: e(T294, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X439)))))))), SCOPE: 27, CLAUSE: 0\n\nT294 is ground\nX439 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: e(T294, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X439)))))))), SCOPE: 27, CLAUSE: 1\n\nT294 is ground\nX439 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: t(T302, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X465))))))))\n\nT302 is ground\nX465 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: t(T302, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X465)))))))), SCOPE: 28, CLAUSE: 2 | t(T302, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X465)))))))), SCOPE: 28, CLAUSE: 3\n\nT302 is ground\nX465 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: t(T302, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X465)))))))), SCOPE: 28, CLAUSE: 2\n\nT302 is ground\nX465 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: t(T302, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X465)))))))), SCOPE: 28, CLAUSE: 3\n\nT302 is ground\nX465 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: n(T314, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X487))))))))\n\nT314 is ground\nX487 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: n(T314, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X487)))))))), SCOPE: 29, CLAUSE: 4 | n(T314, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X487)))))))), SCOPE: 29, CLAUSE: 5\n\nT314 is ground\nX487 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: n(T314, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X487)))))))), SCOPE: 29, CLAUSE: 4\n\nT314 is ground\nX487 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: n(T314, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X487)))))))), SCOPE: 29, CLAUSE: 5\n\nT314 is ground\nX487 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: z(T330)\n\nT330 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: z(T330), SCOPE: 30, CLAUSE: 6 | z(T330), SCOPE: 30, CLAUSE: 7 | z(T330), SCOPE: 30, CLAUSE: 8\n\nT330 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: z(T330), SCOPE: 30, CLAUSE: 6\n\nT330 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: z(T330), SCOPE: 30, CLAUSE: 7 | z(T330), SCOPE: 30, CLAUSE: 8\n\nT330 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: z(T330), SCOPE: 30, CLAUSE: 7\n\nT330 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: z(T330), SCOPE: 30, CLAUSE: 8\n\nT330 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
227 [label="227: e(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))\n\nT335 is ground\nX510 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
229 [label="229: e(T335, .(rbrace, T337))\n\nT335 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: ','(n(T345, .(star, X529)), t(X529, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X530)))))))))\n\nT345 is ground\nX530 is free; \nX529 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: n(T345, .(star, X529))\n\nT345 is ground\nX529 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: t(T349, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X530))))))))\n\nT349 is ground\nX530 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: ','(t(T357, .(plus, X550)), e(X550, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X551)))))))))\n\nT357 is ground\nX551 is free; \nX550 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: t(T357, .(plus, X550))\n\nT357 is ground\nX550 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: e(T359, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X551))))))))\n\nT359 is ground\nX551 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: t(T357, .(plus, X550)), SCOPE: 31, CLAUSE: 2 | t(T357, .(plus, X550)), SCOPE: 31, CLAUSE: 3\n\nT357 is ground\nX550 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: t(T357, .(plus, X550)), SCOPE: 31, CLAUSE: 2\n\nT357 is ground\nX550 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: t(T357, .(plus, X550)), SCOPE: 31, CLAUSE: 3\n\nT357 is ground\nX550 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: n(T371, .(plus, X576))\n\nT371 is ground\nX576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: n(T371, .(plus, X576)), SCOPE: 32, CLAUSE: 4 | n(T371, .(plus, X576)), SCOPE: 32, CLAUSE: 5\n\nT371 is ground\nX576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="241: n(T371, .(plus, X576)), SCOPE: 32, CLAUSE: 4\n\nT371 is ground\nX576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: n(T371, .(plus, X576)), SCOPE: 32, CLAUSE: 5\n\nT371 is ground\nX576 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: z(T387)\n\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: z(T387), SCOPE: 33, CLAUSE: 6 | z(T387), SCOPE: 33, CLAUSE: 7 | z(T387), SCOPE: 33, CLAUSE: 8\n\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: z(T387), SCOPE: 33, CLAUSE: 6\n\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
247 [label="247: z(T387), SCOPE: 33, CLAUSE: 7 | z(T387), SCOPE: 33, CLAUSE: 8\n\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
251 [label="251: z(T387), SCOPE: 33, CLAUSE: 7\n\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: z(T387), SCOPE: 33, CLAUSE: 8\n\nT387 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
257 [label="257: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: e(T392, .(rbrace, .(plus, X599)))\n\nT392 is ground\nX599 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: e(T392, .(rbrace, .(plus, X599))), SCOPE: 34, CLAUSE: 0 | e(T392, .(rbrace, .(plus, X599))), SCOPE: 34, CLAUSE: 1\n\nT392 is ground\nX599 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: e(T392, .(rbrace, .(plus, X599))), SCOPE: 34, CLAUSE: 0\n\nT392 is ground\nX599 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: e(T392, .(rbrace, .(plus, X599))), SCOPE: 34, CLAUSE: 1\n\nT392 is ground\nX599 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: t(T400, .(rbrace, .(plus, X625)))\n\nT400 is ground\nX625 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: t(T400, .(rbrace, .(plus, X625))), SCOPE: 35, CLAUSE: 2 | t(T400, .(rbrace, .(plus, X625))), SCOPE: 35, CLAUSE: 3\n\nT400 is ground\nX625 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: t(T400, .(rbrace, .(plus, X625))), SCOPE: 35, CLAUSE: 2\n\nT400 is ground\nX625 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: t(T400, .(rbrace, .(plus, X625))), SCOPE: 35, CLAUSE: 3\n\nT400 is ground\nX625 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
268 [label="268: n(T412, .(rbrace, .(plus, X647)))\n\nT412 is ground\nX647 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="269: n(T412, .(rbrace, .(plus, X647))), SCOPE: 36, CLAUSE: 4 | n(T412, .(rbrace, .(plus, X647))), SCOPE: 36, CLAUSE: 5\n\nT412 is ground\nX647 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: n(T412, .(rbrace, .(plus, X647))), SCOPE: 36, CLAUSE: 4\n\nT412 is ground\nX647 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: n(T412, .(rbrace, .(plus, X647))), SCOPE: 36, CLAUSE: 5\n\nT412 is ground\nX647 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
272 [label="272: z(T428)\n\nT428 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
274 [label="274: z(T428), SCOPE: 37, CLAUSE: 6 | z(T428), SCOPE: 37, CLAUSE: 7 | z(T428), SCOPE: 37, CLAUSE: 8\n\nT428 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: z(T428), SCOPE: 37, CLAUSE: 6\n\nT428 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: z(T428), SCOPE: 37, CLAUSE: 7 | z(T428), SCOPE: 37, CLAUSE: 8\n\nT428 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: z(T428), SCOPE: 37, CLAUSE: 7\n\nT428 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
281 [label="281: z(T428), SCOPE: 37, CLAUSE: 8\n\nT428 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
283 [label="283: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: e(T433, .(rbrace, .(rbrace, .(plus, X670))))\n\nT433 is ground\nX670 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
289 [label="289: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: e(T433, .(rbrace, .(rbrace, .(plus, X670)))), SCOPE: 38, CLAUSE: 0 | e(T433, .(rbrace, .(rbrace, .(plus, X670)))), SCOPE: 38, CLAUSE: 1\n\nT433 is ground\nX670 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
291 [label="291: e(T433, .(rbrace, .(rbrace, .(plus, X670)))), SCOPE: 38, CLAUSE: 0\n\nT433 is ground\nX670 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: e(T433, .(rbrace, .(rbrace, .(plus, X670)))), SCOPE: 38, CLAUSE: 1\n\nT433 is ground\nX670 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: t(T441, .(rbrace, .(rbrace, .(plus, X696))))\n\nT441 is ground\nX696 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
294 [label="294: t(T441, .(rbrace, .(rbrace, .(plus, X696)))), SCOPE: 39, CLAUSE: 2 | t(T441, .(rbrace, .(rbrace, .(plus, X696)))), SCOPE: 39, CLAUSE: 3\n\nT441 is ground\nX696 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
295 [label="295: t(T441, .(rbrace, .(rbrace, .(plus, X696)))), SCOPE: 39, CLAUSE: 2\n\nT441 is ground\nX696 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="296: t(T441, .(rbrace, .(rbrace, .(plus, X696)))), SCOPE: 39, CLAUSE: 3\n\nT441 is ground\nX696 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: n(T453, .(rbrace, .(rbrace, .(plus, X718))))\n\nT453 is ground\nX718 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: n(T453, .(rbrace, .(rbrace, .(plus, X718)))), SCOPE: 40, CLAUSE: 4 | n(T453, .(rbrace, .(rbrace, .(plus, X718)))), SCOPE: 40, CLAUSE: 5\n\nT453 is ground\nX718 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: n(T453, .(rbrace, .(rbrace, .(plus, X718)))), SCOPE: 40, CLAUSE: 4\n\nT453 is ground\nX718 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="300: n(T453, .(rbrace, .(rbrace, .(plus, X718)))), SCOPE: 40, CLAUSE: 5\n\nT453 is ground\nX718 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: z(T469)\n\nT469 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: z(T469), SCOPE: 41, CLAUSE: 6 | z(T469), SCOPE: 41, CLAUSE: 7 | z(T469), SCOPE: 41, CLAUSE: 8\n\nT469 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: z(T469), SCOPE: 41, CLAUSE: 6\n\nT469 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: z(T469), SCOPE: 41, CLAUSE: 7 | z(T469), SCOPE: 41, CLAUSE: 8\n\nT469 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: z(T469), SCOPE: 41, CLAUSE: 7\n\nT469 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: z(T469), SCOPE: 41, CLAUSE: 8\n\nT469 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
311 [label="311: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
312 [label="312: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
314 [label="314: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: e(T474, .(rbrace, .(rbrace, .(rbrace, .(plus, X741)))))\n\nT474 is ground\nX741 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="318: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
319 [label="319: e(T474, .(rbrace, .(rbrace, .(rbrace, .(plus, X741))))), SCOPE: 42, CLAUSE: 0 | e(T474, .(rbrace, .(rbrace, .(rbrace, .(plus, X741))))), SCOPE: 42, CLAUSE: 1\n\nT474 is ground\nX741 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: e(T474, .(rbrace, .(rbrace, .(rbrace, .(plus, X741))))), SCOPE: 42, CLAUSE: 0\n\nT474 is ground\nX741 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="321: e(T474, .(rbrace, .(rbrace, .(rbrace, .(plus, X741))))), SCOPE: 42, CLAUSE: 1\n\nT474 is ground\nX741 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: t(T482, .(rbrace, .(rbrace, .(rbrace, .(plus, X767)))))\n\nT482 is ground\nX767 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="323: t(T482, .(rbrace, .(rbrace, .(rbrace, .(plus, X767))))), SCOPE: 43, CLAUSE: 2 | t(T482, .(rbrace, .(rbrace, .(rbrace, .(plus, X767))))), SCOPE: 43, CLAUSE: 3\n\nT482 is ground\nX767 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: t(T482, .(rbrace, .(rbrace, .(rbrace, .(plus, X767))))), SCOPE: 43, CLAUSE: 2\n\nT482 is ground\nX767 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: t(T482, .(rbrace, .(rbrace, .(rbrace, .(plus, X767))))), SCOPE: 43, CLAUSE: 3\n\nT482 is ground\nX767 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
326 [label="326: n(T494, .(rbrace, .(rbrace, .(rbrace, .(plus, X789)))))\n\nT494 is ground\nX789 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
327 [label="327: n(T494, .(rbrace, .(rbrace, .(rbrace, .(plus, X789))))), SCOPE: 44, CLAUSE: 4 | n(T494, .(rbrace, .(rbrace, .(rbrace, .(plus, X789))))), SCOPE: 44, CLAUSE: 5\n\nT494 is ground\nX789 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: n(T494, .(rbrace, .(rbrace, .(rbrace, .(plus, X789))))), SCOPE: 44, CLAUSE: 4\n\nT494 is ground\nX789 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: n(T494, .(rbrace, .(rbrace, .(rbrace, .(plus, X789))))), SCOPE: 44, CLAUSE: 5\n\nT494 is ground\nX789 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: z(T510)\n\nT510 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
331 [label="331: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: z(T510), SCOPE: 45, CLAUSE: 6 | z(T510), SCOPE: 45, CLAUSE: 7 | z(T510), SCOPE: 45, CLAUSE: 8\n\nT510 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
333 [label="333: z(T510), SCOPE: 45, CLAUSE: 6\n\nT510 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: z(T510), SCOPE: 45, CLAUSE: 7 | z(T510), SCOPE: 45, CLAUSE: 8\n\nT510 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
335 [label="335: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
336 [label="336: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
337 [label="337: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
338 [label="338: z(T510), SCOPE: 45, CLAUSE: 7\n\nT510 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: z(T510), SCOPE: 45, CLAUSE: 8\n\nT510 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
341 [label="341: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="344: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
345 [label="345: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
346 [label="346: e(T515, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X812))))))\n\nT515 is ground\nX812 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
347 [label="347: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
348 [label="348: e(T515, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X812)))))), SCOPE: 46, CLAUSE: 0 | e(T515, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X812)))))), SCOPE: 46, CLAUSE: 1\n\nT515 is ground\nX812 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
349 [label="349: e(T515, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X812)))))), SCOPE: 46, CLAUSE: 0\n\nT515 is ground\nX812 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
350 [label="350: e(T515, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X812)))))), SCOPE: 46, CLAUSE: 1\n\nT515 is ground\nX812 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
351 [label="351: t(T523, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X838))))))\n\nT523 is ground\nX838 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
352 [label="352: t(T523, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X838)))))), SCOPE: 47, CLAUSE: 2 | t(T523, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X838)))))), SCOPE: 47, CLAUSE: 3\n\nT523 is ground\nX838 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
353 [label="353: t(T523, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X838)))))), SCOPE: 47, CLAUSE: 2\n\nT523 is ground\nX838 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
354 [label="354: t(T523, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X838)))))), SCOPE: 47, CLAUSE: 3\n\nT523 is ground\nX838 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
355 [label="355: n(T535, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X860))))))\n\nT535 is ground\nX860 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
356 [label="356: n(T535, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X860)))))), SCOPE: 48, CLAUSE: 4 | n(T535, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X860)))))), SCOPE: 48, CLAUSE: 5\n\nT535 is ground\nX860 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
357 [label="357: n(T535, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X860)))))), SCOPE: 48, CLAUSE: 4\n\nT535 is ground\nX860 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
358 [label="358: n(T535, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X860)))))), SCOPE: 48, CLAUSE: 5\n\nT535 is ground\nX860 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
359 [label="359: z(T551)\n\nT551 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
360 [label="360: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: z(T551), SCOPE: 49, CLAUSE: 6 | z(T551), SCOPE: 49, CLAUSE: 7 | z(T551), SCOPE: 49, CLAUSE: 8\n\nT551 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
362 [label="362: z(T551), SCOPE: 49, CLAUSE: 6\n\nT551 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
363 [label="363: z(T551), SCOPE: 49, CLAUSE: 7 | z(T551), SCOPE: 49, CLAUSE: 8\n\nT551 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
364 [label="364: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
365 [label="365: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
366 [label="366: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
367 [label="367: z(T551), SCOPE: 49, CLAUSE: 7\n\nT551 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
368 [label="368: z(T551), SCOPE: 49, CLAUSE: 8\n\nT551 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
369 [label="369: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
370 [label="370: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
371 [label="371: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
372 [label="372: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
373 [label="373: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
374 [label="374: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
375 [label="375: e(T556, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X883)))))))\n\nT556 is ground\nX883 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
376 [label="376: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
377 [label="377: e(T556, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X883))))))), SCOPE: 50, CLAUSE: 0 | e(T556, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X883))))))), SCOPE: 50, CLAUSE: 1\n\nT556 is ground\nX883 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
378 [label="378: e(T556, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X883))))))), SCOPE: 50, CLAUSE: 0\n\nT556 is ground\nX883 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
379 [label="379: e(T556, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X883))))))), SCOPE: 50, CLAUSE: 1\n\nT556 is ground\nX883 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
380 [label="380: t(T564, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X909)))))))\n\nT564 is ground\nX909 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: t(T564, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X909))))))), SCOPE: 51, CLAUSE: 2 | t(T564, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X909))))))), SCOPE: 51, CLAUSE: 3\n\nT564 is ground\nX909 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
382 [label="382: t(T564, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X909))))))), SCOPE: 51, CLAUSE: 2\n\nT564 is ground\nX909 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
383 [label="383: t(T564, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X909))))))), SCOPE: 51, CLAUSE: 3\n\nT564 is ground\nX909 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
384 [label="384: n(T576, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X931)))))))\n\nT576 is ground\nX931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
385 [label="385: n(T576, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X931))))))), SCOPE: 52, CLAUSE: 4 | n(T576, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X931))))))), SCOPE: 52, CLAUSE: 5\n\nT576 is ground\nX931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
386 [label="386: n(T576, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X931))))))), SCOPE: 52, CLAUSE: 4\n\nT576 is ground\nX931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
387 [label="387: n(T576, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X931))))))), SCOPE: 52, CLAUSE: 5\n\nT576 is ground\nX931 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: z(T592)\n\nT592 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
389 [label="389: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
390 [label="390: z(T592), SCOPE: 53, CLAUSE: 6 | z(T592), SCOPE: 53, CLAUSE: 7 | z(T592), SCOPE: 53, CLAUSE: 8\n\nT592 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
391 [label="391: z(T592), SCOPE: 53, CLAUSE: 6\n\nT592 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
392 [label="392: z(T592), SCOPE: 53, CLAUSE: 7 | z(T592), SCOPE: 53, CLAUSE: 8\n\nT592 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
393 [label="393: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
394 [label="394: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
395 [label="395: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
396 [label="396: z(T592), SCOPE: 53, CLAUSE: 7\n\nT592 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
397 [label="397: z(T592), SCOPE: 53, CLAUSE: 8\n\nT592 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
398 [label="398: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
399 [label="399: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
400 [label="400: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
401 [label="401: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
402 [label="402: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
403 [label="403: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
404 [label="404: e(T597, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X954))))))))\n\nT597 is ground\nX954 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
405 [label="405: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
406 [label="406: e(T597, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X954)))))))), SCOPE: 54, CLAUSE: 0 | e(T597, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X954)))))))), SCOPE: 54, CLAUSE: 1\n\nT597 is ground\nX954 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
407 [label="407: e(T597, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X954)))))))), SCOPE: 54, CLAUSE: 0\n\nT597 is ground\nX954 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
408 [label="408: e(T597, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X954)))))))), SCOPE: 54, CLAUSE: 1\n\nT597 is ground\nX954 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
409 [label="409: t(T605, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X980))))))))\n\nT605 is ground\nX980 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
410 [label="410: t(T605, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X980)))))))), SCOPE: 55, CLAUSE: 2 | t(T605, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X980)))))))), SCOPE: 55, CLAUSE: 3\n\nT605 is ground\nX980 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
411 [label="411: t(T605, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X980)))))))), SCOPE: 55, CLAUSE: 2\n\nT605 is ground\nX980 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
412 [label="412: t(T605, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X980)))))))), SCOPE: 55, CLAUSE: 3\n\nT605 is ground\nX980 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
413 [label="413: n(T617, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1002))))))))\n\nT617 is ground\nX1002 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
414 [label="414: n(T617, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1002)))))))), SCOPE: 56, CLAUSE: 4 | n(T617, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1002)))))))), SCOPE: 56, CLAUSE: 5\n\nT617 is ground\nX1002 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
415 [label="415: n(T617, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1002)))))))), SCOPE: 56, CLAUSE: 4\n\nT617 is ground\nX1002 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
416 [label="416: n(T617, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1002)))))))), SCOPE: 56, CLAUSE: 5\n\nT617 is ground\nX1002 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
417 [label="417: z(T633)\n\nT633 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
419 [label="419: z(T633), SCOPE: 57, CLAUSE: 6 | z(T633), SCOPE: 57, CLAUSE: 7 | z(T633), SCOPE: 57, CLAUSE: 8\n\nT633 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
420 [label="420: z(T633), SCOPE: 57, CLAUSE: 6\n\nT633 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
421 [label="421: z(T633), SCOPE: 57, CLAUSE: 7 | z(T633), SCOPE: 57, CLAUSE: 8\n\nT633 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
422 [label="422: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
423 [label="423: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
424 [label="424: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
425 [label="425: z(T633), SCOPE: 57, CLAUSE: 7\n\nT633 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
426 [label="426: z(T633), SCOPE: 57, CLAUSE: 8\n\nT633 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
427 [label="427: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
428 [label="428: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
429 [label="429: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
430 [label="430: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
431 [label="431: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
432 [label="432: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
433 [label="433: e(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))\n\nT638 is ground\nX1025 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
434 [label="434: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
435 [label="435: e(T638, .(rbrace, T640))\n\nT638 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
436 [label="436: ','(n(T648, .(star, X1044)), t(X1044, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1045)))))))))\n\nT648 is ground\nX1045 is free; \nX1044 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
437 [label="437: n(T648, .(star, X1044))\n\nT648 is ground\nX1044 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
438 [label="438: t(T652, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1045))))))))\n\nT652 is ground\nX1045 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: ','(t(T660, .(plus, X1065)), e(X1065, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1066)))))))))\n\nT660 is ground\nX1066 is free; \nX1065 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
440 [label="440: t(T660, .(plus, X1065))\n\nT660 is ground\nX1065 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
441 [label="441: e(T662, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1066))))))))\n\nT662 is ground\nX1066 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
442 [label="442: ','(n(T670, .(star, X1087)), t(X1087, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1088))))))))\n\nT670 is ground\nX1088 is free; \nX1087 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
443 [label="443: n(T670, .(star, X1087))\n\nT670 is ground\nX1087 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
444 [label="444: t(T674, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1088)))))))\n\nT674 is ground\nX1088 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
445 [label="445: ','(t(T682, .(plus, X1108)), e(X1108, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1109))))))))\n\nT682 is ground\nX1109 is free; \nX1108 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
446 [label="446: t(T682, .(plus, X1108))\n\nT682 is ground\nX1108 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
447 [label="447: e(T684, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1109)))))))\n\nT684 is ground\nX1109 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
448 [label="448: ','(n(T692, .(star, X1130)), t(X1130, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1131)))))))\n\nT692 is ground\nX1131 is free; \nX1130 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
449 [label="449: n(T692, .(star, X1130))\n\nT692 is ground\nX1130 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
450 [label="450: t(T696, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1131))))))\n\nT696 is ground\nX1131 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
451 [label="451: ','(t(T704, .(plus, X1151)), e(X1151, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1152)))))))\n\nT704 is ground\nX1152 is free; \nX1151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
452 [label="452: t(T704, .(plus, X1151))\n\nT704 is ground\nX1151 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
453 [label="453: e(T706, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1152))))))\n\nT706 is ground\nX1152 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
454 [label="454: ','(n(T714, .(star, X1173)), t(X1173, .(rbrace, .(rbrace, .(rbrace, .(plus, X1174))))))\n\nT714 is ground\nX1174 is free; \nX1173 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
455 [label="455: n(T714, .(star, X1173))\n\nT714 is ground\nX1173 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
456 [label="456: t(T718, .(rbrace, .(rbrace, .(rbrace, .(plus, X1174)))))\n\nT718 is ground\nX1174 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
457 [label="457: ','(t(T726, .(plus, X1194)), e(X1194, .(rbrace, .(rbrace, .(rbrace, .(plus, X1195))))))\n\nT726 is ground\nX1195 is free; \nX1194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
458 [label="458: t(T726, .(plus, X1194))\n\nT726 is ground\nX1194 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: e(T728, .(rbrace, .(rbrace, .(rbrace, .(plus, X1195)))))\n\nT728 is ground\nX1195 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
460 [label="460: ','(n(T736, .(star, X1216)), t(X1216, .(rbrace, .(rbrace, .(plus, X1217)))))\n\nT736 is ground\nX1217 is free; \nX1216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
461 [label="461: n(T736, .(star, X1216))\n\nT736 is ground\nX1216 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
462 [label="462: t(T740, .(rbrace, .(rbrace, .(plus, X1217))))\n\nT740 is ground\nX1217 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
463 [label="463: ','(t(T748, .(plus, X1237)), e(X1237, .(rbrace, .(rbrace, .(plus, X1238)))))\n\nT748 is ground\nX1238 is free; \nX1237 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
464 [label="464: t(T748, .(plus, X1237))\n\nT748 is ground\nX1237 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
465 [label="465: e(T750, .(rbrace, .(rbrace, .(plus, X1238))))\n\nT750 is ground\nX1238 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
466 [label="466: ','(n(T758, .(star, X1259)), t(X1259, .(rbrace, .(plus, X1260))))\n\nT758 is ground\nX1260 is free; \nX1259 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
467 [label="467: n(T758, .(star, X1259))\n\nT758 is ground\nX1259 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
468 [label="468: t(T762, .(rbrace, .(plus, X1260)))\n\nT762 is ground\nX1260 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
469 [label="469: ','(t(T770, .(plus, X1280)), e(X1280, .(rbrace, .(plus, X1281))))\n\nT770 is ground\nX1281 is free; \nX1280 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
470 [label="470: t(T770, .(plus, X1280))\n\nT770 is ground\nX1280 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
471 [label="471: e(T772, .(rbrace, .(plus, X1281)))\n\nT772 is ground\nX1281 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
472 [label="472: ','(n(T780, .(star, X1302)), t(X1302, .(plus, X1303)))\n\nT780 is ground\nX1303 is free; \nX1302 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
473 [label="473: n(T780, .(star, X1302))\n\nT780 is ground\nX1302 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
474 [label="474: t(T784, .(plus, X1303))\n\nT784 is ground\nX1303 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: ','(n(T795, .(star, X1325)), t(X1325, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1326))))))))\n\nT795 is ground\nX1326 is free; \nX1325 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
476 [label="476: n(T795, .(star, X1325))\n\nT795 is ground\nX1325 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
477 [label="477: t(T799, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1326)))))))\n\nT799 is ground\nX1326 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
478 [label="478: ','(t(T807, .(plus, X1346)), e(X1346, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1347))))))))\n\nT807 is ground\nX1347 is free; \nX1346 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
479 [label="479: t(T807, .(plus, X1346))\n\nT807 is ground\nX1346 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
480 [label="480: e(T809, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1347)))))))\n\nT809 is ground\nX1347 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
481 [label="481: ','(n(T817, .(star, X1368)), t(X1368, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1369)))))))\n\nT817 is ground\nX1369 is free; \nX1368 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
482 [label="482: n(T817, .(star, X1368))\n\nT817 is ground\nX1368 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
483 [label="483: t(T821, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1369))))))\n\nT821 is ground\nX1369 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
484 [label="484: ','(t(T829, .(plus, X1389)), e(X1389, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1390)))))))\n\nT829 is ground\nX1390 is free; \nX1389 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
485 [label="485: t(T829, .(plus, X1389))\n\nT829 is ground\nX1389 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
486 [label="486: e(T831, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1390))))))\n\nT831 is ground\nX1390 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
487 [label="487: ','(n(T839, .(star, X1411)), t(X1411, .(rbrace, .(rbrace, .(rbrace, .(star, X1412))))))\n\nT839 is ground\nX1412 is free; \nX1411 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
488 [label="488: n(T839, .(star, X1411))\n\nT839 is ground\nX1411 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
489 [label="489: t(T843, .(rbrace, .(rbrace, .(rbrace, .(star, X1412)))))\n\nT843 is ground\nX1412 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
490 [label="490: ','(t(T851, .(plus, X1432)), e(X1432, .(rbrace, .(rbrace, .(rbrace, .(star, X1433))))))\n\nT851 is ground\nX1433 is free; \nX1432 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
491 [label="491: t(T851, .(plus, X1432))\n\nT851 is ground\nX1432 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
492 [label="492: e(T853, .(rbrace, .(rbrace, .(rbrace, .(star, X1433)))))\n\nT853 is ground\nX1433 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
493 [label="493: ','(n(T861, .(star, X1454)), t(X1454, .(rbrace, .(rbrace, .(star, X1455)))))\n\nT861 is ground\nX1455 is free; \nX1454 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
494 [label="494: n(T861, .(star, X1454))\n\nT861 is ground\nX1454 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
495 [label="495: t(T865, .(rbrace, .(rbrace, .(star, X1455))))\n\nT865 is ground\nX1455 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
496 [label="496: ','(t(T873, .(plus, X1475)), e(X1475, .(rbrace, .(rbrace, .(star, X1476)))))\n\nT873 is ground\nX1476 is free; \nX1475 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
497 [label="497: t(T873, .(plus, X1475))\n\nT873 is ground\nX1475 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
498 [label="498: e(T875, .(rbrace, .(rbrace, .(star, X1476))))\n\nT875 is ground\nX1476 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
499 [label="499: ','(n(T883, .(star, X1497)), t(X1497, .(rbrace, .(star, X1498))))\n\nT883 is ground\nX1498 is free; \nX1497 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
500 [label="500: n(T883, .(star, X1497))\n\nT883 is ground\nX1497 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
501 [label="501: t(T887, .(rbrace, .(star, X1498)))\n\nT887 is ground\nX1498 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
502 [label="502: ','(t(T895, .(plus, X1518)), e(X1518, .(rbrace, .(star, X1519))))\n\nT895 is ground\nX1519 is free; \nX1518 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
503 [label="503: t(T895, .(plus, X1518))\n\nT895 is ground\nX1518 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
504 [label="504: e(T897, .(rbrace, .(star, X1519)))\n\nT897 is ground\nX1519 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
505 [label="505: t(T68, T64), SCOPE: 58, CLAUSE: 2 | t(T68, T64), SCOPE: 58, CLAUSE: 3\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
506 [label="506: t(T68, T64), SCOPE: 58, CLAUSE: 2\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
507 [label="507: t(T68, T64), SCOPE: 58, CLAUSE: 3\n\nT68 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
508 [label="508: n(T916, T918)\n\nT916 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
509 [label="509: ','(n(T929, .(star, X1556)), t(X1556, T931))\n\nT929 is ground\nX1556 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
510 [label="510: e(T5, T2), SCOPE: 1, CLAUSE: 1\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
511 [label="511: ','(t(T941, .(plus, X1569)), e(X1569, T943))\n\nT941 is ground\nX1569 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
512 [label="512: t(T941, .(plus, X1569))\n\nT941 is ground\nX1569 is free; ", fontsize=16, style=filled, fillcolor=lightyellow];
513 [label="513: e(T945, T943)\n\nT945 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
514 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 514 [arrowhead = none ];
514 -> 2;

515 [label="ONLY EVAL with clause\ne(X3, X4) :- t(X3, X4).\nand substitution\nT1 -> T5\nX3 -> T5\nT2 -> T7\nX4 -> T7\nT6 -> T7", fontsize=14, style = filled, fillcolor = white];
2 -> 515 [arrowhead = none ];
515 -> 3;

516 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 516 [arrowhead = none ];
516 -> 4;

517 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 517 [arrowhead = none ];
517 -> 5;

518 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 518 [arrowhead = none ];
518 -> 6;

519 [label="ONLY EVAL with clause\nt(X17, X18) :- n(X17, X18).\nand substitution\nT5 -> T22\nX17 -> T22\nT7 -> T24\nX18 -> T24\nT23 -> T24", fontsize=14, style = filled, fillcolor = white];
5 -> 519 [arrowhead = none ];
519 -> 7;

520 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
6 -> 520 [arrowhead = none ];
520 -> 29;

521 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
6 -> 521 [arrowhead = none ];
521 -> 30;

522 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
7 -> 522 [arrowhead = none ];
522 -> 8;

523 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 523 [arrowhead = none ];
523 -> 9;

524 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
8 -> 524 [arrowhead = none ];
524 -> 10;

525 [label="EVAL with clause\nn(.(X29, X30), X30) :- z(X29).\nand substitution\nX29 -> T35\nX30 -> T36\nT22 -> .(T35, T36)\nT24 -> T36", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 525 [arrowhead = none ];
525 -> 11;

526 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 526 [arrowhead = none ];
526 -> 12;

527 [label="EVAL with clause\nn(.(lbrace, X37), X38) :- e(X37, .(rbrace, X38)).\nand substitution\nX37 -> T41\nT22 -> .(lbrace, T41)\nT24 -> T43\nX38 -> T43\nT42 -> T43", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 527 [arrowhead = none ];
527 -> 27;

528 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 528 [arrowhead = none ];
528 -> 28;

529 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
11 -> 529 [arrowhead = none ];
529 -> 13;

530 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 530 [arrowhead = none ];
530 -> 14;

531 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 531 [arrowhead = none ];
531 -> 15;

532 [label="EVAL with clause\nz(a).\nand substitution\nT35 -> a", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 532 [arrowhead = none ];
532 -> 16;

533 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 533 [arrowhead = none ];
533 -> 17;

534 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 534 [arrowhead = none ];
534 -> 19;

535 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
15 -> 535 [arrowhead = none ];
535 -> 20;

536 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 536 [arrowhead = none ];
536 -> 18;

537 [label="EVAL with clause\nz(b).\nand substitution\nT35 -> b", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 537 [arrowhead = none ];
537 -> 21;

538 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 538 [arrowhead = none ];
538 -> 22;

539 [label="EVAL with clause\nz(c).\nand substitution\nT35 -> c", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 539 [arrowhead = none ];
539 -> 24;

540 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
20 -> 540 [arrowhead = none ];
540 -> 25;

541 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 541 [arrowhead = none ];
541 -> 23;

542 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 542 [arrowhead = none ];
542 -> 26;

543 [label="INSTANCE with matching:\nT1 -> T41\nT2 -> .(rbrace, T43)", fontsize=14, style = filled, fillcolor = lightgrey];
27 -> 543 [arrowhead = none , style=dashed];
543 -> 1[style=dashed];

544 [label="ONLY EVAL with clause\nt(X57, X58) :- ','(n(X57, .(star, X59)), t(X59, X58)).\nand substitution\nT5 -> T62\nX57 -> T62\nT7 -> T64\nX58 -> T64\nT63 -> T64", fontsize=14, style = filled, fillcolor = white];
29 -> 544 [arrowhead = none ];
544 -> 31;

545 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 545 [arrowhead = none ];
545 -> 510;

546 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
31 -> 546 [arrowhead = none ];
546 -> 32;

547 [label="SPLIT 2\nnew knowledge:\nT68 is ground\nreplacements:\nX59 -> T68", fontsize=14, style = filled, fillcolor = violet];
31 -> 547 [arrowhead = none ];
547 -> 33;

548 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
32 -> 548 [arrowhead = none ];
548 -> 34;

549 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
33 -> 549 [arrowhead = none ];
549 -> 505;

550 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
34 -> 550 [arrowhead = none ];
550 -> 35;

551 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
34 -> 551 [arrowhead = none ];
551 -> 36;

552 [label="EVAL with clause\nn(.(X72, X73), X73) :- z(X72).\nand substitution\nX72 -> T84\nX73 -> .(star, T86)\nT62 -> .(T84, .(star, T86))\nX59 -> T86\nT85 -> .(star, T86)", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 552 [arrowhead = none ];
552 -> 37;

553 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 553 [arrowhead = none ];
553 -> 38;

554 [label="EVAL with clause\nn(.(lbrace, X82), X83) :- e(X82, .(rbrace, X83)).\nand substitution\nX82 -> T89\nT62 -> .(lbrace, T89)\nX59 -> X84\nX83 -> .(star, X84)", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 554 [arrowhead = none ];
554 -> 53;

555 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
36 -> 555 [arrowhead = none ];
555 -> 54;

556 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
37 -> 556 [arrowhead = none ];
556 -> 39;

557 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 557 [arrowhead = none ];
557 -> 40;

558 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 558 [arrowhead = none ];
558 -> 41;

559 [label="EVAL with clause\nz(a).\nand substitution\nT84 -> a", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 559 [arrowhead = none ];
559 -> 42;

560 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 560 [arrowhead = none ];
560 -> 43;

561 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
41 -> 561 [arrowhead = none ];
561 -> 45;

562 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
41 -> 562 [arrowhead = none ];
562 -> 46;

563 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
42 -> 563 [arrowhead = none ];
563 -> 44;

564 [label="EVAL with clause\nz(b).\nand substitution\nT84 -> b", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 564 [arrowhead = none ];
564 -> 47;

565 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
45 -> 565 [arrowhead = none ];
565 -> 48;

566 [label="EVAL with clause\nz(c).\nand substitution\nT84 -> c", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 566 [arrowhead = none ];
566 -> 50;

567 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
46 -> 567 [arrowhead = none ];
567 -> 51;

568 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
47 -> 568 [arrowhead = none ];
568 -> 49;

569 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
50 -> 569 [arrowhead = none ];
569 -> 52;

570 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
53 -> 570 [arrowhead = none ];
570 -> 55;

571 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 571 [arrowhead = none ];
571 -> 56;

572 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
55 -> 572 [arrowhead = none ];
572 -> 57;

573 [label="ONLY EVAL with clause\ne(X108, X109) :- t(X108, X109).\nand substitution\nT89 -> T97\nX108 -> T97\nX84 -> X110\nX109 -> .(rbrace, .(star, X110))", fontsize=14, style = filled, fillcolor = white];
56 -> 573 [arrowhead = none ];
573 -> 58;

574 [label="ONLY EVAL with clause\ne(X1516, X1517) :- ','(t(X1516, .(plus, X1518)), e(X1518, X1517)).\nand substitution\nT89 -> T895\nX1516 -> T895\nX84 -> X1519\nX1517 -> .(rbrace, .(star, X1519))", fontsize=14, style = filled, fillcolor = white];
57 -> 574 [arrowhead = none ];
574 -> 502;

575 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
58 -> 575 [arrowhead = none ];
575 -> 59;

576 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
59 -> 576 [arrowhead = none ];
576 -> 60;

577 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
59 -> 577 [arrowhead = none ];
577 -> 61;

578 [label="ONLY EVAL with clause\nt(X130, X131) :- n(X130, X131).\nand substitution\nT97 -> T109\nX130 -> T109\nX110 -> X132\nX131 -> .(rbrace, .(star, X132))", fontsize=14, style = filled, fillcolor = white];
60 -> 578 [arrowhead = none ];
578 -> 62;

579 [label="ONLY EVAL with clause\nt(X1495, X1496) :- ','(n(X1495, .(star, X1497)), t(X1497, X1496)).\nand substitution\nT97 -> T883\nX1495 -> T883\nX110 -> X1498\nX1496 -> .(rbrace, .(star, X1498))", fontsize=14, style = filled, fillcolor = white];
61 -> 579 [arrowhead = none ];
579 -> 499;

580 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
62 -> 580 [arrowhead = none ];
580 -> 63;

581 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
63 -> 581 [arrowhead = none ];
581 -> 64;

582 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
63 -> 582 [arrowhead = none ];
582 -> 65;

583 [label="EVAL with clause\nn(.(X143, X144), X144) :- z(X143).\nand substitution\nX143 -> T125\nX144 -> .(rbrace, .(star, T127))\nT109 -> .(T125, .(rbrace, .(star, T127)))\nX132 -> T127\nT126 -> .(rbrace, .(star, T127))", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 583 [arrowhead = none ];
583 -> 66;

584 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
64 -> 584 [arrowhead = none ];
584 -> 67;

585 [label="EVAL with clause\nn(.(lbrace, X153), X154) :- e(X153, .(rbrace, X154)).\nand substitution\nX153 -> T130\nT109 -> .(lbrace, T130)\nX132 -> X155\nX154 -> .(rbrace, .(star, X155))", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 585 [arrowhead = none ];
585 -> 82;

586 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
65 -> 586 [arrowhead = none ];
586 -> 83;

587 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
66 -> 587 [arrowhead = none ];
587 -> 68;

588 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 588 [arrowhead = none ];
588 -> 69;

589 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 589 [arrowhead = none ];
589 -> 70;

590 [label="EVAL with clause\nz(a).\nand substitution\nT125 -> a", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 590 [arrowhead = none ];
590 -> 71;

591 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 591 [arrowhead = none ];
591 -> 72;

592 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 592 [arrowhead = none ];
592 -> 74;

593 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
70 -> 593 [arrowhead = none ];
593 -> 75;

594 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
71 -> 594 [arrowhead = none ];
594 -> 73;

595 [label="EVAL with clause\nz(b).\nand substitution\nT125 -> b", fontsize=14, style = filled, fillcolor = lightblue];
74 -> 595 [arrowhead = none ];
595 -> 76;

596 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
74 -> 596 [arrowhead = none ];
596 -> 77;

597 [label="EVAL with clause\nz(c).\nand substitution\nT125 -> c", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 597 [arrowhead = none ];
597 -> 79;

598 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 598 [arrowhead = none ];
598 -> 80;

599 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
76 -> 599 [arrowhead = none ];
599 -> 78;

600 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
79 -> 600 [arrowhead = none ];
600 -> 81;

601 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
82 -> 601 [arrowhead = none ];
601 -> 84;

602 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 602 [arrowhead = none ];
602 -> 85;

603 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 603 [arrowhead = none ];
603 -> 86;

604 [label="ONLY EVAL with clause\ne(X179, X180) :- t(X179, X180).\nand substitution\nT130 -> T138\nX179 -> T138\nX155 -> X181\nX180 -> .(rbrace, .(rbrace, .(star, X181)))", fontsize=14, style = filled, fillcolor = white];
85 -> 604 [arrowhead = none ];
604 -> 87;

605 [label="ONLY EVAL with clause\ne(X1473, X1474) :- ','(t(X1473, .(plus, X1475)), e(X1475, X1474)).\nand substitution\nT130 -> T873\nX1473 -> T873\nX155 -> X1476\nX1474 -> .(rbrace, .(rbrace, .(star, X1476)))", fontsize=14, style = filled, fillcolor = white];
86 -> 605 [arrowhead = none ];
605 -> 496;

606 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
87 -> 606 [arrowhead = none ];
606 -> 88;

607 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
88 -> 607 [arrowhead = none ];
607 -> 89;

608 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
88 -> 608 [arrowhead = none ];
608 -> 90;

609 [label="ONLY EVAL with clause\nt(X201, X202) :- n(X201, X202).\nand substitution\nT138 -> T150\nX201 -> T150\nX181 -> X203\nX202 -> .(rbrace, .(rbrace, .(star, X203)))", fontsize=14, style = filled, fillcolor = white];
89 -> 609 [arrowhead = none ];
609 -> 91;

610 [label="ONLY EVAL with clause\nt(X1452, X1453) :- ','(n(X1452, .(star, X1454)), t(X1454, X1453)).\nand substitution\nT138 -> T861\nX1452 -> T861\nX181 -> X1455\nX1453 -> .(rbrace, .(rbrace, .(star, X1455)))", fontsize=14, style = filled, fillcolor = white];
90 -> 610 [arrowhead = none ];
610 -> 493;

611 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
91 -> 611 [arrowhead = none ];
611 -> 92;

612 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
92 -> 612 [arrowhead = none ];
612 -> 93;

613 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
92 -> 613 [arrowhead = none ];
613 -> 94;

614 [label="EVAL with clause\nn(.(X214, X215), X215) :- z(X214).\nand substitution\nX214 -> T166\nX215 -> .(rbrace, .(rbrace, .(star, T168)))\nT150 -> .(T166, .(rbrace, .(rbrace, .(star, T168))))\nX203 -> T168\nT167 -> .(rbrace, .(rbrace, .(star, T168)))", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 614 [arrowhead = none ];
614 -> 95;

615 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
93 -> 615 [arrowhead = none ];
615 -> 96;

616 [label="EVAL with clause\nn(.(lbrace, X224), X225) :- e(X224, .(rbrace, X225)).\nand substitution\nX224 -> T171\nT150 -> .(lbrace, T171)\nX203 -> X226\nX225 -> .(rbrace, .(rbrace, .(star, X226)))", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 616 [arrowhead = none ];
616 -> 111;

617 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
94 -> 617 [arrowhead = none ];
617 -> 112;

618 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
95 -> 618 [arrowhead = none ];
618 -> 97;

619 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
97 -> 619 [arrowhead = none ];
619 -> 98;

620 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
97 -> 620 [arrowhead = none ];
620 -> 99;

621 [label="EVAL with clause\nz(a).\nand substitution\nT166 -> a", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 621 [arrowhead = none ];
621 -> 100;

622 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 622 [arrowhead = none ];
622 -> 101;

623 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
99 -> 623 [arrowhead = none ];
623 -> 103;

624 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
99 -> 624 [arrowhead = none ];
624 -> 104;

625 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
100 -> 625 [arrowhead = none ];
625 -> 102;

626 [label="EVAL with clause\nz(b).\nand substitution\nT166 -> b", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 626 [arrowhead = none ];
626 -> 105;

627 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 627 [arrowhead = none ];
627 -> 106;

628 [label="EVAL with clause\nz(c).\nand substitution\nT166 -> c", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 628 [arrowhead = none ];
628 -> 108;

629 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
104 -> 629 [arrowhead = none ];
629 -> 109;

630 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 630 [arrowhead = none ];
630 -> 107;

631 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
108 -> 631 [arrowhead = none ];
631 -> 110;

632 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
111 -> 632 [arrowhead = none ];
632 -> 113;

633 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 633 [arrowhead = none ];
633 -> 114;

634 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
113 -> 634 [arrowhead = none ];
634 -> 115;

635 [label="ONLY EVAL with clause\ne(X250, X251) :- t(X250, X251).\nand substitution\nT171 -> T179\nX250 -> T179\nX226 -> X252\nX251 -> .(rbrace, .(rbrace, .(rbrace, .(star, X252))))", fontsize=14, style = filled, fillcolor = white];
114 -> 635 [arrowhead = none ];
635 -> 116;

636 [label="ONLY EVAL with clause\ne(X1430, X1431) :- ','(t(X1430, .(plus, X1432)), e(X1432, X1431)).\nand substitution\nT171 -> T851\nX1430 -> T851\nX226 -> X1433\nX1431 -> .(rbrace, .(rbrace, .(rbrace, .(star, X1433))))", fontsize=14, style = filled, fillcolor = white];
115 -> 636 [arrowhead = none ];
636 -> 490;

637 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
116 -> 637 [arrowhead = none ];
637 -> 117;

638 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
117 -> 638 [arrowhead = none ];
638 -> 118;

639 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
117 -> 639 [arrowhead = none ];
639 -> 119;

640 [label="ONLY EVAL with clause\nt(X272, X273) :- n(X272, X273).\nand substitution\nT179 -> T191\nX272 -> T191\nX252 -> X274\nX273 -> .(rbrace, .(rbrace, .(rbrace, .(star, X274))))", fontsize=14, style = filled, fillcolor = white];
118 -> 640 [arrowhead = none ];
640 -> 120;

641 [label="ONLY EVAL with clause\nt(X1409, X1410) :- ','(n(X1409, .(star, X1411)), t(X1411, X1410)).\nand substitution\nT179 -> T839\nX1409 -> T839\nX252 -> X1412\nX1410 -> .(rbrace, .(rbrace, .(rbrace, .(star, X1412))))", fontsize=14, style = filled, fillcolor = white];
119 -> 641 [arrowhead = none ];
641 -> 487;

642 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
120 -> 642 [arrowhead = none ];
642 -> 121;

643 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 643 [arrowhead = none ];
643 -> 122;

644 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
121 -> 644 [arrowhead = none ];
644 -> 123;

645 [label="EVAL with clause\nn(.(X285, X286), X286) :- z(X285).\nand substitution\nX285 -> T207\nX286 -> .(rbrace, .(rbrace, .(rbrace, .(star, T209))))\nT191 -> .(T207, .(rbrace, .(rbrace, .(rbrace, .(star, T209)))))\nX274 -> T209\nT208 -> .(rbrace, .(rbrace, .(rbrace, .(star, T209))))", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 645 [arrowhead = none ];
645 -> 124;

646 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
122 -> 646 [arrowhead = none ];
646 -> 125;

647 [label="EVAL with clause\nn(.(lbrace, X295), X296) :- e(X295, .(rbrace, X296)).\nand substitution\nX295 -> T212\nT191 -> .(lbrace, T212)\nX274 -> X297\nX296 -> .(rbrace, .(rbrace, .(rbrace, .(star, X297))))", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 647 [arrowhead = none ];
647 -> 140;

648 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 648 [arrowhead = none ];
648 -> 141;

649 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
124 -> 649 [arrowhead = none ];
649 -> 126;

650 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
126 -> 650 [arrowhead = none ];
650 -> 127;

651 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
126 -> 651 [arrowhead = none ];
651 -> 128;

652 [label="EVAL with clause\nz(a).\nand substitution\nT207 -> a", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 652 [arrowhead = none ];
652 -> 129;

653 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 653 [arrowhead = none ];
653 -> 130;

654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
128 -> 654 [arrowhead = none ];
654 -> 132;

655 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
128 -> 655 [arrowhead = none ];
655 -> 133;

656 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 656 [arrowhead = none ];
656 -> 131;

657 [label="EVAL with clause\nz(b).\nand substitution\nT207 -> b", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 657 [arrowhead = none ];
657 -> 134;

658 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 658 [arrowhead = none ];
658 -> 135;

659 [label="EVAL with clause\nz(c).\nand substitution\nT207 -> c", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 659 [arrowhead = none ];
659 -> 137;

660 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
133 -> 660 [arrowhead = none ];
660 -> 138;

661 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
134 -> 661 [arrowhead = none ];
661 -> 136;

662 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 662 [arrowhead = none ];
662 -> 139;

663 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
140 -> 663 [arrowhead = none ];
663 -> 142;

664 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 664 [arrowhead = none ];
664 -> 143;

665 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 665 [arrowhead = none ];
665 -> 144;

666 [label="ONLY EVAL with clause\ne(X321, X322) :- t(X321, X322).\nand substitution\nT212 -> T220\nX321 -> T220\nX297 -> X323\nX322 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X323)))))", fontsize=14, style = filled, fillcolor = white];
143 -> 666 [arrowhead = none ];
666 -> 145;

667 [label="ONLY EVAL with clause\ne(X1387, X1388) :- ','(t(X1387, .(plus, X1389)), e(X1389, X1388)).\nand substitution\nT212 -> T829\nX1387 -> T829\nX297 -> X1390\nX1388 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1390)))))", fontsize=14, style = filled, fillcolor = white];
144 -> 667 [arrowhead = none ];
667 -> 484;

668 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
145 -> 668 [arrowhead = none ];
668 -> 146;

669 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
146 -> 669 [arrowhead = none ];
669 -> 147;

670 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
146 -> 670 [arrowhead = none ];
670 -> 148;

671 [label="ONLY EVAL with clause\nt(X343, X344) :- n(X343, X344).\nand substitution\nT220 -> T232\nX343 -> T232\nX323 -> X345\nX344 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X345)))))", fontsize=14, style = filled, fillcolor = white];
147 -> 671 [arrowhead = none ];
671 -> 149;

672 [label="ONLY EVAL with clause\nt(X1366, X1367) :- ','(n(X1366, .(star, X1368)), t(X1368, X1367)).\nand substitution\nT220 -> T817\nX1366 -> T817\nX323 -> X1369\nX1367 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1369)))))", fontsize=14, style = filled, fillcolor = white];
148 -> 672 [arrowhead = none ];
672 -> 481;

673 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
149 -> 673 [arrowhead = none ];
673 -> 150;

674 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
150 -> 674 [arrowhead = none ];
674 -> 151;

675 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
150 -> 675 [arrowhead = none ];
675 -> 152;

676 [label="EVAL with clause\nn(.(X356, X357), X357) :- z(X356).\nand substitution\nX356 -> T248\nX357 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))\nT232 -> .(T248, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250))))))\nX345 -> T250\nT249 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 676 [arrowhead = none ];
676 -> 153;

677 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
151 -> 677 [arrowhead = none ];
677 -> 154;

678 [label="EVAL with clause\nn(.(lbrace, X366), X367) :- e(X366, .(rbrace, X367)).\nand substitution\nX366 -> T253\nT232 -> .(lbrace, T253)\nX345 -> X368\nX367 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X368)))))", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 678 [arrowhead = none ];
678 -> 169;

679 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
152 -> 679 [arrowhead = none ];
679 -> 170;

680 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
153 -> 680 [arrowhead = none ];
680 -> 155;

681 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
155 -> 681 [arrowhead = none ];
681 -> 156;

682 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
155 -> 682 [arrowhead = none ];
682 -> 157;

683 [label="EVAL with clause\nz(a).\nand substitution\nT248 -> a", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 683 [arrowhead = none ];
683 -> 158;

684 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
156 -> 684 [arrowhead = none ];
684 -> 159;

685 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 685 [arrowhead = none ];
685 -> 161;

686 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
157 -> 686 [arrowhead = none ];
686 -> 162;

687 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
158 -> 687 [arrowhead = none ];
687 -> 160;

688 [label="EVAL with clause\nz(b).\nand substitution\nT248 -> b", fontsize=14, style = filled, fillcolor = lightblue];
161 -> 688 [arrowhead = none ];
688 -> 163;

689 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
161 -> 689 [arrowhead = none ];
689 -> 164;

690 [label="EVAL with clause\nz(c).\nand substitution\nT248 -> c", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 690 [arrowhead = none ];
690 -> 166;

691 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
162 -> 691 [arrowhead = none ];
691 -> 167;

692 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
163 -> 692 [arrowhead = none ];
692 -> 165;

693 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
166 -> 693 [arrowhead = none ];
693 -> 168;

694 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
169 -> 694 [arrowhead = none ];
694 -> 171;

695 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
171 -> 695 [arrowhead = none ];
695 -> 172;

696 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
171 -> 696 [arrowhead = none ];
696 -> 173;

697 [label="ONLY EVAL with clause\ne(X392, X393) :- t(X392, X393).\nand substitution\nT253 -> T261\nX392 -> T261\nX368 -> X394\nX393 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X394))))))", fontsize=14, style = filled, fillcolor = white];
172 -> 697 [arrowhead = none ];
697 -> 174;

698 [label="ONLY EVAL with clause\ne(X1344, X1345) :- ','(t(X1344, .(plus, X1346)), e(X1346, X1345)).\nand substitution\nT253 -> T807\nX1344 -> T807\nX368 -> X1347\nX1345 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1347))))))", fontsize=14, style = filled, fillcolor = white];
173 -> 698 [arrowhead = none ];
698 -> 478;

699 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
174 -> 699 [arrowhead = none ];
699 -> 175;

700 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
175 -> 700 [arrowhead = none ];
700 -> 176;

701 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
175 -> 701 [arrowhead = none ];
701 -> 177;

702 [label="ONLY EVAL with clause\nt(X414, X415) :- n(X414, X415).\nand substitution\nT261 -> T273\nX414 -> T273\nX394 -> X416\nX415 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X416))))))", fontsize=14, style = filled, fillcolor = white];
176 -> 702 [arrowhead = none ];
702 -> 178;

703 [label="ONLY EVAL with clause\nt(X1323, X1324) :- ','(n(X1323, .(star, X1325)), t(X1325, X1324)).\nand substitution\nT261 -> T795\nX1323 -> T795\nX394 -> X1326\nX1324 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X1326))))))", fontsize=14, style = filled, fillcolor = white];
177 -> 703 [arrowhead = none ];
703 -> 475;

704 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
178 -> 704 [arrowhead = none ];
704 -> 179;

705 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
179 -> 705 [arrowhead = none ];
705 -> 180;

706 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
179 -> 706 [arrowhead = none ];
706 -> 181;

707 [label="EVAL with clause\nn(.(X427, X428), X428) :- z(X427).\nand substitution\nX427 -> T289\nX428 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))\nT273 -> .(T289, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291)))))))\nX416 -> T291\nT290 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 707 [arrowhead = none ];
707 -> 182;

708 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
180 -> 708 [arrowhead = none ];
708 -> 183;

709 [label="EVAL with clause\nn(.(lbrace, X437), X438) :- e(X437, .(rbrace, X438)).\nand substitution\nX437 -> T294\nT273 -> .(lbrace, T294)\nX416 -> X439\nX438 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X439))))))", fontsize=14, style = filled, fillcolor = lightblue];
181 -> 709 [arrowhead = none ];
709 -> 198;

710 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
181 -> 710 [arrowhead = none ];
710 -> 199;

711 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
182 -> 711 [arrowhead = none ];
711 -> 184;

712 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
184 -> 712 [arrowhead = none ];
712 -> 185;

713 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
184 -> 713 [arrowhead = none ];
713 -> 186;

714 [label="EVAL with clause\nz(a).\nand substitution\nT289 -> a", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 714 [arrowhead = none ];
714 -> 187;

715 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
185 -> 715 [arrowhead = none ];
715 -> 188;

716 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 716 [arrowhead = none ];
716 -> 190;

717 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 717 [arrowhead = none ];
717 -> 191;

718 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
187 -> 718 [arrowhead = none ];
718 -> 189;

719 [label="EVAL with clause\nz(b).\nand substitution\nT289 -> b", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 719 [arrowhead = none ];
719 -> 192;

720 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 720 [arrowhead = none ];
720 -> 193;

721 [label="EVAL with clause\nz(c).\nand substitution\nT289 -> c", fontsize=14, style = filled, fillcolor = lightblue];
191 -> 721 [arrowhead = none ];
721 -> 195;

722 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
191 -> 722 [arrowhead = none ];
722 -> 196;

723 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
192 -> 723 [arrowhead = none ];
723 -> 194;

724 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
195 -> 724 [arrowhead = none ];
724 -> 197;

725 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
198 -> 725 [arrowhead = none ];
725 -> 200;

726 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
200 -> 726 [arrowhead = none ];
726 -> 201;

727 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
200 -> 727 [arrowhead = none ];
727 -> 202;

728 [label="ONLY EVAL with clause\ne(X463, X464) :- t(X463, X464).\nand substitution\nT294 -> T302\nX463 -> T302\nX439 -> X465\nX464 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X465)))))))", fontsize=14, style = filled, fillcolor = white];
201 -> 728 [arrowhead = none ];
728 -> 203;

729 [label="ONLY EVAL with clause\ne(X548, X549) :- ','(t(X548, .(plus, X550)), e(X550, X549)).\nand substitution\nT294 -> T357\nX548 -> T357\nX439 -> X551\nX549 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X551)))))))", fontsize=14, style = filled, fillcolor = white];
202 -> 729 [arrowhead = none ];
729 -> 233;

730 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
203 -> 730 [arrowhead = none ];
730 -> 204;

731 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
204 -> 731 [arrowhead = none ];
731 -> 205;

732 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
204 -> 732 [arrowhead = none ];
732 -> 206;

733 [label="ONLY EVAL with clause\nt(X485, X486) :- n(X485, X486).\nand substitution\nT302 -> T314\nX485 -> T314\nX465 -> X487\nX486 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X487)))))))", fontsize=14, style = filled, fillcolor = white];
205 -> 733 [arrowhead = none ];
733 -> 207;

734 [label="ONLY EVAL with clause\nt(X527, X528) :- ','(n(X527, .(star, X529)), t(X529, X528)).\nand substitution\nT302 -> T345\nX527 -> T345\nX465 -> X530\nX528 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X530)))))))", fontsize=14, style = filled, fillcolor = white];
206 -> 734 [arrowhead = none ];
734 -> 230;

735 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
207 -> 735 [arrowhead = none ];
735 -> 208;

736 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
208 -> 736 [arrowhead = none ];
736 -> 209;

737 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
208 -> 737 [arrowhead = none ];
737 -> 210;

738 [label="EVAL with clause\nn(.(X498, X499), X499) :- z(X498).\nand substitution\nX498 -> T330\nX499 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))\nT314 -> .(T330, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332))))))))\nX487 -> T332\nT331 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))", fontsize=14, style = filled, fillcolor = lightblue];
209 -> 738 [arrowhead = none ];
738 -> 211;

739 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
209 -> 739 [arrowhead = none ];
739 -> 212;

740 [label="EVAL with clause\nn(.(lbrace, X508), X509) :- e(X508, .(rbrace, X509)).\nand substitution\nX508 -> T335\nT314 -> .(lbrace, T335)\nX487 -> X510\nX509 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))", fontsize=14, style = filled, fillcolor = lightblue];
210 -> 740 [arrowhead = none ];
740 -> 227;

741 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
210 -> 741 [arrowhead = none ];
741 -> 228;

742 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
211 -> 742 [arrowhead = none ];
742 -> 213;

743 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
213 -> 743 [arrowhead = none ];
743 -> 214;

744 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
213 -> 744 [arrowhead = none ];
744 -> 215;

745 [label="EVAL with clause\nz(a).\nand substitution\nT330 -> a", fontsize=14, style = filled, fillcolor = lightblue];
214 -> 745 [arrowhead = none ];
745 -> 216;

746 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
214 -> 746 [arrowhead = none ];
746 -> 217;

747 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
215 -> 747 [arrowhead = none ];
747 -> 219;

748 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
215 -> 748 [arrowhead = none ];
748 -> 220;

749 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
216 -> 749 [arrowhead = none ];
749 -> 218;

750 [label="EVAL with clause\nz(b).\nand substitution\nT330 -> b", fontsize=14, style = filled, fillcolor = lightblue];
219 -> 750 [arrowhead = none ];
750 -> 221;

751 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
219 -> 751 [arrowhead = none ];
751 -> 222;

752 [label="EVAL with clause\nz(c).\nand substitution\nT330 -> c", fontsize=14, style = filled, fillcolor = lightblue];
220 -> 752 [arrowhead = none ];
752 -> 224;

753 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
220 -> 753 [arrowhead = none ];
753 -> 225;

754 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
221 -> 754 [arrowhead = none ];
754 -> 223;

755 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
224 -> 755 [arrowhead = none ];
755 -> 226;

756 [label="GENERALIZATION\nT337 <-- .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))", fontsize=14, style = filled, fillcolor = violet];
227 -> 756 [arrowhead = none ];
756 -> 229;

757 [label="INSTANCE with matching:\nT1 -> T335\nT2 -> .(rbrace, T337)", fontsize=14, style = filled, fillcolor = lightgrey];
229 -> 757 [arrowhead = none , style=dashed];
757 -> 1[style=dashed];

758 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
230 -> 758 [arrowhead = none ];
758 -> 231;

759 [label="SPLIT 2\nnew knowledge:\nT349 is ground\nreplacements:\nX529 -> T349", fontsize=14, style = filled, fillcolor = violet];
230 -> 759 [arrowhead = none ];
759 -> 232;

760 [label="INSTANCE with matching:\nT62 -> T345\nX59 -> X529", fontsize=14, style = filled, fillcolor = lightgrey];
231 -> 760 [arrowhead = none , style=dashed];
760 -> 32[style=dashed];

761 [label="INSTANCE with matching:\nT302 -> T349\nX465 -> X530", fontsize=14, style = filled, fillcolor = lightgrey];
232 -> 761 [arrowhead = none , style=dashed];
761 -> 203[style=dashed];

762 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
233 -> 762 [arrowhead = none ];
762 -> 234;

763 [label="SPLIT 2\nnew knowledge:\nT359 is ground\nreplacements:\nX550 -> T359", fontsize=14, style = filled, fillcolor = violet];
233 -> 763 [arrowhead = none ];
763 -> 235;

764 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
234 -> 764 [arrowhead = none ];
764 -> 236;

765 [label="INSTANCE with matching:\nT294 -> T359\nX439 -> X551", fontsize=14, style = filled, fillcolor = lightgrey];
235 -> 765 [arrowhead = none , style=dashed];
765 -> 198[style=dashed];

766 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
236 -> 766 [arrowhead = none ];
766 -> 237;

767 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
236 -> 767 [arrowhead = none ];
767 -> 238;

768 [label="ONLY EVAL with clause\nt(X574, X575) :- n(X574, X575).\nand substitution\nT357 -> T371\nX574 -> T371\nX550 -> X576\nX575 -> .(plus, X576)", fontsize=14, style = filled, fillcolor = white];
237 -> 768 [arrowhead = none ];
768 -> 239;

769 [label="ONLY EVAL with clause\nt(X1300, X1301) :- ','(n(X1300, .(star, X1302)), t(X1302, X1301)).\nand substitution\nT357 -> T780\nX1300 -> T780\nX550 -> X1303\nX1301 -> .(plus, X1303)", fontsize=14, style = filled, fillcolor = white];
238 -> 769 [arrowhead = none ];
769 -> 472;

770 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
239 -> 770 [arrowhead = none ];
770 -> 240;

771 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 771 [arrowhead = none ];
771 -> 241;

772 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 772 [arrowhead = none ];
772 -> 242;

773 [label="EVAL with clause\nn(.(X587, X588), X588) :- z(X587).\nand substitution\nX587 -> T387\nX588 -> .(plus, T389)\nT371 -> .(T387, .(plus, T389))\nX576 -> T389\nT388 -> .(plus, T389)", fontsize=14, style = filled, fillcolor = lightblue];
241 -> 773 [arrowhead = none ];
773 -> 243;

774 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
241 -> 774 [arrowhead = none ];
774 -> 244;

775 [label="EVAL with clause\nn(.(lbrace, X597), X598) :- e(X597, .(rbrace, X598)).\nand substitution\nX597 -> T392\nT371 -> .(lbrace, T392)\nX576 -> X599\nX598 -> .(plus, X599)", fontsize=14, style = filled, fillcolor = lightblue];
242 -> 775 [arrowhead = none ];
775 -> 259;

776 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
242 -> 776 [arrowhead = none ];
776 -> 260;

777 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
243 -> 777 [arrowhead = none ];
777 -> 245;

778 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
245 -> 778 [arrowhead = none ];
778 -> 246;

779 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
245 -> 779 [arrowhead = none ];
779 -> 247;

780 [label="EVAL with clause\nz(a).\nand substitution\nT387 -> a", fontsize=14, style = filled, fillcolor = lightblue];
246 -> 780 [arrowhead = none ];
780 -> 248;

781 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
246 -> 781 [arrowhead = none ];
781 -> 249;

782 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
247 -> 782 [arrowhead = none ];
782 -> 251;

783 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
247 -> 783 [arrowhead = none ];
783 -> 252;

784 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
248 -> 784 [arrowhead = none ];
784 -> 250;

785 [label="EVAL with clause\nz(b).\nand substitution\nT387 -> b", fontsize=14, style = filled, fillcolor = lightblue];
251 -> 785 [arrowhead = none ];
785 -> 253;

786 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
251 -> 786 [arrowhead = none ];
786 -> 254;

787 [label="EVAL with clause\nz(c).\nand substitution\nT387 -> c", fontsize=14, style = filled, fillcolor = lightblue];
252 -> 787 [arrowhead = none ];
787 -> 256;

788 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
252 -> 788 [arrowhead = none ];
788 -> 257;

789 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
253 -> 789 [arrowhead = none ];
789 -> 255;

790 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
256 -> 790 [arrowhead = none ];
790 -> 258;

791 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
259 -> 791 [arrowhead = none ];
791 -> 261;

792 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
261 -> 792 [arrowhead = none ];
792 -> 262;

793 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
261 -> 793 [arrowhead = none ];
793 -> 263;

794 [label="ONLY EVAL with clause\ne(X623, X624) :- t(X623, X624).\nand substitution\nT392 -> T400\nX623 -> T400\nX599 -> X625\nX624 -> .(rbrace, .(plus, X625))", fontsize=14, style = filled, fillcolor = white];
262 -> 794 [arrowhead = none ];
794 -> 264;

795 [label="ONLY EVAL with clause\ne(X1278, X1279) :- ','(t(X1278, .(plus, X1280)), e(X1280, X1279)).\nand substitution\nT392 -> T770\nX1278 -> T770\nX599 -> X1281\nX1279 -> .(rbrace, .(plus, X1281))", fontsize=14, style = filled, fillcolor = white];
263 -> 795 [arrowhead = none ];
795 -> 469;

796 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
264 -> 796 [arrowhead = none ];
796 -> 265;

797 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
265 -> 797 [arrowhead = none ];
797 -> 266;

798 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
265 -> 798 [arrowhead = none ];
798 -> 267;

799 [label="ONLY EVAL with clause\nt(X645, X646) :- n(X645, X646).\nand substitution\nT400 -> T412\nX645 -> T412\nX625 -> X647\nX646 -> .(rbrace, .(plus, X647))", fontsize=14, style = filled, fillcolor = white];
266 -> 799 [arrowhead = none ];
799 -> 268;

800 [label="ONLY EVAL with clause\nt(X1257, X1258) :- ','(n(X1257, .(star, X1259)), t(X1259, X1258)).\nand substitution\nT400 -> T758\nX1257 -> T758\nX625 -> X1260\nX1258 -> .(rbrace, .(plus, X1260))", fontsize=14, style = filled, fillcolor = white];
267 -> 800 [arrowhead = none ];
800 -> 466;

801 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
268 -> 801 [arrowhead = none ];
801 -> 269;

802 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
269 -> 802 [arrowhead = none ];
802 -> 270;

803 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
269 -> 803 [arrowhead = none ];
803 -> 271;

804 [label="EVAL with clause\nn(.(X658, X659), X659) :- z(X658).\nand substitution\nX658 -> T428\nX659 -> .(rbrace, .(plus, T430))\nT412 -> .(T428, .(rbrace, .(plus, T430)))\nX647 -> T430\nT429 -> .(rbrace, .(plus, T430))", fontsize=14, style = filled, fillcolor = lightblue];
270 -> 804 [arrowhead = none ];
804 -> 272;

805 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
270 -> 805 [arrowhead = none ];
805 -> 273;

806 [label="EVAL with clause\nn(.(lbrace, X668), X669) :- e(X668, .(rbrace, X669)).\nand substitution\nX668 -> T433\nT412 -> .(lbrace, T433)\nX647 -> X670\nX669 -> .(rbrace, .(plus, X670))", fontsize=14, style = filled, fillcolor = lightblue];
271 -> 806 [arrowhead = none ];
806 -> 288;

807 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
271 -> 807 [arrowhead = none ];
807 -> 289;

808 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
272 -> 808 [arrowhead = none ];
808 -> 274;

809 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
274 -> 809 [arrowhead = none ];
809 -> 275;

810 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
274 -> 810 [arrowhead = none ];
810 -> 276;

811 [label="EVAL with clause\nz(a).\nand substitution\nT428 -> a", fontsize=14, style = filled, fillcolor = lightblue];
275 -> 811 [arrowhead = none ];
811 -> 277;

812 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
275 -> 812 [arrowhead = none ];
812 -> 278;

813 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
276 -> 813 [arrowhead = none ];
813 -> 280;

814 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
276 -> 814 [arrowhead = none ];
814 -> 281;

815 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
277 -> 815 [arrowhead = none ];
815 -> 279;

816 [label="EVAL with clause\nz(b).\nand substitution\nT428 -> b", fontsize=14, style = filled, fillcolor = lightblue];
280 -> 816 [arrowhead = none ];
816 -> 282;

817 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
280 -> 817 [arrowhead = none ];
817 -> 283;

818 [label="EVAL with clause\nz(c).\nand substitution\nT428 -> c", fontsize=14, style = filled, fillcolor = lightblue];
281 -> 818 [arrowhead = none ];
818 -> 285;

819 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
281 -> 819 [arrowhead = none ];
819 -> 286;

820 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
282 -> 820 [arrowhead = none ];
820 -> 284;

821 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
285 -> 821 [arrowhead = none ];
821 -> 287;

822 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
288 -> 822 [arrowhead = none ];
822 -> 290;

823 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
290 -> 823 [arrowhead = none ];
823 -> 291;

824 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
290 -> 824 [arrowhead = none ];
824 -> 292;

825 [label="ONLY EVAL with clause\ne(X694, X695) :- t(X694, X695).\nand substitution\nT433 -> T441\nX694 -> T441\nX670 -> X696\nX695 -> .(rbrace, .(rbrace, .(plus, X696)))", fontsize=14, style = filled, fillcolor = white];
291 -> 825 [arrowhead = none ];
825 -> 293;

826 [label="ONLY EVAL with clause\ne(X1235, X1236) :- ','(t(X1235, .(plus, X1237)), e(X1237, X1236)).\nand substitution\nT433 -> T748\nX1235 -> T748\nX670 -> X1238\nX1236 -> .(rbrace, .(rbrace, .(plus, X1238)))", fontsize=14, style = filled, fillcolor = white];
292 -> 826 [arrowhead = none ];
826 -> 463;

827 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
293 -> 827 [arrowhead = none ];
827 -> 294;

828 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
294 -> 828 [arrowhead = none ];
828 -> 295;

829 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
294 -> 829 [arrowhead = none ];
829 -> 296;

830 [label="ONLY EVAL with clause\nt(X716, X717) :- n(X716, X717).\nand substitution\nT441 -> T453\nX716 -> T453\nX696 -> X718\nX717 -> .(rbrace, .(rbrace, .(plus, X718)))", fontsize=14, style = filled, fillcolor = white];
295 -> 830 [arrowhead = none ];
830 -> 297;

831 [label="ONLY EVAL with clause\nt(X1214, X1215) :- ','(n(X1214, .(star, X1216)), t(X1216, X1215)).\nand substitution\nT441 -> T736\nX1214 -> T736\nX696 -> X1217\nX1215 -> .(rbrace, .(rbrace, .(plus, X1217)))", fontsize=14, style = filled, fillcolor = white];
296 -> 831 [arrowhead = none ];
831 -> 460;

832 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
297 -> 832 [arrowhead = none ];
832 -> 298;

833 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
298 -> 833 [arrowhead = none ];
833 -> 299;

834 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
298 -> 834 [arrowhead = none ];
834 -> 300;

835 [label="EVAL with clause\nn(.(X729, X730), X730) :- z(X729).\nand substitution\nX729 -> T469\nX730 -> .(rbrace, .(rbrace, .(plus, T471)))\nT453 -> .(T469, .(rbrace, .(rbrace, .(plus, T471))))\nX718 -> T471\nT470 -> .(rbrace, .(rbrace, .(plus, T471)))", fontsize=14, style = filled, fillcolor = lightblue];
299 -> 835 [arrowhead = none ];
835 -> 301;

836 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
299 -> 836 [arrowhead = none ];
836 -> 302;

837 [label="EVAL with clause\nn(.(lbrace, X739), X740) :- e(X739, .(rbrace, X740)).\nand substitution\nX739 -> T474\nT453 -> .(lbrace, T474)\nX718 -> X741\nX740 -> .(rbrace, .(rbrace, .(plus, X741)))", fontsize=14, style = filled, fillcolor = lightblue];
300 -> 837 [arrowhead = none ];
837 -> 317;

838 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
300 -> 838 [arrowhead = none ];
838 -> 318;

839 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
301 -> 839 [arrowhead = none ];
839 -> 303;

840 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
303 -> 840 [arrowhead = none ];
840 -> 304;

841 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
303 -> 841 [arrowhead = none ];
841 -> 305;

842 [label="EVAL with clause\nz(a).\nand substitution\nT469 -> a", fontsize=14, style = filled, fillcolor = lightblue];
304 -> 842 [arrowhead = none ];
842 -> 306;

843 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
304 -> 843 [arrowhead = none ];
843 -> 307;

844 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
305 -> 844 [arrowhead = none ];
844 -> 309;

845 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
305 -> 845 [arrowhead = none ];
845 -> 310;

846 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
306 -> 846 [arrowhead = none ];
846 -> 308;

847 [label="EVAL with clause\nz(b).\nand substitution\nT469 -> b", fontsize=14, style = filled, fillcolor = lightblue];
309 -> 847 [arrowhead = none ];
847 -> 311;

848 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
309 -> 848 [arrowhead = none ];
848 -> 312;

849 [label="EVAL with clause\nz(c).\nand substitution\nT469 -> c", fontsize=14, style = filled, fillcolor = lightblue];
310 -> 849 [arrowhead = none ];
849 -> 314;

850 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
310 -> 850 [arrowhead = none ];
850 -> 315;

851 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
311 -> 851 [arrowhead = none ];
851 -> 313;

852 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
314 -> 852 [arrowhead = none ];
852 -> 316;

853 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
317 -> 853 [arrowhead = none ];
853 -> 319;

854 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
319 -> 854 [arrowhead = none ];
854 -> 320;

855 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
319 -> 855 [arrowhead = none ];
855 -> 321;

856 [label="ONLY EVAL with clause\ne(X765, X766) :- t(X765, X766).\nand substitution\nT474 -> T482\nX765 -> T482\nX741 -> X767\nX766 -> .(rbrace, .(rbrace, .(rbrace, .(plus, X767))))", fontsize=14, style = filled, fillcolor = white];
320 -> 856 [arrowhead = none ];
856 -> 322;

857 [label="ONLY EVAL with clause\ne(X1192, X1193) :- ','(t(X1192, .(plus, X1194)), e(X1194, X1193)).\nand substitution\nT474 -> T726\nX1192 -> T726\nX741 -> X1195\nX1193 -> .(rbrace, .(rbrace, .(rbrace, .(plus, X1195))))", fontsize=14, style = filled, fillcolor = white];
321 -> 857 [arrowhead = none ];
857 -> 457;

858 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
322 -> 858 [arrowhead = none ];
858 -> 323;

859 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
323 -> 859 [arrowhead = none ];
859 -> 324;

860 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
323 -> 860 [arrowhead = none ];
860 -> 325;

861 [label="ONLY EVAL with clause\nt(X787, X788) :- n(X787, X788).\nand substitution\nT482 -> T494\nX787 -> T494\nX767 -> X789\nX788 -> .(rbrace, .(rbrace, .(rbrace, .(plus, X789))))", fontsize=14, style = filled, fillcolor = white];
324 -> 861 [arrowhead = none ];
861 -> 326;

862 [label="ONLY EVAL with clause\nt(X1171, X1172) :- ','(n(X1171, .(star, X1173)), t(X1173, X1172)).\nand substitution\nT482 -> T714\nX1171 -> T714\nX767 -> X1174\nX1172 -> .(rbrace, .(rbrace, .(rbrace, .(plus, X1174))))", fontsize=14, style = filled, fillcolor = white];
325 -> 862 [arrowhead = none ];
862 -> 454;

863 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
326 -> 863 [arrowhead = none ];
863 -> 327;

864 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
327 -> 864 [arrowhead = none ];
864 -> 328;

865 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
327 -> 865 [arrowhead = none ];
865 -> 329;

866 [label="EVAL with clause\nn(.(X800, X801), X801) :- z(X800).\nand substitution\nX800 -> T510\nX801 -> .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))\nT494 -> .(T510, .(rbrace, .(rbrace, .(rbrace, .(plus, T512)))))\nX789 -> T512\nT511 -> .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))", fontsize=14, style = filled, fillcolor = lightblue];
328 -> 866 [arrowhead = none ];
866 -> 330;

867 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
328 -> 867 [arrowhead = none ];
867 -> 331;

868 [label="EVAL with clause\nn(.(lbrace, X810), X811) :- e(X810, .(rbrace, X811)).\nand substitution\nX810 -> T515\nT494 -> .(lbrace, T515)\nX789 -> X812\nX811 -> .(rbrace, .(rbrace, .(rbrace, .(plus, X812))))", fontsize=14, style = filled, fillcolor = lightblue];
329 -> 868 [arrowhead = none ];
868 -> 346;

869 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
329 -> 869 [arrowhead = none ];
869 -> 347;

870 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
330 -> 870 [arrowhead = none ];
870 -> 332;

871 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
332 -> 871 [arrowhead = none ];
871 -> 333;

872 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
332 -> 872 [arrowhead = none ];
872 -> 334;

873 [label="EVAL with clause\nz(a).\nand substitution\nT510 -> a", fontsize=14, style = filled, fillcolor = lightblue];
333 -> 873 [arrowhead = none ];
873 -> 335;

874 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
333 -> 874 [arrowhead = none ];
874 -> 336;

875 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
334 -> 875 [arrowhead = none ];
875 -> 338;

876 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
334 -> 876 [arrowhead = none ];
876 -> 339;

877 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
335 -> 877 [arrowhead = none ];
877 -> 337;

878 [label="EVAL with clause\nz(b).\nand substitution\nT510 -> b", fontsize=14, style = filled, fillcolor = lightblue];
338 -> 878 [arrowhead = none ];
878 -> 340;

879 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
338 -> 879 [arrowhead = none ];
879 -> 341;

880 [label="EVAL with clause\nz(c).\nand substitution\nT510 -> c", fontsize=14, style = filled, fillcolor = lightblue];
339 -> 880 [arrowhead = none ];
880 -> 343;

881 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
339 -> 881 [arrowhead = none ];
881 -> 344;

882 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
340 -> 882 [arrowhead = none ];
882 -> 342;

883 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
343 -> 883 [arrowhead = none ];
883 -> 345;

884 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
346 -> 884 [arrowhead = none ];
884 -> 348;

885 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
348 -> 885 [arrowhead = none ];
885 -> 349;

886 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
348 -> 886 [arrowhead = none ];
886 -> 350;

887 [label="ONLY EVAL with clause\ne(X836, X837) :- t(X836, X837).\nand substitution\nT515 -> T523\nX836 -> T523\nX812 -> X838\nX837 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X838)))))", fontsize=14, style = filled, fillcolor = white];
349 -> 887 [arrowhead = none ];
887 -> 351;

888 [label="ONLY EVAL with clause\ne(X1149, X1150) :- ','(t(X1149, .(plus, X1151)), e(X1151, X1150)).\nand substitution\nT515 -> T704\nX1149 -> T704\nX812 -> X1152\nX1150 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1152)))))", fontsize=14, style = filled, fillcolor = white];
350 -> 888 [arrowhead = none ];
888 -> 451;

889 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
351 -> 889 [arrowhead = none ];
889 -> 352;

890 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
352 -> 890 [arrowhead = none ];
890 -> 353;

891 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
352 -> 891 [arrowhead = none ];
891 -> 354;

892 [label="ONLY EVAL with clause\nt(X858, X859) :- n(X858, X859).\nand substitution\nT523 -> T535\nX858 -> T535\nX838 -> X860\nX859 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X860)))))", fontsize=14, style = filled, fillcolor = white];
353 -> 892 [arrowhead = none ];
892 -> 355;

893 [label="ONLY EVAL with clause\nt(X1128, X1129) :- ','(n(X1128, .(star, X1130)), t(X1130, X1129)).\nand substitution\nT523 -> T692\nX1128 -> T692\nX838 -> X1131\nX1129 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1131)))))", fontsize=14, style = filled, fillcolor = white];
354 -> 893 [arrowhead = none ];
893 -> 448;

894 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
355 -> 894 [arrowhead = none ];
894 -> 356;

895 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
356 -> 895 [arrowhead = none ];
895 -> 357;

896 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
356 -> 896 [arrowhead = none ];
896 -> 358;

897 [label="EVAL with clause\nn(.(X871, X872), X872) :- z(X871).\nand substitution\nX871 -> T551\nX872 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))\nT535 -> .(T551, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553))))))\nX860 -> T553\nT552 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))", fontsize=14, style = filled, fillcolor = lightblue];
357 -> 897 [arrowhead = none ];
897 -> 359;

898 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
357 -> 898 [arrowhead = none ];
898 -> 360;

899 [label="EVAL with clause\nn(.(lbrace, X881), X882) :- e(X881, .(rbrace, X882)).\nand substitution\nX881 -> T556\nT535 -> .(lbrace, T556)\nX860 -> X883\nX882 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X883)))))", fontsize=14, style = filled, fillcolor = lightblue];
358 -> 899 [arrowhead = none ];
899 -> 375;

900 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
358 -> 900 [arrowhead = none ];
900 -> 376;

901 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
359 -> 901 [arrowhead = none ];
901 -> 361;

902 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
361 -> 902 [arrowhead = none ];
902 -> 362;

903 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
361 -> 903 [arrowhead = none ];
903 -> 363;

904 [label="EVAL with clause\nz(a).\nand substitution\nT551 -> a", fontsize=14, style = filled, fillcolor = lightblue];
362 -> 904 [arrowhead = none ];
904 -> 364;

905 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
362 -> 905 [arrowhead = none ];
905 -> 365;

906 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
363 -> 906 [arrowhead = none ];
906 -> 367;

907 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
363 -> 907 [arrowhead = none ];
907 -> 368;

908 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
364 -> 908 [arrowhead = none ];
908 -> 366;

909 [label="EVAL with clause\nz(b).\nand substitution\nT551 -> b", fontsize=14, style = filled, fillcolor = lightblue];
367 -> 909 [arrowhead = none ];
909 -> 369;

910 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
367 -> 910 [arrowhead = none ];
910 -> 370;

911 [label="EVAL with clause\nz(c).\nand substitution\nT551 -> c", fontsize=14, style = filled, fillcolor = lightblue];
368 -> 911 [arrowhead = none ];
911 -> 372;

912 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
368 -> 912 [arrowhead = none ];
912 -> 373;

913 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
369 -> 913 [arrowhead = none ];
913 -> 371;

914 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
372 -> 914 [arrowhead = none ];
914 -> 374;

915 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
375 -> 915 [arrowhead = none ];
915 -> 377;

916 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
377 -> 916 [arrowhead = none ];
916 -> 378;

917 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
377 -> 917 [arrowhead = none ];
917 -> 379;

918 [label="ONLY EVAL with clause\ne(X907, X908) :- t(X907, X908).\nand substitution\nT556 -> T564\nX907 -> T564\nX883 -> X909\nX908 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X909))))))", fontsize=14, style = filled, fillcolor = white];
378 -> 918 [arrowhead = none ];
918 -> 380;

919 [label="ONLY EVAL with clause\ne(X1106, X1107) :- ','(t(X1106, .(plus, X1108)), e(X1108, X1107)).\nand substitution\nT556 -> T682\nX1106 -> T682\nX883 -> X1109\nX1107 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1109))))))", fontsize=14, style = filled, fillcolor = white];
379 -> 919 [arrowhead = none ];
919 -> 445;

920 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
380 -> 920 [arrowhead = none ];
920 -> 381;

921 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
381 -> 921 [arrowhead = none ];
921 -> 382;

922 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
381 -> 922 [arrowhead = none ];
922 -> 383;

923 [label="ONLY EVAL with clause\nt(X929, X930) :- n(X929, X930).\nand substitution\nT564 -> T576\nX929 -> T576\nX909 -> X931\nX930 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X931))))))", fontsize=14, style = filled, fillcolor = white];
382 -> 923 [arrowhead = none ];
923 -> 384;

924 [label="ONLY EVAL with clause\nt(X1085, X1086) :- ','(n(X1085, .(star, X1087)), t(X1087, X1086)).\nand substitution\nT564 -> T670\nX1085 -> T670\nX909 -> X1088\nX1086 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1088))))))", fontsize=14, style = filled, fillcolor = white];
383 -> 924 [arrowhead = none ];
924 -> 442;

925 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
384 -> 925 [arrowhead = none ];
925 -> 385;

926 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
385 -> 926 [arrowhead = none ];
926 -> 386;

927 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
385 -> 927 [arrowhead = none ];
927 -> 387;

928 [label="EVAL with clause\nn(.(X942, X943), X943) :- z(X942).\nand substitution\nX942 -> T592\nX943 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))\nT576 -> .(T592, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594)))))))\nX931 -> T594\nT593 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))", fontsize=14, style = filled, fillcolor = lightblue];
386 -> 928 [arrowhead = none ];
928 -> 388;

929 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
386 -> 929 [arrowhead = none ];
929 -> 389;

930 [label="EVAL with clause\nn(.(lbrace, X952), X953) :- e(X952, .(rbrace, X953)).\nand substitution\nX952 -> T597\nT576 -> .(lbrace, T597)\nX931 -> X954\nX953 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X954))))))", fontsize=14, style = filled, fillcolor = lightblue];
387 -> 930 [arrowhead = none ];
930 -> 404;

931 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
387 -> 931 [arrowhead = none ];
931 -> 405;

932 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
388 -> 932 [arrowhead = none ];
932 -> 390;

933 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
390 -> 933 [arrowhead = none ];
933 -> 391;

934 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
390 -> 934 [arrowhead = none ];
934 -> 392;

935 [label="EVAL with clause\nz(a).\nand substitution\nT592 -> a", fontsize=14, style = filled, fillcolor = lightblue];
391 -> 935 [arrowhead = none ];
935 -> 393;

936 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
391 -> 936 [arrowhead = none ];
936 -> 394;

937 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
392 -> 937 [arrowhead = none ];
937 -> 396;

938 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
392 -> 938 [arrowhead = none ];
938 -> 397;

939 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
393 -> 939 [arrowhead = none ];
939 -> 395;

940 [label="EVAL with clause\nz(b).\nand substitution\nT592 -> b", fontsize=14, style = filled, fillcolor = lightblue];
396 -> 940 [arrowhead = none ];
940 -> 398;

941 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
396 -> 941 [arrowhead = none ];
941 -> 399;

942 [label="EVAL with clause\nz(c).\nand substitution\nT592 -> c", fontsize=14, style = filled, fillcolor = lightblue];
397 -> 942 [arrowhead = none ];
942 -> 401;

943 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
397 -> 943 [arrowhead = none ];
943 -> 402;

944 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
398 -> 944 [arrowhead = none ];
944 -> 400;

945 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
401 -> 945 [arrowhead = none ];
945 -> 403;

946 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
404 -> 946 [arrowhead = none ];
946 -> 406;

947 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
406 -> 947 [arrowhead = none ];
947 -> 407;

948 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
406 -> 948 [arrowhead = none ];
948 -> 408;

949 [label="ONLY EVAL with clause\ne(X978, X979) :- t(X978, X979).\nand substitution\nT597 -> T605\nX978 -> T605\nX954 -> X980\nX979 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X980)))))))", fontsize=14, style = filled, fillcolor = white];
407 -> 949 [arrowhead = none ];
949 -> 409;

950 [label="ONLY EVAL with clause\ne(X1063, X1064) :- ','(t(X1063, .(plus, X1065)), e(X1065, X1064)).\nand substitution\nT597 -> T660\nX1063 -> T660\nX954 -> X1066\nX1064 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1066)))))))", fontsize=14, style = filled, fillcolor = white];
408 -> 950 [arrowhead = none ];
950 -> 439;

951 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
409 -> 951 [arrowhead = none ];
951 -> 410;

952 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
410 -> 952 [arrowhead = none ];
952 -> 411;

953 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
410 -> 953 [arrowhead = none ];
953 -> 412;

954 [label="ONLY EVAL with clause\nt(X1000, X1001) :- n(X1000, X1001).\nand substitution\nT605 -> T617\nX1000 -> T617\nX980 -> X1002\nX1001 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1002)))))))", fontsize=14, style = filled, fillcolor = white];
411 -> 954 [arrowhead = none ];
954 -> 413;

955 [label="ONLY EVAL with clause\nt(X1042, X1043) :- ','(n(X1042, .(star, X1044)), t(X1044, X1043)).\nand substitution\nT605 -> T648\nX1042 -> T648\nX980 -> X1045\nX1043 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1045)))))))", fontsize=14, style = filled, fillcolor = white];
412 -> 955 [arrowhead = none ];
955 -> 436;

956 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
413 -> 956 [arrowhead = none ];
956 -> 414;

957 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
414 -> 957 [arrowhead = none ];
957 -> 415;

958 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
414 -> 958 [arrowhead = none ];
958 -> 416;

959 [label="EVAL with clause\nn(.(X1013, X1014), X1014) :- z(X1013).\nand substitution\nX1013 -> T633\nX1014 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))\nT617 -> .(T633, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635))))))))\nX1002 -> T635\nT634 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))", fontsize=14, style = filled, fillcolor = lightblue];
415 -> 959 [arrowhead = none ];
959 -> 417;

960 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
415 -> 960 [arrowhead = none ];
960 -> 418;

961 [label="EVAL with clause\nn(.(lbrace, X1023), X1024) :- e(X1023, .(rbrace, X1024)).\nand substitution\nX1023 -> T638\nT617 -> .(lbrace, T638)\nX1002 -> X1025\nX1024 -> .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))", fontsize=14, style = filled, fillcolor = lightblue];
416 -> 961 [arrowhead = none ];
961 -> 433;

962 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
416 -> 962 [arrowhead = none ];
962 -> 434;

963 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
417 -> 963 [arrowhead = none ];
963 -> 419;

964 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
419 -> 964 [arrowhead = none ];
964 -> 420;

965 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
419 -> 965 [arrowhead = none ];
965 -> 421;

966 [label="EVAL with clause\nz(a).\nand substitution\nT633 -> a", fontsize=14, style = filled, fillcolor = lightblue];
420 -> 966 [arrowhead = none ];
966 -> 422;

967 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
420 -> 967 [arrowhead = none ];
967 -> 423;

968 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
421 -> 968 [arrowhead = none ];
968 -> 425;

969 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
421 -> 969 [arrowhead = none ];
969 -> 426;

970 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
422 -> 970 [arrowhead = none ];
970 -> 424;

971 [label="EVAL with clause\nz(b).\nand substitution\nT633 -> b", fontsize=14, style = filled, fillcolor = lightblue];
425 -> 971 [arrowhead = none ];
971 -> 427;

972 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
425 -> 972 [arrowhead = none ];
972 -> 428;

973 [label="EVAL with clause\nz(c).\nand substitution\nT633 -> c", fontsize=14, style = filled, fillcolor = lightblue];
426 -> 973 [arrowhead = none ];
973 -> 430;

974 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
426 -> 974 [arrowhead = none ];
974 -> 431;

975 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
427 -> 975 [arrowhead = none ];
975 -> 429;

976 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
430 -> 976 [arrowhead = none ];
976 -> 432;

977 [label="GENERALIZATION\nT640 <-- .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))", fontsize=14, style = filled, fillcolor = violet];
433 -> 977 [arrowhead = none ];
977 -> 435;

978 [label="INSTANCE with matching:\nT1 -> T638\nT2 -> .(rbrace, T640)", fontsize=14, style = filled, fillcolor = lightgrey];
435 -> 978 [arrowhead = none , style=dashed];
978 -> 1[style=dashed];

979 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
436 -> 979 [arrowhead = none ];
979 -> 437;

980 [label="SPLIT 2\nnew knowledge:\nT652 is ground\nreplacements:\nX1044 -> T652", fontsize=14, style = filled, fillcolor = violet];
436 -> 980 [arrowhead = none ];
980 -> 438;

981 [label="INSTANCE with matching:\nT62 -> T648\nX59 -> X1044", fontsize=14, style = filled, fillcolor = lightgrey];
437 -> 981 [arrowhead = none , style=dashed];
981 -> 32[style=dashed];

982 [label="INSTANCE with matching:\nT605 -> T652\nX980 -> X1045", fontsize=14, style = filled, fillcolor = lightgrey];
438 -> 982 [arrowhead = none , style=dashed];
982 -> 409[style=dashed];

983 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
439 -> 983 [arrowhead = none ];
983 -> 440;

984 [label="SPLIT 2\nnew knowledge:\nT662 is ground\nreplacements:\nX1065 -> T662", fontsize=14, style = filled, fillcolor = violet];
439 -> 984 [arrowhead = none ];
984 -> 441;

985 [label="INSTANCE with matching:\nT357 -> T660\nX550 -> X1065", fontsize=14, style = filled, fillcolor = lightgrey];
440 -> 985 [arrowhead = none , style=dashed];
985 -> 234[style=dashed];

986 [label="INSTANCE with matching:\nT597 -> T662\nX954 -> X1066", fontsize=14, style = filled, fillcolor = lightgrey];
441 -> 986 [arrowhead = none , style=dashed];
986 -> 404[style=dashed];

987 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
442 -> 987 [arrowhead = none ];
987 -> 443;

988 [label="SPLIT 2\nnew knowledge:\nT674 is ground\nreplacements:\nX1087 -> T674", fontsize=14, style = filled, fillcolor = violet];
442 -> 988 [arrowhead = none ];
988 -> 444;

989 [label="INSTANCE with matching:\nT62 -> T670\nX59 -> X1087", fontsize=14, style = filled, fillcolor = lightgrey];
443 -> 989 [arrowhead = none , style=dashed];
989 -> 32[style=dashed];

990 [label="INSTANCE with matching:\nT564 -> T674\nX909 -> X1088", fontsize=14, style = filled, fillcolor = lightgrey];
444 -> 990 [arrowhead = none , style=dashed];
990 -> 380[style=dashed];

991 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
445 -> 991 [arrowhead = none ];
991 -> 446;

992 [label="SPLIT 2\nnew knowledge:\nT684 is ground\nreplacements:\nX1108 -> T684", fontsize=14, style = filled, fillcolor = violet];
445 -> 992 [arrowhead = none ];
992 -> 447;

993 [label="INSTANCE with matching:\nT357 -> T682\nX550 -> X1108", fontsize=14, style = filled, fillcolor = lightgrey];
446 -> 993 [arrowhead = none , style=dashed];
993 -> 234[style=dashed];

994 [label="INSTANCE with matching:\nT556 -> T684\nX883 -> X1109", fontsize=14, style = filled, fillcolor = lightgrey];
447 -> 994 [arrowhead = none , style=dashed];
994 -> 375[style=dashed];

995 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
448 -> 995 [arrowhead = none ];
995 -> 449;

996 [label="SPLIT 2\nnew knowledge:\nT696 is ground\nreplacements:\nX1130 -> T696", fontsize=14, style = filled, fillcolor = violet];
448 -> 996 [arrowhead = none ];
996 -> 450;

997 [label="INSTANCE with matching:\nT62 -> T692\nX59 -> X1130", fontsize=14, style = filled, fillcolor = lightgrey];
449 -> 997 [arrowhead = none , style=dashed];
997 -> 32[style=dashed];

998 [label="INSTANCE with matching:\nT523 -> T696\nX838 -> X1131", fontsize=14, style = filled, fillcolor = lightgrey];
450 -> 998 [arrowhead = none , style=dashed];
998 -> 351[style=dashed];

999 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
451 -> 999 [arrowhead = none ];
999 -> 452;

1000 [label="SPLIT 2\nnew knowledge:\nT706 is ground\nreplacements:\nX1151 -> T706", fontsize=14, style = filled, fillcolor = violet];
451 -> 1000 [arrowhead = none ];
1000 -> 453;

1001 [label="INSTANCE with matching:\nT357 -> T704\nX550 -> X1151", fontsize=14, style = filled, fillcolor = lightgrey];
452 -> 1001 [arrowhead = none , style=dashed];
1001 -> 234[style=dashed];

1002 [label="INSTANCE with matching:\nT515 -> T706\nX812 -> X1152", fontsize=14, style = filled, fillcolor = lightgrey];
453 -> 1002 [arrowhead = none , style=dashed];
1002 -> 346[style=dashed];

1003 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
454 -> 1003 [arrowhead = none ];
1003 -> 455;

1004 [label="SPLIT 2\nnew knowledge:\nT718 is ground\nreplacements:\nX1173 -> T718", fontsize=14, style = filled, fillcolor = violet];
454 -> 1004 [arrowhead = none ];
1004 -> 456;

1005 [label="INSTANCE with matching:\nT62 -> T714\nX59 -> X1173", fontsize=14, style = filled, fillcolor = lightgrey];
455 -> 1005 [arrowhead = none , style=dashed];
1005 -> 32[style=dashed];

1006 [label="INSTANCE with matching:\nT482 -> T718\nX767 -> X1174", fontsize=14, style = filled, fillcolor = lightgrey];
456 -> 1006 [arrowhead = none , style=dashed];
1006 -> 322[style=dashed];

1007 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
457 -> 1007 [arrowhead = none ];
1007 -> 458;

1008 [label="SPLIT 2\nnew knowledge:\nT728 is ground\nreplacements:\nX1194 -> T728", fontsize=14, style = filled, fillcolor = violet];
457 -> 1008 [arrowhead = none ];
1008 -> 459;

1009 [label="INSTANCE with matching:\nT357 -> T726\nX550 -> X1194", fontsize=14, style = filled, fillcolor = lightgrey];
458 -> 1009 [arrowhead = none , style=dashed];
1009 -> 234[style=dashed];

1010 [label="INSTANCE with matching:\nT474 -> T728\nX741 -> X1195", fontsize=14, style = filled, fillcolor = lightgrey];
459 -> 1010 [arrowhead = none , style=dashed];
1010 -> 317[style=dashed];

1011 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
460 -> 1011 [arrowhead = none ];
1011 -> 461;

1012 [label="SPLIT 2\nnew knowledge:\nT740 is ground\nreplacements:\nX1216 -> T740", fontsize=14, style = filled, fillcolor = violet];
460 -> 1012 [arrowhead = none ];
1012 -> 462;

1013 [label="INSTANCE with matching:\nT62 -> T736\nX59 -> X1216", fontsize=14, style = filled, fillcolor = lightgrey];
461 -> 1013 [arrowhead = none , style=dashed];
1013 -> 32[style=dashed];

1014 [label="INSTANCE with matching:\nT441 -> T740\nX696 -> X1217", fontsize=14, style = filled, fillcolor = lightgrey];
462 -> 1014 [arrowhead = none , style=dashed];
1014 -> 293[style=dashed];

1015 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
463 -> 1015 [arrowhead = none ];
1015 -> 464;

1016 [label="SPLIT 2\nnew knowledge:\nT750 is ground\nreplacements:\nX1237 -> T750", fontsize=14, style = filled, fillcolor = violet];
463 -> 1016 [arrowhead = none ];
1016 -> 465;

1017 [label="INSTANCE with matching:\nT357 -> T748\nX550 -> X1237", fontsize=14, style = filled, fillcolor = lightgrey];
464 -> 1017 [arrowhead = none , style=dashed];
1017 -> 234[style=dashed];

1018 [label="INSTANCE with matching:\nT433 -> T750\nX670 -> X1238", fontsize=14, style = filled, fillcolor = lightgrey];
465 -> 1018 [arrowhead = none , style=dashed];
1018 -> 288[style=dashed];

1019 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
466 -> 1019 [arrowhead = none ];
1019 -> 467;

1020 [label="SPLIT 2\nnew knowledge:\nT762 is ground\nreplacements:\nX1259 -> T762", fontsize=14, style = filled, fillcolor = violet];
466 -> 1020 [arrowhead = none ];
1020 -> 468;

1021 [label="INSTANCE with matching:\nT62 -> T758\nX59 -> X1259", fontsize=14, style = filled, fillcolor = lightgrey];
467 -> 1021 [arrowhead = none , style=dashed];
1021 -> 32[style=dashed];

1022 [label="INSTANCE with matching:\nT400 -> T762\nX625 -> X1260", fontsize=14, style = filled, fillcolor = lightgrey];
468 -> 1022 [arrowhead = none , style=dashed];
1022 -> 264[style=dashed];

1023 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
469 -> 1023 [arrowhead = none ];
1023 -> 470;

1024 [label="SPLIT 2\nnew knowledge:\nT772 is ground\nreplacements:\nX1280 -> T772", fontsize=14, style = filled, fillcolor = violet];
469 -> 1024 [arrowhead = none ];
1024 -> 471;

1025 [label="INSTANCE with matching:\nT357 -> T770\nX550 -> X1280", fontsize=14, style = filled, fillcolor = lightgrey];
470 -> 1025 [arrowhead = none , style=dashed];
1025 -> 234[style=dashed];

1026 [label="INSTANCE with matching:\nT392 -> T772\nX599 -> X1281", fontsize=14, style = filled, fillcolor = lightgrey];
471 -> 1026 [arrowhead = none , style=dashed];
1026 -> 259[style=dashed];

1027 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
472 -> 1027 [arrowhead = none ];
1027 -> 473;

1028 [label="SPLIT 2\nnew knowledge:\nT784 is ground\nreplacements:\nX1302 -> T784", fontsize=14, style = filled, fillcolor = violet];
472 -> 1028 [arrowhead = none ];
1028 -> 474;

1029 [label="INSTANCE with matching:\nT62 -> T780\nX59 -> X1302", fontsize=14, style = filled, fillcolor = lightgrey];
473 -> 1029 [arrowhead = none , style=dashed];
1029 -> 32[style=dashed];

1030 [label="INSTANCE with matching:\nT357 -> T784\nX550 -> X1303", fontsize=14, style = filled, fillcolor = lightgrey];
474 -> 1030 [arrowhead = none , style=dashed];
1030 -> 234[style=dashed];

1031 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
475 -> 1031 [arrowhead = none ];
1031 -> 476;

1032 [label="SPLIT 2\nnew knowledge:\nT799 is ground\nreplacements:\nX1325 -> T799", fontsize=14, style = filled, fillcolor = violet];
475 -> 1032 [arrowhead = none ];
1032 -> 477;

1033 [label="INSTANCE with matching:\nT62 -> T795\nX59 -> X1325", fontsize=14, style = filled, fillcolor = lightgrey];
476 -> 1033 [arrowhead = none , style=dashed];
1033 -> 32[style=dashed];

1034 [label="INSTANCE with matching:\nT261 -> T799\nX394 -> X1326", fontsize=14, style = filled, fillcolor = lightgrey];
477 -> 1034 [arrowhead = none , style=dashed];
1034 -> 174[style=dashed];

1035 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
478 -> 1035 [arrowhead = none ];
1035 -> 479;

1036 [label="SPLIT 2\nnew knowledge:\nT809 is ground\nreplacements:\nX1346 -> T809", fontsize=14, style = filled, fillcolor = violet];
478 -> 1036 [arrowhead = none ];
1036 -> 480;

1037 [label="INSTANCE with matching:\nT357 -> T807\nX550 -> X1346", fontsize=14, style = filled, fillcolor = lightgrey];
479 -> 1037 [arrowhead = none , style=dashed];
1037 -> 234[style=dashed];

1038 [label="INSTANCE with matching:\nT253 -> T809\nX368 -> X1347", fontsize=14, style = filled, fillcolor = lightgrey];
480 -> 1038 [arrowhead = none , style=dashed];
1038 -> 169[style=dashed];

1039 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
481 -> 1039 [arrowhead = none ];
1039 -> 482;

1040 [label="SPLIT 2\nnew knowledge:\nT821 is ground\nreplacements:\nX1368 -> T821", fontsize=14, style = filled, fillcolor = violet];
481 -> 1040 [arrowhead = none ];
1040 -> 483;

1041 [label="INSTANCE with matching:\nT62 -> T817\nX59 -> X1368", fontsize=14, style = filled, fillcolor = lightgrey];
482 -> 1041 [arrowhead = none , style=dashed];
1041 -> 32[style=dashed];

1042 [label="INSTANCE with matching:\nT220 -> T821\nX323 -> X1369", fontsize=14, style = filled, fillcolor = lightgrey];
483 -> 1042 [arrowhead = none , style=dashed];
1042 -> 145[style=dashed];

1043 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
484 -> 1043 [arrowhead = none ];
1043 -> 485;

1044 [label="SPLIT 2\nnew knowledge:\nT831 is ground\nreplacements:\nX1389 -> T831", fontsize=14, style = filled, fillcolor = violet];
484 -> 1044 [arrowhead = none ];
1044 -> 486;

1045 [label="INSTANCE with matching:\nT807 -> T829\nX1346 -> X1389", fontsize=14, style = filled, fillcolor = lightgrey];
485 -> 1045 [arrowhead = none , style=dashed];
1045 -> 479[style=dashed];

1046 [label="INSTANCE with matching:\nT212 -> T831\nX297 -> X1390", fontsize=14, style = filled, fillcolor = lightgrey];
486 -> 1046 [arrowhead = none , style=dashed];
1046 -> 140[style=dashed];

1047 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
487 -> 1047 [arrowhead = none ];
1047 -> 488;

1048 [label="SPLIT 2\nnew knowledge:\nT843 is ground\nreplacements:\nX1411 -> T843", fontsize=14, style = filled, fillcolor = violet];
487 -> 1048 [arrowhead = none ];
1048 -> 489;

1049 [label="INSTANCE with matching:\nT62 -> T839\nX59 -> X1411", fontsize=14, style = filled, fillcolor = lightgrey];
488 -> 1049 [arrowhead = none , style=dashed];
1049 -> 32[style=dashed];

1050 [label="INSTANCE with matching:\nT179 -> T843\nX252 -> X1412", fontsize=14, style = filled, fillcolor = lightgrey];
489 -> 1050 [arrowhead = none , style=dashed];
1050 -> 116[style=dashed];

1051 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
490 -> 1051 [arrowhead = none ];
1051 -> 491;

1052 [label="SPLIT 2\nnew knowledge:\nT853 is ground\nreplacements:\nX1432 -> T853", fontsize=14, style = filled, fillcolor = violet];
490 -> 1052 [arrowhead = none ];
1052 -> 492;

1053 [label="INSTANCE with matching:\nT829 -> T851\nX1389 -> X1432", fontsize=14, style = filled, fillcolor = lightgrey];
491 -> 1053 [arrowhead = none , style=dashed];
1053 -> 485[style=dashed];

1054 [label="INSTANCE with matching:\nT171 -> T853\nX226 -> X1433", fontsize=14, style = filled, fillcolor = lightgrey];
492 -> 1054 [arrowhead = none , style=dashed];
1054 -> 111[style=dashed];

1055 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
493 -> 1055 [arrowhead = none ];
1055 -> 494;

1056 [label="SPLIT 2\nnew knowledge:\nT865 is ground\nreplacements:\nX1454 -> T865", fontsize=14, style = filled, fillcolor = violet];
493 -> 1056 [arrowhead = none ];
1056 -> 495;

1057 [label="INSTANCE with matching:\nT62 -> T861\nX59 -> X1454", fontsize=14, style = filled, fillcolor = lightgrey];
494 -> 1057 [arrowhead = none , style=dashed];
1057 -> 32[style=dashed];

1058 [label="INSTANCE with matching:\nT138 -> T865\nX181 -> X1455", fontsize=14, style = filled, fillcolor = lightgrey];
495 -> 1058 [arrowhead = none , style=dashed];
1058 -> 87[style=dashed];

1059 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
496 -> 1059 [arrowhead = none ];
1059 -> 497;

1060 [label="SPLIT 2\nnew knowledge:\nT875 is ground\nreplacements:\nX1475 -> T875", fontsize=14, style = filled, fillcolor = violet];
496 -> 1060 [arrowhead = none ];
1060 -> 498;

1061 [label="INSTANCE with matching:\nT851 -> T873\nX1432 -> X1475", fontsize=14, style = filled, fillcolor = lightgrey];
497 -> 1061 [arrowhead = none , style=dashed];
1061 -> 491[style=dashed];

1062 [label="INSTANCE with matching:\nT130 -> T875\nX155 -> X1476", fontsize=14, style = filled, fillcolor = lightgrey];
498 -> 1062 [arrowhead = none , style=dashed];
1062 -> 82[style=dashed];

1063 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
499 -> 1063 [arrowhead = none ];
1063 -> 500;

1064 [label="SPLIT 2\nnew knowledge:\nT887 is ground\nreplacements:\nX1497 -> T887", fontsize=14, style = filled, fillcolor = violet];
499 -> 1064 [arrowhead = none ];
1064 -> 501;

1065 [label="INSTANCE with matching:\nT62 -> T883\nX59 -> X1497", fontsize=14, style = filled, fillcolor = lightgrey];
500 -> 1065 [arrowhead = none , style=dashed];
1065 -> 32[style=dashed];

1066 [label="INSTANCE with matching:\nT97 -> T887\nX110 -> X1498", fontsize=14, style = filled, fillcolor = lightgrey];
501 -> 1066 [arrowhead = none , style=dashed];
1066 -> 58[style=dashed];

1067 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
502 -> 1067 [arrowhead = none ];
1067 -> 503;

1068 [label="SPLIT 2\nnew knowledge:\nT897 is ground\nreplacements:\nX1518 -> T897", fontsize=14, style = filled, fillcolor = violet];
502 -> 1068 [arrowhead = none ];
1068 -> 504;

1069 [label="INSTANCE with matching:\nT873 -> T895\nX1475 -> X1518", fontsize=14, style = filled, fillcolor = lightgrey];
503 -> 1069 [arrowhead = none , style=dashed];
1069 -> 497[style=dashed];

1070 [label="INSTANCE with matching:\nT89 -> T897\nX84 -> X1519", fontsize=14, style = filled, fillcolor = lightgrey];
504 -> 1070 [arrowhead = none , style=dashed];
1070 -> 53[style=dashed];

1071 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
505 -> 1071 [arrowhead = none ];
1071 -> 506;

1072 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
505 -> 1072 [arrowhead = none ];
1072 -> 507;

1073 [label="ONLY EVAL with clause\nt(X1543, X1544) :- n(X1543, X1544).\nand substitution\nT68 -> T916\nX1543 -> T916\nT64 -> T918\nX1544 -> T918\nT917 -> T918", fontsize=14, style = filled, fillcolor = white];
506 -> 1073 [arrowhead = none ];
1073 -> 508;

1074 [label="ONLY EVAL with clause\nt(X1554, X1555) :- ','(n(X1554, .(star, X1556)), t(X1556, X1555)).\nand substitution\nT68 -> T929\nX1554 -> T929\nT64 -> T931\nX1555 -> T931\nT930 -> T931", fontsize=14, style = filled, fillcolor = white];
507 -> 1074 [arrowhead = none ];
1074 -> 509;

1075 [label="INSTANCE with matching:\nT22 -> T916\nT24 -> T918", fontsize=14, style = filled, fillcolor = lightgrey];
508 -> 1075 [arrowhead = none , style=dashed];
1075 -> 7[style=dashed];

1076 [label="INSTANCE with matching:\nT62 -> T929\nX59 -> X1556\nT64 -> T931", fontsize=14, style = filled, fillcolor = lightgrey];
509 -> 1076 [arrowhead = none , style=dashed];
1076 -> 31[style=dashed];

1077 [label="ONLY EVAL with clause\ne(X1567, X1568) :- ','(t(X1567, .(plus, X1569)), e(X1569, X1568)).\nand substitution\nT5 -> T941\nX1567 -> T941\nT2 -> T943\nX1568 -> T943\nT942 -> T943", fontsize=14, style = filled, fillcolor = white];
510 -> 1077 [arrowhead = none ];
1077 -> 511;

1078 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
511 -> 1078 [arrowhead = none ];
1078 -> 512;

1079 [label="SPLIT 2\nnew knowledge:\nT945 is ground\nreplacements:\nX1569 -> T945", fontsize=14, style = filled, fillcolor = violet];
511 -> 1079 [arrowhead = none ];
1079 -> 513;

1080 [label="INSTANCE with matching:\nT895 -> T941\nX1518 -> X1569", fontsize=14, style = filled, fillcolor = lightgrey];
512 -> 1080 [arrowhead = none , style=dashed];
1080 -> 503[style=dashed];

1081 [label="INSTANCE with matching:\nT1 -> T945\nT2 -> T943", fontsize=14, style = filled, fillcolor = lightgrey];
513 -> 1081 [arrowhead = none , style=dashed];
1081 -> 1[style=dashed];

}

(2) Obligation:

Clauses:

n32(.(a, .(star, T86)), T86).
n32(.(b, .(star, T86)), T86).
n32(.(c, .(star, T86)), T86).
n32(.(lbrace, T89), X84) :- e53(T89, X84).
t203(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332).
t203(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332).
t203(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332).
t203(.(lbrace, T335), X510) :- e1(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))).
t203(T345, X530) :- n32(T345, X529).
t203(T345, X530) :- ','(n32(T345, T349), t203(T349, X530)).
e198(T302, X465) :- t203(T302, X465).
e198(T357, X551) :- t234(T357, X550).
e198(T357, X551) :- ','(t234(T357, T359), e198(T359, X551)).
t409(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635).
t409(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635).
t409(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635).
t409(.(lbrace, T638), X1025) :- e1(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))).
t409(T648, X1045) :- n32(T648, X1044).
t409(T648, X1045) :- ','(n32(T648, T652), t409(T652, X1045)).
t234(.(a, .(plus, T389)), T389).
t234(.(b, .(plus, T389)), T389).
t234(.(c, .(plus, T389)), T389).
t234(.(lbrace, T392), X599) :- e259(T392, X599).
t234(T780, X1303) :- n32(T780, X1302).
t234(T780, X1303) :- ','(n32(T780, T784), t234(T784, X1303)).
e404(T605, X980) :- t409(T605, X980).
e404(T660, X1066) :- t234(T660, X1065).
e404(T660, X1066) :- ','(t234(T660, T662), e404(T662, X1066)).
t380(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594).
t380(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594).
t380(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594).
t380(.(lbrace, T597), X954) :- e404(T597, X954).
t380(T670, X1088) :- n32(T670, X1087).
t380(T670, X1088) :- ','(n32(T670, T674), t380(T674, X1088)).
e375(T564, X909) :- t380(T564, X909).
e375(T682, X1109) :- t234(T682, X1108).
e375(T682, X1109) :- ','(t234(T682, T684), e375(T684, X1109)).
t351(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553).
t351(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553).
t351(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553).
t351(.(lbrace, T556), X883) :- e375(T556, X883).
t351(T692, X1131) :- n32(T692, X1130).
t351(T692, X1131) :- ','(n32(T692, T696), t351(T696, X1131)).
e346(T523, X838) :- t351(T523, X838).
e346(T704, X1152) :- t234(T704, X1151).
e346(T704, X1152) :- ','(t234(T704, T706), e346(T706, X1152)).
t322(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512).
t322(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512).
t322(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512).
t322(.(lbrace, T515), X812) :- e346(T515, X812).
t322(T714, X1174) :- n32(T714, X1173).
t322(T714, X1174) :- ','(n32(T714, T718), t322(T718, X1174)).
e317(T482, X767) :- t322(T482, X767).
e317(T726, X1195) :- t234(T726, X1194).
e317(T726, X1195) :- ','(t234(T726, T728), e317(T728, X1195)).
t293(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471).
t293(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471).
t293(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471).
t293(.(lbrace, T474), X741) :- e317(T474, X741).
t293(T736, X1217) :- n32(T736, X1216).
t293(T736, X1217) :- ','(n32(T736, T740), t293(T740, X1217)).
e288(T441, X696) :- t293(T441, X696).
e288(T748, X1238) :- t234(T748, X1237).
e288(T748, X1238) :- ','(t234(T748, T750), e288(T750, X1238)).
t264(.(a, .(rbrace, .(plus, T430))), T430).
t264(.(b, .(rbrace, .(plus, T430))), T430).
t264(.(c, .(rbrace, .(plus, T430))), T430).
t264(.(lbrace, T433), X670) :- e288(T433, X670).
t264(T758, X1260) :- n32(T758, X1259).
t264(T758, X1260) :- ','(n32(T758, T762), t264(T762, X1260)).
e259(T400, X625) :- t264(T400, X625).
e259(T770, X1281) :- t234(T770, X1280).
e259(T770, X1281) :- ','(t234(T770, T772), e259(T772, X1281)).
t174(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291).
t174(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291).
t174(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291).
t174(.(lbrace, T294), X439) :- e198(T294, X439).
t174(T795, X1326) :- n32(T795, X1325).
t174(T795, X1326) :- ','(n32(T795, T799), t174(T799, X1326)).
e169(T261, X394) :- t174(T261, X394).
e169(T807, X1347) :- t234(T807, X1346).
e169(T807, X1347) :- ','(t234(T807, T809), e169(T809, X1347)).
t145(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250).
t145(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250).
t145(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250).
t145(.(lbrace, T253), X368) :- e169(T253, X368).
t145(T817, X1369) :- n32(T817, X1368).
t145(T817, X1369) :- ','(n32(T817, T821), t145(T821, X1369)).
e140(T220, X323) :- t145(T220, X323).
e140(T829, X1390) :- t234(T829, X1389).
e140(T829, X1390) :- ','(t234(T829, T831), e140(T831, X1390)).
t116(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209).
t116(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209).
t116(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209).
t116(.(lbrace, T212), X297) :- e140(T212, X297).
t116(T839, X1412) :- n32(T839, X1411).
t116(T839, X1412) :- ','(n32(T839, T843), t116(T843, X1412)).
e111(T179, X252) :- t116(T179, X252).
e111(T851, X1433) :- t234(T851, X1432).
e111(T851, X1433) :- ','(t234(T851, T853), e111(T853, X1433)).
t87(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168).
t87(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168).
t87(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168).
t87(.(lbrace, T171), X226) :- e111(T171, X226).
t87(T861, X1455) :- n32(T861, X1454).
t87(T861, X1455) :- ','(n32(T861, T865), t87(T865, X1455)).
e82(T138, X181) :- t87(T138, X181).
e82(T873, X1476) :- t234(T873, X1475).
e82(T873, X1476) :- ','(t234(T873, T875), e82(T875, X1476)).
t58(.(a, .(rbrace, .(star, T127))), T127).
t58(.(b, .(rbrace, .(star, T127))), T127).
t58(.(c, .(rbrace, .(star, T127))), T127).
t58(.(lbrace, T130), X155) :- e82(T130, X155).
t58(T883, X1498) :- n32(T883, X1497).
t58(T883, X1498) :- ','(n32(T883, T887), t58(T887, X1498)).
e53(T97, X110) :- t58(T97, X110).
e53(T895, X1519) :- t234(T895, X1518).
e53(T895, X1519) :- ','(t234(T895, T897), e53(T897, X1519)).
n7(.(a, T36), T36).
n7(.(b, T36), T36).
n7(.(c, T36), T36).
n7(.(lbrace, T41), T43) :- e1(T41, .(rbrace, T43)).
p31(T62, X59, T64) :- n32(T62, X59).
p31(T62, T916, T918) :- ','(n32(T62, T916), n7(T916, T918)).
p31(T62, T929, T931) :- ','(n32(T62, T929), p31(T929, X1556, T931)).
e1(T22, T24) :- n7(T22, T24).
e1(T62, T64) :- p31(T62, X59, T64).
e1(T941, T943) :- t234(T941, X1569).
e1(T941, T943) :- ','(t234(T941, T945), e1(T945, T943)).

Queries:

e1(g,a).

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
e1_in: (b,f) (f,f)
n7_in: (b,f) (f,f)
p31_in: (b,f,f) (f,f,f)
n32_in: (b,f) (f,f)
e53_in: (b,f) (f,f)
t58_in: (b,f) (f,f)
e82_in: (b,f) (f,f)
t87_in: (b,f) (f,f)
e111_in: (b,f) (f,f)
t116_in: (b,f) (f,f)
e140_in: (b,f) (f,f)
t145_in: (b,f) (f,f)
e169_in: (b,f) (f,f)
t174_in: (b,f) (f,f)
e198_in: (b,f) (f,f)
t203_in: (b,f) (f,f)
t234_in: (b,f) (f,f)
e259_in: (b,f) (f,f)
t264_in: (b,f) (f,f)
e288_in: (b,f) (f,f)
t293_in: (b,f) (f,f)
e317_in: (b,f) (f,f)
t322_in: (b,f) (f,f)
e346_in: (b,f) (f,f)
t351_in: (b,f) (f,f)
e375_in: (b,f) (f,f)
t380_in: (b,f) (f,f)
e404_in: (b,f) (f,f)
t409_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:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x1, x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga(x1)
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x1, x3)
U109_ga(x1, x2, x3)  =  U109_ga(x1, x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x1, x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x1, x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga(x1)
U94_ga(x1, x2, x3)  =  U94_ga(x1, x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x1, x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga(x1)
U86_ga(x1, x2, x3)  =  U86_ga(x1, x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x1, x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x1, x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga(x1)
U70_ga(x1, x2, x3)  =  U70_ga(x1, x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga(x1)
U62_ga(x1, x2, x3)  =  U62_ga(x1, x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga(x1)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga(x1)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x1, x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga(x1)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga(x1)
U38_ga(x1, x2, x3)  =  U38_ga(x1, x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x1, x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga(x1)
U30_ga(x1, x2, x3)  =  U30_ga(x1, x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga(x1)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U111_ga(x1, x2, x3)  =  U111_ga(x1, x3)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U112_ga(x1, x2, x3)  =  U112_ga(x1, x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
e404_out_ga(x1, x2)  =  e404_out_ga(x1)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
e375_out_ga(x1, x2)  =  e375_out_ga(x1)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
U28_ga(x1, x2, x3)  =  U28_ga(x1, x3)
U29_ga(x1, x2, x3)  =  U29_ga(x1, x3)
U31_ga(x1, x2, x3)  =  U31_ga(x1, x3)
U32_ga(x1, x2, x3)  =  U32_ga(x1, x3)
U33_ga(x1, x2, x3)  =  U33_ga(x1, x3)
e346_out_ga(x1, x2)  =  e346_out_ga(x1)
U35_ga(x1, x2, x3)  =  U35_ga(x1, x3)
U36_ga(x1, x2, x3)  =  U36_ga(x1, x3)
U37_ga(x1, x2, x3)  =  U37_ga(x1, x3)
U39_ga(x1, x2, x3)  =  U39_ga(x1, x3)
U40_ga(x1, x2, x3)  =  U40_ga(x1, x3)
U41_ga(x1, x2, x3)  =  U41_ga(x1, x3)
e317_out_ga(x1, x2)  =  e317_out_ga(x1)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
e288_out_ga(x1, x2)  =  e288_out_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
e259_out_ga(x1, x2)  =  e259_out_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
U60_ga(x1, x2, x3)  =  U60_ga(x1, x3)
U61_ga(x1, x2, x3)  =  U61_ga(x1, x3)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
e198_out_ga(x1, x2)  =  e198_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U63_ga(x1, x2, x3)  =  U63_ga(x1, x3)
U64_ga(x1, x2, x3)  =  U64_ga(x1, x3)
U65_ga(x1, x2, x3)  =  U65_ga(x1, x3)
e169_out_ga(x1, x2)  =  e169_out_ga(x1)
U67_ga(x1, x2, x3)  =  U67_ga(x1, x3)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
U69_ga(x1, x2, x3)  =  U69_ga(x1, x3)
U71_ga(x1, x2, x3)  =  U71_ga(x1, x3)
U72_ga(x1, x2, x3)  =  U72_ga(x1, x3)
U73_ga(x1, x2, x3)  =  U73_ga(x1, x3)
e140_out_ga(x1, x2)  =  e140_out_ga(x1)
U75_ga(x1, x2, x3)  =  U75_ga(x1, x3)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
U77_ga(x1, x2, x3)  =  U77_ga(x1, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x3)
U80_ga(x1, x2, x3)  =  U80_ga(x1, x3)
U81_ga(x1, x2, x3)  =  U81_ga(x1, x3)
e111_out_ga(x1, x2)  =  e111_out_ga(x1)
U83_ga(x1, x2, x3)  =  U83_ga(x1, x3)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
U85_ga(x1, x2, x3)  =  U85_ga(x1, x3)
U87_ga(x1, x2, x3)  =  U87_ga(x1, x3)
U88_ga(x1, x2, x3)  =  U88_ga(x1, x3)
U89_ga(x1, x2, x3)  =  U89_ga(x1, x3)
e82_out_ga(x1, x2)  =  e82_out_ga(x1)
U91_ga(x1, x2, x3)  =  U91_ga(x1, x3)
U92_ga(x1, x2, x3)  =  U92_ga(x1, x3)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
U95_ga(x1, x2, x3)  =  U95_ga(x1, x3)
U96_ga(x1, x2, x3)  =  U96_ga(x1, x3)
U97_ga(x1, x2, x3)  =  U97_ga(x1, x3)
e53_out_ga(x1, x2)  =  e53_out_ga(x1)
U99_ga(x1, x2, x3)  =  U99_ga(x1, x3)
U100_ga(x1, x2, x3)  =  U100_ga(x1, x3)
U101_ga(x1, x2, x3)  =  U101_ga(x1, x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa(x1)
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x1, x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x1, x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x1, x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x1, x4)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x1, x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga(x1)
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x1, x3)
U109_ga(x1, x2, x3)  =  U109_ga(x1, x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x1, x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x1, x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga(x1)
U94_ga(x1, x2, x3)  =  U94_ga(x1, x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x1, x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga(x1)
U86_ga(x1, x2, x3)  =  U86_ga(x1, x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x1, x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x1, x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga(x1)
U70_ga(x1, x2, x3)  =  U70_ga(x1, x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga(x1)
U62_ga(x1, x2, x3)  =  U62_ga(x1, x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga(x1)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga(x1)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x1, x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga(x1)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga(x1)
U38_ga(x1, x2, x3)  =  U38_ga(x1, x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x1, x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga(x1)
U30_ga(x1, x2, x3)  =  U30_ga(x1, x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga(x1)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U111_ga(x1, x2, x3)  =  U111_ga(x1, x3)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U112_ga(x1, x2, x3)  =  U112_ga(x1, x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
e404_out_ga(x1, x2)  =  e404_out_ga(x1)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
e375_out_ga(x1, x2)  =  e375_out_ga(x1)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
U28_ga(x1, x2, x3)  =  U28_ga(x1, x3)
U29_ga(x1, x2, x3)  =  U29_ga(x1, x3)
U31_ga(x1, x2, x3)  =  U31_ga(x1, x3)
U32_ga(x1, x2, x3)  =  U32_ga(x1, x3)
U33_ga(x1, x2, x3)  =  U33_ga(x1, x3)
e346_out_ga(x1, x2)  =  e346_out_ga(x1)
U35_ga(x1, x2, x3)  =  U35_ga(x1, x3)
U36_ga(x1, x2, x3)  =  U36_ga(x1, x3)
U37_ga(x1, x2, x3)  =  U37_ga(x1, x3)
U39_ga(x1, x2, x3)  =  U39_ga(x1, x3)
U40_ga(x1, x2, x3)  =  U40_ga(x1, x3)
U41_ga(x1, x2, x3)  =  U41_ga(x1, x3)
e317_out_ga(x1, x2)  =  e317_out_ga(x1)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
e288_out_ga(x1, x2)  =  e288_out_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
e259_out_ga(x1, x2)  =  e259_out_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
U60_ga(x1, x2, x3)  =  U60_ga(x1, x3)
U61_ga(x1, x2, x3)  =  U61_ga(x1, x3)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
e198_out_ga(x1, x2)  =  e198_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U63_ga(x1, x2, x3)  =  U63_ga(x1, x3)
U64_ga(x1, x2, x3)  =  U64_ga(x1, x3)
U65_ga(x1, x2, x3)  =  U65_ga(x1, x3)
e169_out_ga(x1, x2)  =  e169_out_ga(x1)
U67_ga(x1, x2, x3)  =  U67_ga(x1, x3)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
U69_ga(x1, x2, x3)  =  U69_ga(x1, x3)
U71_ga(x1, x2, x3)  =  U71_ga(x1, x3)
U72_ga(x1, x2, x3)  =  U72_ga(x1, x3)
U73_ga(x1, x2, x3)  =  U73_ga(x1, x3)
e140_out_ga(x1, x2)  =  e140_out_ga(x1)
U75_ga(x1, x2, x3)  =  U75_ga(x1, x3)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
U77_ga(x1, x2, x3)  =  U77_ga(x1, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x3)
U80_ga(x1, x2, x3)  =  U80_ga(x1, x3)
U81_ga(x1, x2, x3)  =  U81_ga(x1, x3)
e111_out_ga(x1, x2)  =  e111_out_ga(x1)
U83_ga(x1, x2, x3)  =  U83_ga(x1, x3)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
U85_ga(x1, x2, x3)  =  U85_ga(x1, x3)
U87_ga(x1, x2, x3)  =  U87_ga(x1, x3)
U88_ga(x1, x2, x3)  =  U88_ga(x1, x3)
U89_ga(x1, x2, x3)  =  U89_ga(x1, x3)
e82_out_ga(x1, x2)  =  e82_out_ga(x1)
U91_ga(x1, x2, x3)  =  U91_ga(x1, x3)
U92_ga(x1, x2, x3)  =  U92_ga(x1, x3)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
U95_ga(x1, x2, x3)  =  U95_ga(x1, x3)
U96_ga(x1, x2, x3)  =  U96_ga(x1, x3)
U97_ga(x1, x2, x3)  =  U97_ga(x1, x3)
e53_out_ga(x1, x2)  =  e53_out_ga(x1)
U99_ga(x1, x2, x3)  =  U99_ga(x1, x3)
U100_ga(x1, x2, x3)  =  U100_ga(x1, x3)
U101_ga(x1, x2, x3)  =  U101_ga(x1, x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa(x1)
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x1, x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x1, x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x1, x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x1, x4)

(5) DependencyPairsProof (EQUIVALENT transformation)

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

E1_IN_GA(T22, T24) → U108_GA(T22, T24, n7_in_ga(T22, T24))
E1_IN_GA(T22, T24) → N7_IN_GA(T22, T24)
N7_IN_GA(.(lbrace, T41), T43) → U102_GA(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
N7_IN_GA(.(lbrace, T41), T43) → E1_IN_GA(T41, .(rbrace, T43))
E1_IN_GA(T62, T64) → U109_GA(T62, T64, p31_in_gaa(T62, X59, T64))
E1_IN_GA(T62, T64) → P31_IN_GAA(T62, X59, T64)
P31_IN_GAA(T62, X59, T64) → U103_GAA(T62, X59, T64, n32_in_ga(T62, X59))
P31_IN_GAA(T62, X59, T64) → N32_IN_GA(T62, X59)
N32_IN_GA(.(lbrace, T89), X84) → U1_GA(T89, X84, e53_in_ga(T89, X84))
N32_IN_GA(.(lbrace, T89), X84) → E53_IN_GA(T89, X84)
E53_IN_GA(T97, X110) → U98_GA(T97, X110, t58_in_ga(T97, X110))
E53_IN_GA(T97, X110) → T58_IN_GA(T97, X110)
T58_IN_GA(.(lbrace, T130), X155) → U94_GA(T130, X155, e82_in_ga(T130, X155))
T58_IN_GA(.(lbrace, T130), X155) → E82_IN_GA(T130, X155)
E82_IN_GA(T138, X181) → U90_GA(T138, X181, t87_in_ga(T138, X181))
E82_IN_GA(T138, X181) → T87_IN_GA(T138, X181)
T87_IN_GA(.(lbrace, T171), X226) → U86_GA(T171, X226, e111_in_ga(T171, X226))
T87_IN_GA(.(lbrace, T171), X226) → E111_IN_GA(T171, X226)
E111_IN_GA(T179, X252) → U82_GA(T179, X252, t116_in_ga(T179, X252))
E111_IN_GA(T179, X252) → T116_IN_GA(T179, X252)
T116_IN_GA(.(lbrace, T212), X297) → U78_GA(T212, X297, e140_in_ga(T212, X297))
T116_IN_GA(.(lbrace, T212), X297) → E140_IN_GA(T212, X297)
E140_IN_GA(T220, X323) → U74_GA(T220, X323, t145_in_ga(T220, X323))
E140_IN_GA(T220, X323) → T145_IN_GA(T220, X323)
T145_IN_GA(.(lbrace, T253), X368) → U70_GA(T253, X368, e169_in_ga(T253, X368))
T145_IN_GA(.(lbrace, T253), X368) → E169_IN_GA(T253, X368)
E169_IN_GA(T261, X394) → U66_GA(T261, X394, t174_in_ga(T261, X394))
E169_IN_GA(T261, X394) → T174_IN_GA(T261, X394)
T174_IN_GA(.(lbrace, T294), X439) → U62_GA(T294, X439, e198_in_ga(T294, X439))
T174_IN_GA(.(lbrace, T294), X439) → E198_IN_GA(T294, X439)
E198_IN_GA(T302, X465) → U6_GA(T302, X465, t203_in_ga(T302, X465))
E198_IN_GA(T302, X465) → T203_IN_GA(T302, X465)
T203_IN_GA(.(lbrace, T335), X510) → U2_GA(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
T203_IN_GA(.(lbrace, T335), X510) → E1_IN_GA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_GA(T941, T943) → U110_GA(T941, T943, t234_in_ga(T941, X1569))
E1_IN_GA(T941, T943) → T234_IN_GA(T941, X1569)
T234_IN_GA(.(lbrace, T392), X599) → U14_GA(T392, X599, e259_in_ga(T392, X599))
T234_IN_GA(.(lbrace, T392), X599) → E259_IN_GA(T392, X599)
E259_IN_GA(T400, X625) → U58_GA(T400, X625, t264_in_ga(T400, X625))
E259_IN_GA(T400, X625) → T264_IN_GA(T400, X625)
T264_IN_GA(.(lbrace, T433), X670) → U54_GA(T433, X670, e288_in_ga(T433, X670))
T264_IN_GA(.(lbrace, T433), X670) → E288_IN_GA(T433, X670)
E288_IN_GA(T441, X696) → U50_GA(T441, X696, t293_in_ga(T441, X696))
E288_IN_GA(T441, X696) → T293_IN_GA(T441, X696)
T293_IN_GA(.(lbrace, T474), X741) → U46_GA(T474, X741, e317_in_ga(T474, X741))
T293_IN_GA(.(lbrace, T474), X741) → E317_IN_GA(T474, X741)
E317_IN_GA(T482, X767) → U42_GA(T482, X767, t322_in_ga(T482, X767))
E317_IN_GA(T482, X767) → T322_IN_GA(T482, X767)
T322_IN_GA(.(lbrace, T515), X812) → U38_GA(T515, X812, e346_in_ga(T515, X812))
T322_IN_GA(.(lbrace, T515), X812) → E346_IN_GA(T515, X812)
E346_IN_GA(T523, X838) → U34_GA(T523, X838, t351_in_ga(T523, X838))
E346_IN_GA(T523, X838) → T351_IN_GA(T523, X838)
T351_IN_GA(.(lbrace, T556), X883) → U30_GA(T556, X883, e375_in_ga(T556, X883))
T351_IN_GA(.(lbrace, T556), X883) → E375_IN_GA(T556, X883)
E375_IN_GA(T564, X909) → U26_GA(T564, X909, t380_in_ga(T564, X909))
E375_IN_GA(T564, X909) → T380_IN_GA(T564, X909)
T380_IN_GA(.(lbrace, T597), X954) → U22_GA(T597, X954, e404_in_ga(T597, X954))
T380_IN_GA(.(lbrace, T597), X954) → E404_IN_GA(T597, X954)
E404_IN_GA(T605, X980) → U18_GA(T605, X980, t409_in_ga(T605, X980))
E404_IN_GA(T605, X980) → T409_IN_GA(T605, X980)
T409_IN_GA(.(lbrace, T638), X1025) → U10_GA(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
T409_IN_GA(.(lbrace, T638), X1025) → E1_IN_GA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_GA(T941, T943) → U111_GA(T941, T943, t234_in_ga(T941, T945))
T234_IN_GA(T780, X1303) → U15_GA(T780, X1303, n32_in_ga(T780, X1302))
T234_IN_GA(T780, X1303) → N32_IN_GA(T780, X1302)
T234_IN_GA(T780, X1303) → U16_GA(T780, X1303, n32_in_ga(T780, T784))
U16_GA(T780, X1303, n32_out_ga(T780, T784)) → U17_GA(T780, X1303, t234_in_aa(T784, X1303))
U16_GA(T780, X1303, n32_out_ga(T780, T784)) → T234_IN_AA(T784, X1303)
T234_IN_AA(.(lbrace, T392), X599) → U14_AA(T392, X599, e259_in_aa(T392, X599))
T234_IN_AA(.(lbrace, T392), X599) → E259_IN_AA(T392, X599)
E259_IN_AA(T400, X625) → U58_AA(T400, X625, t264_in_aa(T400, X625))
E259_IN_AA(T400, X625) → T264_IN_AA(T400, X625)
T264_IN_AA(.(lbrace, T433), X670) → U54_AA(T433, X670, e288_in_aa(T433, X670))
T264_IN_AA(.(lbrace, T433), X670) → E288_IN_AA(T433, X670)
E288_IN_AA(T441, X696) → U50_AA(T441, X696, t293_in_aa(T441, X696))
E288_IN_AA(T441, X696) → T293_IN_AA(T441, X696)
T293_IN_AA(.(lbrace, T474), X741) → U46_AA(T474, X741, e317_in_aa(T474, X741))
T293_IN_AA(.(lbrace, T474), X741) → E317_IN_AA(T474, X741)
E317_IN_AA(T482, X767) → U42_AA(T482, X767, t322_in_aa(T482, X767))
E317_IN_AA(T482, X767) → T322_IN_AA(T482, X767)
T322_IN_AA(.(lbrace, T515), X812) → U38_AA(T515, X812, e346_in_aa(T515, X812))
T322_IN_AA(.(lbrace, T515), X812) → E346_IN_AA(T515, X812)
E346_IN_AA(T523, X838) → U34_AA(T523, X838, t351_in_aa(T523, X838))
E346_IN_AA(T523, X838) → T351_IN_AA(T523, X838)
T351_IN_AA(.(lbrace, T556), X883) → U30_AA(T556, X883, e375_in_aa(T556, X883))
T351_IN_AA(.(lbrace, T556), X883) → E375_IN_AA(T556, X883)
E375_IN_AA(T564, X909) → U26_AA(T564, X909, t380_in_aa(T564, X909))
E375_IN_AA(T564, X909) → T380_IN_AA(T564, X909)
T380_IN_AA(.(lbrace, T597), X954) → U22_AA(T597, X954, e404_in_aa(T597, X954))
T380_IN_AA(.(lbrace, T597), X954) → E404_IN_AA(T597, X954)
E404_IN_AA(T605, X980) → U18_AA(T605, X980, t409_in_aa(T605, X980))
E404_IN_AA(T605, X980) → T409_IN_AA(T605, X980)
T409_IN_AA(.(lbrace, T638), X1025) → U10_AA(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
T409_IN_AA(.(lbrace, T638), X1025) → E1_IN_AA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_AA(T22, T24) → U108_AA(T22, T24, n7_in_aa(T22, T24))
E1_IN_AA(T22, T24) → N7_IN_AA(T22, T24)
N7_IN_AA(.(lbrace, T41), T43) → U102_AA(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
N7_IN_AA(.(lbrace, T41), T43) → E1_IN_AA(T41, .(rbrace, T43))
E1_IN_AA(T62, T64) → U109_AA(T62, T64, p31_in_aaa(T62, X59, T64))
E1_IN_AA(T62, T64) → P31_IN_AAA(T62, X59, T64)
P31_IN_AAA(T62, X59, T64) → U103_AAA(T62, X59, T64, n32_in_aa(T62, X59))
P31_IN_AAA(T62, X59, T64) → N32_IN_AA(T62, X59)
N32_IN_AA(.(lbrace, T89), X84) → U1_AA(T89, X84, e53_in_aa(T89, X84))
N32_IN_AA(.(lbrace, T89), X84) → E53_IN_AA(T89, X84)
E53_IN_AA(T97, X110) → U98_AA(T97, X110, t58_in_aa(T97, X110))
E53_IN_AA(T97, X110) → T58_IN_AA(T97, X110)
T58_IN_AA(.(lbrace, T130), X155) → U94_AA(T130, X155, e82_in_aa(T130, X155))
T58_IN_AA(.(lbrace, T130), X155) → E82_IN_AA(T130, X155)
E82_IN_AA(T138, X181) → U90_AA(T138, X181, t87_in_aa(T138, X181))
E82_IN_AA(T138, X181) → T87_IN_AA(T138, X181)
T87_IN_AA(.(lbrace, T171), X226) → U86_AA(T171, X226, e111_in_aa(T171, X226))
T87_IN_AA(.(lbrace, T171), X226) → E111_IN_AA(T171, X226)
E111_IN_AA(T179, X252) → U82_AA(T179, X252, t116_in_aa(T179, X252))
E111_IN_AA(T179, X252) → T116_IN_AA(T179, X252)
T116_IN_AA(.(lbrace, T212), X297) → U78_AA(T212, X297, e140_in_aa(T212, X297))
T116_IN_AA(.(lbrace, T212), X297) → E140_IN_AA(T212, X297)
E140_IN_AA(T220, X323) → U74_AA(T220, X323, t145_in_aa(T220, X323))
E140_IN_AA(T220, X323) → T145_IN_AA(T220, X323)
T145_IN_AA(.(lbrace, T253), X368) → U70_AA(T253, X368, e169_in_aa(T253, X368))
T145_IN_AA(.(lbrace, T253), X368) → E169_IN_AA(T253, X368)
E169_IN_AA(T261, X394) → U66_AA(T261, X394, t174_in_aa(T261, X394))
E169_IN_AA(T261, X394) → T174_IN_AA(T261, X394)
T174_IN_AA(.(lbrace, T294), X439) → U62_AA(T294, X439, e198_in_aa(T294, X439))
T174_IN_AA(.(lbrace, T294), X439) → E198_IN_AA(T294, X439)
E198_IN_AA(T302, X465) → U6_AA(T302, X465, t203_in_aa(T302, X465))
E198_IN_AA(T302, X465) → T203_IN_AA(T302, X465)
T203_IN_AA(.(lbrace, T335), X510) → U2_AA(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
T203_IN_AA(.(lbrace, T335), X510) → E1_IN_AA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_AA(T941, T943) → U110_AA(T941, T943, t234_in_aa(T941, X1569))
E1_IN_AA(T941, T943) → T234_IN_AA(T941, X1569)
T234_IN_AA(T780, X1303) → U15_AA(T780, X1303, n32_in_aa(T780, X1302))
T234_IN_AA(T780, X1303) → N32_IN_AA(T780, X1302)
T234_IN_AA(T780, X1303) → U16_AA(T780, X1303, n32_in_aa(T780, T784))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → U17_AA(T780, X1303, t234_in_aa(T784, X1303))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → T234_IN_AA(T784, X1303)
E1_IN_AA(T941, T943) → U111_AA(T941, T943, t234_in_aa(T941, T945))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → U112_AA(T941, T943, e1_in_aa(T945, T943))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → E1_IN_AA(T945, T943)
T203_IN_AA(T345, X530) → U3_AA(T345, X530, n32_in_aa(T345, X529))
T203_IN_AA(T345, X530) → N32_IN_AA(T345, X529)
T203_IN_AA(T345, X530) → U4_AA(T345, X530, n32_in_aa(T345, T349))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → U5_AA(T345, X530, t203_in_aa(T349, X530))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_AA(T357, X551) → U7_AA(T357, X551, t234_in_aa(T357, X550))
E198_IN_AA(T357, X551) → T234_IN_AA(T357, X550)
E198_IN_AA(T357, X551) → U8_AA(T357, X551, t234_in_aa(T357, T359))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → U9_AA(T357, X551, e198_in_aa(T359, X551))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_AA(T795, X1326) → U63_AA(T795, X1326, n32_in_aa(T795, X1325))
T174_IN_AA(T795, X1326) → N32_IN_AA(T795, X1325)
T174_IN_AA(T795, X1326) → U64_AA(T795, X1326, n32_in_aa(T795, T799))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → U65_AA(T795, X1326, t174_in_aa(T799, X1326))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_AA(T807, X1347) → U67_AA(T807, X1347, t234_in_aa(T807, X1346))
E169_IN_AA(T807, X1347) → T234_IN_AA(T807, X1346)
E169_IN_AA(T807, X1347) → U68_AA(T807, X1347, t234_in_aa(T807, T809))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → U69_AA(T807, X1347, e169_in_aa(T809, X1347))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_AA(T817, X1369) → U71_AA(T817, X1369, n32_in_aa(T817, X1368))
T145_IN_AA(T817, X1369) → N32_IN_AA(T817, X1368)
T145_IN_AA(T817, X1369) → U72_AA(T817, X1369, n32_in_aa(T817, T821))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → U73_AA(T817, X1369, t145_in_aa(T821, X1369))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_AA(T829, X1390) → U75_AA(T829, X1390, t234_in_aa(T829, X1389))
E140_IN_AA(T829, X1390) → T234_IN_AA(T829, X1389)
E140_IN_AA(T829, X1390) → U76_AA(T829, X1390, t234_in_aa(T829, T831))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → U77_AA(T829, X1390, e140_in_aa(T831, X1390))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_AA(T839, X1412) → U79_AA(T839, X1412, n32_in_aa(T839, X1411))
T116_IN_AA(T839, X1412) → N32_IN_AA(T839, X1411)
T116_IN_AA(T839, X1412) → U80_AA(T839, X1412, n32_in_aa(T839, T843))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → U81_AA(T839, X1412, t116_in_aa(T843, X1412))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_AA(T851, X1433) → U83_AA(T851, X1433, t234_in_aa(T851, X1432))
E111_IN_AA(T851, X1433) → T234_IN_AA(T851, X1432)
E111_IN_AA(T851, X1433) → U84_AA(T851, X1433, t234_in_aa(T851, T853))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → U85_AA(T851, X1433, e111_in_aa(T853, X1433))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_AA(T861, X1455) → U87_AA(T861, X1455, n32_in_aa(T861, X1454))
T87_IN_AA(T861, X1455) → N32_IN_AA(T861, X1454)
T87_IN_AA(T861, X1455) → U88_AA(T861, X1455, n32_in_aa(T861, T865))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → U89_AA(T861, X1455, t87_in_aa(T865, X1455))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_AA(T873, X1476) → U91_AA(T873, X1476, t234_in_aa(T873, X1475))
E82_IN_AA(T873, X1476) → T234_IN_AA(T873, X1475)
E82_IN_AA(T873, X1476) → U92_AA(T873, X1476, t234_in_aa(T873, T875))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → U93_AA(T873, X1476, e82_in_aa(T875, X1476))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_AA(T883, X1498) → U95_AA(T883, X1498, n32_in_aa(T883, X1497))
T58_IN_AA(T883, X1498) → N32_IN_AA(T883, X1497)
T58_IN_AA(T883, X1498) → U96_AA(T883, X1498, n32_in_aa(T883, T887))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → U97_AA(T883, X1498, t58_in_aa(T887, X1498))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_AA(T895, X1519) → U99_AA(T895, X1519, t234_in_aa(T895, X1518))
E53_IN_AA(T895, X1519) → T234_IN_AA(T895, X1518)
E53_IN_AA(T895, X1519) → U100_AA(T895, X1519, t234_in_aa(T895, T897))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → U101_AA(T895, X1519, e53_in_aa(T897, X1519))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_AAA(T62, T916, T918) → U104_AAA(T62, T916, T918, n32_in_aa(T62, T916))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → U105_AAA(T62, T916, T918, n7_in_aa(T916, T918))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_AAA(T62, T929, T931) → U106_AAA(T62, T929, T931, n32_in_aa(T62, T929))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → U107_AAA(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → P31_IN_AAA(T929, X1556, T931)
T409_IN_AA(T648, X1045) → U11_AA(T648, X1045, n32_in_aa(T648, X1044))
T409_IN_AA(T648, X1045) → N32_IN_AA(T648, X1044)
T409_IN_AA(T648, X1045) → U12_AA(T648, X1045, n32_in_aa(T648, T652))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → U13_AA(T648, X1045, t409_in_aa(T652, X1045))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_AA(T660, X1066) → U19_AA(T660, X1066, t234_in_aa(T660, X1065))
E404_IN_AA(T660, X1066) → T234_IN_AA(T660, X1065)
E404_IN_AA(T660, X1066) → U20_AA(T660, X1066, t234_in_aa(T660, T662))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → U21_AA(T660, X1066, e404_in_aa(T662, X1066))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_AA(T670, X1088) → U23_AA(T670, X1088, n32_in_aa(T670, X1087))
T380_IN_AA(T670, X1088) → N32_IN_AA(T670, X1087)
T380_IN_AA(T670, X1088) → U24_AA(T670, X1088, n32_in_aa(T670, T674))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → U25_AA(T670, X1088, t380_in_aa(T674, X1088))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_AA(T682, X1109) → U27_AA(T682, X1109, t234_in_aa(T682, X1108))
E375_IN_AA(T682, X1109) → T234_IN_AA(T682, X1108)
E375_IN_AA(T682, X1109) → U28_AA(T682, X1109, t234_in_aa(T682, T684))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → U29_AA(T682, X1109, e375_in_aa(T684, X1109))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_AA(T692, X1131) → U31_AA(T692, X1131, n32_in_aa(T692, X1130))
T351_IN_AA(T692, X1131) → N32_IN_AA(T692, X1130)
T351_IN_AA(T692, X1131) → U32_AA(T692, X1131, n32_in_aa(T692, T696))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → U33_AA(T692, X1131, t351_in_aa(T696, X1131))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_AA(T704, X1152) → U35_AA(T704, X1152, t234_in_aa(T704, X1151))
E346_IN_AA(T704, X1152) → T234_IN_AA(T704, X1151)
E346_IN_AA(T704, X1152) → U36_AA(T704, X1152, t234_in_aa(T704, T706))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → U37_AA(T704, X1152, e346_in_aa(T706, X1152))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_AA(T714, X1174) → U39_AA(T714, X1174, n32_in_aa(T714, X1173))
T322_IN_AA(T714, X1174) → N32_IN_AA(T714, X1173)
T322_IN_AA(T714, X1174) → U40_AA(T714, X1174, n32_in_aa(T714, T718))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → U41_AA(T714, X1174, t322_in_aa(T718, X1174))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_AA(T726, X1195) → U43_AA(T726, X1195, t234_in_aa(T726, X1194))
E317_IN_AA(T726, X1195) → T234_IN_AA(T726, X1194)
E317_IN_AA(T726, X1195) → U44_AA(T726, X1195, t234_in_aa(T726, T728))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → U45_AA(T726, X1195, e317_in_aa(T728, X1195))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_AA(T736, X1217) → U47_AA(T736, X1217, n32_in_aa(T736, X1216))
T293_IN_AA(T736, X1217) → N32_IN_AA(T736, X1216)
T293_IN_AA(T736, X1217) → U48_AA(T736, X1217, n32_in_aa(T736, T740))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → U49_AA(T736, X1217, t293_in_aa(T740, X1217))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_AA(T748, X1238) → U51_AA(T748, X1238, t234_in_aa(T748, X1237))
E288_IN_AA(T748, X1238) → T234_IN_AA(T748, X1237)
E288_IN_AA(T748, X1238) → U52_AA(T748, X1238, t234_in_aa(T748, T750))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → U53_AA(T748, X1238, e288_in_aa(T750, X1238))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_AA(T758, X1260) → U55_AA(T758, X1260, n32_in_aa(T758, X1259))
T264_IN_AA(T758, X1260) → N32_IN_AA(T758, X1259)
T264_IN_AA(T758, X1260) → U56_AA(T758, X1260, n32_in_aa(T758, T762))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → U57_AA(T758, X1260, t264_in_aa(T762, X1260))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_AA(T770, X1281) → U59_AA(T770, X1281, t234_in_aa(T770, X1280))
E259_IN_AA(T770, X1281) → T234_IN_AA(T770, X1280)
E259_IN_AA(T770, X1281) → U60_AA(T770, X1281, t234_in_aa(T770, T772))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → U61_AA(T770, X1281, e259_in_aa(T772, X1281))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → E259_IN_AA(T772, X1281)
U111_GA(T941, T943, t234_out_ga(T941, T945)) → U112_GA(T941, T943, e1_in_aa(T945, T943))
U111_GA(T941, T943, t234_out_ga(T941, T945)) → E1_IN_AA(T945, T943)
T409_IN_GA(T648, X1045) → U11_GA(T648, X1045, n32_in_ga(T648, X1044))
T409_IN_GA(T648, X1045) → N32_IN_GA(T648, X1044)
T409_IN_GA(T648, X1045) → U12_GA(T648, X1045, n32_in_ga(T648, T652))
U12_GA(T648, X1045, n32_out_ga(T648, T652)) → U13_GA(T648, X1045, t409_in_aa(T652, X1045))
U12_GA(T648, X1045, n32_out_ga(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_GA(T660, X1066) → U19_GA(T660, X1066, t234_in_ga(T660, X1065))
E404_IN_GA(T660, X1066) → T234_IN_GA(T660, X1065)
E404_IN_GA(T660, X1066) → U20_GA(T660, X1066, t234_in_ga(T660, T662))
U20_GA(T660, X1066, t234_out_ga(T660, T662)) → U21_GA(T660, X1066, e404_in_aa(T662, X1066))
U20_GA(T660, X1066, t234_out_ga(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_GA(T670, X1088) → U23_GA(T670, X1088, n32_in_ga(T670, X1087))
T380_IN_GA(T670, X1088) → N32_IN_GA(T670, X1087)
T380_IN_GA(T670, X1088) → U24_GA(T670, X1088, n32_in_ga(T670, T674))
U24_GA(T670, X1088, n32_out_ga(T670, T674)) → U25_GA(T670, X1088, t380_in_aa(T674, X1088))
U24_GA(T670, X1088, n32_out_ga(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_GA(T682, X1109) → U27_GA(T682, X1109, t234_in_ga(T682, X1108))
E375_IN_GA(T682, X1109) → T234_IN_GA(T682, X1108)
E375_IN_GA(T682, X1109) → U28_GA(T682, X1109, t234_in_ga(T682, T684))
U28_GA(T682, X1109, t234_out_ga(T682, T684)) → U29_GA(T682, X1109, e375_in_aa(T684, X1109))
U28_GA(T682, X1109, t234_out_ga(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_GA(T692, X1131) → U31_GA(T692, X1131, n32_in_ga(T692, X1130))
T351_IN_GA(T692, X1131) → N32_IN_GA(T692, X1130)
T351_IN_GA(T692, X1131) → U32_GA(T692, X1131, n32_in_ga(T692, T696))
U32_GA(T692, X1131, n32_out_ga(T692, T696)) → U33_GA(T692, X1131, t351_in_aa(T696, X1131))
U32_GA(T692, X1131, n32_out_ga(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_GA(T704, X1152) → U35_GA(T704, X1152, t234_in_ga(T704, X1151))
E346_IN_GA(T704, X1152) → T234_IN_GA(T704, X1151)
E346_IN_GA(T704, X1152) → U36_GA(T704, X1152, t234_in_ga(T704, T706))
U36_GA(T704, X1152, t234_out_ga(T704, T706)) → U37_GA(T704, X1152, e346_in_aa(T706, X1152))
U36_GA(T704, X1152, t234_out_ga(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_GA(T714, X1174) → U39_GA(T714, X1174, n32_in_ga(T714, X1173))
T322_IN_GA(T714, X1174) → N32_IN_GA(T714, X1173)
T322_IN_GA(T714, X1174) → U40_GA(T714, X1174, n32_in_ga(T714, T718))
U40_GA(T714, X1174, n32_out_ga(T714, T718)) → U41_GA(T714, X1174, t322_in_aa(T718, X1174))
U40_GA(T714, X1174, n32_out_ga(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_GA(T726, X1195) → U43_GA(T726, X1195, t234_in_ga(T726, X1194))
E317_IN_GA(T726, X1195) → T234_IN_GA(T726, X1194)
E317_IN_GA(T726, X1195) → U44_GA(T726, X1195, t234_in_ga(T726, T728))
U44_GA(T726, X1195, t234_out_ga(T726, T728)) → U45_GA(T726, X1195, e317_in_aa(T728, X1195))
U44_GA(T726, X1195, t234_out_ga(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_GA(T736, X1217) → U47_GA(T736, X1217, n32_in_ga(T736, X1216))
T293_IN_GA(T736, X1217) → N32_IN_GA(T736, X1216)
T293_IN_GA(T736, X1217) → U48_GA(T736, X1217, n32_in_ga(T736, T740))
U48_GA(T736, X1217, n32_out_ga(T736, T740)) → U49_GA(T736, X1217, t293_in_aa(T740, X1217))
U48_GA(T736, X1217, n32_out_ga(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_GA(T748, X1238) → U51_GA(T748, X1238, t234_in_ga(T748, X1237))
E288_IN_GA(T748, X1238) → T234_IN_GA(T748, X1237)
E288_IN_GA(T748, X1238) → U52_GA(T748, X1238, t234_in_ga(T748, T750))
U52_GA(T748, X1238, t234_out_ga(T748, T750)) → U53_GA(T748, X1238, e288_in_aa(T750, X1238))
U52_GA(T748, X1238, t234_out_ga(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_GA(T758, X1260) → U55_GA(T758, X1260, n32_in_ga(T758, X1259))
T264_IN_GA(T758, X1260) → N32_IN_GA(T758, X1259)
T264_IN_GA(T758, X1260) → U56_GA(T758, X1260, n32_in_ga(T758, T762))
U56_GA(T758, X1260, n32_out_ga(T758, T762)) → U57_GA(T758, X1260, t264_in_aa(T762, X1260))
U56_GA(T758, X1260, n32_out_ga(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_GA(T770, X1281) → U59_GA(T770, X1281, t234_in_ga(T770, X1280))
E259_IN_GA(T770, X1281) → T234_IN_GA(T770, X1280)
E259_IN_GA(T770, X1281) → U60_GA(T770, X1281, t234_in_ga(T770, T772))
U60_GA(T770, X1281, t234_out_ga(T770, T772)) → U61_GA(T770, X1281, e259_in_aa(T772, X1281))
U60_GA(T770, X1281, t234_out_ga(T770, T772)) → E259_IN_AA(T772, X1281)
T203_IN_GA(T345, X530) → U3_GA(T345, X530, n32_in_ga(T345, X529))
T203_IN_GA(T345, X530) → N32_IN_GA(T345, X529)
T203_IN_GA(T345, X530) → U4_GA(T345, X530, n32_in_ga(T345, T349))
U4_GA(T345, X530, n32_out_ga(T345, T349)) → U5_GA(T345, X530, t203_in_aa(T349, X530))
U4_GA(T345, X530, n32_out_ga(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_GA(T357, X551) → U7_GA(T357, X551, t234_in_ga(T357, X550))
E198_IN_GA(T357, X551) → T234_IN_GA(T357, X550)
E198_IN_GA(T357, X551) → U8_GA(T357, X551, t234_in_ga(T357, T359))
U8_GA(T357, X551, t234_out_ga(T357, T359)) → U9_GA(T357, X551, e198_in_aa(T359, X551))
U8_GA(T357, X551, t234_out_ga(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_GA(T795, X1326) → U63_GA(T795, X1326, n32_in_ga(T795, X1325))
T174_IN_GA(T795, X1326) → N32_IN_GA(T795, X1325)
T174_IN_GA(T795, X1326) → U64_GA(T795, X1326, n32_in_ga(T795, T799))
U64_GA(T795, X1326, n32_out_ga(T795, T799)) → U65_GA(T795, X1326, t174_in_aa(T799, X1326))
U64_GA(T795, X1326, n32_out_ga(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_GA(T807, X1347) → U67_GA(T807, X1347, t234_in_ga(T807, X1346))
E169_IN_GA(T807, X1347) → T234_IN_GA(T807, X1346)
E169_IN_GA(T807, X1347) → U68_GA(T807, X1347, t234_in_ga(T807, T809))
U68_GA(T807, X1347, t234_out_ga(T807, T809)) → U69_GA(T807, X1347, e169_in_aa(T809, X1347))
U68_GA(T807, X1347, t234_out_ga(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_GA(T817, X1369) → U71_GA(T817, X1369, n32_in_ga(T817, X1368))
T145_IN_GA(T817, X1369) → N32_IN_GA(T817, X1368)
T145_IN_GA(T817, X1369) → U72_GA(T817, X1369, n32_in_ga(T817, T821))
U72_GA(T817, X1369, n32_out_ga(T817, T821)) → U73_GA(T817, X1369, t145_in_aa(T821, X1369))
U72_GA(T817, X1369, n32_out_ga(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_GA(T829, X1390) → U75_GA(T829, X1390, t234_in_ga(T829, X1389))
E140_IN_GA(T829, X1390) → T234_IN_GA(T829, X1389)
E140_IN_GA(T829, X1390) → U76_GA(T829, X1390, t234_in_ga(T829, T831))
U76_GA(T829, X1390, t234_out_ga(T829, T831)) → U77_GA(T829, X1390, e140_in_aa(T831, X1390))
U76_GA(T829, X1390, t234_out_ga(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_GA(T839, X1412) → U79_GA(T839, X1412, n32_in_ga(T839, X1411))
T116_IN_GA(T839, X1412) → N32_IN_GA(T839, X1411)
T116_IN_GA(T839, X1412) → U80_GA(T839, X1412, n32_in_ga(T839, T843))
U80_GA(T839, X1412, n32_out_ga(T839, T843)) → U81_GA(T839, X1412, t116_in_aa(T843, X1412))
U80_GA(T839, X1412, n32_out_ga(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_GA(T851, X1433) → U83_GA(T851, X1433, t234_in_ga(T851, X1432))
E111_IN_GA(T851, X1433) → T234_IN_GA(T851, X1432)
E111_IN_GA(T851, X1433) → U84_GA(T851, X1433, t234_in_ga(T851, T853))
U84_GA(T851, X1433, t234_out_ga(T851, T853)) → U85_GA(T851, X1433, e111_in_aa(T853, X1433))
U84_GA(T851, X1433, t234_out_ga(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_GA(T861, X1455) → U87_GA(T861, X1455, n32_in_ga(T861, X1454))
T87_IN_GA(T861, X1455) → N32_IN_GA(T861, X1454)
T87_IN_GA(T861, X1455) → U88_GA(T861, X1455, n32_in_ga(T861, T865))
U88_GA(T861, X1455, n32_out_ga(T861, T865)) → U89_GA(T861, X1455, t87_in_aa(T865, X1455))
U88_GA(T861, X1455, n32_out_ga(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_GA(T873, X1476) → U91_GA(T873, X1476, t234_in_ga(T873, X1475))
E82_IN_GA(T873, X1476) → T234_IN_GA(T873, X1475)
E82_IN_GA(T873, X1476) → U92_GA(T873, X1476, t234_in_ga(T873, T875))
U92_GA(T873, X1476, t234_out_ga(T873, T875)) → U93_GA(T873, X1476, e82_in_aa(T875, X1476))
U92_GA(T873, X1476, t234_out_ga(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_GA(T883, X1498) → U95_GA(T883, X1498, n32_in_ga(T883, X1497))
T58_IN_GA(T883, X1498) → N32_IN_GA(T883, X1497)
T58_IN_GA(T883, X1498) → U96_GA(T883, X1498, n32_in_ga(T883, T887))
U96_GA(T883, X1498, n32_out_ga(T883, T887)) → U97_GA(T883, X1498, t58_in_aa(T887, X1498))
U96_GA(T883, X1498, n32_out_ga(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_GA(T895, X1519) → U99_GA(T895, X1519, t234_in_ga(T895, X1518))
E53_IN_GA(T895, X1519) → T234_IN_GA(T895, X1518)
E53_IN_GA(T895, X1519) → U100_GA(T895, X1519, t234_in_ga(T895, T897))
U100_GA(T895, X1519, t234_out_ga(T895, T897)) → U101_GA(T895, X1519, e53_in_aa(T897, X1519))
U100_GA(T895, X1519, t234_out_ga(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_GAA(T62, T916, T918) → U104_GAA(T62, T916, T918, n32_in_ga(T62, T916))
U104_GAA(T62, T916, T918, n32_out_ga(T62, T916)) → U105_GAA(T62, T916, T918, n7_in_aa(T916, T918))
U104_GAA(T62, T916, T918, n32_out_ga(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_GAA(T62, T929, T931) → U106_GAA(T62, T929, T931, n32_in_ga(T62, T929))
U106_GAA(T62, T929, T931, n32_out_ga(T62, T929)) → U107_GAA(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U106_GAA(T62, T929, T931, n32_out_ga(T62, T929)) → P31_IN_AAA(T929, X1556, T931)

The TRS R consists of the following rules:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x1, x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga(x1)
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x1, x3)
U109_ga(x1, x2, x3)  =  U109_ga(x1, x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x1, x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x1, x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga(x1)
U94_ga(x1, x2, x3)  =  U94_ga(x1, x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x1, x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga(x1)
U86_ga(x1, x2, x3)  =  U86_ga(x1, x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x1, x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x1, x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga(x1)
U70_ga(x1, x2, x3)  =  U70_ga(x1, x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga(x1)
U62_ga(x1, x2, x3)  =  U62_ga(x1, x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga(x1)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga(x1)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x1, x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga(x1)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga(x1)
U38_ga(x1, x2, x3)  =  U38_ga(x1, x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x1, x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga(x1)
U30_ga(x1, x2, x3)  =  U30_ga(x1, x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga(x1)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U111_ga(x1, x2, x3)  =  U111_ga(x1, x3)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U112_ga(x1, x2, x3)  =  U112_ga(x1, x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
e404_out_ga(x1, x2)  =  e404_out_ga(x1)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
e375_out_ga(x1, x2)  =  e375_out_ga(x1)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
U28_ga(x1, x2, x3)  =  U28_ga(x1, x3)
U29_ga(x1, x2, x3)  =  U29_ga(x1, x3)
U31_ga(x1, x2, x3)  =  U31_ga(x1, x3)
U32_ga(x1, x2, x3)  =  U32_ga(x1, x3)
U33_ga(x1, x2, x3)  =  U33_ga(x1, x3)
e346_out_ga(x1, x2)  =  e346_out_ga(x1)
U35_ga(x1, x2, x3)  =  U35_ga(x1, x3)
U36_ga(x1, x2, x3)  =  U36_ga(x1, x3)
U37_ga(x1, x2, x3)  =  U37_ga(x1, x3)
U39_ga(x1, x2, x3)  =  U39_ga(x1, x3)
U40_ga(x1, x2, x3)  =  U40_ga(x1, x3)
U41_ga(x1, x2, x3)  =  U41_ga(x1, x3)
e317_out_ga(x1, x2)  =  e317_out_ga(x1)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
e288_out_ga(x1, x2)  =  e288_out_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
e259_out_ga(x1, x2)  =  e259_out_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
U60_ga(x1, x2, x3)  =  U60_ga(x1, x3)
U61_ga(x1, x2, x3)  =  U61_ga(x1, x3)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
e198_out_ga(x1, x2)  =  e198_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U63_ga(x1, x2, x3)  =  U63_ga(x1, x3)
U64_ga(x1, x2, x3)  =  U64_ga(x1, x3)
U65_ga(x1, x2, x3)  =  U65_ga(x1, x3)
e169_out_ga(x1, x2)  =  e169_out_ga(x1)
U67_ga(x1, x2, x3)  =  U67_ga(x1, x3)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
U69_ga(x1, x2, x3)  =  U69_ga(x1, x3)
U71_ga(x1, x2, x3)  =  U71_ga(x1, x3)
U72_ga(x1, x2, x3)  =  U72_ga(x1, x3)
U73_ga(x1, x2, x3)  =  U73_ga(x1, x3)
e140_out_ga(x1, x2)  =  e140_out_ga(x1)
U75_ga(x1, x2, x3)  =  U75_ga(x1, x3)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
U77_ga(x1, x2, x3)  =  U77_ga(x1, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x3)
U80_ga(x1, x2, x3)  =  U80_ga(x1, x3)
U81_ga(x1, x2, x3)  =  U81_ga(x1, x3)
e111_out_ga(x1, x2)  =  e111_out_ga(x1)
U83_ga(x1, x2, x3)  =  U83_ga(x1, x3)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
U85_ga(x1, x2, x3)  =  U85_ga(x1, x3)
U87_ga(x1, x2, x3)  =  U87_ga(x1, x3)
U88_ga(x1, x2, x3)  =  U88_ga(x1, x3)
U89_ga(x1, x2, x3)  =  U89_ga(x1, x3)
e82_out_ga(x1, x2)  =  e82_out_ga(x1)
U91_ga(x1, x2, x3)  =  U91_ga(x1, x3)
U92_ga(x1, x2, x3)  =  U92_ga(x1, x3)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
U95_ga(x1, x2, x3)  =  U95_ga(x1, x3)
U96_ga(x1, x2, x3)  =  U96_ga(x1, x3)
U97_ga(x1, x2, x3)  =  U97_ga(x1, x3)
e53_out_ga(x1, x2)  =  e53_out_ga(x1)
U99_ga(x1, x2, x3)  =  U99_ga(x1, x3)
U100_ga(x1, x2, x3)  =  U100_ga(x1, x3)
U101_ga(x1, x2, x3)  =  U101_ga(x1, x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa(x1)
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x1, x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x1, x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x1, x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x1, x4)
E1_IN_GA(x1, x2)  =  E1_IN_GA(x1)
U108_GA(x1, x2, x3)  =  U108_GA(x1, x3)
N7_IN_GA(x1, x2)  =  N7_IN_GA(x1)
U102_GA(x1, x2, x3)  =  U102_GA(x1, x3)
U109_GA(x1, x2, x3)  =  U109_GA(x1, x3)
P31_IN_GAA(x1, x2, x3)  =  P31_IN_GAA(x1)
U103_GAA(x1, x2, x3, x4)  =  U103_GAA(x1, x4)
N32_IN_GA(x1, x2)  =  N32_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x1, x3)
E53_IN_GA(x1, x2)  =  E53_IN_GA(x1)
U98_GA(x1, x2, x3)  =  U98_GA(x1, x3)
T58_IN_GA(x1, x2)  =  T58_IN_GA(x1)
U94_GA(x1, x2, x3)  =  U94_GA(x1, x3)
E82_IN_GA(x1, x2)  =  E82_IN_GA(x1)
U90_GA(x1, x2, x3)  =  U90_GA(x1, x3)
T87_IN_GA(x1, x2)  =  T87_IN_GA(x1)
U86_GA(x1, x2, x3)  =  U86_GA(x1, x3)
E111_IN_GA(x1, x2)  =  E111_IN_GA(x1)
U82_GA(x1, x2, x3)  =  U82_GA(x1, x3)
T116_IN_GA(x1, x2)  =  T116_IN_GA(x1)
U78_GA(x1, x2, x3)  =  U78_GA(x1, x3)
E140_IN_GA(x1, x2)  =  E140_IN_GA(x1)
U74_GA(x1, x2, x3)  =  U74_GA(x1, x3)
T145_IN_GA(x1, x2)  =  T145_IN_GA(x1)
U70_GA(x1, x2, x3)  =  U70_GA(x1, x3)
E169_IN_GA(x1, x2)  =  E169_IN_GA(x1)
U66_GA(x1, x2, x3)  =  U66_GA(x1, x3)
T174_IN_GA(x1, x2)  =  T174_IN_GA(x1)
U62_GA(x1, x2, x3)  =  U62_GA(x1, x3)
E198_IN_GA(x1, x2)  =  E198_IN_GA(x1)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x3)
T203_IN_GA(x1, x2)  =  T203_IN_GA(x1)
U2_GA(x1, x2, x3)  =  U2_GA(x1, x3)
U110_GA(x1, x2, x3)  =  U110_GA(x1, x3)
T234_IN_GA(x1, x2)  =  T234_IN_GA(x1)
U14_GA(x1, x2, x3)  =  U14_GA(x1, x3)
E259_IN_GA(x1, x2)  =  E259_IN_GA(x1)
U58_GA(x1, x2, x3)  =  U58_GA(x1, x3)
T264_IN_GA(x1, x2)  =  T264_IN_GA(x1)
U54_GA(x1, x2, x3)  =  U54_GA(x1, x3)
E288_IN_GA(x1, x2)  =  E288_IN_GA(x1)
U50_GA(x1, x2, x3)  =  U50_GA(x1, x3)
T293_IN_GA(x1, x2)  =  T293_IN_GA(x1)
U46_GA(x1, x2, x3)  =  U46_GA(x1, x3)
E317_IN_GA(x1, x2)  =  E317_IN_GA(x1)
U42_GA(x1, x2, x3)  =  U42_GA(x1, x3)
T322_IN_GA(x1, x2)  =  T322_IN_GA(x1)
U38_GA(x1, x2, x3)  =  U38_GA(x1, x3)
E346_IN_GA(x1, x2)  =  E346_IN_GA(x1)
U34_GA(x1, x2, x3)  =  U34_GA(x1, x3)
T351_IN_GA(x1, x2)  =  T351_IN_GA(x1)
U30_GA(x1, x2, x3)  =  U30_GA(x1, x3)
E375_IN_GA(x1, x2)  =  E375_IN_GA(x1)
U26_GA(x1, x2, x3)  =  U26_GA(x1, x3)
T380_IN_GA(x1, x2)  =  T380_IN_GA(x1)
U22_GA(x1, x2, x3)  =  U22_GA(x1, x3)
E404_IN_GA(x1, x2)  =  E404_IN_GA(x1)
U18_GA(x1, x2, x3)  =  U18_GA(x1, x3)
T409_IN_GA(x1, x2)  =  T409_IN_GA(x1)
U10_GA(x1, x2, x3)  =  U10_GA(x1, x3)
U111_GA(x1, x2, x3)  =  U111_GA(x1, x3)
U15_GA(x1, x2, x3)  =  U15_GA(x1, x3)
U16_GA(x1, x2, x3)  =  U16_GA(x1, x3)
U17_GA(x1, x2, x3)  =  U17_GA(x1, x3)
T234_IN_AA(x1, x2)  =  T234_IN_AA
U14_AA(x1, x2, x3)  =  U14_AA(x3)
E259_IN_AA(x1, x2)  =  E259_IN_AA
U58_AA(x1, x2, x3)  =  U58_AA(x3)
T264_IN_AA(x1, x2)  =  T264_IN_AA
U54_AA(x1, x2, x3)  =  U54_AA(x3)
E288_IN_AA(x1, x2)  =  E288_IN_AA
U50_AA(x1, x2, x3)  =  U50_AA(x3)
T293_IN_AA(x1, x2)  =  T293_IN_AA
U46_AA(x1, x2, x3)  =  U46_AA(x3)
E317_IN_AA(x1, x2)  =  E317_IN_AA
U42_AA(x1, x2, x3)  =  U42_AA(x3)
T322_IN_AA(x1, x2)  =  T322_IN_AA
U38_AA(x1, x2, x3)  =  U38_AA(x3)
E346_IN_AA(x1, x2)  =  E346_IN_AA
U34_AA(x1, x2, x3)  =  U34_AA(x3)
T351_IN_AA(x1, x2)  =  T351_IN_AA
U30_AA(x1, x2, x3)  =  U30_AA(x3)
E375_IN_AA(x1, x2)  =  E375_IN_AA
U26_AA(x1, x2, x3)  =  U26_AA(x3)
T380_IN_AA(x1, x2)  =  T380_IN_AA
U22_AA(x1, x2, x3)  =  U22_AA(x3)
E404_IN_AA(x1, x2)  =  E404_IN_AA
U18_AA(x1, x2, x3)  =  U18_AA(x3)
T409_IN_AA(x1, x2)  =  T409_IN_AA
U10_AA(x1, x2, x3)  =  U10_AA(x3)
E1_IN_AA(x1, x2)  =  E1_IN_AA
U108_AA(x1, x2, x3)  =  U108_AA(x3)
N7_IN_AA(x1, x2)  =  N7_IN_AA
U102_AA(x1, x2, x3)  =  U102_AA(x3)
U109_AA(x1, x2, x3)  =  U109_AA(x3)
P31_IN_AAA(x1, x2, x3)  =  P31_IN_AAA
U103_AAA(x1, x2, x3, x4)  =  U103_AAA(x4)
N32_IN_AA(x1, x2)  =  N32_IN_AA
U1_AA(x1, x2, x3)  =  U1_AA(x3)
E53_IN_AA(x1, x2)  =  E53_IN_AA
U98_AA(x1, x2, x3)  =  U98_AA(x3)
T58_IN_AA(x1, x2)  =  T58_IN_AA
U94_AA(x1, x2, x3)  =  U94_AA(x3)
E82_IN_AA(x1, x2)  =  E82_IN_AA
U90_AA(x1, x2, x3)  =  U90_AA(x3)
T87_IN_AA(x1, x2)  =  T87_IN_AA
U86_AA(x1, x2, x3)  =  U86_AA(x3)
E111_IN_AA(x1, x2)  =  E111_IN_AA
U82_AA(x1, x2, x3)  =  U82_AA(x3)
T116_IN_AA(x1, x2)  =  T116_IN_AA
U78_AA(x1, x2, x3)  =  U78_AA(x3)
E140_IN_AA(x1, x2)  =  E140_IN_AA
U74_AA(x1, x2, x3)  =  U74_AA(x3)
T145_IN_AA(x1, x2)  =  T145_IN_AA
U70_AA(x1, x2, x3)  =  U70_AA(x3)
E169_IN_AA(x1, x2)  =  E169_IN_AA
U66_AA(x1, x2, x3)  =  U66_AA(x3)
T174_IN_AA(x1, x2)  =  T174_IN_AA
U62_AA(x1, x2, x3)  =  U62_AA(x3)
E198_IN_AA(x1, x2)  =  E198_IN_AA
U6_AA(x1, x2, x3)  =  U6_AA(x3)
T203_IN_AA(x1, x2)  =  T203_IN_AA
U2_AA(x1, x2, x3)  =  U2_AA(x3)
U110_AA(x1, x2, x3)  =  U110_AA(x3)
U15_AA(x1, x2, x3)  =  U15_AA(x3)
U16_AA(x1, x2, x3)  =  U16_AA(x3)
U17_AA(x1, x2, x3)  =  U17_AA(x3)
U111_AA(x1, x2, x3)  =  U111_AA(x3)
U112_AA(x1, x2, x3)  =  U112_AA(x3)
U3_AA(x1, x2, x3)  =  U3_AA(x3)
U4_AA(x1, x2, x3)  =  U4_AA(x3)
U5_AA(x1, x2, x3)  =  U5_AA(x3)
U7_AA(x1, x2, x3)  =  U7_AA(x3)
U8_AA(x1, x2, x3)  =  U8_AA(x3)
U9_AA(x1, x2, x3)  =  U9_AA(x3)
U63_AA(x1, x2, x3)  =  U63_AA(x3)
U64_AA(x1, x2, x3)  =  U64_AA(x3)
U65_AA(x1, x2, x3)  =  U65_AA(x3)
U67_AA(x1, x2, x3)  =  U67_AA(x3)
U68_AA(x1, x2, x3)  =  U68_AA(x3)
U69_AA(x1, x2, x3)  =  U69_AA(x3)
U71_AA(x1, x2, x3)  =  U71_AA(x3)
U72_AA(x1, x2, x3)  =  U72_AA(x3)
U73_AA(x1, x2, x3)  =  U73_AA(x3)
U75_AA(x1, x2, x3)  =  U75_AA(x3)
U76_AA(x1, x2, x3)  =  U76_AA(x3)
U77_AA(x1, x2, x3)  =  U77_AA(x3)
U79_AA(x1, x2, x3)  =  U79_AA(x3)
U80_AA(x1, x2, x3)  =  U80_AA(x3)
U81_AA(x1, x2, x3)  =  U81_AA(x3)
U83_AA(x1, x2, x3)  =  U83_AA(x3)
U84_AA(x1, x2, x3)  =  U84_AA(x3)
U85_AA(x1, x2, x3)  =  U85_AA(x3)
U87_AA(x1, x2, x3)  =  U87_AA(x3)
U88_AA(x1, x2, x3)  =  U88_AA(x3)
U89_AA(x1, x2, x3)  =  U89_AA(x3)
U91_AA(x1, x2, x3)  =  U91_AA(x3)
U92_AA(x1, x2, x3)  =  U92_AA(x3)
U93_AA(x1, x2, x3)  =  U93_AA(x3)
U95_AA(x1, x2, x3)  =  U95_AA(x3)
U96_AA(x1, x2, x3)  =  U96_AA(x3)
U97_AA(x1, x2, x3)  =  U97_AA(x3)
U99_AA(x1, x2, x3)  =  U99_AA(x3)
U100_AA(x1, x2, x3)  =  U100_AA(x3)
U101_AA(x1, x2, x3)  =  U101_AA(x3)
U104_AAA(x1, x2, x3, x4)  =  U104_AAA(x4)
U105_AAA(x1, x2, x3, x4)  =  U105_AAA(x4)
U106_AAA(x1, x2, x3, x4)  =  U106_AAA(x4)
U107_AAA(x1, x2, x3, x4)  =  U107_AAA(x4)
U11_AA(x1, x2, x3)  =  U11_AA(x3)
U12_AA(x1, x2, x3)  =  U12_AA(x3)
U13_AA(x1, x2, x3)  =  U13_AA(x3)
U19_AA(x1, x2, x3)  =  U19_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U23_AA(x1, x2, x3)  =  U23_AA(x3)
U24_AA(x1, x2, x3)  =  U24_AA(x3)
U25_AA(x1, x2, x3)  =  U25_AA(x3)
U27_AA(x1, x2, x3)  =  U27_AA(x3)
U28_AA(x1, x2, x3)  =  U28_AA(x3)
U29_AA(x1, x2, x3)  =  U29_AA(x3)
U31_AA(x1, x2, x3)  =  U31_AA(x3)
U32_AA(x1, x2, x3)  =  U32_AA(x3)
U33_AA(x1, x2, x3)  =  U33_AA(x3)
U35_AA(x1, x2, x3)  =  U35_AA(x3)
U36_AA(x1, x2, x3)  =  U36_AA(x3)
U37_AA(x1, x2, x3)  =  U37_AA(x3)
U39_AA(x1, x2, x3)  =  U39_AA(x3)
U40_AA(x1, x2, x3)  =  U40_AA(x3)
U41_AA(x1, x2, x3)  =  U41_AA(x3)
U43_AA(x1, x2, x3)  =  U43_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U45_AA(x1, x2, x3)  =  U45_AA(x3)
U47_AA(x1, x2, x3)  =  U47_AA(x3)
U48_AA(x1, x2, x3)  =  U48_AA(x3)
U49_AA(x1, x2, x3)  =  U49_AA(x3)
U51_AA(x1, x2, x3)  =  U51_AA(x3)
U52_AA(x1, x2, x3)  =  U52_AA(x3)
U53_AA(x1, x2, x3)  =  U53_AA(x3)
U55_AA(x1, x2, x3)  =  U55_AA(x3)
U56_AA(x1, x2, x3)  =  U56_AA(x3)
U57_AA(x1, x2, x3)  =  U57_AA(x3)
U59_AA(x1, x2, x3)  =  U59_AA(x3)
U60_AA(x1, x2, x3)  =  U60_AA(x3)
U61_AA(x1, x2, x3)  =  U61_AA(x3)
U112_GA(x1, x2, x3)  =  U112_GA(x1, x3)
U11_GA(x1, x2, x3)  =  U11_GA(x1, x3)
U12_GA(x1, x2, x3)  =  U12_GA(x1, x3)
U13_GA(x1, x2, x3)  =  U13_GA(x1, x3)
U19_GA(x1, x2, x3)  =  U19_GA(x1, x3)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x3)
U23_GA(x1, x2, x3)  =  U23_GA(x1, x3)
U24_GA(x1, x2, x3)  =  U24_GA(x1, x3)
U25_GA(x1, x2, x3)  =  U25_GA(x1, x3)
U27_GA(x1, x2, x3)  =  U27_GA(x1, x3)
U28_GA(x1, x2, x3)  =  U28_GA(x1, x3)
U29_GA(x1, x2, x3)  =  U29_GA(x1, x3)
U31_GA(x1, x2, x3)  =  U31_GA(x1, x3)
U32_GA(x1, x2, x3)  =  U32_GA(x1, x3)
U33_GA(x1, x2, x3)  =  U33_GA(x1, x3)
U35_GA(x1, x2, x3)  =  U35_GA(x1, x3)
U36_GA(x1, x2, x3)  =  U36_GA(x1, x3)
U37_GA(x1, x2, x3)  =  U37_GA(x1, x3)
U39_GA(x1, x2, x3)  =  U39_GA(x1, x3)
U40_GA(x1, x2, x3)  =  U40_GA(x1, x3)
U41_GA(x1, x2, x3)  =  U41_GA(x1, x3)
U43_GA(x1, x2, x3)  =  U43_GA(x1, x3)
U44_GA(x1, x2, x3)  =  U44_GA(x1, x3)
U45_GA(x1, x2, x3)  =  U45_GA(x1, x3)
U47_GA(x1, x2, x3)  =  U47_GA(x1, x3)
U48_GA(x1, x2, x3)  =  U48_GA(x1, x3)
U49_GA(x1, x2, x3)  =  U49_GA(x1, x3)
U51_GA(x1, x2, x3)  =  U51_GA(x1, x3)
U52_GA(x1, x2, x3)  =  U52_GA(x1, x3)
U53_GA(x1, x2, x3)  =  U53_GA(x1, x3)
U55_GA(x1, x2, x3)  =  U55_GA(x1, x3)
U56_GA(x1, x2, x3)  =  U56_GA(x1, x3)
U57_GA(x1, x2, x3)  =  U57_GA(x1, x3)
U59_GA(x1, x2, x3)  =  U59_GA(x1, x3)
U60_GA(x1, x2, x3)  =  U60_GA(x1, x3)
U61_GA(x1, x2, x3)  =  U61_GA(x1, x3)
U3_GA(x1, x2, x3)  =  U3_GA(x1, x3)
U4_GA(x1, x2, x3)  =  U4_GA(x1, x3)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x3)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x3)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x3)
U63_GA(x1, x2, x3)  =  U63_GA(x1, x3)
U64_GA(x1, x2, x3)  =  U64_GA(x1, x3)
U65_GA(x1, x2, x3)  =  U65_GA(x1, x3)
U67_GA(x1, x2, x3)  =  U67_GA(x1, x3)
U68_GA(x1, x2, x3)  =  U68_GA(x1, x3)
U69_GA(x1, x2, x3)  =  U69_GA(x1, x3)
U71_GA(x1, x2, x3)  =  U71_GA(x1, x3)
U72_GA(x1, x2, x3)  =  U72_GA(x1, x3)
U73_GA(x1, x2, x3)  =  U73_GA(x1, x3)
U75_GA(x1, x2, x3)  =  U75_GA(x1, x3)
U76_GA(x1, x2, x3)  =  U76_GA(x1, x3)
U77_GA(x1, x2, x3)  =  U77_GA(x1, x3)
U79_GA(x1, x2, x3)  =  U79_GA(x1, x3)
U80_GA(x1, x2, x3)  =  U80_GA(x1, x3)
U81_GA(x1, x2, x3)  =  U81_GA(x1, x3)
U83_GA(x1, x2, x3)  =  U83_GA(x1, x3)
U84_GA(x1, x2, x3)  =  U84_GA(x1, x3)
U85_GA(x1, x2, x3)  =  U85_GA(x1, x3)
U87_GA(x1, x2, x3)  =  U87_GA(x1, x3)
U88_GA(x1, x2, x3)  =  U88_GA(x1, x3)
U89_GA(x1, x2, x3)  =  U89_GA(x1, x3)
U91_GA(x1, x2, x3)  =  U91_GA(x1, x3)
U92_GA(x1, x2, x3)  =  U92_GA(x1, x3)
U93_GA(x1, x2, x3)  =  U93_GA(x1, x3)
U95_GA(x1, x2, x3)  =  U95_GA(x1, x3)
U96_GA(x1, x2, x3)  =  U96_GA(x1, x3)
U97_GA(x1, x2, x3)  =  U97_GA(x1, x3)
U99_GA(x1, x2, x3)  =  U99_GA(x1, x3)
U100_GA(x1, x2, x3)  =  U100_GA(x1, x3)
U101_GA(x1, x2, x3)  =  U101_GA(x1, x3)
U104_GAA(x1, x2, x3, x4)  =  U104_GAA(x1, x4)
U105_GAA(x1, x2, x3, x4)  =  U105_GAA(x1, x4)
U106_GAA(x1, x2, x3, x4)  =  U106_GAA(x1, x4)
U107_GAA(x1, x2, x3, x4)  =  U107_GAA(x1, x4)

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

(6) Obligation:

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

E1_IN_GA(T22, T24) → U108_GA(T22, T24, n7_in_ga(T22, T24))
E1_IN_GA(T22, T24) → N7_IN_GA(T22, T24)
N7_IN_GA(.(lbrace, T41), T43) → U102_GA(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
N7_IN_GA(.(lbrace, T41), T43) → E1_IN_GA(T41, .(rbrace, T43))
E1_IN_GA(T62, T64) → U109_GA(T62, T64, p31_in_gaa(T62, X59, T64))
E1_IN_GA(T62, T64) → P31_IN_GAA(T62, X59, T64)
P31_IN_GAA(T62, X59, T64) → U103_GAA(T62, X59, T64, n32_in_ga(T62, X59))
P31_IN_GAA(T62, X59, T64) → N32_IN_GA(T62, X59)
N32_IN_GA(.(lbrace, T89), X84) → U1_GA(T89, X84, e53_in_ga(T89, X84))
N32_IN_GA(.(lbrace, T89), X84) → E53_IN_GA(T89, X84)
E53_IN_GA(T97, X110) → U98_GA(T97, X110, t58_in_ga(T97, X110))
E53_IN_GA(T97, X110) → T58_IN_GA(T97, X110)
T58_IN_GA(.(lbrace, T130), X155) → U94_GA(T130, X155, e82_in_ga(T130, X155))
T58_IN_GA(.(lbrace, T130), X155) → E82_IN_GA(T130, X155)
E82_IN_GA(T138, X181) → U90_GA(T138, X181, t87_in_ga(T138, X181))
E82_IN_GA(T138, X181) → T87_IN_GA(T138, X181)
T87_IN_GA(.(lbrace, T171), X226) → U86_GA(T171, X226, e111_in_ga(T171, X226))
T87_IN_GA(.(lbrace, T171), X226) → E111_IN_GA(T171, X226)
E111_IN_GA(T179, X252) → U82_GA(T179, X252, t116_in_ga(T179, X252))
E111_IN_GA(T179, X252) → T116_IN_GA(T179, X252)
T116_IN_GA(.(lbrace, T212), X297) → U78_GA(T212, X297, e140_in_ga(T212, X297))
T116_IN_GA(.(lbrace, T212), X297) → E140_IN_GA(T212, X297)
E140_IN_GA(T220, X323) → U74_GA(T220, X323, t145_in_ga(T220, X323))
E140_IN_GA(T220, X323) → T145_IN_GA(T220, X323)
T145_IN_GA(.(lbrace, T253), X368) → U70_GA(T253, X368, e169_in_ga(T253, X368))
T145_IN_GA(.(lbrace, T253), X368) → E169_IN_GA(T253, X368)
E169_IN_GA(T261, X394) → U66_GA(T261, X394, t174_in_ga(T261, X394))
E169_IN_GA(T261, X394) → T174_IN_GA(T261, X394)
T174_IN_GA(.(lbrace, T294), X439) → U62_GA(T294, X439, e198_in_ga(T294, X439))
T174_IN_GA(.(lbrace, T294), X439) → E198_IN_GA(T294, X439)
E198_IN_GA(T302, X465) → U6_GA(T302, X465, t203_in_ga(T302, X465))
E198_IN_GA(T302, X465) → T203_IN_GA(T302, X465)
T203_IN_GA(.(lbrace, T335), X510) → U2_GA(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
T203_IN_GA(.(lbrace, T335), X510) → E1_IN_GA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_GA(T941, T943) → U110_GA(T941, T943, t234_in_ga(T941, X1569))
E1_IN_GA(T941, T943) → T234_IN_GA(T941, X1569)
T234_IN_GA(.(lbrace, T392), X599) → U14_GA(T392, X599, e259_in_ga(T392, X599))
T234_IN_GA(.(lbrace, T392), X599) → E259_IN_GA(T392, X599)
E259_IN_GA(T400, X625) → U58_GA(T400, X625, t264_in_ga(T400, X625))
E259_IN_GA(T400, X625) → T264_IN_GA(T400, X625)
T264_IN_GA(.(lbrace, T433), X670) → U54_GA(T433, X670, e288_in_ga(T433, X670))
T264_IN_GA(.(lbrace, T433), X670) → E288_IN_GA(T433, X670)
E288_IN_GA(T441, X696) → U50_GA(T441, X696, t293_in_ga(T441, X696))
E288_IN_GA(T441, X696) → T293_IN_GA(T441, X696)
T293_IN_GA(.(lbrace, T474), X741) → U46_GA(T474, X741, e317_in_ga(T474, X741))
T293_IN_GA(.(lbrace, T474), X741) → E317_IN_GA(T474, X741)
E317_IN_GA(T482, X767) → U42_GA(T482, X767, t322_in_ga(T482, X767))
E317_IN_GA(T482, X767) → T322_IN_GA(T482, X767)
T322_IN_GA(.(lbrace, T515), X812) → U38_GA(T515, X812, e346_in_ga(T515, X812))
T322_IN_GA(.(lbrace, T515), X812) → E346_IN_GA(T515, X812)
E346_IN_GA(T523, X838) → U34_GA(T523, X838, t351_in_ga(T523, X838))
E346_IN_GA(T523, X838) → T351_IN_GA(T523, X838)
T351_IN_GA(.(lbrace, T556), X883) → U30_GA(T556, X883, e375_in_ga(T556, X883))
T351_IN_GA(.(lbrace, T556), X883) → E375_IN_GA(T556, X883)
E375_IN_GA(T564, X909) → U26_GA(T564, X909, t380_in_ga(T564, X909))
E375_IN_GA(T564, X909) → T380_IN_GA(T564, X909)
T380_IN_GA(.(lbrace, T597), X954) → U22_GA(T597, X954, e404_in_ga(T597, X954))
T380_IN_GA(.(lbrace, T597), X954) → E404_IN_GA(T597, X954)
E404_IN_GA(T605, X980) → U18_GA(T605, X980, t409_in_ga(T605, X980))
E404_IN_GA(T605, X980) → T409_IN_GA(T605, X980)
T409_IN_GA(.(lbrace, T638), X1025) → U10_GA(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
T409_IN_GA(.(lbrace, T638), X1025) → E1_IN_GA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_GA(T941, T943) → U111_GA(T941, T943, t234_in_ga(T941, T945))
T234_IN_GA(T780, X1303) → U15_GA(T780, X1303, n32_in_ga(T780, X1302))
T234_IN_GA(T780, X1303) → N32_IN_GA(T780, X1302)
T234_IN_GA(T780, X1303) → U16_GA(T780, X1303, n32_in_ga(T780, T784))
U16_GA(T780, X1303, n32_out_ga(T780, T784)) → U17_GA(T780, X1303, t234_in_aa(T784, X1303))
U16_GA(T780, X1303, n32_out_ga(T780, T784)) → T234_IN_AA(T784, X1303)
T234_IN_AA(.(lbrace, T392), X599) → U14_AA(T392, X599, e259_in_aa(T392, X599))
T234_IN_AA(.(lbrace, T392), X599) → E259_IN_AA(T392, X599)
E259_IN_AA(T400, X625) → U58_AA(T400, X625, t264_in_aa(T400, X625))
E259_IN_AA(T400, X625) → T264_IN_AA(T400, X625)
T264_IN_AA(.(lbrace, T433), X670) → U54_AA(T433, X670, e288_in_aa(T433, X670))
T264_IN_AA(.(lbrace, T433), X670) → E288_IN_AA(T433, X670)
E288_IN_AA(T441, X696) → U50_AA(T441, X696, t293_in_aa(T441, X696))
E288_IN_AA(T441, X696) → T293_IN_AA(T441, X696)
T293_IN_AA(.(lbrace, T474), X741) → U46_AA(T474, X741, e317_in_aa(T474, X741))
T293_IN_AA(.(lbrace, T474), X741) → E317_IN_AA(T474, X741)
E317_IN_AA(T482, X767) → U42_AA(T482, X767, t322_in_aa(T482, X767))
E317_IN_AA(T482, X767) → T322_IN_AA(T482, X767)
T322_IN_AA(.(lbrace, T515), X812) → U38_AA(T515, X812, e346_in_aa(T515, X812))
T322_IN_AA(.(lbrace, T515), X812) → E346_IN_AA(T515, X812)
E346_IN_AA(T523, X838) → U34_AA(T523, X838, t351_in_aa(T523, X838))
E346_IN_AA(T523, X838) → T351_IN_AA(T523, X838)
T351_IN_AA(.(lbrace, T556), X883) → U30_AA(T556, X883, e375_in_aa(T556, X883))
T351_IN_AA(.(lbrace, T556), X883) → E375_IN_AA(T556, X883)
E375_IN_AA(T564, X909) → U26_AA(T564, X909, t380_in_aa(T564, X909))
E375_IN_AA(T564, X909) → T380_IN_AA(T564, X909)
T380_IN_AA(.(lbrace, T597), X954) → U22_AA(T597, X954, e404_in_aa(T597, X954))
T380_IN_AA(.(lbrace, T597), X954) → E404_IN_AA(T597, X954)
E404_IN_AA(T605, X980) → U18_AA(T605, X980, t409_in_aa(T605, X980))
E404_IN_AA(T605, X980) → T409_IN_AA(T605, X980)
T409_IN_AA(.(lbrace, T638), X1025) → U10_AA(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
T409_IN_AA(.(lbrace, T638), X1025) → E1_IN_AA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_AA(T22, T24) → U108_AA(T22, T24, n7_in_aa(T22, T24))
E1_IN_AA(T22, T24) → N7_IN_AA(T22, T24)
N7_IN_AA(.(lbrace, T41), T43) → U102_AA(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
N7_IN_AA(.(lbrace, T41), T43) → E1_IN_AA(T41, .(rbrace, T43))
E1_IN_AA(T62, T64) → U109_AA(T62, T64, p31_in_aaa(T62, X59, T64))
E1_IN_AA(T62, T64) → P31_IN_AAA(T62, X59, T64)
P31_IN_AAA(T62, X59, T64) → U103_AAA(T62, X59, T64, n32_in_aa(T62, X59))
P31_IN_AAA(T62, X59, T64) → N32_IN_AA(T62, X59)
N32_IN_AA(.(lbrace, T89), X84) → U1_AA(T89, X84, e53_in_aa(T89, X84))
N32_IN_AA(.(lbrace, T89), X84) → E53_IN_AA(T89, X84)
E53_IN_AA(T97, X110) → U98_AA(T97, X110, t58_in_aa(T97, X110))
E53_IN_AA(T97, X110) → T58_IN_AA(T97, X110)
T58_IN_AA(.(lbrace, T130), X155) → U94_AA(T130, X155, e82_in_aa(T130, X155))
T58_IN_AA(.(lbrace, T130), X155) → E82_IN_AA(T130, X155)
E82_IN_AA(T138, X181) → U90_AA(T138, X181, t87_in_aa(T138, X181))
E82_IN_AA(T138, X181) → T87_IN_AA(T138, X181)
T87_IN_AA(.(lbrace, T171), X226) → U86_AA(T171, X226, e111_in_aa(T171, X226))
T87_IN_AA(.(lbrace, T171), X226) → E111_IN_AA(T171, X226)
E111_IN_AA(T179, X252) → U82_AA(T179, X252, t116_in_aa(T179, X252))
E111_IN_AA(T179, X252) → T116_IN_AA(T179, X252)
T116_IN_AA(.(lbrace, T212), X297) → U78_AA(T212, X297, e140_in_aa(T212, X297))
T116_IN_AA(.(lbrace, T212), X297) → E140_IN_AA(T212, X297)
E140_IN_AA(T220, X323) → U74_AA(T220, X323, t145_in_aa(T220, X323))
E140_IN_AA(T220, X323) → T145_IN_AA(T220, X323)
T145_IN_AA(.(lbrace, T253), X368) → U70_AA(T253, X368, e169_in_aa(T253, X368))
T145_IN_AA(.(lbrace, T253), X368) → E169_IN_AA(T253, X368)
E169_IN_AA(T261, X394) → U66_AA(T261, X394, t174_in_aa(T261, X394))
E169_IN_AA(T261, X394) → T174_IN_AA(T261, X394)
T174_IN_AA(.(lbrace, T294), X439) → U62_AA(T294, X439, e198_in_aa(T294, X439))
T174_IN_AA(.(lbrace, T294), X439) → E198_IN_AA(T294, X439)
E198_IN_AA(T302, X465) → U6_AA(T302, X465, t203_in_aa(T302, X465))
E198_IN_AA(T302, X465) → T203_IN_AA(T302, X465)
T203_IN_AA(.(lbrace, T335), X510) → U2_AA(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
T203_IN_AA(.(lbrace, T335), X510) → E1_IN_AA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_AA(T941, T943) → U110_AA(T941, T943, t234_in_aa(T941, X1569))
E1_IN_AA(T941, T943) → T234_IN_AA(T941, X1569)
T234_IN_AA(T780, X1303) → U15_AA(T780, X1303, n32_in_aa(T780, X1302))
T234_IN_AA(T780, X1303) → N32_IN_AA(T780, X1302)
T234_IN_AA(T780, X1303) → U16_AA(T780, X1303, n32_in_aa(T780, T784))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → U17_AA(T780, X1303, t234_in_aa(T784, X1303))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → T234_IN_AA(T784, X1303)
E1_IN_AA(T941, T943) → U111_AA(T941, T943, t234_in_aa(T941, T945))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → U112_AA(T941, T943, e1_in_aa(T945, T943))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → E1_IN_AA(T945, T943)
T203_IN_AA(T345, X530) → U3_AA(T345, X530, n32_in_aa(T345, X529))
T203_IN_AA(T345, X530) → N32_IN_AA(T345, X529)
T203_IN_AA(T345, X530) → U4_AA(T345, X530, n32_in_aa(T345, T349))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → U5_AA(T345, X530, t203_in_aa(T349, X530))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_AA(T357, X551) → U7_AA(T357, X551, t234_in_aa(T357, X550))
E198_IN_AA(T357, X551) → T234_IN_AA(T357, X550)
E198_IN_AA(T357, X551) → U8_AA(T357, X551, t234_in_aa(T357, T359))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → U9_AA(T357, X551, e198_in_aa(T359, X551))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_AA(T795, X1326) → U63_AA(T795, X1326, n32_in_aa(T795, X1325))
T174_IN_AA(T795, X1326) → N32_IN_AA(T795, X1325)
T174_IN_AA(T795, X1326) → U64_AA(T795, X1326, n32_in_aa(T795, T799))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → U65_AA(T795, X1326, t174_in_aa(T799, X1326))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_AA(T807, X1347) → U67_AA(T807, X1347, t234_in_aa(T807, X1346))
E169_IN_AA(T807, X1347) → T234_IN_AA(T807, X1346)
E169_IN_AA(T807, X1347) → U68_AA(T807, X1347, t234_in_aa(T807, T809))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → U69_AA(T807, X1347, e169_in_aa(T809, X1347))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_AA(T817, X1369) → U71_AA(T817, X1369, n32_in_aa(T817, X1368))
T145_IN_AA(T817, X1369) → N32_IN_AA(T817, X1368)
T145_IN_AA(T817, X1369) → U72_AA(T817, X1369, n32_in_aa(T817, T821))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → U73_AA(T817, X1369, t145_in_aa(T821, X1369))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_AA(T829, X1390) → U75_AA(T829, X1390, t234_in_aa(T829, X1389))
E140_IN_AA(T829, X1390) → T234_IN_AA(T829, X1389)
E140_IN_AA(T829, X1390) → U76_AA(T829, X1390, t234_in_aa(T829, T831))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → U77_AA(T829, X1390, e140_in_aa(T831, X1390))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_AA(T839, X1412) → U79_AA(T839, X1412, n32_in_aa(T839, X1411))
T116_IN_AA(T839, X1412) → N32_IN_AA(T839, X1411)
T116_IN_AA(T839, X1412) → U80_AA(T839, X1412, n32_in_aa(T839, T843))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → U81_AA(T839, X1412, t116_in_aa(T843, X1412))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_AA(T851, X1433) → U83_AA(T851, X1433, t234_in_aa(T851, X1432))
E111_IN_AA(T851, X1433) → T234_IN_AA(T851, X1432)
E111_IN_AA(T851, X1433) → U84_AA(T851, X1433, t234_in_aa(T851, T853))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → U85_AA(T851, X1433, e111_in_aa(T853, X1433))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_AA(T861, X1455) → U87_AA(T861, X1455, n32_in_aa(T861, X1454))
T87_IN_AA(T861, X1455) → N32_IN_AA(T861, X1454)
T87_IN_AA(T861, X1455) → U88_AA(T861, X1455, n32_in_aa(T861, T865))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → U89_AA(T861, X1455, t87_in_aa(T865, X1455))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_AA(T873, X1476) → U91_AA(T873, X1476, t234_in_aa(T873, X1475))
E82_IN_AA(T873, X1476) → T234_IN_AA(T873, X1475)
E82_IN_AA(T873, X1476) → U92_AA(T873, X1476, t234_in_aa(T873, T875))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → U93_AA(T873, X1476, e82_in_aa(T875, X1476))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_AA(T883, X1498) → U95_AA(T883, X1498, n32_in_aa(T883, X1497))
T58_IN_AA(T883, X1498) → N32_IN_AA(T883, X1497)
T58_IN_AA(T883, X1498) → U96_AA(T883, X1498, n32_in_aa(T883, T887))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → U97_AA(T883, X1498, t58_in_aa(T887, X1498))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_AA(T895, X1519) → U99_AA(T895, X1519, t234_in_aa(T895, X1518))
E53_IN_AA(T895, X1519) → T234_IN_AA(T895, X1518)
E53_IN_AA(T895, X1519) → U100_AA(T895, X1519, t234_in_aa(T895, T897))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → U101_AA(T895, X1519, e53_in_aa(T897, X1519))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_AAA(T62, T916, T918) → U104_AAA(T62, T916, T918, n32_in_aa(T62, T916))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → U105_AAA(T62, T916, T918, n7_in_aa(T916, T918))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_AAA(T62, T929, T931) → U106_AAA(T62, T929, T931, n32_in_aa(T62, T929))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → U107_AAA(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → P31_IN_AAA(T929, X1556, T931)
T409_IN_AA(T648, X1045) → U11_AA(T648, X1045, n32_in_aa(T648, X1044))
T409_IN_AA(T648, X1045) → N32_IN_AA(T648, X1044)
T409_IN_AA(T648, X1045) → U12_AA(T648, X1045, n32_in_aa(T648, T652))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → U13_AA(T648, X1045, t409_in_aa(T652, X1045))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_AA(T660, X1066) → U19_AA(T660, X1066, t234_in_aa(T660, X1065))
E404_IN_AA(T660, X1066) → T234_IN_AA(T660, X1065)
E404_IN_AA(T660, X1066) → U20_AA(T660, X1066, t234_in_aa(T660, T662))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → U21_AA(T660, X1066, e404_in_aa(T662, X1066))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_AA(T670, X1088) → U23_AA(T670, X1088, n32_in_aa(T670, X1087))
T380_IN_AA(T670, X1088) → N32_IN_AA(T670, X1087)
T380_IN_AA(T670, X1088) → U24_AA(T670, X1088, n32_in_aa(T670, T674))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → U25_AA(T670, X1088, t380_in_aa(T674, X1088))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_AA(T682, X1109) → U27_AA(T682, X1109, t234_in_aa(T682, X1108))
E375_IN_AA(T682, X1109) → T234_IN_AA(T682, X1108)
E375_IN_AA(T682, X1109) → U28_AA(T682, X1109, t234_in_aa(T682, T684))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → U29_AA(T682, X1109, e375_in_aa(T684, X1109))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_AA(T692, X1131) → U31_AA(T692, X1131, n32_in_aa(T692, X1130))
T351_IN_AA(T692, X1131) → N32_IN_AA(T692, X1130)
T351_IN_AA(T692, X1131) → U32_AA(T692, X1131, n32_in_aa(T692, T696))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → U33_AA(T692, X1131, t351_in_aa(T696, X1131))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_AA(T704, X1152) → U35_AA(T704, X1152, t234_in_aa(T704, X1151))
E346_IN_AA(T704, X1152) → T234_IN_AA(T704, X1151)
E346_IN_AA(T704, X1152) → U36_AA(T704, X1152, t234_in_aa(T704, T706))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → U37_AA(T704, X1152, e346_in_aa(T706, X1152))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_AA(T714, X1174) → U39_AA(T714, X1174, n32_in_aa(T714, X1173))
T322_IN_AA(T714, X1174) → N32_IN_AA(T714, X1173)
T322_IN_AA(T714, X1174) → U40_AA(T714, X1174, n32_in_aa(T714, T718))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → U41_AA(T714, X1174, t322_in_aa(T718, X1174))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_AA(T726, X1195) → U43_AA(T726, X1195, t234_in_aa(T726, X1194))
E317_IN_AA(T726, X1195) → T234_IN_AA(T726, X1194)
E317_IN_AA(T726, X1195) → U44_AA(T726, X1195, t234_in_aa(T726, T728))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → U45_AA(T726, X1195, e317_in_aa(T728, X1195))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_AA(T736, X1217) → U47_AA(T736, X1217, n32_in_aa(T736, X1216))
T293_IN_AA(T736, X1217) → N32_IN_AA(T736, X1216)
T293_IN_AA(T736, X1217) → U48_AA(T736, X1217, n32_in_aa(T736, T740))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → U49_AA(T736, X1217, t293_in_aa(T740, X1217))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_AA(T748, X1238) → U51_AA(T748, X1238, t234_in_aa(T748, X1237))
E288_IN_AA(T748, X1238) → T234_IN_AA(T748, X1237)
E288_IN_AA(T748, X1238) → U52_AA(T748, X1238, t234_in_aa(T748, T750))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → U53_AA(T748, X1238, e288_in_aa(T750, X1238))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_AA(T758, X1260) → U55_AA(T758, X1260, n32_in_aa(T758, X1259))
T264_IN_AA(T758, X1260) → N32_IN_AA(T758, X1259)
T264_IN_AA(T758, X1260) → U56_AA(T758, X1260, n32_in_aa(T758, T762))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → U57_AA(T758, X1260, t264_in_aa(T762, X1260))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_AA(T770, X1281) → U59_AA(T770, X1281, t234_in_aa(T770, X1280))
E259_IN_AA(T770, X1281) → T234_IN_AA(T770, X1280)
E259_IN_AA(T770, X1281) → U60_AA(T770, X1281, t234_in_aa(T770, T772))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → U61_AA(T770, X1281, e259_in_aa(T772, X1281))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → E259_IN_AA(T772, X1281)
U111_GA(T941, T943, t234_out_ga(T941, T945)) → U112_GA(T941, T943, e1_in_aa(T945, T943))
U111_GA(T941, T943, t234_out_ga(T941, T945)) → E1_IN_AA(T945, T943)
T409_IN_GA(T648, X1045) → U11_GA(T648, X1045, n32_in_ga(T648, X1044))
T409_IN_GA(T648, X1045) → N32_IN_GA(T648, X1044)
T409_IN_GA(T648, X1045) → U12_GA(T648, X1045, n32_in_ga(T648, T652))
U12_GA(T648, X1045, n32_out_ga(T648, T652)) → U13_GA(T648, X1045, t409_in_aa(T652, X1045))
U12_GA(T648, X1045, n32_out_ga(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_GA(T660, X1066) → U19_GA(T660, X1066, t234_in_ga(T660, X1065))
E404_IN_GA(T660, X1066) → T234_IN_GA(T660, X1065)
E404_IN_GA(T660, X1066) → U20_GA(T660, X1066, t234_in_ga(T660, T662))
U20_GA(T660, X1066, t234_out_ga(T660, T662)) → U21_GA(T660, X1066, e404_in_aa(T662, X1066))
U20_GA(T660, X1066, t234_out_ga(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_GA(T670, X1088) → U23_GA(T670, X1088, n32_in_ga(T670, X1087))
T380_IN_GA(T670, X1088) → N32_IN_GA(T670, X1087)
T380_IN_GA(T670, X1088) → U24_GA(T670, X1088, n32_in_ga(T670, T674))
U24_GA(T670, X1088, n32_out_ga(T670, T674)) → U25_GA(T670, X1088, t380_in_aa(T674, X1088))
U24_GA(T670, X1088, n32_out_ga(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_GA(T682, X1109) → U27_GA(T682, X1109, t234_in_ga(T682, X1108))
E375_IN_GA(T682, X1109) → T234_IN_GA(T682, X1108)
E375_IN_GA(T682, X1109) → U28_GA(T682, X1109, t234_in_ga(T682, T684))
U28_GA(T682, X1109, t234_out_ga(T682, T684)) → U29_GA(T682, X1109, e375_in_aa(T684, X1109))
U28_GA(T682, X1109, t234_out_ga(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_GA(T692, X1131) → U31_GA(T692, X1131, n32_in_ga(T692, X1130))
T351_IN_GA(T692, X1131) → N32_IN_GA(T692, X1130)
T351_IN_GA(T692, X1131) → U32_GA(T692, X1131, n32_in_ga(T692, T696))
U32_GA(T692, X1131, n32_out_ga(T692, T696)) → U33_GA(T692, X1131, t351_in_aa(T696, X1131))
U32_GA(T692, X1131, n32_out_ga(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_GA(T704, X1152) → U35_GA(T704, X1152, t234_in_ga(T704, X1151))
E346_IN_GA(T704, X1152) → T234_IN_GA(T704, X1151)
E346_IN_GA(T704, X1152) → U36_GA(T704, X1152, t234_in_ga(T704, T706))
U36_GA(T704, X1152, t234_out_ga(T704, T706)) → U37_GA(T704, X1152, e346_in_aa(T706, X1152))
U36_GA(T704, X1152, t234_out_ga(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_GA(T714, X1174) → U39_GA(T714, X1174, n32_in_ga(T714, X1173))
T322_IN_GA(T714, X1174) → N32_IN_GA(T714, X1173)
T322_IN_GA(T714, X1174) → U40_GA(T714, X1174, n32_in_ga(T714, T718))
U40_GA(T714, X1174, n32_out_ga(T714, T718)) → U41_GA(T714, X1174, t322_in_aa(T718, X1174))
U40_GA(T714, X1174, n32_out_ga(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_GA(T726, X1195) → U43_GA(T726, X1195, t234_in_ga(T726, X1194))
E317_IN_GA(T726, X1195) → T234_IN_GA(T726, X1194)
E317_IN_GA(T726, X1195) → U44_GA(T726, X1195, t234_in_ga(T726, T728))
U44_GA(T726, X1195, t234_out_ga(T726, T728)) → U45_GA(T726, X1195, e317_in_aa(T728, X1195))
U44_GA(T726, X1195, t234_out_ga(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_GA(T736, X1217) → U47_GA(T736, X1217, n32_in_ga(T736, X1216))
T293_IN_GA(T736, X1217) → N32_IN_GA(T736, X1216)
T293_IN_GA(T736, X1217) → U48_GA(T736, X1217, n32_in_ga(T736, T740))
U48_GA(T736, X1217, n32_out_ga(T736, T740)) → U49_GA(T736, X1217, t293_in_aa(T740, X1217))
U48_GA(T736, X1217, n32_out_ga(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_GA(T748, X1238) → U51_GA(T748, X1238, t234_in_ga(T748, X1237))
E288_IN_GA(T748, X1238) → T234_IN_GA(T748, X1237)
E288_IN_GA(T748, X1238) → U52_GA(T748, X1238, t234_in_ga(T748, T750))
U52_GA(T748, X1238, t234_out_ga(T748, T750)) → U53_GA(T748, X1238, e288_in_aa(T750, X1238))
U52_GA(T748, X1238, t234_out_ga(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_GA(T758, X1260) → U55_GA(T758, X1260, n32_in_ga(T758, X1259))
T264_IN_GA(T758, X1260) → N32_IN_GA(T758, X1259)
T264_IN_GA(T758, X1260) → U56_GA(T758, X1260, n32_in_ga(T758, T762))
U56_GA(T758, X1260, n32_out_ga(T758, T762)) → U57_GA(T758, X1260, t264_in_aa(T762, X1260))
U56_GA(T758, X1260, n32_out_ga(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_GA(T770, X1281) → U59_GA(T770, X1281, t234_in_ga(T770, X1280))
E259_IN_GA(T770, X1281) → T234_IN_GA(T770, X1280)
E259_IN_GA(T770, X1281) → U60_GA(T770, X1281, t234_in_ga(T770, T772))
U60_GA(T770, X1281, t234_out_ga(T770, T772)) → U61_GA(T770, X1281, e259_in_aa(T772, X1281))
U60_GA(T770, X1281, t234_out_ga(T770, T772)) → E259_IN_AA(T772, X1281)
T203_IN_GA(T345, X530) → U3_GA(T345, X530, n32_in_ga(T345, X529))
T203_IN_GA(T345, X530) → N32_IN_GA(T345, X529)
T203_IN_GA(T345, X530) → U4_GA(T345, X530, n32_in_ga(T345, T349))
U4_GA(T345, X530, n32_out_ga(T345, T349)) → U5_GA(T345, X530, t203_in_aa(T349, X530))
U4_GA(T345, X530, n32_out_ga(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_GA(T357, X551) → U7_GA(T357, X551, t234_in_ga(T357, X550))
E198_IN_GA(T357, X551) → T234_IN_GA(T357, X550)
E198_IN_GA(T357, X551) → U8_GA(T357, X551, t234_in_ga(T357, T359))
U8_GA(T357, X551, t234_out_ga(T357, T359)) → U9_GA(T357, X551, e198_in_aa(T359, X551))
U8_GA(T357, X551, t234_out_ga(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_GA(T795, X1326) → U63_GA(T795, X1326, n32_in_ga(T795, X1325))
T174_IN_GA(T795, X1326) → N32_IN_GA(T795, X1325)
T174_IN_GA(T795, X1326) → U64_GA(T795, X1326, n32_in_ga(T795, T799))
U64_GA(T795, X1326, n32_out_ga(T795, T799)) → U65_GA(T795, X1326, t174_in_aa(T799, X1326))
U64_GA(T795, X1326, n32_out_ga(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_GA(T807, X1347) → U67_GA(T807, X1347, t234_in_ga(T807, X1346))
E169_IN_GA(T807, X1347) → T234_IN_GA(T807, X1346)
E169_IN_GA(T807, X1347) → U68_GA(T807, X1347, t234_in_ga(T807, T809))
U68_GA(T807, X1347, t234_out_ga(T807, T809)) → U69_GA(T807, X1347, e169_in_aa(T809, X1347))
U68_GA(T807, X1347, t234_out_ga(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_GA(T817, X1369) → U71_GA(T817, X1369, n32_in_ga(T817, X1368))
T145_IN_GA(T817, X1369) → N32_IN_GA(T817, X1368)
T145_IN_GA(T817, X1369) → U72_GA(T817, X1369, n32_in_ga(T817, T821))
U72_GA(T817, X1369, n32_out_ga(T817, T821)) → U73_GA(T817, X1369, t145_in_aa(T821, X1369))
U72_GA(T817, X1369, n32_out_ga(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_GA(T829, X1390) → U75_GA(T829, X1390, t234_in_ga(T829, X1389))
E140_IN_GA(T829, X1390) → T234_IN_GA(T829, X1389)
E140_IN_GA(T829, X1390) → U76_GA(T829, X1390, t234_in_ga(T829, T831))
U76_GA(T829, X1390, t234_out_ga(T829, T831)) → U77_GA(T829, X1390, e140_in_aa(T831, X1390))
U76_GA(T829, X1390, t234_out_ga(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_GA(T839, X1412) → U79_GA(T839, X1412, n32_in_ga(T839, X1411))
T116_IN_GA(T839, X1412) → N32_IN_GA(T839, X1411)
T116_IN_GA(T839, X1412) → U80_GA(T839, X1412, n32_in_ga(T839, T843))
U80_GA(T839, X1412, n32_out_ga(T839, T843)) → U81_GA(T839, X1412, t116_in_aa(T843, X1412))
U80_GA(T839, X1412, n32_out_ga(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_GA(T851, X1433) → U83_GA(T851, X1433, t234_in_ga(T851, X1432))
E111_IN_GA(T851, X1433) → T234_IN_GA(T851, X1432)
E111_IN_GA(T851, X1433) → U84_GA(T851, X1433, t234_in_ga(T851, T853))
U84_GA(T851, X1433, t234_out_ga(T851, T853)) → U85_GA(T851, X1433, e111_in_aa(T853, X1433))
U84_GA(T851, X1433, t234_out_ga(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_GA(T861, X1455) → U87_GA(T861, X1455, n32_in_ga(T861, X1454))
T87_IN_GA(T861, X1455) → N32_IN_GA(T861, X1454)
T87_IN_GA(T861, X1455) → U88_GA(T861, X1455, n32_in_ga(T861, T865))
U88_GA(T861, X1455, n32_out_ga(T861, T865)) → U89_GA(T861, X1455, t87_in_aa(T865, X1455))
U88_GA(T861, X1455, n32_out_ga(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_GA(T873, X1476) → U91_GA(T873, X1476, t234_in_ga(T873, X1475))
E82_IN_GA(T873, X1476) → T234_IN_GA(T873, X1475)
E82_IN_GA(T873, X1476) → U92_GA(T873, X1476, t234_in_ga(T873, T875))
U92_GA(T873, X1476, t234_out_ga(T873, T875)) → U93_GA(T873, X1476, e82_in_aa(T875, X1476))
U92_GA(T873, X1476, t234_out_ga(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_GA(T883, X1498) → U95_GA(T883, X1498, n32_in_ga(T883, X1497))
T58_IN_GA(T883, X1498) → N32_IN_GA(T883, X1497)
T58_IN_GA(T883, X1498) → U96_GA(T883, X1498, n32_in_ga(T883, T887))
U96_GA(T883, X1498, n32_out_ga(T883, T887)) → U97_GA(T883, X1498, t58_in_aa(T887, X1498))
U96_GA(T883, X1498, n32_out_ga(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_GA(T895, X1519) → U99_GA(T895, X1519, t234_in_ga(T895, X1518))
E53_IN_GA(T895, X1519) → T234_IN_GA(T895, X1518)
E53_IN_GA(T895, X1519) → U100_GA(T895, X1519, t234_in_ga(T895, T897))
U100_GA(T895, X1519, t234_out_ga(T895, T897)) → U101_GA(T895, X1519, e53_in_aa(T897, X1519))
U100_GA(T895, X1519, t234_out_ga(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_GAA(T62, T916, T918) → U104_GAA(T62, T916, T918, n32_in_ga(T62, T916))
U104_GAA(T62, T916, T918, n32_out_ga(T62, T916)) → U105_GAA(T62, T916, T918, n7_in_aa(T916, T918))
U104_GAA(T62, T916, T918, n32_out_ga(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_GAA(T62, T929, T931) → U106_GAA(T62, T929, T931, n32_in_ga(T62, T929))
U106_GAA(T62, T929, T931, n32_out_ga(T62, T929)) → U107_GAA(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U106_GAA(T62, T929, T931, n32_out_ga(T62, T929)) → P31_IN_AAA(T929, X1556, T931)

The TRS R consists of the following rules:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x1, x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga(x1)
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x1, x3)
U109_ga(x1, x2, x3)  =  U109_ga(x1, x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x1, x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x1, x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga(x1)
U94_ga(x1, x2, x3)  =  U94_ga(x1, x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x1, x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga(x1)
U86_ga(x1, x2, x3)  =  U86_ga(x1, x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x1, x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x1, x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga(x1)
U70_ga(x1, x2, x3)  =  U70_ga(x1, x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga(x1)
U62_ga(x1, x2, x3)  =  U62_ga(x1, x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga(x1)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga(x1)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x1, x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga(x1)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga(x1)
U38_ga(x1, x2, x3)  =  U38_ga(x1, x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x1, x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga(x1)
U30_ga(x1, x2, x3)  =  U30_ga(x1, x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga(x1)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U111_ga(x1, x2, x3)  =  U111_ga(x1, x3)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U112_ga(x1, x2, x3)  =  U112_ga(x1, x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
e404_out_ga(x1, x2)  =  e404_out_ga(x1)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
e375_out_ga(x1, x2)  =  e375_out_ga(x1)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
U28_ga(x1, x2, x3)  =  U28_ga(x1, x3)
U29_ga(x1, x2, x3)  =  U29_ga(x1, x3)
U31_ga(x1, x2, x3)  =  U31_ga(x1, x3)
U32_ga(x1, x2, x3)  =  U32_ga(x1, x3)
U33_ga(x1, x2, x3)  =  U33_ga(x1, x3)
e346_out_ga(x1, x2)  =  e346_out_ga(x1)
U35_ga(x1, x2, x3)  =  U35_ga(x1, x3)
U36_ga(x1, x2, x3)  =  U36_ga(x1, x3)
U37_ga(x1, x2, x3)  =  U37_ga(x1, x3)
U39_ga(x1, x2, x3)  =  U39_ga(x1, x3)
U40_ga(x1, x2, x3)  =  U40_ga(x1, x3)
U41_ga(x1, x2, x3)  =  U41_ga(x1, x3)
e317_out_ga(x1, x2)  =  e317_out_ga(x1)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
e288_out_ga(x1, x2)  =  e288_out_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
e259_out_ga(x1, x2)  =  e259_out_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
U60_ga(x1, x2, x3)  =  U60_ga(x1, x3)
U61_ga(x1, x2, x3)  =  U61_ga(x1, x3)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
e198_out_ga(x1, x2)  =  e198_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U63_ga(x1, x2, x3)  =  U63_ga(x1, x3)
U64_ga(x1, x2, x3)  =  U64_ga(x1, x3)
U65_ga(x1, x2, x3)  =  U65_ga(x1, x3)
e169_out_ga(x1, x2)  =  e169_out_ga(x1)
U67_ga(x1, x2, x3)  =  U67_ga(x1, x3)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
U69_ga(x1, x2, x3)  =  U69_ga(x1, x3)
U71_ga(x1, x2, x3)  =  U71_ga(x1, x3)
U72_ga(x1, x2, x3)  =  U72_ga(x1, x3)
U73_ga(x1, x2, x3)  =  U73_ga(x1, x3)
e140_out_ga(x1, x2)  =  e140_out_ga(x1)
U75_ga(x1, x2, x3)  =  U75_ga(x1, x3)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
U77_ga(x1, x2, x3)  =  U77_ga(x1, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x3)
U80_ga(x1, x2, x3)  =  U80_ga(x1, x3)
U81_ga(x1, x2, x3)  =  U81_ga(x1, x3)
e111_out_ga(x1, x2)  =  e111_out_ga(x1)
U83_ga(x1, x2, x3)  =  U83_ga(x1, x3)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
U85_ga(x1, x2, x3)  =  U85_ga(x1, x3)
U87_ga(x1, x2, x3)  =  U87_ga(x1, x3)
U88_ga(x1, x2, x3)  =  U88_ga(x1, x3)
U89_ga(x1, x2, x3)  =  U89_ga(x1, x3)
e82_out_ga(x1, x2)  =  e82_out_ga(x1)
U91_ga(x1, x2, x3)  =  U91_ga(x1, x3)
U92_ga(x1, x2, x3)  =  U92_ga(x1, x3)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
U95_ga(x1, x2, x3)  =  U95_ga(x1, x3)
U96_ga(x1, x2, x3)  =  U96_ga(x1, x3)
U97_ga(x1, x2, x3)  =  U97_ga(x1, x3)
e53_out_ga(x1, x2)  =  e53_out_ga(x1)
U99_ga(x1, x2, x3)  =  U99_ga(x1, x3)
U100_ga(x1, x2, x3)  =  U100_ga(x1, x3)
U101_ga(x1, x2, x3)  =  U101_ga(x1, x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa(x1)
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x1, x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x1, x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x1, x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x1, x4)
E1_IN_GA(x1, x2)  =  E1_IN_GA(x1)
U108_GA(x1, x2, x3)  =  U108_GA(x1, x3)
N7_IN_GA(x1, x2)  =  N7_IN_GA(x1)
U102_GA(x1, x2, x3)  =  U102_GA(x1, x3)
U109_GA(x1, x2, x3)  =  U109_GA(x1, x3)
P31_IN_GAA(x1, x2, x3)  =  P31_IN_GAA(x1)
U103_GAA(x1, x2, x3, x4)  =  U103_GAA(x1, x4)
N32_IN_GA(x1, x2)  =  N32_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x1, x3)
E53_IN_GA(x1, x2)  =  E53_IN_GA(x1)
U98_GA(x1, x2, x3)  =  U98_GA(x1, x3)
T58_IN_GA(x1, x2)  =  T58_IN_GA(x1)
U94_GA(x1, x2, x3)  =  U94_GA(x1, x3)
E82_IN_GA(x1, x2)  =  E82_IN_GA(x1)
U90_GA(x1, x2, x3)  =  U90_GA(x1, x3)
T87_IN_GA(x1, x2)  =  T87_IN_GA(x1)
U86_GA(x1, x2, x3)  =  U86_GA(x1, x3)
E111_IN_GA(x1, x2)  =  E111_IN_GA(x1)
U82_GA(x1, x2, x3)  =  U82_GA(x1, x3)
T116_IN_GA(x1, x2)  =  T116_IN_GA(x1)
U78_GA(x1, x2, x3)  =  U78_GA(x1, x3)
E140_IN_GA(x1, x2)  =  E140_IN_GA(x1)
U74_GA(x1, x2, x3)  =  U74_GA(x1, x3)
T145_IN_GA(x1, x2)  =  T145_IN_GA(x1)
U70_GA(x1, x2, x3)  =  U70_GA(x1, x3)
E169_IN_GA(x1, x2)  =  E169_IN_GA(x1)
U66_GA(x1, x2, x3)  =  U66_GA(x1, x3)
T174_IN_GA(x1, x2)  =  T174_IN_GA(x1)
U62_GA(x1, x2, x3)  =  U62_GA(x1, x3)
E198_IN_GA(x1, x2)  =  E198_IN_GA(x1)
U6_GA(x1, x2, x3)  =  U6_GA(x1, x3)
T203_IN_GA(x1, x2)  =  T203_IN_GA(x1)
U2_GA(x1, x2, x3)  =  U2_GA(x1, x3)
U110_GA(x1, x2, x3)  =  U110_GA(x1, x3)
T234_IN_GA(x1, x2)  =  T234_IN_GA(x1)
U14_GA(x1, x2, x3)  =  U14_GA(x1, x3)
E259_IN_GA(x1, x2)  =  E259_IN_GA(x1)
U58_GA(x1, x2, x3)  =  U58_GA(x1, x3)
T264_IN_GA(x1, x2)  =  T264_IN_GA(x1)
U54_GA(x1, x2, x3)  =  U54_GA(x1, x3)
E288_IN_GA(x1, x2)  =  E288_IN_GA(x1)
U50_GA(x1, x2, x3)  =  U50_GA(x1, x3)
T293_IN_GA(x1, x2)  =  T293_IN_GA(x1)
U46_GA(x1, x2, x3)  =  U46_GA(x1, x3)
E317_IN_GA(x1, x2)  =  E317_IN_GA(x1)
U42_GA(x1, x2, x3)  =  U42_GA(x1, x3)
T322_IN_GA(x1, x2)  =  T322_IN_GA(x1)
U38_GA(x1, x2, x3)  =  U38_GA(x1, x3)
E346_IN_GA(x1, x2)  =  E346_IN_GA(x1)
U34_GA(x1, x2, x3)  =  U34_GA(x1, x3)
T351_IN_GA(x1, x2)  =  T351_IN_GA(x1)
U30_GA(x1, x2, x3)  =  U30_GA(x1, x3)
E375_IN_GA(x1, x2)  =  E375_IN_GA(x1)
U26_GA(x1, x2, x3)  =  U26_GA(x1, x3)
T380_IN_GA(x1, x2)  =  T380_IN_GA(x1)
U22_GA(x1, x2, x3)  =  U22_GA(x1, x3)
E404_IN_GA(x1, x2)  =  E404_IN_GA(x1)
U18_GA(x1, x2, x3)  =  U18_GA(x1, x3)
T409_IN_GA(x1, x2)  =  T409_IN_GA(x1)
U10_GA(x1, x2, x3)  =  U10_GA(x1, x3)
U111_GA(x1, x2, x3)  =  U111_GA(x1, x3)
U15_GA(x1, x2, x3)  =  U15_GA(x1, x3)
U16_GA(x1, x2, x3)  =  U16_GA(x1, x3)
U17_GA(x1, x2, x3)  =  U17_GA(x1, x3)
T234_IN_AA(x1, x2)  =  T234_IN_AA
U14_AA(x1, x2, x3)  =  U14_AA(x3)
E259_IN_AA(x1, x2)  =  E259_IN_AA
U58_AA(x1, x2, x3)  =  U58_AA(x3)
T264_IN_AA(x1, x2)  =  T264_IN_AA
U54_AA(x1, x2, x3)  =  U54_AA(x3)
E288_IN_AA(x1, x2)  =  E288_IN_AA
U50_AA(x1, x2, x3)  =  U50_AA(x3)
T293_IN_AA(x1, x2)  =  T293_IN_AA
U46_AA(x1, x2, x3)  =  U46_AA(x3)
E317_IN_AA(x1, x2)  =  E317_IN_AA
U42_AA(x1, x2, x3)  =  U42_AA(x3)
T322_IN_AA(x1, x2)  =  T322_IN_AA
U38_AA(x1, x2, x3)  =  U38_AA(x3)
E346_IN_AA(x1, x2)  =  E346_IN_AA
U34_AA(x1, x2, x3)  =  U34_AA(x3)
T351_IN_AA(x1, x2)  =  T351_IN_AA
U30_AA(x1, x2, x3)  =  U30_AA(x3)
E375_IN_AA(x1, x2)  =  E375_IN_AA
U26_AA(x1, x2, x3)  =  U26_AA(x3)
T380_IN_AA(x1, x2)  =  T380_IN_AA
U22_AA(x1, x2, x3)  =  U22_AA(x3)
E404_IN_AA(x1, x2)  =  E404_IN_AA
U18_AA(x1, x2, x3)  =  U18_AA(x3)
T409_IN_AA(x1, x2)  =  T409_IN_AA
U10_AA(x1, x2, x3)  =  U10_AA(x3)
E1_IN_AA(x1, x2)  =  E1_IN_AA
U108_AA(x1, x2, x3)  =  U108_AA(x3)
N7_IN_AA(x1, x2)  =  N7_IN_AA
U102_AA(x1, x2, x3)  =  U102_AA(x3)
U109_AA(x1, x2, x3)  =  U109_AA(x3)
P31_IN_AAA(x1, x2, x3)  =  P31_IN_AAA
U103_AAA(x1, x2, x3, x4)  =  U103_AAA(x4)
N32_IN_AA(x1, x2)  =  N32_IN_AA
U1_AA(x1, x2, x3)  =  U1_AA(x3)
E53_IN_AA(x1, x2)  =  E53_IN_AA
U98_AA(x1, x2, x3)  =  U98_AA(x3)
T58_IN_AA(x1, x2)  =  T58_IN_AA
U94_AA(x1, x2, x3)  =  U94_AA(x3)
E82_IN_AA(x1, x2)  =  E82_IN_AA
U90_AA(x1, x2, x3)  =  U90_AA(x3)
T87_IN_AA(x1, x2)  =  T87_IN_AA
U86_AA(x1, x2, x3)  =  U86_AA(x3)
E111_IN_AA(x1, x2)  =  E111_IN_AA
U82_AA(x1, x2, x3)  =  U82_AA(x3)
T116_IN_AA(x1, x2)  =  T116_IN_AA
U78_AA(x1, x2, x3)  =  U78_AA(x3)
E140_IN_AA(x1, x2)  =  E140_IN_AA
U74_AA(x1, x2, x3)  =  U74_AA(x3)
T145_IN_AA(x1, x2)  =  T145_IN_AA
U70_AA(x1, x2, x3)  =  U70_AA(x3)
E169_IN_AA(x1, x2)  =  E169_IN_AA
U66_AA(x1, x2, x3)  =  U66_AA(x3)
T174_IN_AA(x1, x2)  =  T174_IN_AA
U62_AA(x1, x2, x3)  =  U62_AA(x3)
E198_IN_AA(x1, x2)  =  E198_IN_AA
U6_AA(x1, x2, x3)  =  U6_AA(x3)
T203_IN_AA(x1, x2)  =  T203_IN_AA
U2_AA(x1, x2, x3)  =  U2_AA(x3)
U110_AA(x1, x2, x3)  =  U110_AA(x3)
U15_AA(x1, x2, x3)  =  U15_AA(x3)
U16_AA(x1, x2, x3)  =  U16_AA(x3)
U17_AA(x1, x2, x3)  =  U17_AA(x3)
U111_AA(x1, x2, x3)  =  U111_AA(x3)
U112_AA(x1, x2, x3)  =  U112_AA(x3)
U3_AA(x1, x2, x3)  =  U3_AA(x3)
U4_AA(x1, x2, x3)  =  U4_AA(x3)
U5_AA(x1, x2, x3)  =  U5_AA(x3)
U7_AA(x1, x2, x3)  =  U7_AA(x3)
U8_AA(x1, x2, x3)  =  U8_AA(x3)
U9_AA(x1, x2, x3)  =  U9_AA(x3)
U63_AA(x1, x2, x3)  =  U63_AA(x3)
U64_AA(x1, x2, x3)  =  U64_AA(x3)
U65_AA(x1, x2, x3)  =  U65_AA(x3)
U67_AA(x1, x2, x3)  =  U67_AA(x3)
U68_AA(x1, x2, x3)  =  U68_AA(x3)
U69_AA(x1, x2, x3)  =  U69_AA(x3)
U71_AA(x1, x2, x3)  =  U71_AA(x3)
U72_AA(x1, x2, x3)  =  U72_AA(x3)
U73_AA(x1, x2, x3)  =  U73_AA(x3)
U75_AA(x1, x2, x3)  =  U75_AA(x3)
U76_AA(x1, x2, x3)  =  U76_AA(x3)
U77_AA(x1, x2, x3)  =  U77_AA(x3)
U79_AA(x1, x2, x3)  =  U79_AA(x3)
U80_AA(x1, x2, x3)  =  U80_AA(x3)
U81_AA(x1, x2, x3)  =  U81_AA(x3)
U83_AA(x1, x2, x3)  =  U83_AA(x3)
U84_AA(x1, x2, x3)  =  U84_AA(x3)
U85_AA(x1, x2, x3)  =  U85_AA(x3)
U87_AA(x1, x2, x3)  =  U87_AA(x3)
U88_AA(x1, x2, x3)  =  U88_AA(x3)
U89_AA(x1, x2, x3)  =  U89_AA(x3)
U91_AA(x1, x2, x3)  =  U91_AA(x3)
U92_AA(x1, x2, x3)  =  U92_AA(x3)
U93_AA(x1, x2, x3)  =  U93_AA(x3)
U95_AA(x1, x2, x3)  =  U95_AA(x3)
U96_AA(x1, x2, x3)  =  U96_AA(x3)
U97_AA(x1, x2, x3)  =  U97_AA(x3)
U99_AA(x1, x2, x3)  =  U99_AA(x3)
U100_AA(x1, x2, x3)  =  U100_AA(x3)
U101_AA(x1, x2, x3)  =  U101_AA(x3)
U104_AAA(x1, x2, x3, x4)  =  U104_AAA(x4)
U105_AAA(x1, x2, x3, x4)  =  U105_AAA(x4)
U106_AAA(x1, x2, x3, x4)  =  U106_AAA(x4)
U107_AAA(x1, x2, x3, x4)  =  U107_AAA(x4)
U11_AA(x1, x2, x3)  =  U11_AA(x3)
U12_AA(x1, x2, x3)  =  U12_AA(x3)
U13_AA(x1, x2, x3)  =  U13_AA(x3)
U19_AA(x1, x2, x3)  =  U19_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U23_AA(x1, x2, x3)  =  U23_AA(x3)
U24_AA(x1, x2, x3)  =  U24_AA(x3)
U25_AA(x1, x2, x3)  =  U25_AA(x3)
U27_AA(x1, x2, x3)  =  U27_AA(x3)
U28_AA(x1, x2, x3)  =  U28_AA(x3)
U29_AA(x1, x2, x3)  =  U29_AA(x3)
U31_AA(x1, x2, x3)  =  U31_AA(x3)
U32_AA(x1, x2, x3)  =  U32_AA(x3)
U33_AA(x1, x2, x3)  =  U33_AA(x3)
U35_AA(x1, x2, x3)  =  U35_AA(x3)
U36_AA(x1, x2, x3)  =  U36_AA(x3)
U37_AA(x1, x2, x3)  =  U37_AA(x3)
U39_AA(x1, x2, x3)  =  U39_AA(x3)
U40_AA(x1, x2, x3)  =  U40_AA(x3)
U41_AA(x1, x2, x3)  =  U41_AA(x3)
U43_AA(x1, x2, x3)  =  U43_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U45_AA(x1, x2, x3)  =  U45_AA(x3)
U47_AA(x1, x2, x3)  =  U47_AA(x3)
U48_AA(x1, x2, x3)  =  U48_AA(x3)
U49_AA(x1, x2, x3)  =  U49_AA(x3)
U51_AA(x1, x2, x3)  =  U51_AA(x3)
U52_AA(x1, x2, x3)  =  U52_AA(x3)
U53_AA(x1, x2, x3)  =  U53_AA(x3)
U55_AA(x1, x2, x3)  =  U55_AA(x3)
U56_AA(x1, x2, x3)  =  U56_AA(x3)
U57_AA(x1, x2, x3)  =  U57_AA(x3)
U59_AA(x1, x2, x3)  =  U59_AA(x3)
U60_AA(x1, x2, x3)  =  U60_AA(x3)
U61_AA(x1, x2, x3)  =  U61_AA(x3)
U112_GA(x1, x2, x3)  =  U112_GA(x1, x3)
U11_GA(x1, x2, x3)  =  U11_GA(x1, x3)
U12_GA(x1, x2, x3)  =  U12_GA(x1, x3)
U13_GA(x1, x2, x3)  =  U13_GA(x1, x3)
U19_GA(x1, x2, x3)  =  U19_GA(x1, x3)
U20_GA(x1, x2, x3)  =  U20_GA(x1, x3)
U21_GA(x1, x2, x3)  =  U21_GA(x1, x3)
U23_GA(x1, x2, x3)  =  U23_GA(x1, x3)
U24_GA(x1, x2, x3)  =  U24_GA(x1, x3)
U25_GA(x1, x2, x3)  =  U25_GA(x1, x3)
U27_GA(x1, x2, x3)  =  U27_GA(x1, x3)
U28_GA(x1, x2, x3)  =  U28_GA(x1, x3)
U29_GA(x1, x2, x3)  =  U29_GA(x1, x3)
U31_GA(x1, x2, x3)  =  U31_GA(x1, x3)
U32_GA(x1, x2, x3)  =  U32_GA(x1, x3)
U33_GA(x1, x2, x3)  =  U33_GA(x1, x3)
U35_GA(x1, x2, x3)  =  U35_GA(x1, x3)
U36_GA(x1, x2, x3)  =  U36_GA(x1, x3)
U37_GA(x1, x2, x3)  =  U37_GA(x1, x3)
U39_GA(x1, x2, x3)  =  U39_GA(x1, x3)
U40_GA(x1, x2, x3)  =  U40_GA(x1, x3)
U41_GA(x1, x2, x3)  =  U41_GA(x1, x3)
U43_GA(x1, x2, x3)  =  U43_GA(x1, x3)
U44_GA(x1, x2, x3)  =  U44_GA(x1, x3)
U45_GA(x1, x2, x3)  =  U45_GA(x1, x3)
U47_GA(x1, x2, x3)  =  U47_GA(x1, x3)
U48_GA(x1, x2, x3)  =  U48_GA(x1, x3)
U49_GA(x1, x2, x3)  =  U49_GA(x1, x3)
U51_GA(x1, x2, x3)  =  U51_GA(x1, x3)
U52_GA(x1, x2, x3)  =  U52_GA(x1, x3)
U53_GA(x1, x2, x3)  =  U53_GA(x1, x3)
U55_GA(x1, x2, x3)  =  U55_GA(x1, x3)
U56_GA(x1, x2, x3)  =  U56_GA(x1, x3)
U57_GA(x1, x2, x3)  =  U57_GA(x1, x3)
U59_GA(x1, x2, x3)  =  U59_GA(x1, x3)
U60_GA(x1, x2, x3)  =  U60_GA(x1, x3)
U61_GA(x1, x2, x3)  =  U61_GA(x1, x3)
U3_GA(x1, x2, x3)  =  U3_GA(x1, x3)
U4_GA(x1, x2, x3)  =  U4_GA(x1, x3)
U5_GA(x1, x2, x3)  =  U5_GA(x1, x3)
U7_GA(x1, x2, x3)  =  U7_GA(x1, x3)
U8_GA(x1, x2, x3)  =  U8_GA(x1, x3)
U9_GA(x1, x2, x3)  =  U9_GA(x1, x3)
U63_GA(x1, x2, x3)  =  U63_GA(x1, x3)
U64_GA(x1, x2, x3)  =  U64_GA(x1, x3)
U65_GA(x1, x2, x3)  =  U65_GA(x1, x3)
U67_GA(x1, x2, x3)  =  U67_GA(x1, x3)
U68_GA(x1, x2, x3)  =  U68_GA(x1, x3)
U69_GA(x1, x2, x3)  =  U69_GA(x1, x3)
U71_GA(x1, x2, x3)  =  U71_GA(x1, x3)
U72_GA(x1, x2, x3)  =  U72_GA(x1, x3)
U73_GA(x1, x2, x3)  =  U73_GA(x1, x3)
U75_GA(x1, x2, x3)  =  U75_GA(x1, x3)
U76_GA(x1, x2, x3)  =  U76_GA(x1, x3)
U77_GA(x1, x2, x3)  =  U77_GA(x1, x3)
U79_GA(x1, x2, x3)  =  U79_GA(x1, x3)
U80_GA(x1, x2, x3)  =  U80_GA(x1, x3)
U81_GA(x1, x2, x3)  =  U81_GA(x1, x3)
U83_GA(x1, x2, x3)  =  U83_GA(x1, x3)
U84_GA(x1, x2, x3)  =  U84_GA(x1, x3)
U85_GA(x1, x2, x3)  =  U85_GA(x1, x3)
U87_GA(x1, x2, x3)  =  U87_GA(x1, x3)
U88_GA(x1, x2, x3)  =  U88_GA(x1, x3)
U89_GA(x1, x2, x3)  =  U89_GA(x1, x3)
U91_GA(x1, x2, x3)  =  U91_GA(x1, x3)
U92_GA(x1, x2, x3)  =  U92_GA(x1, x3)
U93_GA(x1, x2, x3)  =  U93_GA(x1, x3)
U95_GA(x1, x2, x3)  =  U95_GA(x1, x3)
U96_GA(x1, x2, x3)  =  U96_GA(x1, x3)
U97_GA(x1, x2, x3)  =  U97_GA(x1, x3)
U99_GA(x1, x2, x3)  =  U99_GA(x1, x3)
U100_GA(x1, x2, x3)  =  U100_GA(x1, x3)
U101_GA(x1, x2, x3)  =  U101_GA(x1, x3)
U104_GAA(x1, x2, x3, x4)  =  U104_GAA(x1, x4)
U105_GAA(x1, x2, x3, x4)  =  U105_GAA(x1, x4)
U106_GAA(x1, x2, x3, x4)  =  U106_GAA(x1, x4)
U107_GAA(x1, x2, x3, x4)  =  U107_GAA(x1, x4)

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

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 224 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

T234_IN_AA(.(lbrace, T392), X599) → E259_IN_AA(T392, X599)
E259_IN_AA(T400, X625) → T264_IN_AA(T400, X625)
T264_IN_AA(.(lbrace, T433), X670) → E288_IN_AA(T433, X670)
E288_IN_AA(T441, X696) → T293_IN_AA(T441, X696)
T293_IN_AA(.(lbrace, T474), X741) → E317_IN_AA(T474, X741)
E317_IN_AA(T482, X767) → T322_IN_AA(T482, X767)
T322_IN_AA(.(lbrace, T515), X812) → E346_IN_AA(T515, X812)
E346_IN_AA(T523, X838) → T351_IN_AA(T523, X838)
T351_IN_AA(.(lbrace, T556), X883) → E375_IN_AA(T556, X883)
E375_IN_AA(T564, X909) → T380_IN_AA(T564, X909)
T380_IN_AA(.(lbrace, T597), X954) → E404_IN_AA(T597, X954)
E404_IN_AA(T605, X980) → T409_IN_AA(T605, X980)
T409_IN_AA(.(lbrace, T638), X1025) → E1_IN_AA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_AA(T22, T24) → N7_IN_AA(T22, T24)
N7_IN_AA(.(lbrace, T41), T43) → E1_IN_AA(T41, .(rbrace, T43))
E1_IN_AA(T62, T64) → P31_IN_AAA(T62, X59, T64)
P31_IN_AAA(T62, X59, T64) → N32_IN_AA(T62, X59)
N32_IN_AA(.(lbrace, T89), X84) → E53_IN_AA(T89, X84)
E53_IN_AA(T97, X110) → T58_IN_AA(T97, X110)
T58_IN_AA(.(lbrace, T130), X155) → E82_IN_AA(T130, X155)
E82_IN_AA(T138, X181) → T87_IN_AA(T138, X181)
T87_IN_AA(.(lbrace, T171), X226) → E111_IN_AA(T171, X226)
E111_IN_AA(T179, X252) → T116_IN_AA(T179, X252)
T116_IN_AA(.(lbrace, T212), X297) → E140_IN_AA(T212, X297)
E140_IN_AA(T220, X323) → T145_IN_AA(T220, X323)
T145_IN_AA(.(lbrace, T253), X368) → E169_IN_AA(T253, X368)
E169_IN_AA(T261, X394) → T174_IN_AA(T261, X394)
T174_IN_AA(.(lbrace, T294), X439) → E198_IN_AA(T294, X439)
E198_IN_AA(T302, X465) → T203_IN_AA(T302, X465)
T203_IN_AA(.(lbrace, T335), X510) → E1_IN_AA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_AA(T941, T943) → T234_IN_AA(T941, X1569)
T234_IN_AA(T780, X1303) → N32_IN_AA(T780, X1302)
T234_IN_AA(T780, X1303) → U16_AA(T780, X1303, n32_in_aa(T780, T784))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → T234_IN_AA(T784, X1303)
E1_IN_AA(T941, T943) → U111_AA(T941, T943, t234_in_aa(T941, T945))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → E1_IN_AA(T945, T943)
T203_IN_AA(T345, X530) → N32_IN_AA(T345, X529)
T203_IN_AA(T345, X530) → U4_AA(T345, X530, n32_in_aa(T345, T349))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_AA(T357, X551) → T234_IN_AA(T357, X550)
E198_IN_AA(T357, X551) → U8_AA(T357, X551, t234_in_aa(T357, T359))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_AA(T795, X1326) → N32_IN_AA(T795, X1325)
T174_IN_AA(T795, X1326) → U64_AA(T795, X1326, n32_in_aa(T795, T799))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_AA(T807, X1347) → T234_IN_AA(T807, X1346)
E169_IN_AA(T807, X1347) → U68_AA(T807, X1347, t234_in_aa(T807, T809))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_AA(T817, X1369) → N32_IN_AA(T817, X1368)
T145_IN_AA(T817, X1369) → U72_AA(T817, X1369, n32_in_aa(T817, T821))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_AA(T829, X1390) → T234_IN_AA(T829, X1389)
E140_IN_AA(T829, X1390) → U76_AA(T829, X1390, t234_in_aa(T829, T831))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_AA(T839, X1412) → N32_IN_AA(T839, X1411)
T116_IN_AA(T839, X1412) → U80_AA(T839, X1412, n32_in_aa(T839, T843))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_AA(T851, X1433) → T234_IN_AA(T851, X1432)
E111_IN_AA(T851, X1433) → U84_AA(T851, X1433, t234_in_aa(T851, T853))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_AA(T861, X1455) → N32_IN_AA(T861, X1454)
T87_IN_AA(T861, X1455) → U88_AA(T861, X1455, n32_in_aa(T861, T865))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_AA(T873, X1476) → T234_IN_AA(T873, X1475)
E82_IN_AA(T873, X1476) → U92_AA(T873, X1476, t234_in_aa(T873, T875))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_AA(T883, X1498) → N32_IN_AA(T883, X1497)
T58_IN_AA(T883, X1498) → U96_AA(T883, X1498, n32_in_aa(T883, T887))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_AA(T895, X1519) → T234_IN_AA(T895, X1518)
E53_IN_AA(T895, X1519) → U100_AA(T895, X1519, t234_in_aa(T895, T897))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_AAA(T62, T916, T918) → U104_AAA(T62, T916, T918, n32_in_aa(T62, T916))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_AAA(T62, T929, T931) → U106_AAA(T62, T929, T931, n32_in_aa(T62, T929))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → P31_IN_AAA(T929, X1556, T931)
T409_IN_AA(T648, X1045) → N32_IN_AA(T648, X1044)
T409_IN_AA(T648, X1045) → U12_AA(T648, X1045, n32_in_aa(T648, T652))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_AA(T660, X1066) → T234_IN_AA(T660, X1065)
E404_IN_AA(T660, X1066) → U20_AA(T660, X1066, t234_in_aa(T660, T662))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_AA(T670, X1088) → N32_IN_AA(T670, X1087)
T380_IN_AA(T670, X1088) → U24_AA(T670, X1088, n32_in_aa(T670, T674))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_AA(T682, X1109) → T234_IN_AA(T682, X1108)
E375_IN_AA(T682, X1109) → U28_AA(T682, X1109, t234_in_aa(T682, T684))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_AA(T692, X1131) → N32_IN_AA(T692, X1130)
T351_IN_AA(T692, X1131) → U32_AA(T692, X1131, n32_in_aa(T692, T696))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_AA(T704, X1152) → T234_IN_AA(T704, X1151)
E346_IN_AA(T704, X1152) → U36_AA(T704, X1152, t234_in_aa(T704, T706))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_AA(T714, X1174) → N32_IN_AA(T714, X1173)
T322_IN_AA(T714, X1174) → U40_AA(T714, X1174, n32_in_aa(T714, T718))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_AA(T726, X1195) → T234_IN_AA(T726, X1194)
E317_IN_AA(T726, X1195) → U44_AA(T726, X1195, t234_in_aa(T726, T728))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_AA(T736, X1217) → N32_IN_AA(T736, X1216)
T293_IN_AA(T736, X1217) → U48_AA(T736, X1217, n32_in_aa(T736, T740))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_AA(T748, X1238) → T234_IN_AA(T748, X1237)
E288_IN_AA(T748, X1238) → U52_AA(T748, X1238, t234_in_aa(T748, T750))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_AA(T758, X1260) → N32_IN_AA(T758, X1259)
T264_IN_AA(T758, X1260) → U56_AA(T758, X1260, n32_in_aa(T758, T762))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_AA(T770, X1281) → T234_IN_AA(T770, X1280)
E259_IN_AA(T770, X1281) → U60_AA(T770, X1281, t234_in_aa(T770, T772))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → E259_IN_AA(T772, X1281)

The TRS R consists of the following rules:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x1, x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga(x1)
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x1, x3)
U109_ga(x1, x2, x3)  =  U109_ga(x1, x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x1, x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x1, x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga(x1)
U94_ga(x1, x2, x3)  =  U94_ga(x1, x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x1, x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga(x1)
U86_ga(x1, x2, x3)  =  U86_ga(x1, x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x1, x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x1, x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga(x1)
U70_ga(x1, x2, x3)  =  U70_ga(x1, x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga(x1)
U62_ga(x1, x2, x3)  =  U62_ga(x1, x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga(x1)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga(x1)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x1, x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga(x1)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga(x1)
U38_ga(x1, x2, x3)  =  U38_ga(x1, x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x1, x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga(x1)
U30_ga(x1, x2, x3)  =  U30_ga(x1, x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga(x1)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U111_ga(x1, x2, x3)  =  U111_ga(x1, x3)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U112_ga(x1, x2, x3)  =  U112_ga(x1, x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
e404_out_ga(x1, x2)  =  e404_out_ga(x1)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
e375_out_ga(x1, x2)  =  e375_out_ga(x1)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
U28_ga(x1, x2, x3)  =  U28_ga(x1, x3)
U29_ga(x1, x2, x3)  =  U29_ga(x1, x3)
U31_ga(x1, x2, x3)  =  U31_ga(x1, x3)
U32_ga(x1, x2, x3)  =  U32_ga(x1, x3)
U33_ga(x1, x2, x3)  =  U33_ga(x1, x3)
e346_out_ga(x1, x2)  =  e346_out_ga(x1)
U35_ga(x1, x2, x3)  =  U35_ga(x1, x3)
U36_ga(x1, x2, x3)  =  U36_ga(x1, x3)
U37_ga(x1, x2, x3)  =  U37_ga(x1, x3)
U39_ga(x1, x2, x3)  =  U39_ga(x1, x3)
U40_ga(x1, x2, x3)  =  U40_ga(x1, x3)
U41_ga(x1, x2, x3)  =  U41_ga(x1, x3)
e317_out_ga(x1, x2)  =  e317_out_ga(x1)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
e288_out_ga(x1, x2)  =  e288_out_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
e259_out_ga(x1, x2)  =  e259_out_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
U60_ga(x1, x2, x3)  =  U60_ga(x1, x3)
U61_ga(x1, x2, x3)  =  U61_ga(x1, x3)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
e198_out_ga(x1, x2)  =  e198_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U63_ga(x1, x2, x3)  =  U63_ga(x1, x3)
U64_ga(x1, x2, x3)  =  U64_ga(x1, x3)
U65_ga(x1, x2, x3)  =  U65_ga(x1, x3)
e169_out_ga(x1, x2)  =  e169_out_ga(x1)
U67_ga(x1, x2, x3)  =  U67_ga(x1, x3)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
U69_ga(x1, x2, x3)  =  U69_ga(x1, x3)
U71_ga(x1, x2, x3)  =  U71_ga(x1, x3)
U72_ga(x1, x2, x3)  =  U72_ga(x1, x3)
U73_ga(x1, x2, x3)  =  U73_ga(x1, x3)
e140_out_ga(x1, x2)  =  e140_out_ga(x1)
U75_ga(x1, x2, x3)  =  U75_ga(x1, x3)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
U77_ga(x1, x2, x3)  =  U77_ga(x1, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x3)
U80_ga(x1, x2, x3)  =  U80_ga(x1, x3)
U81_ga(x1, x2, x3)  =  U81_ga(x1, x3)
e111_out_ga(x1, x2)  =  e111_out_ga(x1)
U83_ga(x1, x2, x3)  =  U83_ga(x1, x3)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
U85_ga(x1, x2, x3)  =  U85_ga(x1, x3)
U87_ga(x1, x2, x3)  =  U87_ga(x1, x3)
U88_ga(x1, x2, x3)  =  U88_ga(x1, x3)
U89_ga(x1, x2, x3)  =  U89_ga(x1, x3)
e82_out_ga(x1, x2)  =  e82_out_ga(x1)
U91_ga(x1, x2, x3)  =  U91_ga(x1, x3)
U92_ga(x1, x2, x3)  =  U92_ga(x1, x3)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
U95_ga(x1, x2, x3)  =  U95_ga(x1, x3)
U96_ga(x1, x2, x3)  =  U96_ga(x1, x3)
U97_ga(x1, x2, x3)  =  U97_ga(x1, x3)
e53_out_ga(x1, x2)  =  e53_out_ga(x1)
U99_ga(x1, x2, x3)  =  U99_ga(x1, x3)
U100_ga(x1, x2, x3)  =  U100_ga(x1, x3)
U101_ga(x1, x2, x3)  =  U101_ga(x1, x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa(x1)
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x1, x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x1, x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x1, x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x1, x4)
T234_IN_AA(x1, x2)  =  T234_IN_AA
E259_IN_AA(x1, x2)  =  E259_IN_AA
T264_IN_AA(x1, x2)  =  T264_IN_AA
E288_IN_AA(x1, x2)  =  E288_IN_AA
T293_IN_AA(x1, x2)  =  T293_IN_AA
E317_IN_AA(x1, x2)  =  E317_IN_AA
T322_IN_AA(x1, x2)  =  T322_IN_AA
E346_IN_AA(x1, x2)  =  E346_IN_AA
T351_IN_AA(x1, x2)  =  T351_IN_AA
E375_IN_AA(x1, x2)  =  E375_IN_AA
T380_IN_AA(x1, x2)  =  T380_IN_AA
E404_IN_AA(x1, x2)  =  E404_IN_AA
T409_IN_AA(x1, x2)  =  T409_IN_AA
E1_IN_AA(x1, x2)  =  E1_IN_AA
N7_IN_AA(x1, x2)  =  N7_IN_AA
P31_IN_AAA(x1, x2, x3)  =  P31_IN_AAA
N32_IN_AA(x1, x2)  =  N32_IN_AA
E53_IN_AA(x1, x2)  =  E53_IN_AA
T58_IN_AA(x1, x2)  =  T58_IN_AA
E82_IN_AA(x1, x2)  =  E82_IN_AA
T87_IN_AA(x1, x2)  =  T87_IN_AA
E111_IN_AA(x1, x2)  =  E111_IN_AA
T116_IN_AA(x1, x2)  =  T116_IN_AA
E140_IN_AA(x1, x2)  =  E140_IN_AA
T145_IN_AA(x1, x2)  =  T145_IN_AA
E169_IN_AA(x1, x2)  =  E169_IN_AA
T174_IN_AA(x1, x2)  =  T174_IN_AA
E198_IN_AA(x1, x2)  =  E198_IN_AA
T203_IN_AA(x1, x2)  =  T203_IN_AA
U16_AA(x1, x2, x3)  =  U16_AA(x3)
U111_AA(x1, x2, x3)  =  U111_AA(x3)
U4_AA(x1, x2, x3)  =  U4_AA(x3)
U8_AA(x1, x2, x3)  =  U8_AA(x3)
U64_AA(x1, x2, x3)  =  U64_AA(x3)
U68_AA(x1, x2, x3)  =  U68_AA(x3)
U72_AA(x1, x2, x3)  =  U72_AA(x3)
U76_AA(x1, x2, x3)  =  U76_AA(x3)
U80_AA(x1, x2, x3)  =  U80_AA(x3)
U84_AA(x1, x2, x3)  =  U84_AA(x3)
U88_AA(x1, x2, x3)  =  U88_AA(x3)
U92_AA(x1, x2, x3)  =  U92_AA(x3)
U96_AA(x1, x2, x3)  =  U96_AA(x3)
U100_AA(x1, x2, x3)  =  U100_AA(x3)
U104_AAA(x1, x2, x3, x4)  =  U104_AAA(x4)
U106_AAA(x1, x2, x3, x4)  =  U106_AAA(x4)
U12_AA(x1, x2, x3)  =  U12_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U24_AA(x1, x2, x3)  =  U24_AA(x3)
U28_AA(x1, x2, x3)  =  U28_AA(x3)
U32_AA(x1, x2, x3)  =  U32_AA(x3)
U36_AA(x1, x2, x3)  =  U36_AA(x3)
U40_AA(x1, x2, x3)  =  U40_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U48_AA(x1, x2, x3)  =  U48_AA(x3)
U52_AA(x1, x2, x3)  =  U52_AA(x3)
U56_AA(x1, x2, x3)  =  U56_AA(x3)
U60_AA(x1, x2, x3)  =  U60_AA(x3)

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:

T234_IN_AA(.(lbrace, T392), X599) → E259_IN_AA(T392, X599)
E259_IN_AA(T400, X625) → T264_IN_AA(T400, X625)
T264_IN_AA(.(lbrace, T433), X670) → E288_IN_AA(T433, X670)
E288_IN_AA(T441, X696) → T293_IN_AA(T441, X696)
T293_IN_AA(.(lbrace, T474), X741) → E317_IN_AA(T474, X741)
E317_IN_AA(T482, X767) → T322_IN_AA(T482, X767)
T322_IN_AA(.(lbrace, T515), X812) → E346_IN_AA(T515, X812)
E346_IN_AA(T523, X838) → T351_IN_AA(T523, X838)
T351_IN_AA(.(lbrace, T556), X883) → E375_IN_AA(T556, X883)
E375_IN_AA(T564, X909) → T380_IN_AA(T564, X909)
T380_IN_AA(.(lbrace, T597), X954) → E404_IN_AA(T597, X954)
E404_IN_AA(T605, X980) → T409_IN_AA(T605, X980)
T409_IN_AA(.(lbrace, T638), X1025) → E1_IN_AA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_AA(T22, T24) → N7_IN_AA(T22, T24)
N7_IN_AA(.(lbrace, T41), T43) → E1_IN_AA(T41, .(rbrace, T43))
E1_IN_AA(T62, T64) → P31_IN_AAA(T62, X59, T64)
P31_IN_AAA(T62, X59, T64) → N32_IN_AA(T62, X59)
N32_IN_AA(.(lbrace, T89), X84) → E53_IN_AA(T89, X84)
E53_IN_AA(T97, X110) → T58_IN_AA(T97, X110)
T58_IN_AA(.(lbrace, T130), X155) → E82_IN_AA(T130, X155)
E82_IN_AA(T138, X181) → T87_IN_AA(T138, X181)
T87_IN_AA(.(lbrace, T171), X226) → E111_IN_AA(T171, X226)
E111_IN_AA(T179, X252) → T116_IN_AA(T179, X252)
T116_IN_AA(.(lbrace, T212), X297) → E140_IN_AA(T212, X297)
E140_IN_AA(T220, X323) → T145_IN_AA(T220, X323)
T145_IN_AA(.(lbrace, T253), X368) → E169_IN_AA(T253, X368)
E169_IN_AA(T261, X394) → T174_IN_AA(T261, X394)
T174_IN_AA(.(lbrace, T294), X439) → E198_IN_AA(T294, X439)
E198_IN_AA(T302, X465) → T203_IN_AA(T302, X465)
T203_IN_AA(.(lbrace, T335), X510) → E1_IN_AA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_AA(T941, T943) → T234_IN_AA(T941, X1569)
T234_IN_AA(T780, X1303) → N32_IN_AA(T780, X1302)
T234_IN_AA(T780, X1303) → U16_AA(T780, X1303, n32_in_aa(T780, T784))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → T234_IN_AA(T784, X1303)
E1_IN_AA(T941, T943) → U111_AA(T941, T943, t234_in_aa(T941, T945))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → E1_IN_AA(T945, T943)
T203_IN_AA(T345, X530) → N32_IN_AA(T345, X529)
T203_IN_AA(T345, X530) → U4_AA(T345, X530, n32_in_aa(T345, T349))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_AA(T357, X551) → T234_IN_AA(T357, X550)
E198_IN_AA(T357, X551) → U8_AA(T357, X551, t234_in_aa(T357, T359))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_AA(T795, X1326) → N32_IN_AA(T795, X1325)
T174_IN_AA(T795, X1326) → U64_AA(T795, X1326, n32_in_aa(T795, T799))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_AA(T807, X1347) → T234_IN_AA(T807, X1346)
E169_IN_AA(T807, X1347) → U68_AA(T807, X1347, t234_in_aa(T807, T809))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_AA(T817, X1369) → N32_IN_AA(T817, X1368)
T145_IN_AA(T817, X1369) → U72_AA(T817, X1369, n32_in_aa(T817, T821))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_AA(T829, X1390) → T234_IN_AA(T829, X1389)
E140_IN_AA(T829, X1390) → U76_AA(T829, X1390, t234_in_aa(T829, T831))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_AA(T839, X1412) → N32_IN_AA(T839, X1411)
T116_IN_AA(T839, X1412) → U80_AA(T839, X1412, n32_in_aa(T839, T843))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_AA(T851, X1433) → T234_IN_AA(T851, X1432)
E111_IN_AA(T851, X1433) → U84_AA(T851, X1433, t234_in_aa(T851, T853))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_AA(T861, X1455) → N32_IN_AA(T861, X1454)
T87_IN_AA(T861, X1455) → U88_AA(T861, X1455, n32_in_aa(T861, T865))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_AA(T873, X1476) → T234_IN_AA(T873, X1475)
E82_IN_AA(T873, X1476) → U92_AA(T873, X1476, t234_in_aa(T873, T875))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_AA(T883, X1498) → N32_IN_AA(T883, X1497)
T58_IN_AA(T883, X1498) → U96_AA(T883, X1498, n32_in_aa(T883, T887))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_AA(T895, X1519) → T234_IN_AA(T895, X1518)
E53_IN_AA(T895, X1519) → U100_AA(T895, X1519, t234_in_aa(T895, T897))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_AAA(T62, T916, T918) → U104_AAA(T62, T916, T918, n32_in_aa(T62, T916))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_AAA(T62, T929, T931) → U106_AAA(T62, T929, T931, n32_in_aa(T62, T929))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → P31_IN_AAA(T929, X1556, T931)
T409_IN_AA(T648, X1045) → N32_IN_AA(T648, X1044)
T409_IN_AA(T648, X1045) → U12_AA(T648, X1045, n32_in_aa(T648, T652))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_AA(T660, X1066) → T234_IN_AA(T660, X1065)
E404_IN_AA(T660, X1066) → U20_AA(T660, X1066, t234_in_aa(T660, T662))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_AA(T670, X1088) → N32_IN_AA(T670, X1087)
T380_IN_AA(T670, X1088) → U24_AA(T670, X1088, n32_in_aa(T670, T674))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_AA(T682, X1109) → T234_IN_AA(T682, X1108)
E375_IN_AA(T682, X1109) → U28_AA(T682, X1109, t234_in_aa(T682, T684))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_AA(T692, X1131) → N32_IN_AA(T692, X1130)
T351_IN_AA(T692, X1131) → U32_AA(T692, X1131, n32_in_aa(T692, T696))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_AA(T704, X1152) → T234_IN_AA(T704, X1151)
E346_IN_AA(T704, X1152) → U36_AA(T704, X1152, t234_in_aa(T704, T706))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_AA(T714, X1174) → N32_IN_AA(T714, X1173)
T322_IN_AA(T714, X1174) → U40_AA(T714, X1174, n32_in_aa(T714, T718))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_AA(T726, X1195) → T234_IN_AA(T726, X1194)
E317_IN_AA(T726, X1195) → U44_AA(T726, X1195, t234_in_aa(T726, T728))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_AA(T736, X1217) → N32_IN_AA(T736, X1216)
T293_IN_AA(T736, X1217) → U48_AA(T736, X1217, n32_in_aa(T736, T740))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_AA(T748, X1238) → T234_IN_AA(T748, X1237)
E288_IN_AA(T748, X1238) → U52_AA(T748, X1238, t234_in_aa(T748, T750))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_AA(T758, X1260) → N32_IN_AA(T758, X1259)
T264_IN_AA(T758, X1260) → U56_AA(T758, X1260, n32_in_aa(T758, T762))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_AA(T770, X1281) → T234_IN_AA(T770, X1280)
E259_IN_AA(T770, X1281) → U60_AA(T770, X1281, t234_in_aa(T770, T772))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → E259_IN_AA(T772, X1281)

The TRS R consists of the following rules:

n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
a  =  a
b  =  b
c  =  c
lbrace  =  lbrace
star  =  star
rbrace  =  rbrace
plus  =  plus
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
T234_IN_AA(x1, x2)  =  T234_IN_AA
E259_IN_AA(x1, x2)  =  E259_IN_AA
T264_IN_AA(x1, x2)  =  T264_IN_AA
E288_IN_AA(x1, x2)  =  E288_IN_AA
T293_IN_AA(x1, x2)  =  T293_IN_AA
E317_IN_AA(x1, x2)  =  E317_IN_AA
T322_IN_AA(x1, x2)  =  T322_IN_AA
E346_IN_AA(x1, x2)  =  E346_IN_AA
T351_IN_AA(x1, x2)  =  T351_IN_AA
E375_IN_AA(x1, x2)  =  E375_IN_AA
T380_IN_AA(x1, x2)  =  T380_IN_AA
E404_IN_AA(x1, x2)  =  E404_IN_AA
T409_IN_AA(x1, x2)  =  T409_IN_AA
E1_IN_AA(x1, x2)  =  E1_IN_AA
N7_IN_AA(x1, x2)  =  N7_IN_AA
P31_IN_AAA(x1, x2, x3)  =  P31_IN_AAA
N32_IN_AA(x1, x2)  =  N32_IN_AA
E53_IN_AA(x1, x2)  =  E53_IN_AA
T58_IN_AA(x1, x2)  =  T58_IN_AA
E82_IN_AA(x1, x2)  =  E82_IN_AA
T87_IN_AA(x1, x2)  =  T87_IN_AA
E111_IN_AA(x1, x2)  =  E111_IN_AA
T116_IN_AA(x1, x2)  =  T116_IN_AA
E140_IN_AA(x1, x2)  =  E140_IN_AA
T145_IN_AA(x1, x2)  =  T145_IN_AA
E169_IN_AA(x1, x2)  =  E169_IN_AA
T174_IN_AA(x1, x2)  =  T174_IN_AA
E198_IN_AA(x1, x2)  =  E198_IN_AA
T203_IN_AA(x1, x2)  =  T203_IN_AA
U16_AA(x1, x2, x3)  =  U16_AA(x3)
U111_AA(x1, x2, x3)  =  U111_AA(x3)
U4_AA(x1, x2, x3)  =  U4_AA(x3)
U8_AA(x1, x2, x3)  =  U8_AA(x3)
U64_AA(x1, x2, x3)  =  U64_AA(x3)
U68_AA(x1, x2, x3)  =  U68_AA(x3)
U72_AA(x1, x2, x3)  =  U72_AA(x3)
U76_AA(x1, x2, x3)  =  U76_AA(x3)
U80_AA(x1, x2, x3)  =  U80_AA(x3)
U84_AA(x1, x2, x3)  =  U84_AA(x3)
U88_AA(x1, x2, x3)  =  U88_AA(x3)
U92_AA(x1, x2, x3)  =  U92_AA(x3)
U96_AA(x1, x2, x3)  =  U96_AA(x3)
U100_AA(x1, x2, x3)  =  U100_AA(x3)
U104_AAA(x1, x2, x3, x4)  =  U104_AAA(x4)
U106_AAA(x1, x2, x3, x4)  =  U106_AAA(x4)
U12_AA(x1, x2, x3)  =  U12_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U24_AA(x1, x2, x3)  =  U24_AA(x3)
U28_AA(x1, x2, x3)  =  U28_AA(x3)
U32_AA(x1, x2, x3)  =  U32_AA(x3)
U36_AA(x1, x2, x3)  =  U36_AA(x3)
U40_AA(x1, x2, x3)  =  U40_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U48_AA(x1, x2, x3)  =  U48_AA(x3)
U52_AA(x1, x2, x3)  =  U52_AA(x3)
U56_AA(x1, x2, x3)  =  U56_AA(x3)
U60_AA(x1, x2, x3)  =  U60_AA(x3)

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:

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
T234_IN_AA → U16_AA(n32_in_aa)
U16_AA(n32_out_aa) → T234_IN_AA
E1_IN_AA → U111_AA(t234_in_aa)
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
T203_IN_AA → U4_AA(n32_in_aa)
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
E198_IN_AA → U8_AA(t234_in_aa)
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(14) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T234_IN_AA → U16_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))

(15) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
E1_IN_AA → U111_AA(t234_in_aa)
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
T203_IN_AA → U4_AA(n32_in_aa)
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
E198_IN_AA → U8_AA(t234_in_aa)
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(16) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E1_IN_AA → U111_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))

(17) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
T203_IN_AA → U4_AA(n32_in_aa)
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
E198_IN_AA → U8_AA(t234_in_aa)
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(18) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T203_IN_AA → U4_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))

(19) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
E198_IN_AA → U8_AA(t234_in_aa)
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(20) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E198_IN_AA → U8_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))

(21) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(22) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T174_IN_AA → U64_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))

(23) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(24) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E169_IN_AA → U68_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))

(25) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(26) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T145_IN_AA → U72_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))

(27) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(28) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E140_IN_AA → U76_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))

(29) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(30) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T116_IN_AA → U80_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))

(31) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(32) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E111_IN_AA → U84_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))

(33) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(34) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T87_IN_AA → U88_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))

(35) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(36) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E82_IN_AA → U92_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))

(37) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(38) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T58_IN_AA → U96_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))

(39) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(40) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E53_IN_AA → U100_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))

(41) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(42) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P31_IN_AAA → U104_AAA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))

(43) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(44) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P31_IN_AAA → U106_AAA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))

(45) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(46) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T409_IN_AA → U12_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))

(47) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(48) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E404_IN_AA → U20_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))

(49) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(50) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T380_IN_AA → U24_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))

(51) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(52) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E375_IN_AA → U28_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))

(53) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(54) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T351_IN_AA → U32_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))

(55) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(56) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E346_IN_AA → U36_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))

(57) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(58) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T322_IN_AA → U40_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))

(59) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(60) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E317_IN_AA → U44_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))

(61) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(62) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T293_IN_AA → U48_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))

(63) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))
T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(64) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E288_IN_AA → U52_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E288_IN_AA → U52_AA(t234_out_aa)
E288_IN_AA → U52_AA(U14_aa(e259_in_aa))
E288_IN_AA → U52_AA(U15_aa(n32_in_aa))
E288_IN_AA → U52_AA(U16_aa(n32_in_aa))

(65) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))
T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))
E288_IN_AA → U52_AA(t234_out_aa)
E288_IN_AA → U52_AA(U14_aa(e259_in_aa))
E288_IN_AA → U52_AA(U15_aa(n32_in_aa))
E288_IN_AA → U52_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(66) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T264_IN_AA → U56_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T264_IN_AA → U56_AA(n32_out_aa)
T264_IN_AA → U56_AA(U1_aa(e53_in_aa))

(67) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))
T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))
E288_IN_AA → U52_AA(t234_out_aa)
E288_IN_AA → U52_AA(U14_aa(e259_in_aa))
E288_IN_AA → U52_AA(U15_aa(n32_in_aa))
E288_IN_AA → U52_AA(U16_aa(n32_in_aa))
T264_IN_AA → U56_AA(n32_out_aa)
T264_IN_AA → U56_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(68) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E259_IN_AA → U60_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E259_IN_AA → U60_AA(t234_out_aa)
E259_IN_AA → U60_AA(U14_aa(e259_in_aa))
E259_IN_AA → U60_AA(U15_aa(n32_in_aa))
E259_IN_AA → U60_AA(U16_aa(n32_in_aa))

(69) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))
T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))
E288_IN_AA → U52_AA(t234_out_aa)
E288_IN_AA → U52_AA(U14_aa(e259_in_aa))
E288_IN_AA → U52_AA(U15_aa(n32_in_aa))
E288_IN_AA → U52_AA(U16_aa(n32_in_aa))
T264_IN_AA → U56_AA(n32_out_aa)
T264_IN_AA → U56_AA(U1_aa(e53_in_aa))
E259_IN_AA → U60_AA(t234_out_aa)
E259_IN_AA → U60_AA(U14_aa(e259_in_aa))
E259_IN_AA → U60_AA(U15_aa(n32_in_aa))
E259_IN_AA → U60_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(70) Obligation:

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

E1_IN_GA(T22, T24) → N7_IN_GA(T22, T24)
N7_IN_GA(.(lbrace, T41), T43) → E1_IN_GA(T41, .(rbrace, T43))
E1_IN_GA(T62, T64) → P31_IN_GAA(T62, X59, T64)
P31_IN_GAA(T62, X59, T64) → N32_IN_GA(T62, X59)
N32_IN_GA(.(lbrace, T89), X84) → E53_IN_GA(T89, X84)
E53_IN_GA(T97, X110) → T58_IN_GA(T97, X110)
T58_IN_GA(.(lbrace, T130), X155) → E82_IN_GA(T130, X155)
E82_IN_GA(T138, X181) → T87_IN_GA(T138, X181)
T87_IN_GA(.(lbrace, T171), X226) → E111_IN_GA(T171, X226)
E111_IN_GA(T179, X252) → T116_IN_GA(T179, X252)
T116_IN_GA(.(lbrace, T212), X297) → E140_IN_GA(T212, X297)
E140_IN_GA(T220, X323) → T145_IN_GA(T220, X323)
T145_IN_GA(.(lbrace, T253), X368) → E169_IN_GA(T253, X368)
E169_IN_GA(T261, X394) → T174_IN_GA(T261, X394)
T174_IN_GA(.(lbrace, T294), X439) → E198_IN_GA(T294, X439)
E198_IN_GA(T302, X465) → T203_IN_GA(T302, X465)
T203_IN_GA(.(lbrace, T335), X510) → E1_IN_GA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_GA(T941, T943) → T234_IN_GA(T941, X1569)
T234_IN_GA(.(lbrace, T392), X599) → E259_IN_GA(T392, X599)
E259_IN_GA(T400, X625) → T264_IN_GA(T400, X625)
T264_IN_GA(.(lbrace, T433), X670) → E288_IN_GA(T433, X670)
E288_IN_GA(T441, X696) → T293_IN_GA(T441, X696)
T293_IN_GA(.(lbrace, T474), X741) → E317_IN_GA(T474, X741)
E317_IN_GA(T482, X767) → T322_IN_GA(T482, X767)
T322_IN_GA(.(lbrace, T515), X812) → E346_IN_GA(T515, X812)
E346_IN_GA(T523, X838) → T351_IN_GA(T523, X838)
T351_IN_GA(.(lbrace, T556), X883) → E375_IN_GA(T556, X883)
E375_IN_GA(T564, X909) → T380_IN_GA(T564, X909)
T380_IN_GA(.(lbrace, T597), X954) → E404_IN_GA(T597, X954)
E404_IN_GA(T605, X980) → T409_IN_GA(T605, X980)
T409_IN_GA(.(lbrace, T638), X1025) → E1_IN_GA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
T409_IN_GA(T648, X1045) → N32_IN_GA(T648, X1044)
E404_IN_GA(T660, X1066) → T234_IN_GA(T660, X1065)
T234_IN_GA(T780, X1303) → N32_IN_GA(T780, X1302)
T380_IN_GA(T670, X1088) → N32_IN_GA(T670, X1087)
E375_IN_GA(T682, X1109) → T234_IN_GA(T682, X1108)
T351_IN_GA(T692, X1131) → N32_IN_GA(T692, X1130)
E346_IN_GA(T704, X1152) → T234_IN_GA(T704, X1151)
T322_IN_GA(T714, X1174) → N32_IN_GA(T714, X1173)
E317_IN_GA(T726, X1195) → T234_IN_GA(T726, X1194)
T293_IN_GA(T736, X1217) → N32_IN_GA(T736, X1216)
E288_IN_GA(T748, X1238) → T234_IN_GA(T748, X1237)
T264_IN_GA(T758, X1260) → N32_IN_GA(T758, X1259)
E259_IN_GA(T770, X1281) → T234_IN_GA(T770, X1280)
T203_IN_GA(T345, X530) → N32_IN_GA(T345, X529)
E198_IN_GA(T357, X551) → T234_IN_GA(T357, X550)
T174_IN_GA(T795, X1326) → N32_IN_GA(T795, X1325)
E169_IN_GA(T807, X1347) → T234_IN_GA(T807, X1346)
T145_IN_GA(T817, X1369) → N32_IN_GA(T817, X1368)
E140_IN_GA(T829, X1390) → T234_IN_GA(T829, X1389)
T116_IN_GA(T839, X1412) → N32_IN_GA(T839, X1411)
E111_IN_GA(T851, X1433) → T234_IN_GA(T851, X1432)
T87_IN_GA(T861, X1455) → N32_IN_GA(T861, X1454)
E82_IN_GA(T873, X1476) → T234_IN_GA(T873, X1475)
T58_IN_GA(T883, X1498) → N32_IN_GA(T883, X1497)
E53_IN_GA(T895, X1519) → T234_IN_GA(T895, X1518)

The TRS R consists of the following rules:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x1, x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga(x1)
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x1, x3)
U109_ga(x1, x2, x3)  =  U109_ga(x1, x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x1, x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga(x1)
U1_ga(x1, x2, x3)  =  U1_ga(x1, x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x1, x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga(x1)
U94_ga(x1, x2, x3)  =  U94_ga(x1, x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x1, x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga(x1)
U86_ga(x1, x2, x3)  =  U86_ga(x1, x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x1, x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga(x1)
U78_ga(x1, x2, x3)  =  U78_ga(x1, x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x1, x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga(x1)
U70_ga(x1, x2, x3)  =  U70_ga(x1, x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x1, x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga(x1)
U62_ga(x1, x2, x3)  =  U62_ga(x1, x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x1, x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga(x1)
U2_ga(x1, x2, x3)  =  U2_ga(x1, x3)
U110_ga(x1, x2, x3)  =  U110_ga(x1, x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga(x1)
U14_ga(x1, x2, x3)  =  U14_ga(x1, x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x1, x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga(x1)
U54_ga(x1, x2, x3)  =  U54_ga(x1, x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x1, x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga(x1)
U46_ga(x1, x2, x3)  =  U46_ga(x1, x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x1, x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga(x1)
U38_ga(x1, x2, x3)  =  U38_ga(x1, x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x1, x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga(x1)
U30_ga(x1, x2, x3)  =  U30_ga(x1, x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x1, x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga(x1)
U22_ga(x1, x2, x3)  =  U22_ga(x1, x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x1, x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga(x1)
U10_ga(x1, x2, x3)  =  U10_ga(x1, x3)
U111_ga(x1, x2, x3)  =  U111_ga(x1, x3)
U15_ga(x1, x2, x3)  =  U15_ga(x1, x3)
U16_ga(x1, x2, x3)  =  U16_ga(x1, x3)
U17_ga(x1, x2, x3)  =  U17_ga(x1, x3)
U112_ga(x1, x2, x3)  =  U112_ga(x1, x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga(x1)
U11_ga(x1, x2, x3)  =  U11_ga(x1, x3)
U12_ga(x1, x2, x3)  =  U12_ga(x1, x3)
U13_ga(x1, x2, x3)  =  U13_ga(x1, x3)
e404_out_ga(x1, x2)  =  e404_out_ga(x1)
U19_ga(x1, x2, x3)  =  U19_ga(x1, x3)
U20_ga(x1, x2, x3)  =  U20_ga(x1, x3)
U21_ga(x1, x2, x3)  =  U21_ga(x1, x3)
U23_ga(x1, x2, x3)  =  U23_ga(x1, x3)
U24_ga(x1, x2, x3)  =  U24_ga(x1, x3)
U25_ga(x1, x2, x3)  =  U25_ga(x1, x3)
e375_out_ga(x1, x2)  =  e375_out_ga(x1)
U27_ga(x1, x2, x3)  =  U27_ga(x1, x3)
U28_ga(x1, x2, x3)  =  U28_ga(x1, x3)
U29_ga(x1, x2, x3)  =  U29_ga(x1, x3)
U31_ga(x1, x2, x3)  =  U31_ga(x1, x3)
U32_ga(x1, x2, x3)  =  U32_ga(x1, x3)
U33_ga(x1, x2, x3)  =  U33_ga(x1, x3)
e346_out_ga(x1, x2)  =  e346_out_ga(x1)
U35_ga(x1, x2, x3)  =  U35_ga(x1, x3)
U36_ga(x1, x2, x3)  =  U36_ga(x1, x3)
U37_ga(x1, x2, x3)  =  U37_ga(x1, x3)
U39_ga(x1, x2, x3)  =  U39_ga(x1, x3)
U40_ga(x1, x2, x3)  =  U40_ga(x1, x3)
U41_ga(x1, x2, x3)  =  U41_ga(x1, x3)
e317_out_ga(x1, x2)  =  e317_out_ga(x1)
U43_ga(x1, x2, x3)  =  U43_ga(x1, x3)
U44_ga(x1, x2, x3)  =  U44_ga(x1, x3)
U45_ga(x1, x2, x3)  =  U45_ga(x1, x3)
U47_ga(x1, x2, x3)  =  U47_ga(x1, x3)
U48_ga(x1, x2, x3)  =  U48_ga(x1, x3)
U49_ga(x1, x2, x3)  =  U49_ga(x1, x3)
e288_out_ga(x1, x2)  =  e288_out_ga(x1)
U51_ga(x1, x2, x3)  =  U51_ga(x1, x3)
U52_ga(x1, x2, x3)  =  U52_ga(x1, x3)
U53_ga(x1, x2, x3)  =  U53_ga(x1, x3)
U55_ga(x1, x2, x3)  =  U55_ga(x1, x3)
U56_ga(x1, x2, x3)  =  U56_ga(x1, x3)
U57_ga(x1, x2, x3)  =  U57_ga(x1, x3)
e259_out_ga(x1, x2)  =  e259_out_ga(x1)
U59_ga(x1, x2, x3)  =  U59_ga(x1, x3)
U60_ga(x1, x2, x3)  =  U60_ga(x1, x3)
U61_ga(x1, x2, x3)  =  U61_ga(x1, x3)
U3_ga(x1, x2, x3)  =  U3_ga(x1, x3)
U4_ga(x1, x2, x3)  =  U4_ga(x1, x3)
U5_ga(x1, x2, x3)  =  U5_ga(x1, x3)
e198_out_ga(x1, x2)  =  e198_out_ga(x1)
U7_ga(x1, x2, x3)  =  U7_ga(x1, x3)
U8_ga(x1, x2, x3)  =  U8_ga(x1, x3)
U9_ga(x1, x2, x3)  =  U9_ga(x1, x3)
U63_ga(x1, x2, x3)  =  U63_ga(x1, x3)
U64_ga(x1, x2, x3)  =  U64_ga(x1, x3)
U65_ga(x1, x2, x3)  =  U65_ga(x1, x3)
e169_out_ga(x1, x2)  =  e169_out_ga(x1)
U67_ga(x1, x2, x3)  =  U67_ga(x1, x3)
U68_ga(x1, x2, x3)  =  U68_ga(x1, x3)
U69_ga(x1, x2, x3)  =  U69_ga(x1, x3)
U71_ga(x1, x2, x3)  =  U71_ga(x1, x3)
U72_ga(x1, x2, x3)  =  U72_ga(x1, x3)
U73_ga(x1, x2, x3)  =  U73_ga(x1, x3)
e140_out_ga(x1, x2)  =  e140_out_ga(x1)
U75_ga(x1, x2, x3)  =  U75_ga(x1, x3)
U76_ga(x1, x2, x3)  =  U76_ga(x1, x3)
U77_ga(x1, x2, x3)  =  U77_ga(x1, x3)
U79_ga(x1, x2, x3)  =  U79_ga(x1, x3)
U80_ga(x1, x2, x3)  =  U80_ga(x1, x3)
U81_ga(x1, x2, x3)  =  U81_ga(x1, x3)
e111_out_ga(x1, x2)  =  e111_out_ga(x1)
U83_ga(x1, x2, x3)  =  U83_ga(x1, x3)
U84_ga(x1, x2, x3)  =  U84_ga(x1, x3)
U85_ga(x1, x2, x3)  =  U85_ga(x1, x3)
U87_ga(x1, x2, x3)  =  U87_ga(x1, x3)
U88_ga(x1, x2, x3)  =  U88_ga(x1, x3)
U89_ga(x1, x2, x3)  =  U89_ga(x1, x3)
e82_out_ga(x1, x2)  =  e82_out_ga(x1)
U91_ga(x1, x2, x3)  =  U91_ga(x1, x3)
U92_ga(x1, x2, x3)  =  U92_ga(x1, x3)
U93_ga(x1, x2, x3)  =  U93_ga(x1, x3)
U95_ga(x1, x2, x3)  =  U95_ga(x1, x3)
U96_ga(x1, x2, x3)  =  U96_ga(x1, x3)
U97_ga(x1, x2, x3)  =  U97_ga(x1, x3)
e53_out_ga(x1, x2)  =  e53_out_ga(x1)
U99_ga(x1, x2, x3)  =  U99_ga(x1, x3)
U100_ga(x1, x2, x3)  =  U100_ga(x1, x3)
U101_ga(x1, x2, x3)  =  U101_ga(x1, x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa(x1)
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x1, x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x1, x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x1, x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x1, x4)
E1_IN_GA(x1, x2)  =  E1_IN_GA(x1)
N7_IN_GA(x1, x2)  =  N7_IN_GA(x1)
P31_IN_GAA(x1, x2, x3)  =  P31_IN_GAA(x1)
N32_IN_GA(x1, x2)  =  N32_IN_GA(x1)
E53_IN_GA(x1, x2)  =  E53_IN_GA(x1)
T58_IN_GA(x1, x2)  =  T58_IN_GA(x1)
E82_IN_GA(x1, x2)  =  E82_IN_GA(x1)
T87_IN_GA(x1, x2)  =  T87_IN_GA(x1)
E111_IN_GA(x1, x2)  =  E111_IN_GA(x1)
T116_IN_GA(x1, x2)  =  T116_IN_GA(x1)
E140_IN_GA(x1, x2)  =  E140_IN_GA(x1)
T145_IN_GA(x1, x2)  =  T145_IN_GA(x1)
E169_IN_GA(x1, x2)  =  E169_IN_GA(x1)
T174_IN_GA(x1, x2)  =  T174_IN_GA(x1)
E198_IN_GA(x1, x2)  =  E198_IN_GA(x1)
T203_IN_GA(x1, x2)  =  T203_IN_GA(x1)
T234_IN_GA(x1, x2)  =  T234_IN_GA(x1)
E259_IN_GA(x1, x2)  =  E259_IN_GA(x1)
T264_IN_GA(x1, x2)  =  T264_IN_GA(x1)
E288_IN_GA(x1, x2)  =  E288_IN_GA(x1)
T293_IN_GA(x1, x2)  =  T293_IN_GA(x1)
E317_IN_GA(x1, x2)  =  E317_IN_GA(x1)
T322_IN_GA(x1, x2)  =  T322_IN_GA(x1)
E346_IN_GA(x1, x2)  =  E346_IN_GA(x1)
T351_IN_GA(x1, x2)  =  T351_IN_GA(x1)
E375_IN_GA(x1, x2)  =  E375_IN_GA(x1)
T380_IN_GA(x1, x2)  =  T380_IN_GA(x1)
E404_IN_GA(x1, x2)  =  E404_IN_GA(x1)
T409_IN_GA(x1, x2)  =  T409_IN_GA(x1)

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

(71) UsableRulesProof (EQUIVALENT transformation)

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

(72) Obligation:

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

E1_IN_GA(T22, T24) → N7_IN_GA(T22, T24)
N7_IN_GA(.(lbrace, T41), T43) → E1_IN_GA(T41, .(rbrace, T43))
E1_IN_GA(T62, T64) → P31_IN_GAA(T62, X59, T64)
P31_IN_GAA(T62, X59, T64) → N32_IN_GA(T62, X59)
N32_IN_GA(.(lbrace, T89), X84) → E53_IN_GA(T89, X84)
E53_IN_GA(T97, X110) → T58_IN_GA(T97, X110)
T58_IN_GA(.(lbrace, T130), X155) → E82_IN_GA(T130, X155)
E82_IN_GA(T138, X181) → T87_IN_GA(T138, X181)
T87_IN_GA(.(lbrace, T171), X226) → E111_IN_GA(T171, X226)
E111_IN_GA(T179, X252) → T116_IN_GA(T179, X252)
T116_IN_GA(.(lbrace, T212), X297) → E140_IN_GA(T212, X297)
E140_IN_GA(T220, X323) → T145_IN_GA(T220, X323)
T145_IN_GA(.(lbrace, T253), X368) → E169_IN_GA(T253, X368)
E169_IN_GA(T261, X394) → T174_IN_GA(T261, X394)
T174_IN_GA(.(lbrace, T294), X439) → E198_IN_GA(T294, X439)
E198_IN_GA(T302, X465) → T203_IN_GA(T302, X465)
T203_IN_GA(.(lbrace, T335), X510) → E1_IN_GA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_GA(T941, T943) → T234_IN_GA(T941, X1569)
T234_IN_GA(.(lbrace, T392), X599) → E259_IN_GA(T392, X599)
E259_IN_GA(T400, X625) → T264_IN_GA(T400, X625)
T264_IN_GA(.(lbrace, T433), X670) → E288_IN_GA(T433, X670)
E288_IN_GA(T441, X696) → T293_IN_GA(T441, X696)
T293_IN_GA(.(lbrace, T474), X741) → E317_IN_GA(T474, X741)
E317_IN_GA(T482, X767) → T322_IN_GA(T482, X767)
T322_IN_GA(.(lbrace, T515), X812) → E346_IN_GA(T515, X812)
E346_IN_GA(T523, X838) → T351_IN_GA(T523, X838)
T351_IN_GA(.(lbrace, T556), X883) → E375_IN_GA(T556, X883)
E375_IN_GA(T564, X909) → T380_IN_GA(T564, X909)
T380_IN_GA(.(lbrace, T597), X954) → E404_IN_GA(T597, X954)
E404_IN_GA(T605, X980) → T409_IN_GA(T605, X980)
T409_IN_GA(.(lbrace, T638), X1025) → E1_IN_GA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
T409_IN_GA(T648, X1045) → N32_IN_GA(T648, X1044)
E404_IN_GA(T660, X1066) → T234_IN_GA(T660, X1065)
T234_IN_GA(T780, X1303) → N32_IN_GA(T780, X1302)
T380_IN_GA(T670, X1088) → N32_IN_GA(T670, X1087)
E375_IN_GA(T682, X1109) → T234_IN_GA(T682, X1108)
T351_IN_GA(T692, X1131) → N32_IN_GA(T692, X1130)
E346_IN_GA(T704, X1152) → T234_IN_GA(T704, X1151)
T322_IN_GA(T714, X1174) → N32_IN_GA(T714, X1173)
E317_IN_GA(T726, X1195) → T234_IN_GA(T726, X1194)
T293_IN_GA(T736, X1217) → N32_IN_GA(T736, X1216)
E288_IN_GA(T748, X1238) → T234_IN_GA(T748, X1237)
T264_IN_GA(T758, X1260) → N32_IN_GA(T758, X1259)
E259_IN_GA(T770, X1281) → T234_IN_GA(T770, X1280)
T203_IN_GA(T345, X530) → N32_IN_GA(T345, X529)
E198_IN_GA(T357, X551) → T234_IN_GA(T357, X550)
T174_IN_GA(T795, X1326) → N32_IN_GA(T795, X1325)
E169_IN_GA(T807, X1347) → T234_IN_GA(T807, X1346)
T145_IN_GA(T817, X1369) → N32_IN_GA(T817, X1368)
E140_IN_GA(T829, X1390) → T234_IN_GA(T829, X1389)
T116_IN_GA(T839, X1412) → N32_IN_GA(T839, X1411)
E111_IN_GA(T851, X1433) → T234_IN_GA(T851, X1432)
T87_IN_GA(T861, X1455) → N32_IN_GA(T861, X1454)
E82_IN_GA(T873, X1476) → T234_IN_GA(T873, X1475)
T58_IN_GA(T883, X1498) → N32_IN_GA(T883, X1497)
E53_IN_GA(T895, X1519) → T234_IN_GA(T895, X1518)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
lbrace  =  lbrace
star  =  star
rbrace  =  rbrace
plus  =  plus
E1_IN_GA(x1, x2)  =  E1_IN_GA(x1)
N7_IN_GA(x1, x2)  =  N7_IN_GA(x1)
P31_IN_GAA(x1, x2, x3)  =  P31_IN_GAA(x1)
N32_IN_GA(x1, x2)  =  N32_IN_GA(x1)
E53_IN_GA(x1, x2)  =  E53_IN_GA(x1)
T58_IN_GA(x1, x2)  =  T58_IN_GA(x1)
E82_IN_GA(x1, x2)  =  E82_IN_GA(x1)
T87_IN_GA(x1, x2)  =  T87_IN_GA(x1)
E111_IN_GA(x1, x2)  =  E111_IN_GA(x1)
T116_IN_GA(x1, x2)  =  T116_IN_GA(x1)
E140_IN_GA(x1, x2)  =  E140_IN_GA(x1)
T145_IN_GA(x1, x2)  =  T145_IN_GA(x1)
E169_IN_GA(x1, x2)  =  E169_IN_GA(x1)
T174_IN_GA(x1, x2)  =  T174_IN_GA(x1)
E198_IN_GA(x1, x2)  =  E198_IN_GA(x1)
T203_IN_GA(x1, x2)  =  T203_IN_GA(x1)
T234_IN_GA(x1, x2)  =  T234_IN_GA(x1)
E259_IN_GA(x1, x2)  =  E259_IN_GA(x1)
T264_IN_GA(x1, x2)  =  T264_IN_GA(x1)
E288_IN_GA(x1, x2)  =  E288_IN_GA(x1)
T293_IN_GA(x1, x2)  =  T293_IN_GA(x1)
E317_IN_GA(x1, x2)  =  E317_IN_GA(x1)
T322_IN_GA(x1, x2)  =  T322_IN_GA(x1)
E346_IN_GA(x1, x2)  =  E346_IN_GA(x1)
T351_IN_GA(x1, x2)  =  T351_IN_GA(x1)
E375_IN_GA(x1, x2)  =  E375_IN_GA(x1)
T380_IN_GA(x1, x2)  =  T380_IN_GA(x1)
E404_IN_GA(x1, x2)  =  E404_IN_GA(x1)
T409_IN_GA(x1, x2)  =  T409_IN_GA(x1)

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

(73) PrologToPiTRSProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
e1_in: (b,f) (f,f)
n7_in: (b,f) (f,f)
p31_in: (b,f,f) (f,f,f)
n32_in: (b,f) (f,f)
e53_in: (b,f) (f,f)
t58_in: (b,f) (f,f)
e82_in: (b,f) (f,f)
t87_in: (b,f) (f,f)
e111_in: (b,f) (f,f)
t116_in: (b,f) (f,f)
e140_in: (b,f) (f,f)
t145_in: (b,f) (f,f)
e169_in: (b,f) (f,f)
t174_in: (b,f) (f,f)
e198_in: (b,f) (f,f)
t203_in: (b,f) (f,f)
t234_in: (b,f) (f,f)
e259_in: (b,f) (f,f)
t264_in: (b,f) (f,f)
e288_in: (b,f) (f,f)
t293_in: (b,f) (f,f)
e317_in: (b,f) (f,f)
t322_in: (b,f) (f,f)
e346_in: (b,f) (f,f)
t351_in: (b,f) (f,f)
e375_in: (b,f) (f,f)
t380_in: (b,f) (f,f)
e404_in: (b,f) (f,f)
t409_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:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x3)
U109_ga(x1, x2, x3)  =  U109_ga(x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga
U1_ga(x1, x2, x3)  =  U1_ga(x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga
U94_ga(x1, x2, x3)  =  U94_ga(x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga
U86_ga(x1, x2, x3)  =  U86_ga(x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga
U78_ga(x1, x2, x3)  =  U78_ga(x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga
U70_ga(x1, x2, x3)  =  U70_ga(x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga
U62_ga(x1, x2, x3)  =  U62_ga(x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U110_ga(x1, x2, x3)  =  U110_ga(x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga
U14_ga(x1, x2, x3)  =  U14_ga(x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga
U54_ga(x1, x2, x3)  =  U54_ga(x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga
U46_ga(x1, x2, x3)  =  U46_ga(x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga
U38_ga(x1, x2, x3)  =  U38_ga(x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga
U30_ga(x1, x2, x3)  =  U30_ga(x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga
U22_ga(x1, x2, x3)  =  U22_ga(x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U111_ga(x1, x2, x3)  =  U111_ga(x3)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U112_ga(x1, x2, x3)  =  U112_ga(x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
e404_out_ga(x1, x2)  =  e404_out_ga
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
e375_out_ga(x1, x2)  =  e375_out_ga
U27_ga(x1, x2, x3)  =  U27_ga(x3)
U28_ga(x1, x2, x3)  =  U28_ga(x3)
U29_ga(x1, x2, x3)  =  U29_ga(x3)
U31_ga(x1, x2, x3)  =  U31_ga(x3)
U32_ga(x1, x2, x3)  =  U32_ga(x3)
U33_ga(x1, x2, x3)  =  U33_ga(x3)
e346_out_ga(x1, x2)  =  e346_out_ga
U35_ga(x1, x2, x3)  =  U35_ga(x3)
U36_ga(x1, x2, x3)  =  U36_ga(x3)
U37_ga(x1, x2, x3)  =  U37_ga(x3)
U39_ga(x1, x2, x3)  =  U39_ga(x3)
U40_ga(x1, x2, x3)  =  U40_ga(x3)
U41_ga(x1, x2, x3)  =  U41_ga(x3)
e317_out_ga(x1, x2)  =  e317_out_ga
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U49_ga(x1, x2, x3)  =  U49_ga(x3)
e288_out_ga(x1, x2)  =  e288_out_ga
U51_ga(x1, x2, x3)  =  U51_ga(x3)
U52_ga(x1, x2, x3)  =  U52_ga(x3)
U53_ga(x1, x2, x3)  =  U53_ga(x3)
U55_ga(x1, x2, x3)  =  U55_ga(x3)
U56_ga(x1, x2, x3)  =  U56_ga(x3)
U57_ga(x1, x2, x3)  =  U57_ga(x3)
e259_out_ga(x1, x2)  =  e259_out_ga
U59_ga(x1, x2, x3)  =  U59_ga(x3)
U60_ga(x1, x2, x3)  =  U60_ga(x3)
U61_ga(x1, x2, x3)  =  U61_ga(x3)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
e198_out_ga(x1, x2)  =  e198_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U63_ga(x1, x2, x3)  =  U63_ga(x3)
U64_ga(x1, x2, x3)  =  U64_ga(x3)
U65_ga(x1, x2, x3)  =  U65_ga(x3)
e169_out_ga(x1, x2)  =  e169_out_ga
U67_ga(x1, x2, x3)  =  U67_ga(x3)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
U69_ga(x1, x2, x3)  =  U69_ga(x3)
U71_ga(x1, x2, x3)  =  U71_ga(x3)
U72_ga(x1, x2, x3)  =  U72_ga(x3)
U73_ga(x1, x2, x3)  =  U73_ga(x3)
e140_out_ga(x1, x2)  =  e140_out_ga
U75_ga(x1, x2, x3)  =  U75_ga(x3)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
U77_ga(x1, x2, x3)  =  U77_ga(x3)
U79_ga(x1, x2, x3)  =  U79_ga(x3)
U80_ga(x1, x2, x3)  =  U80_ga(x3)
U81_ga(x1, x2, x3)  =  U81_ga(x3)
e111_out_ga(x1, x2)  =  e111_out_ga
U83_ga(x1, x2, x3)  =  U83_ga(x3)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
U85_ga(x1, x2, x3)  =  U85_ga(x3)
U87_ga(x1, x2, x3)  =  U87_ga(x3)
U88_ga(x1, x2, x3)  =  U88_ga(x3)
U89_ga(x1, x2, x3)  =  U89_ga(x3)
e82_out_ga(x1, x2)  =  e82_out_ga
U91_ga(x1, x2, x3)  =  U91_ga(x3)
U92_ga(x1, x2, x3)  =  U92_ga(x3)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
U95_ga(x1, x2, x3)  =  U95_ga(x3)
U96_ga(x1, x2, x3)  =  U96_ga(x3)
U97_ga(x1, x2, x3)  =  U97_ga(x3)
e53_out_ga(x1, x2)  =  e53_out_ga
U99_ga(x1, x2, x3)  =  U99_ga(x3)
U100_ga(x1, x2, x3)  =  U100_ga(x3)
U101_ga(x1, x2, x3)  =  U101_ga(x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x4)

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(74) Obligation:

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

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x3)
U109_ga(x1, x2, x3)  =  U109_ga(x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga
U1_ga(x1, x2, x3)  =  U1_ga(x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga
U94_ga(x1, x2, x3)  =  U94_ga(x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga
U86_ga(x1, x2, x3)  =  U86_ga(x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga
U78_ga(x1, x2, x3)  =  U78_ga(x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga
U70_ga(x1, x2, x3)  =  U70_ga(x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga
U62_ga(x1, x2, x3)  =  U62_ga(x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U110_ga(x1, x2, x3)  =  U110_ga(x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga
U14_ga(x1, x2, x3)  =  U14_ga(x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga
U54_ga(x1, x2, x3)  =  U54_ga(x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga
U46_ga(x1, x2, x3)  =  U46_ga(x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga
U38_ga(x1, x2, x3)  =  U38_ga(x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga
U30_ga(x1, x2, x3)  =  U30_ga(x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga
U22_ga(x1, x2, x3)  =  U22_ga(x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U111_ga(x1, x2, x3)  =  U111_ga(x3)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U112_ga(x1, x2, x3)  =  U112_ga(x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
e404_out_ga(x1, x2)  =  e404_out_ga
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
e375_out_ga(x1, x2)  =  e375_out_ga
U27_ga(x1, x2, x3)  =  U27_ga(x3)
U28_ga(x1, x2, x3)  =  U28_ga(x3)
U29_ga(x1, x2, x3)  =  U29_ga(x3)
U31_ga(x1, x2, x3)  =  U31_ga(x3)
U32_ga(x1, x2, x3)  =  U32_ga(x3)
U33_ga(x1, x2, x3)  =  U33_ga(x3)
e346_out_ga(x1, x2)  =  e346_out_ga
U35_ga(x1, x2, x3)  =  U35_ga(x3)
U36_ga(x1, x2, x3)  =  U36_ga(x3)
U37_ga(x1, x2, x3)  =  U37_ga(x3)
U39_ga(x1, x2, x3)  =  U39_ga(x3)
U40_ga(x1, x2, x3)  =  U40_ga(x3)
U41_ga(x1, x2, x3)  =  U41_ga(x3)
e317_out_ga(x1, x2)  =  e317_out_ga
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U49_ga(x1, x2, x3)  =  U49_ga(x3)
e288_out_ga(x1, x2)  =  e288_out_ga
U51_ga(x1, x2, x3)  =  U51_ga(x3)
U52_ga(x1, x2, x3)  =  U52_ga(x3)
U53_ga(x1, x2, x3)  =  U53_ga(x3)
U55_ga(x1, x2, x3)  =  U55_ga(x3)
U56_ga(x1, x2, x3)  =  U56_ga(x3)
U57_ga(x1, x2, x3)  =  U57_ga(x3)
e259_out_ga(x1, x2)  =  e259_out_ga
U59_ga(x1, x2, x3)  =  U59_ga(x3)
U60_ga(x1, x2, x3)  =  U60_ga(x3)
U61_ga(x1, x2, x3)  =  U61_ga(x3)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
e198_out_ga(x1, x2)  =  e198_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U63_ga(x1, x2, x3)  =  U63_ga(x3)
U64_ga(x1, x2, x3)  =  U64_ga(x3)
U65_ga(x1, x2, x3)  =  U65_ga(x3)
e169_out_ga(x1, x2)  =  e169_out_ga
U67_ga(x1, x2, x3)  =  U67_ga(x3)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
U69_ga(x1, x2, x3)  =  U69_ga(x3)
U71_ga(x1, x2, x3)  =  U71_ga(x3)
U72_ga(x1, x2, x3)  =  U72_ga(x3)
U73_ga(x1, x2, x3)  =  U73_ga(x3)
e140_out_ga(x1, x2)  =  e140_out_ga
U75_ga(x1, x2, x3)  =  U75_ga(x3)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
U77_ga(x1, x2, x3)  =  U77_ga(x3)
U79_ga(x1, x2, x3)  =  U79_ga(x3)
U80_ga(x1, x2, x3)  =  U80_ga(x3)
U81_ga(x1, x2, x3)  =  U81_ga(x3)
e111_out_ga(x1, x2)  =  e111_out_ga
U83_ga(x1, x2, x3)  =  U83_ga(x3)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
U85_ga(x1, x2, x3)  =  U85_ga(x3)
U87_ga(x1, x2, x3)  =  U87_ga(x3)
U88_ga(x1, x2, x3)  =  U88_ga(x3)
U89_ga(x1, x2, x3)  =  U89_ga(x3)
e82_out_ga(x1, x2)  =  e82_out_ga
U91_ga(x1, x2, x3)  =  U91_ga(x3)
U92_ga(x1, x2, x3)  =  U92_ga(x3)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
U95_ga(x1, x2, x3)  =  U95_ga(x3)
U96_ga(x1, x2, x3)  =  U96_ga(x3)
U97_ga(x1, x2, x3)  =  U97_ga(x3)
e53_out_ga(x1, x2)  =  e53_out_ga
U99_ga(x1, x2, x3)  =  U99_ga(x3)
U100_ga(x1, x2, x3)  =  U100_ga(x3)
U101_ga(x1, x2, x3)  =  U101_ga(x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x4)

(75) 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:

E1_IN_GA(T22, T24) → U108_GA(T22, T24, n7_in_ga(T22, T24))
E1_IN_GA(T22, T24) → N7_IN_GA(T22, T24)
N7_IN_GA(.(lbrace, T41), T43) → U102_GA(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
N7_IN_GA(.(lbrace, T41), T43) → E1_IN_GA(T41, .(rbrace, T43))
E1_IN_GA(T62, T64) → U109_GA(T62, T64, p31_in_gaa(T62, X59, T64))
E1_IN_GA(T62, T64) → P31_IN_GAA(T62, X59, T64)
P31_IN_GAA(T62, X59, T64) → U103_GAA(T62, X59, T64, n32_in_ga(T62, X59))
P31_IN_GAA(T62, X59, T64) → N32_IN_GA(T62, X59)
N32_IN_GA(.(lbrace, T89), X84) → U1_GA(T89, X84, e53_in_ga(T89, X84))
N32_IN_GA(.(lbrace, T89), X84) → E53_IN_GA(T89, X84)
E53_IN_GA(T97, X110) → U98_GA(T97, X110, t58_in_ga(T97, X110))
E53_IN_GA(T97, X110) → T58_IN_GA(T97, X110)
T58_IN_GA(.(lbrace, T130), X155) → U94_GA(T130, X155, e82_in_ga(T130, X155))
T58_IN_GA(.(lbrace, T130), X155) → E82_IN_GA(T130, X155)
E82_IN_GA(T138, X181) → U90_GA(T138, X181, t87_in_ga(T138, X181))
E82_IN_GA(T138, X181) → T87_IN_GA(T138, X181)
T87_IN_GA(.(lbrace, T171), X226) → U86_GA(T171, X226, e111_in_ga(T171, X226))
T87_IN_GA(.(lbrace, T171), X226) → E111_IN_GA(T171, X226)
E111_IN_GA(T179, X252) → U82_GA(T179, X252, t116_in_ga(T179, X252))
E111_IN_GA(T179, X252) → T116_IN_GA(T179, X252)
T116_IN_GA(.(lbrace, T212), X297) → U78_GA(T212, X297, e140_in_ga(T212, X297))
T116_IN_GA(.(lbrace, T212), X297) → E140_IN_GA(T212, X297)
E140_IN_GA(T220, X323) → U74_GA(T220, X323, t145_in_ga(T220, X323))
E140_IN_GA(T220, X323) → T145_IN_GA(T220, X323)
T145_IN_GA(.(lbrace, T253), X368) → U70_GA(T253, X368, e169_in_ga(T253, X368))
T145_IN_GA(.(lbrace, T253), X368) → E169_IN_GA(T253, X368)
E169_IN_GA(T261, X394) → U66_GA(T261, X394, t174_in_ga(T261, X394))
E169_IN_GA(T261, X394) → T174_IN_GA(T261, X394)
T174_IN_GA(.(lbrace, T294), X439) → U62_GA(T294, X439, e198_in_ga(T294, X439))
T174_IN_GA(.(lbrace, T294), X439) → E198_IN_GA(T294, X439)
E198_IN_GA(T302, X465) → U6_GA(T302, X465, t203_in_ga(T302, X465))
E198_IN_GA(T302, X465) → T203_IN_GA(T302, X465)
T203_IN_GA(.(lbrace, T335), X510) → U2_GA(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
T203_IN_GA(.(lbrace, T335), X510) → E1_IN_GA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_GA(T941, T943) → U110_GA(T941, T943, t234_in_ga(T941, X1569))
E1_IN_GA(T941, T943) → T234_IN_GA(T941, X1569)
T234_IN_GA(.(lbrace, T392), X599) → U14_GA(T392, X599, e259_in_ga(T392, X599))
T234_IN_GA(.(lbrace, T392), X599) → E259_IN_GA(T392, X599)
E259_IN_GA(T400, X625) → U58_GA(T400, X625, t264_in_ga(T400, X625))
E259_IN_GA(T400, X625) → T264_IN_GA(T400, X625)
T264_IN_GA(.(lbrace, T433), X670) → U54_GA(T433, X670, e288_in_ga(T433, X670))
T264_IN_GA(.(lbrace, T433), X670) → E288_IN_GA(T433, X670)
E288_IN_GA(T441, X696) → U50_GA(T441, X696, t293_in_ga(T441, X696))
E288_IN_GA(T441, X696) → T293_IN_GA(T441, X696)
T293_IN_GA(.(lbrace, T474), X741) → U46_GA(T474, X741, e317_in_ga(T474, X741))
T293_IN_GA(.(lbrace, T474), X741) → E317_IN_GA(T474, X741)
E317_IN_GA(T482, X767) → U42_GA(T482, X767, t322_in_ga(T482, X767))
E317_IN_GA(T482, X767) → T322_IN_GA(T482, X767)
T322_IN_GA(.(lbrace, T515), X812) → U38_GA(T515, X812, e346_in_ga(T515, X812))
T322_IN_GA(.(lbrace, T515), X812) → E346_IN_GA(T515, X812)
E346_IN_GA(T523, X838) → U34_GA(T523, X838, t351_in_ga(T523, X838))
E346_IN_GA(T523, X838) → T351_IN_GA(T523, X838)
T351_IN_GA(.(lbrace, T556), X883) → U30_GA(T556, X883, e375_in_ga(T556, X883))
T351_IN_GA(.(lbrace, T556), X883) → E375_IN_GA(T556, X883)
E375_IN_GA(T564, X909) → U26_GA(T564, X909, t380_in_ga(T564, X909))
E375_IN_GA(T564, X909) → T380_IN_GA(T564, X909)
T380_IN_GA(.(lbrace, T597), X954) → U22_GA(T597, X954, e404_in_ga(T597, X954))
T380_IN_GA(.(lbrace, T597), X954) → E404_IN_GA(T597, X954)
E404_IN_GA(T605, X980) → U18_GA(T605, X980, t409_in_ga(T605, X980))
E404_IN_GA(T605, X980) → T409_IN_GA(T605, X980)
T409_IN_GA(.(lbrace, T638), X1025) → U10_GA(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
T409_IN_GA(.(lbrace, T638), X1025) → E1_IN_GA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_GA(T941, T943) → U111_GA(T941, T943, t234_in_ga(T941, T945))
T234_IN_GA(T780, X1303) → U15_GA(T780, X1303, n32_in_ga(T780, X1302))
T234_IN_GA(T780, X1303) → N32_IN_GA(T780, X1302)
T234_IN_GA(T780, X1303) → U16_GA(T780, X1303, n32_in_ga(T780, T784))
U16_GA(T780, X1303, n32_out_ga(T780, T784)) → U17_GA(T780, X1303, t234_in_aa(T784, X1303))
U16_GA(T780, X1303, n32_out_ga(T780, T784)) → T234_IN_AA(T784, X1303)
T234_IN_AA(.(lbrace, T392), X599) → U14_AA(T392, X599, e259_in_aa(T392, X599))
T234_IN_AA(.(lbrace, T392), X599) → E259_IN_AA(T392, X599)
E259_IN_AA(T400, X625) → U58_AA(T400, X625, t264_in_aa(T400, X625))
E259_IN_AA(T400, X625) → T264_IN_AA(T400, X625)
T264_IN_AA(.(lbrace, T433), X670) → U54_AA(T433, X670, e288_in_aa(T433, X670))
T264_IN_AA(.(lbrace, T433), X670) → E288_IN_AA(T433, X670)
E288_IN_AA(T441, X696) → U50_AA(T441, X696, t293_in_aa(T441, X696))
E288_IN_AA(T441, X696) → T293_IN_AA(T441, X696)
T293_IN_AA(.(lbrace, T474), X741) → U46_AA(T474, X741, e317_in_aa(T474, X741))
T293_IN_AA(.(lbrace, T474), X741) → E317_IN_AA(T474, X741)
E317_IN_AA(T482, X767) → U42_AA(T482, X767, t322_in_aa(T482, X767))
E317_IN_AA(T482, X767) → T322_IN_AA(T482, X767)
T322_IN_AA(.(lbrace, T515), X812) → U38_AA(T515, X812, e346_in_aa(T515, X812))
T322_IN_AA(.(lbrace, T515), X812) → E346_IN_AA(T515, X812)
E346_IN_AA(T523, X838) → U34_AA(T523, X838, t351_in_aa(T523, X838))
E346_IN_AA(T523, X838) → T351_IN_AA(T523, X838)
T351_IN_AA(.(lbrace, T556), X883) → U30_AA(T556, X883, e375_in_aa(T556, X883))
T351_IN_AA(.(lbrace, T556), X883) → E375_IN_AA(T556, X883)
E375_IN_AA(T564, X909) → U26_AA(T564, X909, t380_in_aa(T564, X909))
E375_IN_AA(T564, X909) → T380_IN_AA(T564, X909)
T380_IN_AA(.(lbrace, T597), X954) → U22_AA(T597, X954, e404_in_aa(T597, X954))
T380_IN_AA(.(lbrace, T597), X954) → E404_IN_AA(T597, X954)
E404_IN_AA(T605, X980) → U18_AA(T605, X980, t409_in_aa(T605, X980))
E404_IN_AA(T605, X980) → T409_IN_AA(T605, X980)
T409_IN_AA(.(lbrace, T638), X1025) → U10_AA(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
T409_IN_AA(.(lbrace, T638), X1025) → E1_IN_AA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_AA(T22, T24) → U108_AA(T22, T24, n7_in_aa(T22, T24))
E1_IN_AA(T22, T24) → N7_IN_AA(T22, T24)
N7_IN_AA(.(lbrace, T41), T43) → U102_AA(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
N7_IN_AA(.(lbrace, T41), T43) → E1_IN_AA(T41, .(rbrace, T43))
E1_IN_AA(T62, T64) → U109_AA(T62, T64, p31_in_aaa(T62, X59, T64))
E1_IN_AA(T62, T64) → P31_IN_AAA(T62, X59, T64)
P31_IN_AAA(T62, X59, T64) → U103_AAA(T62, X59, T64, n32_in_aa(T62, X59))
P31_IN_AAA(T62, X59, T64) → N32_IN_AA(T62, X59)
N32_IN_AA(.(lbrace, T89), X84) → U1_AA(T89, X84, e53_in_aa(T89, X84))
N32_IN_AA(.(lbrace, T89), X84) → E53_IN_AA(T89, X84)
E53_IN_AA(T97, X110) → U98_AA(T97, X110, t58_in_aa(T97, X110))
E53_IN_AA(T97, X110) → T58_IN_AA(T97, X110)
T58_IN_AA(.(lbrace, T130), X155) → U94_AA(T130, X155, e82_in_aa(T130, X155))
T58_IN_AA(.(lbrace, T130), X155) → E82_IN_AA(T130, X155)
E82_IN_AA(T138, X181) → U90_AA(T138, X181, t87_in_aa(T138, X181))
E82_IN_AA(T138, X181) → T87_IN_AA(T138, X181)
T87_IN_AA(.(lbrace, T171), X226) → U86_AA(T171, X226, e111_in_aa(T171, X226))
T87_IN_AA(.(lbrace, T171), X226) → E111_IN_AA(T171, X226)
E111_IN_AA(T179, X252) → U82_AA(T179, X252, t116_in_aa(T179, X252))
E111_IN_AA(T179, X252) → T116_IN_AA(T179, X252)
T116_IN_AA(.(lbrace, T212), X297) → U78_AA(T212, X297, e140_in_aa(T212, X297))
T116_IN_AA(.(lbrace, T212), X297) → E140_IN_AA(T212, X297)
E140_IN_AA(T220, X323) → U74_AA(T220, X323, t145_in_aa(T220, X323))
E140_IN_AA(T220, X323) → T145_IN_AA(T220, X323)
T145_IN_AA(.(lbrace, T253), X368) → U70_AA(T253, X368, e169_in_aa(T253, X368))
T145_IN_AA(.(lbrace, T253), X368) → E169_IN_AA(T253, X368)
E169_IN_AA(T261, X394) → U66_AA(T261, X394, t174_in_aa(T261, X394))
E169_IN_AA(T261, X394) → T174_IN_AA(T261, X394)
T174_IN_AA(.(lbrace, T294), X439) → U62_AA(T294, X439, e198_in_aa(T294, X439))
T174_IN_AA(.(lbrace, T294), X439) → E198_IN_AA(T294, X439)
E198_IN_AA(T302, X465) → U6_AA(T302, X465, t203_in_aa(T302, X465))
E198_IN_AA(T302, X465) → T203_IN_AA(T302, X465)
T203_IN_AA(.(lbrace, T335), X510) → U2_AA(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
T203_IN_AA(.(lbrace, T335), X510) → E1_IN_AA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_AA(T941, T943) → U110_AA(T941, T943, t234_in_aa(T941, X1569))
E1_IN_AA(T941, T943) → T234_IN_AA(T941, X1569)
T234_IN_AA(T780, X1303) → U15_AA(T780, X1303, n32_in_aa(T780, X1302))
T234_IN_AA(T780, X1303) → N32_IN_AA(T780, X1302)
T234_IN_AA(T780, X1303) → U16_AA(T780, X1303, n32_in_aa(T780, T784))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → U17_AA(T780, X1303, t234_in_aa(T784, X1303))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → T234_IN_AA(T784, X1303)
E1_IN_AA(T941, T943) → U111_AA(T941, T943, t234_in_aa(T941, T945))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → U112_AA(T941, T943, e1_in_aa(T945, T943))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → E1_IN_AA(T945, T943)
T203_IN_AA(T345, X530) → U3_AA(T345, X530, n32_in_aa(T345, X529))
T203_IN_AA(T345, X530) → N32_IN_AA(T345, X529)
T203_IN_AA(T345, X530) → U4_AA(T345, X530, n32_in_aa(T345, T349))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → U5_AA(T345, X530, t203_in_aa(T349, X530))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_AA(T357, X551) → U7_AA(T357, X551, t234_in_aa(T357, X550))
E198_IN_AA(T357, X551) → T234_IN_AA(T357, X550)
E198_IN_AA(T357, X551) → U8_AA(T357, X551, t234_in_aa(T357, T359))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → U9_AA(T357, X551, e198_in_aa(T359, X551))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_AA(T795, X1326) → U63_AA(T795, X1326, n32_in_aa(T795, X1325))
T174_IN_AA(T795, X1326) → N32_IN_AA(T795, X1325)
T174_IN_AA(T795, X1326) → U64_AA(T795, X1326, n32_in_aa(T795, T799))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → U65_AA(T795, X1326, t174_in_aa(T799, X1326))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_AA(T807, X1347) → U67_AA(T807, X1347, t234_in_aa(T807, X1346))
E169_IN_AA(T807, X1347) → T234_IN_AA(T807, X1346)
E169_IN_AA(T807, X1347) → U68_AA(T807, X1347, t234_in_aa(T807, T809))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → U69_AA(T807, X1347, e169_in_aa(T809, X1347))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_AA(T817, X1369) → U71_AA(T817, X1369, n32_in_aa(T817, X1368))
T145_IN_AA(T817, X1369) → N32_IN_AA(T817, X1368)
T145_IN_AA(T817, X1369) → U72_AA(T817, X1369, n32_in_aa(T817, T821))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → U73_AA(T817, X1369, t145_in_aa(T821, X1369))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_AA(T829, X1390) → U75_AA(T829, X1390, t234_in_aa(T829, X1389))
E140_IN_AA(T829, X1390) → T234_IN_AA(T829, X1389)
E140_IN_AA(T829, X1390) → U76_AA(T829, X1390, t234_in_aa(T829, T831))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → U77_AA(T829, X1390, e140_in_aa(T831, X1390))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_AA(T839, X1412) → U79_AA(T839, X1412, n32_in_aa(T839, X1411))
T116_IN_AA(T839, X1412) → N32_IN_AA(T839, X1411)
T116_IN_AA(T839, X1412) → U80_AA(T839, X1412, n32_in_aa(T839, T843))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → U81_AA(T839, X1412, t116_in_aa(T843, X1412))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_AA(T851, X1433) → U83_AA(T851, X1433, t234_in_aa(T851, X1432))
E111_IN_AA(T851, X1433) → T234_IN_AA(T851, X1432)
E111_IN_AA(T851, X1433) → U84_AA(T851, X1433, t234_in_aa(T851, T853))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → U85_AA(T851, X1433, e111_in_aa(T853, X1433))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_AA(T861, X1455) → U87_AA(T861, X1455, n32_in_aa(T861, X1454))
T87_IN_AA(T861, X1455) → N32_IN_AA(T861, X1454)
T87_IN_AA(T861, X1455) → U88_AA(T861, X1455, n32_in_aa(T861, T865))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → U89_AA(T861, X1455, t87_in_aa(T865, X1455))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_AA(T873, X1476) → U91_AA(T873, X1476, t234_in_aa(T873, X1475))
E82_IN_AA(T873, X1476) → T234_IN_AA(T873, X1475)
E82_IN_AA(T873, X1476) → U92_AA(T873, X1476, t234_in_aa(T873, T875))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → U93_AA(T873, X1476, e82_in_aa(T875, X1476))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_AA(T883, X1498) → U95_AA(T883, X1498, n32_in_aa(T883, X1497))
T58_IN_AA(T883, X1498) → N32_IN_AA(T883, X1497)
T58_IN_AA(T883, X1498) → U96_AA(T883, X1498, n32_in_aa(T883, T887))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → U97_AA(T883, X1498, t58_in_aa(T887, X1498))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_AA(T895, X1519) → U99_AA(T895, X1519, t234_in_aa(T895, X1518))
E53_IN_AA(T895, X1519) → T234_IN_AA(T895, X1518)
E53_IN_AA(T895, X1519) → U100_AA(T895, X1519, t234_in_aa(T895, T897))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → U101_AA(T895, X1519, e53_in_aa(T897, X1519))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_AAA(T62, T916, T918) → U104_AAA(T62, T916, T918, n32_in_aa(T62, T916))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → U105_AAA(T62, T916, T918, n7_in_aa(T916, T918))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_AAA(T62, T929, T931) → U106_AAA(T62, T929, T931, n32_in_aa(T62, T929))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → U107_AAA(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → P31_IN_AAA(T929, X1556, T931)
T409_IN_AA(T648, X1045) → U11_AA(T648, X1045, n32_in_aa(T648, X1044))
T409_IN_AA(T648, X1045) → N32_IN_AA(T648, X1044)
T409_IN_AA(T648, X1045) → U12_AA(T648, X1045, n32_in_aa(T648, T652))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → U13_AA(T648, X1045, t409_in_aa(T652, X1045))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_AA(T660, X1066) → U19_AA(T660, X1066, t234_in_aa(T660, X1065))
E404_IN_AA(T660, X1066) → T234_IN_AA(T660, X1065)
E404_IN_AA(T660, X1066) → U20_AA(T660, X1066, t234_in_aa(T660, T662))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → U21_AA(T660, X1066, e404_in_aa(T662, X1066))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_AA(T670, X1088) → U23_AA(T670, X1088, n32_in_aa(T670, X1087))
T380_IN_AA(T670, X1088) → N32_IN_AA(T670, X1087)
T380_IN_AA(T670, X1088) → U24_AA(T670, X1088, n32_in_aa(T670, T674))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → U25_AA(T670, X1088, t380_in_aa(T674, X1088))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_AA(T682, X1109) → U27_AA(T682, X1109, t234_in_aa(T682, X1108))
E375_IN_AA(T682, X1109) → T234_IN_AA(T682, X1108)
E375_IN_AA(T682, X1109) → U28_AA(T682, X1109, t234_in_aa(T682, T684))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → U29_AA(T682, X1109, e375_in_aa(T684, X1109))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_AA(T692, X1131) → U31_AA(T692, X1131, n32_in_aa(T692, X1130))
T351_IN_AA(T692, X1131) → N32_IN_AA(T692, X1130)
T351_IN_AA(T692, X1131) → U32_AA(T692, X1131, n32_in_aa(T692, T696))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → U33_AA(T692, X1131, t351_in_aa(T696, X1131))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_AA(T704, X1152) → U35_AA(T704, X1152, t234_in_aa(T704, X1151))
E346_IN_AA(T704, X1152) → T234_IN_AA(T704, X1151)
E346_IN_AA(T704, X1152) → U36_AA(T704, X1152, t234_in_aa(T704, T706))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → U37_AA(T704, X1152, e346_in_aa(T706, X1152))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_AA(T714, X1174) → U39_AA(T714, X1174, n32_in_aa(T714, X1173))
T322_IN_AA(T714, X1174) → N32_IN_AA(T714, X1173)
T322_IN_AA(T714, X1174) → U40_AA(T714, X1174, n32_in_aa(T714, T718))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → U41_AA(T714, X1174, t322_in_aa(T718, X1174))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_AA(T726, X1195) → U43_AA(T726, X1195, t234_in_aa(T726, X1194))
E317_IN_AA(T726, X1195) → T234_IN_AA(T726, X1194)
E317_IN_AA(T726, X1195) → U44_AA(T726, X1195, t234_in_aa(T726, T728))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → U45_AA(T726, X1195, e317_in_aa(T728, X1195))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_AA(T736, X1217) → U47_AA(T736, X1217, n32_in_aa(T736, X1216))
T293_IN_AA(T736, X1217) → N32_IN_AA(T736, X1216)
T293_IN_AA(T736, X1217) → U48_AA(T736, X1217, n32_in_aa(T736, T740))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → U49_AA(T736, X1217, t293_in_aa(T740, X1217))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_AA(T748, X1238) → U51_AA(T748, X1238, t234_in_aa(T748, X1237))
E288_IN_AA(T748, X1238) → T234_IN_AA(T748, X1237)
E288_IN_AA(T748, X1238) → U52_AA(T748, X1238, t234_in_aa(T748, T750))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → U53_AA(T748, X1238, e288_in_aa(T750, X1238))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_AA(T758, X1260) → U55_AA(T758, X1260, n32_in_aa(T758, X1259))
T264_IN_AA(T758, X1260) → N32_IN_AA(T758, X1259)
T264_IN_AA(T758, X1260) → U56_AA(T758, X1260, n32_in_aa(T758, T762))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → U57_AA(T758, X1260, t264_in_aa(T762, X1260))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_AA(T770, X1281) → U59_AA(T770, X1281, t234_in_aa(T770, X1280))
E259_IN_AA(T770, X1281) → T234_IN_AA(T770, X1280)
E259_IN_AA(T770, X1281) → U60_AA(T770, X1281, t234_in_aa(T770, T772))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → U61_AA(T770, X1281, e259_in_aa(T772, X1281))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → E259_IN_AA(T772, X1281)
U111_GA(T941, T943, t234_out_ga(T941, T945)) → U112_GA(T941, T943, e1_in_aa(T945, T943))
U111_GA(T941, T943, t234_out_ga(T941, T945)) → E1_IN_AA(T945, T943)
T409_IN_GA(T648, X1045) → U11_GA(T648, X1045, n32_in_ga(T648, X1044))
T409_IN_GA(T648, X1045) → N32_IN_GA(T648, X1044)
T409_IN_GA(T648, X1045) → U12_GA(T648, X1045, n32_in_ga(T648, T652))
U12_GA(T648, X1045, n32_out_ga(T648, T652)) → U13_GA(T648, X1045, t409_in_aa(T652, X1045))
U12_GA(T648, X1045, n32_out_ga(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_GA(T660, X1066) → U19_GA(T660, X1066, t234_in_ga(T660, X1065))
E404_IN_GA(T660, X1066) → T234_IN_GA(T660, X1065)
E404_IN_GA(T660, X1066) → U20_GA(T660, X1066, t234_in_ga(T660, T662))
U20_GA(T660, X1066, t234_out_ga(T660, T662)) → U21_GA(T660, X1066, e404_in_aa(T662, X1066))
U20_GA(T660, X1066, t234_out_ga(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_GA(T670, X1088) → U23_GA(T670, X1088, n32_in_ga(T670, X1087))
T380_IN_GA(T670, X1088) → N32_IN_GA(T670, X1087)
T380_IN_GA(T670, X1088) → U24_GA(T670, X1088, n32_in_ga(T670, T674))
U24_GA(T670, X1088, n32_out_ga(T670, T674)) → U25_GA(T670, X1088, t380_in_aa(T674, X1088))
U24_GA(T670, X1088, n32_out_ga(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_GA(T682, X1109) → U27_GA(T682, X1109, t234_in_ga(T682, X1108))
E375_IN_GA(T682, X1109) → T234_IN_GA(T682, X1108)
E375_IN_GA(T682, X1109) → U28_GA(T682, X1109, t234_in_ga(T682, T684))
U28_GA(T682, X1109, t234_out_ga(T682, T684)) → U29_GA(T682, X1109, e375_in_aa(T684, X1109))
U28_GA(T682, X1109, t234_out_ga(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_GA(T692, X1131) → U31_GA(T692, X1131, n32_in_ga(T692, X1130))
T351_IN_GA(T692, X1131) → N32_IN_GA(T692, X1130)
T351_IN_GA(T692, X1131) → U32_GA(T692, X1131, n32_in_ga(T692, T696))
U32_GA(T692, X1131, n32_out_ga(T692, T696)) → U33_GA(T692, X1131, t351_in_aa(T696, X1131))
U32_GA(T692, X1131, n32_out_ga(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_GA(T704, X1152) → U35_GA(T704, X1152, t234_in_ga(T704, X1151))
E346_IN_GA(T704, X1152) → T234_IN_GA(T704, X1151)
E346_IN_GA(T704, X1152) → U36_GA(T704, X1152, t234_in_ga(T704, T706))
U36_GA(T704, X1152, t234_out_ga(T704, T706)) → U37_GA(T704, X1152, e346_in_aa(T706, X1152))
U36_GA(T704, X1152, t234_out_ga(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_GA(T714, X1174) → U39_GA(T714, X1174, n32_in_ga(T714, X1173))
T322_IN_GA(T714, X1174) → N32_IN_GA(T714, X1173)
T322_IN_GA(T714, X1174) → U40_GA(T714, X1174, n32_in_ga(T714, T718))
U40_GA(T714, X1174, n32_out_ga(T714, T718)) → U41_GA(T714, X1174, t322_in_aa(T718, X1174))
U40_GA(T714, X1174, n32_out_ga(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_GA(T726, X1195) → U43_GA(T726, X1195, t234_in_ga(T726, X1194))
E317_IN_GA(T726, X1195) → T234_IN_GA(T726, X1194)
E317_IN_GA(T726, X1195) → U44_GA(T726, X1195, t234_in_ga(T726, T728))
U44_GA(T726, X1195, t234_out_ga(T726, T728)) → U45_GA(T726, X1195, e317_in_aa(T728, X1195))
U44_GA(T726, X1195, t234_out_ga(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_GA(T736, X1217) → U47_GA(T736, X1217, n32_in_ga(T736, X1216))
T293_IN_GA(T736, X1217) → N32_IN_GA(T736, X1216)
T293_IN_GA(T736, X1217) → U48_GA(T736, X1217, n32_in_ga(T736, T740))
U48_GA(T736, X1217, n32_out_ga(T736, T740)) → U49_GA(T736, X1217, t293_in_aa(T740, X1217))
U48_GA(T736, X1217, n32_out_ga(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_GA(T748, X1238) → U51_GA(T748, X1238, t234_in_ga(T748, X1237))
E288_IN_GA(T748, X1238) → T234_IN_GA(T748, X1237)
E288_IN_GA(T748, X1238) → U52_GA(T748, X1238, t234_in_ga(T748, T750))
U52_GA(T748, X1238, t234_out_ga(T748, T750)) → U53_GA(T748, X1238, e288_in_aa(T750, X1238))
U52_GA(T748, X1238, t234_out_ga(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_GA(T758, X1260) → U55_GA(T758, X1260, n32_in_ga(T758, X1259))
T264_IN_GA(T758, X1260) → N32_IN_GA(T758, X1259)
T264_IN_GA(T758, X1260) → U56_GA(T758, X1260, n32_in_ga(T758, T762))
U56_GA(T758, X1260, n32_out_ga(T758, T762)) → U57_GA(T758, X1260, t264_in_aa(T762, X1260))
U56_GA(T758, X1260, n32_out_ga(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_GA(T770, X1281) → U59_GA(T770, X1281, t234_in_ga(T770, X1280))
E259_IN_GA(T770, X1281) → T234_IN_GA(T770, X1280)
E259_IN_GA(T770, X1281) → U60_GA(T770, X1281, t234_in_ga(T770, T772))
U60_GA(T770, X1281, t234_out_ga(T770, T772)) → U61_GA(T770, X1281, e259_in_aa(T772, X1281))
U60_GA(T770, X1281, t234_out_ga(T770, T772)) → E259_IN_AA(T772, X1281)
T203_IN_GA(T345, X530) → U3_GA(T345, X530, n32_in_ga(T345, X529))
T203_IN_GA(T345, X530) → N32_IN_GA(T345, X529)
T203_IN_GA(T345, X530) → U4_GA(T345, X530, n32_in_ga(T345, T349))
U4_GA(T345, X530, n32_out_ga(T345, T349)) → U5_GA(T345, X530, t203_in_aa(T349, X530))
U4_GA(T345, X530, n32_out_ga(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_GA(T357, X551) → U7_GA(T357, X551, t234_in_ga(T357, X550))
E198_IN_GA(T357, X551) → T234_IN_GA(T357, X550)
E198_IN_GA(T357, X551) → U8_GA(T357, X551, t234_in_ga(T357, T359))
U8_GA(T357, X551, t234_out_ga(T357, T359)) → U9_GA(T357, X551, e198_in_aa(T359, X551))
U8_GA(T357, X551, t234_out_ga(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_GA(T795, X1326) → U63_GA(T795, X1326, n32_in_ga(T795, X1325))
T174_IN_GA(T795, X1326) → N32_IN_GA(T795, X1325)
T174_IN_GA(T795, X1326) → U64_GA(T795, X1326, n32_in_ga(T795, T799))
U64_GA(T795, X1326, n32_out_ga(T795, T799)) → U65_GA(T795, X1326, t174_in_aa(T799, X1326))
U64_GA(T795, X1326, n32_out_ga(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_GA(T807, X1347) → U67_GA(T807, X1347, t234_in_ga(T807, X1346))
E169_IN_GA(T807, X1347) → T234_IN_GA(T807, X1346)
E169_IN_GA(T807, X1347) → U68_GA(T807, X1347, t234_in_ga(T807, T809))
U68_GA(T807, X1347, t234_out_ga(T807, T809)) → U69_GA(T807, X1347, e169_in_aa(T809, X1347))
U68_GA(T807, X1347, t234_out_ga(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_GA(T817, X1369) → U71_GA(T817, X1369, n32_in_ga(T817, X1368))
T145_IN_GA(T817, X1369) → N32_IN_GA(T817, X1368)
T145_IN_GA(T817, X1369) → U72_GA(T817, X1369, n32_in_ga(T817, T821))
U72_GA(T817, X1369, n32_out_ga(T817, T821)) → U73_GA(T817, X1369, t145_in_aa(T821, X1369))
U72_GA(T817, X1369, n32_out_ga(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_GA(T829, X1390) → U75_GA(T829, X1390, t234_in_ga(T829, X1389))
E140_IN_GA(T829, X1390) → T234_IN_GA(T829, X1389)
E140_IN_GA(T829, X1390) → U76_GA(T829, X1390, t234_in_ga(T829, T831))
U76_GA(T829, X1390, t234_out_ga(T829, T831)) → U77_GA(T829, X1390, e140_in_aa(T831, X1390))
U76_GA(T829, X1390, t234_out_ga(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_GA(T839, X1412) → U79_GA(T839, X1412, n32_in_ga(T839, X1411))
T116_IN_GA(T839, X1412) → N32_IN_GA(T839, X1411)
T116_IN_GA(T839, X1412) → U80_GA(T839, X1412, n32_in_ga(T839, T843))
U80_GA(T839, X1412, n32_out_ga(T839, T843)) → U81_GA(T839, X1412, t116_in_aa(T843, X1412))
U80_GA(T839, X1412, n32_out_ga(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_GA(T851, X1433) → U83_GA(T851, X1433, t234_in_ga(T851, X1432))
E111_IN_GA(T851, X1433) → T234_IN_GA(T851, X1432)
E111_IN_GA(T851, X1433) → U84_GA(T851, X1433, t234_in_ga(T851, T853))
U84_GA(T851, X1433, t234_out_ga(T851, T853)) → U85_GA(T851, X1433, e111_in_aa(T853, X1433))
U84_GA(T851, X1433, t234_out_ga(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_GA(T861, X1455) → U87_GA(T861, X1455, n32_in_ga(T861, X1454))
T87_IN_GA(T861, X1455) → N32_IN_GA(T861, X1454)
T87_IN_GA(T861, X1455) → U88_GA(T861, X1455, n32_in_ga(T861, T865))
U88_GA(T861, X1455, n32_out_ga(T861, T865)) → U89_GA(T861, X1455, t87_in_aa(T865, X1455))
U88_GA(T861, X1455, n32_out_ga(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_GA(T873, X1476) → U91_GA(T873, X1476, t234_in_ga(T873, X1475))
E82_IN_GA(T873, X1476) → T234_IN_GA(T873, X1475)
E82_IN_GA(T873, X1476) → U92_GA(T873, X1476, t234_in_ga(T873, T875))
U92_GA(T873, X1476, t234_out_ga(T873, T875)) → U93_GA(T873, X1476, e82_in_aa(T875, X1476))
U92_GA(T873, X1476, t234_out_ga(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_GA(T883, X1498) → U95_GA(T883, X1498, n32_in_ga(T883, X1497))
T58_IN_GA(T883, X1498) → N32_IN_GA(T883, X1497)
T58_IN_GA(T883, X1498) → U96_GA(T883, X1498, n32_in_ga(T883, T887))
U96_GA(T883, X1498, n32_out_ga(T883, T887)) → U97_GA(T883, X1498, t58_in_aa(T887, X1498))
U96_GA(T883, X1498, n32_out_ga(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_GA(T895, X1519) → U99_GA(T895, X1519, t234_in_ga(T895, X1518))
E53_IN_GA(T895, X1519) → T234_IN_GA(T895, X1518)
E53_IN_GA(T895, X1519) → U100_GA(T895, X1519, t234_in_ga(T895, T897))
U100_GA(T895, X1519, t234_out_ga(T895, T897)) → U101_GA(T895, X1519, e53_in_aa(T897, X1519))
U100_GA(T895, X1519, t234_out_ga(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_GAA(T62, T916, T918) → U104_GAA(T62, T916, T918, n32_in_ga(T62, T916))
U104_GAA(T62, T916, T918, n32_out_ga(T62, T916)) → U105_GAA(T62, T916, T918, n7_in_aa(T916, T918))
U104_GAA(T62, T916, T918, n32_out_ga(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_GAA(T62, T929, T931) → U106_GAA(T62, T929, T931, n32_in_ga(T62, T929))
U106_GAA(T62, T929, T931, n32_out_ga(T62, T929)) → U107_GAA(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U106_GAA(T62, T929, T931, n32_out_ga(T62, T929)) → P31_IN_AAA(T929, X1556, T931)

The TRS R consists of the following rules:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x3)
U109_ga(x1, x2, x3)  =  U109_ga(x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga
U1_ga(x1, x2, x3)  =  U1_ga(x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga
U94_ga(x1, x2, x3)  =  U94_ga(x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga
U86_ga(x1, x2, x3)  =  U86_ga(x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga
U78_ga(x1, x2, x3)  =  U78_ga(x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga
U70_ga(x1, x2, x3)  =  U70_ga(x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga
U62_ga(x1, x2, x3)  =  U62_ga(x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U110_ga(x1, x2, x3)  =  U110_ga(x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga
U14_ga(x1, x2, x3)  =  U14_ga(x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga
U54_ga(x1, x2, x3)  =  U54_ga(x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga
U46_ga(x1, x2, x3)  =  U46_ga(x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga
U38_ga(x1, x2, x3)  =  U38_ga(x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga
U30_ga(x1, x2, x3)  =  U30_ga(x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga
U22_ga(x1, x2, x3)  =  U22_ga(x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U111_ga(x1, x2, x3)  =  U111_ga(x3)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U112_ga(x1, x2, x3)  =  U112_ga(x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
e404_out_ga(x1, x2)  =  e404_out_ga
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
e375_out_ga(x1, x2)  =  e375_out_ga
U27_ga(x1, x2, x3)  =  U27_ga(x3)
U28_ga(x1, x2, x3)  =  U28_ga(x3)
U29_ga(x1, x2, x3)  =  U29_ga(x3)
U31_ga(x1, x2, x3)  =  U31_ga(x3)
U32_ga(x1, x2, x3)  =  U32_ga(x3)
U33_ga(x1, x2, x3)  =  U33_ga(x3)
e346_out_ga(x1, x2)  =  e346_out_ga
U35_ga(x1, x2, x3)  =  U35_ga(x3)
U36_ga(x1, x2, x3)  =  U36_ga(x3)
U37_ga(x1, x2, x3)  =  U37_ga(x3)
U39_ga(x1, x2, x3)  =  U39_ga(x3)
U40_ga(x1, x2, x3)  =  U40_ga(x3)
U41_ga(x1, x2, x3)  =  U41_ga(x3)
e317_out_ga(x1, x2)  =  e317_out_ga
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U49_ga(x1, x2, x3)  =  U49_ga(x3)
e288_out_ga(x1, x2)  =  e288_out_ga
U51_ga(x1, x2, x3)  =  U51_ga(x3)
U52_ga(x1, x2, x3)  =  U52_ga(x3)
U53_ga(x1, x2, x3)  =  U53_ga(x3)
U55_ga(x1, x2, x3)  =  U55_ga(x3)
U56_ga(x1, x2, x3)  =  U56_ga(x3)
U57_ga(x1, x2, x3)  =  U57_ga(x3)
e259_out_ga(x1, x2)  =  e259_out_ga
U59_ga(x1, x2, x3)  =  U59_ga(x3)
U60_ga(x1, x2, x3)  =  U60_ga(x3)
U61_ga(x1, x2, x3)  =  U61_ga(x3)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
e198_out_ga(x1, x2)  =  e198_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U63_ga(x1, x2, x3)  =  U63_ga(x3)
U64_ga(x1, x2, x3)  =  U64_ga(x3)
U65_ga(x1, x2, x3)  =  U65_ga(x3)
e169_out_ga(x1, x2)  =  e169_out_ga
U67_ga(x1, x2, x3)  =  U67_ga(x3)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
U69_ga(x1, x2, x3)  =  U69_ga(x3)
U71_ga(x1, x2, x3)  =  U71_ga(x3)
U72_ga(x1, x2, x3)  =  U72_ga(x3)
U73_ga(x1, x2, x3)  =  U73_ga(x3)
e140_out_ga(x1, x2)  =  e140_out_ga
U75_ga(x1, x2, x3)  =  U75_ga(x3)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
U77_ga(x1, x2, x3)  =  U77_ga(x3)
U79_ga(x1, x2, x3)  =  U79_ga(x3)
U80_ga(x1, x2, x3)  =  U80_ga(x3)
U81_ga(x1, x2, x3)  =  U81_ga(x3)
e111_out_ga(x1, x2)  =  e111_out_ga
U83_ga(x1, x2, x3)  =  U83_ga(x3)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
U85_ga(x1, x2, x3)  =  U85_ga(x3)
U87_ga(x1, x2, x3)  =  U87_ga(x3)
U88_ga(x1, x2, x3)  =  U88_ga(x3)
U89_ga(x1, x2, x3)  =  U89_ga(x3)
e82_out_ga(x1, x2)  =  e82_out_ga
U91_ga(x1, x2, x3)  =  U91_ga(x3)
U92_ga(x1, x2, x3)  =  U92_ga(x3)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
U95_ga(x1, x2, x3)  =  U95_ga(x3)
U96_ga(x1, x2, x3)  =  U96_ga(x3)
U97_ga(x1, x2, x3)  =  U97_ga(x3)
e53_out_ga(x1, x2)  =  e53_out_ga
U99_ga(x1, x2, x3)  =  U99_ga(x3)
U100_ga(x1, x2, x3)  =  U100_ga(x3)
U101_ga(x1, x2, x3)  =  U101_ga(x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x4)
E1_IN_GA(x1, x2)  =  E1_IN_GA(x1)
U108_GA(x1, x2, x3)  =  U108_GA(x3)
N7_IN_GA(x1, x2)  =  N7_IN_GA(x1)
U102_GA(x1, x2, x3)  =  U102_GA(x3)
U109_GA(x1, x2, x3)  =  U109_GA(x3)
P31_IN_GAA(x1, x2, x3)  =  P31_IN_GAA(x1)
U103_GAA(x1, x2, x3, x4)  =  U103_GAA(x4)
N32_IN_GA(x1, x2)  =  N32_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x3)
E53_IN_GA(x1, x2)  =  E53_IN_GA(x1)
U98_GA(x1, x2, x3)  =  U98_GA(x3)
T58_IN_GA(x1, x2)  =  T58_IN_GA(x1)
U94_GA(x1, x2, x3)  =  U94_GA(x3)
E82_IN_GA(x1, x2)  =  E82_IN_GA(x1)
U90_GA(x1, x2, x3)  =  U90_GA(x3)
T87_IN_GA(x1, x2)  =  T87_IN_GA(x1)
U86_GA(x1, x2, x3)  =  U86_GA(x3)
E111_IN_GA(x1, x2)  =  E111_IN_GA(x1)
U82_GA(x1, x2, x3)  =  U82_GA(x3)
T116_IN_GA(x1, x2)  =  T116_IN_GA(x1)
U78_GA(x1, x2, x3)  =  U78_GA(x3)
E140_IN_GA(x1, x2)  =  E140_IN_GA(x1)
U74_GA(x1, x2, x3)  =  U74_GA(x3)
T145_IN_GA(x1, x2)  =  T145_IN_GA(x1)
U70_GA(x1, x2, x3)  =  U70_GA(x3)
E169_IN_GA(x1, x2)  =  E169_IN_GA(x1)
U66_GA(x1, x2, x3)  =  U66_GA(x3)
T174_IN_GA(x1, x2)  =  T174_IN_GA(x1)
U62_GA(x1, x2, x3)  =  U62_GA(x3)
E198_IN_GA(x1, x2)  =  E198_IN_GA(x1)
U6_GA(x1, x2, x3)  =  U6_GA(x3)
T203_IN_GA(x1, x2)  =  T203_IN_GA(x1)
U2_GA(x1, x2, x3)  =  U2_GA(x3)
U110_GA(x1, x2, x3)  =  U110_GA(x3)
T234_IN_GA(x1, x2)  =  T234_IN_GA(x1)
U14_GA(x1, x2, x3)  =  U14_GA(x3)
E259_IN_GA(x1, x2)  =  E259_IN_GA(x1)
U58_GA(x1, x2, x3)  =  U58_GA(x3)
T264_IN_GA(x1, x2)  =  T264_IN_GA(x1)
U54_GA(x1, x2, x3)  =  U54_GA(x3)
E288_IN_GA(x1, x2)  =  E288_IN_GA(x1)
U50_GA(x1, x2, x3)  =  U50_GA(x3)
T293_IN_GA(x1, x2)  =  T293_IN_GA(x1)
U46_GA(x1, x2, x3)  =  U46_GA(x3)
E317_IN_GA(x1, x2)  =  E317_IN_GA(x1)
U42_GA(x1, x2, x3)  =  U42_GA(x3)
T322_IN_GA(x1, x2)  =  T322_IN_GA(x1)
U38_GA(x1, x2, x3)  =  U38_GA(x3)
E346_IN_GA(x1, x2)  =  E346_IN_GA(x1)
U34_GA(x1, x2, x3)  =  U34_GA(x3)
T351_IN_GA(x1, x2)  =  T351_IN_GA(x1)
U30_GA(x1, x2, x3)  =  U30_GA(x3)
E375_IN_GA(x1, x2)  =  E375_IN_GA(x1)
U26_GA(x1, x2, x3)  =  U26_GA(x3)
T380_IN_GA(x1, x2)  =  T380_IN_GA(x1)
U22_GA(x1, x2, x3)  =  U22_GA(x3)
E404_IN_GA(x1, x2)  =  E404_IN_GA(x1)
U18_GA(x1, x2, x3)  =  U18_GA(x3)
T409_IN_GA(x1, x2)  =  T409_IN_GA(x1)
U10_GA(x1, x2, x3)  =  U10_GA(x3)
U111_GA(x1, x2, x3)  =  U111_GA(x3)
U15_GA(x1, x2, x3)  =  U15_GA(x3)
U16_GA(x1, x2, x3)  =  U16_GA(x3)
U17_GA(x1, x2, x3)  =  U17_GA(x3)
T234_IN_AA(x1, x2)  =  T234_IN_AA
U14_AA(x1, x2, x3)  =  U14_AA(x3)
E259_IN_AA(x1, x2)  =  E259_IN_AA
U58_AA(x1, x2, x3)  =  U58_AA(x3)
T264_IN_AA(x1, x2)  =  T264_IN_AA
U54_AA(x1, x2, x3)  =  U54_AA(x3)
E288_IN_AA(x1, x2)  =  E288_IN_AA
U50_AA(x1, x2, x3)  =  U50_AA(x3)
T293_IN_AA(x1, x2)  =  T293_IN_AA
U46_AA(x1, x2, x3)  =  U46_AA(x3)
E317_IN_AA(x1, x2)  =  E317_IN_AA
U42_AA(x1, x2, x3)  =  U42_AA(x3)
T322_IN_AA(x1, x2)  =  T322_IN_AA
U38_AA(x1, x2, x3)  =  U38_AA(x3)
E346_IN_AA(x1, x2)  =  E346_IN_AA
U34_AA(x1, x2, x3)  =  U34_AA(x3)
T351_IN_AA(x1, x2)  =  T351_IN_AA
U30_AA(x1, x2, x3)  =  U30_AA(x3)
E375_IN_AA(x1, x2)  =  E375_IN_AA
U26_AA(x1, x2, x3)  =  U26_AA(x3)
T380_IN_AA(x1, x2)  =  T380_IN_AA
U22_AA(x1, x2, x3)  =  U22_AA(x3)
E404_IN_AA(x1, x2)  =  E404_IN_AA
U18_AA(x1, x2, x3)  =  U18_AA(x3)
T409_IN_AA(x1, x2)  =  T409_IN_AA
U10_AA(x1, x2, x3)  =  U10_AA(x3)
E1_IN_AA(x1, x2)  =  E1_IN_AA
U108_AA(x1, x2, x3)  =  U108_AA(x3)
N7_IN_AA(x1, x2)  =  N7_IN_AA
U102_AA(x1, x2, x3)  =  U102_AA(x3)
U109_AA(x1, x2, x3)  =  U109_AA(x3)
P31_IN_AAA(x1, x2, x3)  =  P31_IN_AAA
U103_AAA(x1, x2, x3, x4)  =  U103_AAA(x4)
N32_IN_AA(x1, x2)  =  N32_IN_AA
U1_AA(x1, x2, x3)  =  U1_AA(x3)
E53_IN_AA(x1, x2)  =  E53_IN_AA
U98_AA(x1, x2, x3)  =  U98_AA(x3)
T58_IN_AA(x1, x2)  =  T58_IN_AA
U94_AA(x1, x2, x3)  =  U94_AA(x3)
E82_IN_AA(x1, x2)  =  E82_IN_AA
U90_AA(x1, x2, x3)  =  U90_AA(x3)
T87_IN_AA(x1, x2)  =  T87_IN_AA
U86_AA(x1, x2, x3)  =  U86_AA(x3)
E111_IN_AA(x1, x2)  =  E111_IN_AA
U82_AA(x1, x2, x3)  =  U82_AA(x3)
T116_IN_AA(x1, x2)  =  T116_IN_AA
U78_AA(x1, x2, x3)  =  U78_AA(x3)
E140_IN_AA(x1, x2)  =  E140_IN_AA
U74_AA(x1, x2, x3)  =  U74_AA(x3)
T145_IN_AA(x1, x2)  =  T145_IN_AA
U70_AA(x1, x2, x3)  =  U70_AA(x3)
E169_IN_AA(x1, x2)  =  E169_IN_AA
U66_AA(x1, x2, x3)  =  U66_AA(x3)
T174_IN_AA(x1, x2)  =  T174_IN_AA
U62_AA(x1, x2, x3)  =  U62_AA(x3)
E198_IN_AA(x1, x2)  =  E198_IN_AA
U6_AA(x1, x2, x3)  =  U6_AA(x3)
T203_IN_AA(x1, x2)  =  T203_IN_AA
U2_AA(x1, x2, x3)  =  U2_AA(x3)
U110_AA(x1, x2, x3)  =  U110_AA(x3)
U15_AA(x1, x2, x3)  =  U15_AA(x3)
U16_AA(x1, x2, x3)  =  U16_AA(x3)
U17_AA(x1, x2, x3)  =  U17_AA(x3)
U111_AA(x1, x2, x3)  =  U111_AA(x3)
U112_AA(x1, x2, x3)  =  U112_AA(x3)
U3_AA(x1, x2, x3)  =  U3_AA(x3)
U4_AA(x1, x2, x3)  =  U4_AA(x3)
U5_AA(x1, x2, x3)  =  U5_AA(x3)
U7_AA(x1, x2, x3)  =  U7_AA(x3)
U8_AA(x1, x2, x3)  =  U8_AA(x3)
U9_AA(x1, x2, x3)  =  U9_AA(x3)
U63_AA(x1, x2, x3)  =  U63_AA(x3)
U64_AA(x1, x2, x3)  =  U64_AA(x3)
U65_AA(x1, x2, x3)  =  U65_AA(x3)
U67_AA(x1, x2, x3)  =  U67_AA(x3)
U68_AA(x1, x2, x3)  =  U68_AA(x3)
U69_AA(x1, x2, x3)  =  U69_AA(x3)
U71_AA(x1, x2, x3)  =  U71_AA(x3)
U72_AA(x1, x2, x3)  =  U72_AA(x3)
U73_AA(x1, x2, x3)  =  U73_AA(x3)
U75_AA(x1, x2, x3)  =  U75_AA(x3)
U76_AA(x1, x2, x3)  =  U76_AA(x3)
U77_AA(x1, x2, x3)  =  U77_AA(x3)
U79_AA(x1, x2, x3)  =  U79_AA(x3)
U80_AA(x1, x2, x3)  =  U80_AA(x3)
U81_AA(x1, x2, x3)  =  U81_AA(x3)
U83_AA(x1, x2, x3)  =  U83_AA(x3)
U84_AA(x1, x2, x3)  =  U84_AA(x3)
U85_AA(x1, x2, x3)  =  U85_AA(x3)
U87_AA(x1, x2, x3)  =  U87_AA(x3)
U88_AA(x1, x2, x3)  =  U88_AA(x3)
U89_AA(x1, x2, x3)  =  U89_AA(x3)
U91_AA(x1, x2, x3)  =  U91_AA(x3)
U92_AA(x1, x2, x3)  =  U92_AA(x3)
U93_AA(x1, x2, x3)  =  U93_AA(x3)
U95_AA(x1, x2, x3)  =  U95_AA(x3)
U96_AA(x1, x2, x3)  =  U96_AA(x3)
U97_AA(x1, x2, x3)  =  U97_AA(x3)
U99_AA(x1, x2, x3)  =  U99_AA(x3)
U100_AA(x1, x2, x3)  =  U100_AA(x3)
U101_AA(x1, x2, x3)  =  U101_AA(x3)
U104_AAA(x1, x2, x3, x4)  =  U104_AAA(x4)
U105_AAA(x1, x2, x3, x4)  =  U105_AAA(x4)
U106_AAA(x1, x2, x3, x4)  =  U106_AAA(x4)
U107_AAA(x1, x2, x3, x4)  =  U107_AAA(x4)
U11_AA(x1, x2, x3)  =  U11_AA(x3)
U12_AA(x1, x2, x3)  =  U12_AA(x3)
U13_AA(x1, x2, x3)  =  U13_AA(x3)
U19_AA(x1, x2, x3)  =  U19_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U23_AA(x1, x2, x3)  =  U23_AA(x3)
U24_AA(x1, x2, x3)  =  U24_AA(x3)
U25_AA(x1, x2, x3)  =  U25_AA(x3)
U27_AA(x1, x2, x3)  =  U27_AA(x3)
U28_AA(x1, x2, x3)  =  U28_AA(x3)
U29_AA(x1, x2, x3)  =  U29_AA(x3)
U31_AA(x1, x2, x3)  =  U31_AA(x3)
U32_AA(x1, x2, x3)  =  U32_AA(x3)
U33_AA(x1, x2, x3)  =  U33_AA(x3)
U35_AA(x1, x2, x3)  =  U35_AA(x3)
U36_AA(x1, x2, x3)  =  U36_AA(x3)
U37_AA(x1, x2, x3)  =  U37_AA(x3)
U39_AA(x1, x2, x3)  =  U39_AA(x3)
U40_AA(x1, x2, x3)  =  U40_AA(x3)
U41_AA(x1, x2, x3)  =  U41_AA(x3)
U43_AA(x1, x2, x3)  =  U43_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U45_AA(x1, x2, x3)  =  U45_AA(x3)
U47_AA(x1, x2, x3)  =  U47_AA(x3)
U48_AA(x1, x2, x3)  =  U48_AA(x3)
U49_AA(x1, x2, x3)  =  U49_AA(x3)
U51_AA(x1, x2, x3)  =  U51_AA(x3)
U52_AA(x1, x2, x3)  =  U52_AA(x3)
U53_AA(x1, x2, x3)  =  U53_AA(x3)
U55_AA(x1, x2, x3)  =  U55_AA(x3)
U56_AA(x1, x2, x3)  =  U56_AA(x3)
U57_AA(x1, x2, x3)  =  U57_AA(x3)
U59_AA(x1, x2, x3)  =  U59_AA(x3)
U60_AA(x1, x2, x3)  =  U60_AA(x3)
U61_AA(x1, x2, x3)  =  U61_AA(x3)
U112_GA(x1, x2, x3)  =  U112_GA(x3)
U11_GA(x1, x2, x3)  =  U11_GA(x3)
U12_GA(x1, x2, x3)  =  U12_GA(x3)
U13_GA(x1, x2, x3)  =  U13_GA(x3)
U19_GA(x1, x2, x3)  =  U19_GA(x3)
U20_GA(x1, x2, x3)  =  U20_GA(x3)
U21_GA(x1, x2, x3)  =  U21_GA(x3)
U23_GA(x1, x2, x3)  =  U23_GA(x3)
U24_GA(x1, x2, x3)  =  U24_GA(x3)
U25_GA(x1, x2, x3)  =  U25_GA(x3)
U27_GA(x1, x2, x3)  =  U27_GA(x3)
U28_GA(x1, x2, x3)  =  U28_GA(x3)
U29_GA(x1, x2, x3)  =  U29_GA(x3)
U31_GA(x1, x2, x3)  =  U31_GA(x3)
U32_GA(x1, x2, x3)  =  U32_GA(x3)
U33_GA(x1, x2, x3)  =  U33_GA(x3)
U35_GA(x1, x2, x3)  =  U35_GA(x3)
U36_GA(x1, x2, x3)  =  U36_GA(x3)
U37_GA(x1, x2, x3)  =  U37_GA(x3)
U39_GA(x1, x2, x3)  =  U39_GA(x3)
U40_GA(x1, x2, x3)  =  U40_GA(x3)
U41_GA(x1, x2, x3)  =  U41_GA(x3)
U43_GA(x1, x2, x3)  =  U43_GA(x3)
U44_GA(x1, x2, x3)  =  U44_GA(x3)
U45_GA(x1, x2, x3)  =  U45_GA(x3)
U47_GA(x1, x2, x3)  =  U47_GA(x3)
U48_GA(x1, x2, x3)  =  U48_GA(x3)
U49_GA(x1, x2, x3)  =  U49_GA(x3)
U51_GA(x1, x2, x3)  =  U51_GA(x3)
U52_GA(x1, x2, x3)  =  U52_GA(x3)
U53_GA(x1, x2, x3)  =  U53_GA(x3)
U55_GA(x1, x2, x3)  =  U55_GA(x3)
U56_GA(x1, x2, x3)  =  U56_GA(x3)
U57_GA(x1, x2, x3)  =  U57_GA(x3)
U59_GA(x1, x2, x3)  =  U59_GA(x3)
U60_GA(x1, x2, x3)  =  U60_GA(x3)
U61_GA(x1, x2, x3)  =  U61_GA(x3)
U3_GA(x1, x2, x3)  =  U3_GA(x3)
U4_GA(x1, x2, x3)  =  U4_GA(x3)
U5_GA(x1, x2, x3)  =  U5_GA(x3)
U7_GA(x1, x2, x3)  =  U7_GA(x3)
U8_GA(x1, x2, x3)  =  U8_GA(x3)
U9_GA(x1, x2, x3)  =  U9_GA(x3)
U63_GA(x1, x2, x3)  =  U63_GA(x3)
U64_GA(x1, x2, x3)  =  U64_GA(x3)
U65_GA(x1, x2, x3)  =  U65_GA(x3)
U67_GA(x1, x2, x3)  =  U67_GA(x3)
U68_GA(x1, x2, x3)  =  U68_GA(x3)
U69_GA(x1, x2, x3)  =  U69_GA(x3)
U71_GA(x1, x2, x3)  =  U71_GA(x3)
U72_GA(x1, x2, x3)  =  U72_GA(x3)
U73_GA(x1, x2, x3)  =  U73_GA(x3)
U75_GA(x1, x2, x3)  =  U75_GA(x3)
U76_GA(x1, x2, x3)  =  U76_GA(x3)
U77_GA(x1, x2, x3)  =  U77_GA(x3)
U79_GA(x1, x2, x3)  =  U79_GA(x3)
U80_GA(x1, x2, x3)  =  U80_GA(x3)
U81_GA(x1, x2, x3)  =  U81_GA(x3)
U83_GA(x1, x2, x3)  =  U83_GA(x3)
U84_GA(x1, x2, x3)  =  U84_GA(x3)
U85_GA(x1, x2, x3)  =  U85_GA(x3)
U87_GA(x1, x2, x3)  =  U87_GA(x3)
U88_GA(x1, x2, x3)  =  U88_GA(x3)
U89_GA(x1, x2, x3)  =  U89_GA(x3)
U91_GA(x1, x2, x3)  =  U91_GA(x3)
U92_GA(x1, x2, x3)  =  U92_GA(x3)
U93_GA(x1, x2, x3)  =  U93_GA(x3)
U95_GA(x1, x2, x3)  =  U95_GA(x3)
U96_GA(x1, x2, x3)  =  U96_GA(x3)
U97_GA(x1, x2, x3)  =  U97_GA(x3)
U99_GA(x1, x2, x3)  =  U99_GA(x3)
U100_GA(x1, x2, x3)  =  U100_GA(x3)
U101_GA(x1, x2, x3)  =  U101_GA(x3)
U104_GAA(x1, x2, x3, x4)  =  U104_GAA(x4)
U105_GAA(x1, x2, x3, x4)  =  U105_GAA(x4)
U106_GAA(x1, x2, x3, x4)  =  U106_GAA(x4)
U107_GAA(x1, x2, x3, x4)  =  U107_GAA(x4)

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

(76) Obligation:

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

E1_IN_GA(T22, T24) → U108_GA(T22, T24, n7_in_ga(T22, T24))
E1_IN_GA(T22, T24) → N7_IN_GA(T22, T24)
N7_IN_GA(.(lbrace, T41), T43) → U102_GA(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
N7_IN_GA(.(lbrace, T41), T43) → E1_IN_GA(T41, .(rbrace, T43))
E1_IN_GA(T62, T64) → U109_GA(T62, T64, p31_in_gaa(T62, X59, T64))
E1_IN_GA(T62, T64) → P31_IN_GAA(T62, X59, T64)
P31_IN_GAA(T62, X59, T64) → U103_GAA(T62, X59, T64, n32_in_ga(T62, X59))
P31_IN_GAA(T62, X59, T64) → N32_IN_GA(T62, X59)
N32_IN_GA(.(lbrace, T89), X84) → U1_GA(T89, X84, e53_in_ga(T89, X84))
N32_IN_GA(.(lbrace, T89), X84) → E53_IN_GA(T89, X84)
E53_IN_GA(T97, X110) → U98_GA(T97, X110, t58_in_ga(T97, X110))
E53_IN_GA(T97, X110) → T58_IN_GA(T97, X110)
T58_IN_GA(.(lbrace, T130), X155) → U94_GA(T130, X155, e82_in_ga(T130, X155))
T58_IN_GA(.(lbrace, T130), X155) → E82_IN_GA(T130, X155)
E82_IN_GA(T138, X181) → U90_GA(T138, X181, t87_in_ga(T138, X181))
E82_IN_GA(T138, X181) → T87_IN_GA(T138, X181)
T87_IN_GA(.(lbrace, T171), X226) → U86_GA(T171, X226, e111_in_ga(T171, X226))
T87_IN_GA(.(lbrace, T171), X226) → E111_IN_GA(T171, X226)
E111_IN_GA(T179, X252) → U82_GA(T179, X252, t116_in_ga(T179, X252))
E111_IN_GA(T179, X252) → T116_IN_GA(T179, X252)
T116_IN_GA(.(lbrace, T212), X297) → U78_GA(T212, X297, e140_in_ga(T212, X297))
T116_IN_GA(.(lbrace, T212), X297) → E140_IN_GA(T212, X297)
E140_IN_GA(T220, X323) → U74_GA(T220, X323, t145_in_ga(T220, X323))
E140_IN_GA(T220, X323) → T145_IN_GA(T220, X323)
T145_IN_GA(.(lbrace, T253), X368) → U70_GA(T253, X368, e169_in_ga(T253, X368))
T145_IN_GA(.(lbrace, T253), X368) → E169_IN_GA(T253, X368)
E169_IN_GA(T261, X394) → U66_GA(T261, X394, t174_in_ga(T261, X394))
E169_IN_GA(T261, X394) → T174_IN_GA(T261, X394)
T174_IN_GA(.(lbrace, T294), X439) → U62_GA(T294, X439, e198_in_ga(T294, X439))
T174_IN_GA(.(lbrace, T294), X439) → E198_IN_GA(T294, X439)
E198_IN_GA(T302, X465) → U6_GA(T302, X465, t203_in_ga(T302, X465))
E198_IN_GA(T302, X465) → T203_IN_GA(T302, X465)
T203_IN_GA(.(lbrace, T335), X510) → U2_GA(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
T203_IN_GA(.(lbrace, T335), X510) → E1_IN_GA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_GA(T941, T943) → U110_GA(T941, T943, t234_in_ga(T941, X1569))
E1_IN_GA(T941, T943) → T234_IN_GA(T941, X1569)
T234_IN_GA(.(lbrace, T392), X599) → U14_GA(T392, X599, e259_in_ga(T392, X599))
T234_IN_GA(.(lbrace, T392), X599) → E259_IN_GA(T392, X599)
E259_IN_GA(T400, X625) → U58_GA(T400, X625, t264_in_ga(T400, X625))
E259_IN_GA(T400, X625) → T264_IN_GA(T400, X625)
T264_IN_GA(.(lbrace, T433), X670) → U54_GA(T433, X670, e288_in_ga(T433, X670))
T264_IN_GA(.(lbrace, T433), X670) → E288_IN_GA(T433, X670)
E288_IN_GA(T441, X696) → U50_GA(T441, X696, t293_in_ga(T441, X696))
E288_IN_GA(T441, X696) → T293_IN_GA(T441, X696)
T293_IN_GA(.(lbrace, T474), X741) → U46_GA(T474, X741, e317_in_ga(T474, X741))
T293_IN_GA(.(lbrace, T474), X741) → E317_IN_GA(T474, X741)
E317_IN_GA(T482, X767) → U42_GA(T482, X767, t322_in_ga(T482, X767))
E317_IN_GA(T482, X767) → T322_IN_GA(T482, X767)
T322_IN_GA(.(lbrace, T515), X812) → U38_GA(T515, X812, e346_in_ga(T515, X812))
T322_IN_GA(.(lbrace, T515), X812) → E346_IN_GA(T515, X812)
E346_IN_GA(T523, X838) → U34_GA(T523, X838, t351_in_ga(T523, X838))
E346_IN_GA(T523, X838) → T351_IN_GA(T523, X838)
T351_IN_GA(.(lbrace, T556), X883) → U30_GA(T556, X883, e375_in_ga(T556, X883))
T351_IN_GA(.(lbrace, T556), X883) → E375_IN_GA(T556, X883)
E375_IN_GA(T564, X909) → U26_GA(T564, X909, t380_in_ga(T564, X909))
E375_IN_GA(T564, X909) → T380_IN_GA(T564, X909)
T380_IN_GA(.(lbrace, T597), X954) → U22_GA(T597, X954, e404_in_ga(T597, X954))
T380_IN_GA(.(lbrace, T597), X954) → E404_IN_GA(T597, X954)
E404_IN_GA(T605, X980) → U18_GA(T605, X980, t409_in_ga(T605, X980))
E404_IN_GA(T605, X980) → T409_IN_GA(T605, X980)
T409_IN_GA(.(lbrace, T638), X1025) → U10_GA(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
T409_IN_GA(.(lbrace, T638), X1025) → E1_IN_GA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_GA(T941, T943) → U111_GA(T941, T943, t234_in_ga(T941, T945))
T234_IN_GA(T780, X1303) → U15_GA(T780, X1303, n32_in_ga(T780, X1302))
T234_IN_GA(T780, X1303) → N32_IN_GA(T780, X1302)
T234_IN_GA(T780, X1303) → U16_GA(T780, X1303, n32_in_ga(T780, T784))
U16_GA(T780, X1303, n32_out_ga(T780, T784)) → U17_GA(T780, X1303, t234_in_aa(T784, X1303))
U16_GA(T780, X1303, n32_out_ga(T780, T784)) → T234_IN_AA(T784, X1303)
T234_IN_AA(.(lbrace, T392), X599) → U14_AA(T392, X599, e259_in_aa(T392, X599))
T234_IN_AA(.(lbrace, T392), X599) → E259_IN_AA(T392, X599)
E259_IN_AA(T400, X625) → U58_AA(T400, X625, t264_in_aa(T400, X625))
E259_IN_AA(T400, X625) → T264_IN_AA(T400, X625)
T264_IN_AA(.(lbrace, T433), X670) → U54_AA(T433, X670, e288_in_aa(T433, X670))
T264_IN_AA(.(lbrace, T433), X670) → E288_IN_AA(T433, X670)
E288_IN_AA(T441, X696) → U50_AA(T441, X696, t293_in_aa(T441, X696))
E288_IN_AA(T441, X696) → T293_IN_AA(T441, X696)
T293_IN_AA(.(lbrace, T474), X741) → U46_AA(T474, X741, e317_in_aa(T474, X741))
T293_IN_AA(.(lbrace, T474), X741) → E317_IN_AA(T474, X741)
E317_IN_AA(T482, X767) → U42_AA(T482, X767, t322_in_aa(T482, X767))
E317_IN_AA(T482, X767) → T322_IN_AA(T482, X767)
T322_IN_AA(.(lbrace, T515), X812) → U38_AA(T515, X812, e346_in_aa(T515, X812))
T322_IN_AA(.(lbrace, T515), X812) → E346_IN_AA(T515, X812)
E346_IN_AA(T523, X838) → U34_AA(T523, X838, t351_in_aa(T523, X838))
E346_IN_AA(T523, X838) → T351_IN_AA(T523, X838)
T351_IN_AA(.(lbrace, T556), X883) → U30_AA(T556, X883, e375_in_aa(T556, X883))
T351_IN_AA(.(lbrace, T556), X883) → E375_IN_AA(T556, X883)
E375_IN_AA(T564, X909) → U26_AA(T564, X909, t380_in_aa(T564, X909))
E375_IN_AA(T564, X909) → T380_IN_AA(T564, X909)
T380_IN_AA(.(lbrace, T597), X954) → U22_AA(T597, X954, e404_in_aa(T597, X954))
T380_IN_AA(.(lbrace, T597), X954) → E404_IN_AA(T597, X954)
E404_IN_AA(T605, X980) → U18_AA(T605, X980, t409_in_aa(T605, X980))
E404_IN_AA(T605, X980) → T409_IN_AA(T605, X980)
T409_IN_AA(.(lbrace, T638), X1025) → U10_AA(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
T409_IN_AA(.(lbrace, T638), X1025) → E1_IN_AA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_AA(T22, T24) → U108_AA(T22, T24, n7_in_aa(T22, T24))
E1_IN_AA(T22, T24) → N7_IN_AA(T22, T24)
N7_IN_AA(.(lbrace, T41), T43) → U102_AA(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
N7_IN_AA(.(lbrace, T41), T43) → E1_IN_AA(T41, .(rbrace, T43))
E1_IN_AA(T62, T64) → U109_AA(T62, T64, p31_in_aaa(T62, X59, T64))
E1_IN_AA(T62, T64) → P31_IN_AAA(T62, X59, T64)
P31_IN_AAA(T62, X59, T64) → U103_AAA(T62, X59, T64, n32_in_aa(T62, X59))
P31_IN_AAA(T62, X59, T64) → N32_IN_AA(T62, X59)
N32_IN_AA(.(lbrace, T89), X84) → U1_AA(T89, X84, e53_in_aa(T89, X84))
N32_IN_AA(.(lbrace, T89), X84) → E53_IN_AA(T89, X84)
E53_IN_AA(T97, X110) → U98_AA(T97, X110, t58_in_aa(T97, X110))
E53_IN_AA(T97, X110) → T58_IN_AA(T97, X110)
T58_IN_AA(.(lbrace, T130), X155) → U94_AA(T130, X155, e82_in_aa(T130, X155))
T58_IN_AA(.(lbrace, T130), X155) → E82_IN_AA(T130, X155)
E82_IN_AA(T138, X181) → U90_AA(T138, X181, t87_in_aa(T138, X181))
E82_IN_AA(T138, X181) → T87_IN_AA(T138, X181)
T87_IN_AA(.(lbrace, T171), X226) → U86_AA(T171, X226, e111_in_aa(T171, X226))
T87_IN_AA(.(lbrace, T171), X226) → E111_IN_AA(T171, X226)
E111_IN_AA(T179, X252) → U82_AA(T179, X252, t116_in_aa(T179, X252))
E111_IN_AA(T179, X252) → T116_IN_AA(T179, X252)
T116_IN_AA(.(lbrace, T212), X297) → U78_AA(T212, X297, e140_in_aa(T212, X297))
T116_IN_AA(.(lbrace, T212), X297) → E140_IN_AA(T212, X297)
E140_IN_AA(T220, X323) → U74_AA(T220, X323, t145_in_aa(T220, X323))
E140_IN_AA(T220, X323) → T145_IN_AA(T220, X323)
T145_IN_AA(.(lbrace, T253), X368) → U70_AA(T253, X368, e169_in_aa(T253, X368))
T145_IN_AA(.(lbrace, T253), X368) → E169_IN_AA(T253, X368)
E169_IN_AA(T261, X394) → U66_AA(T261, X394, t174_in_aa(T261, X394))
E169_IN_AA(T261, X394) → T174_IN_AA(T261, X394)
T174_IN_AA(.(lbrace, T294), X439) → U62_AA(T294, X439, e198_in_aa(T294, X439))
T174_IN_AA(.(lbrace, T294), X439) → E198_IN_AA(T294, X439)
E198_IN_AA(T302, X465) → U6_AA(T302, X465, t203_in_aa(T302, X465))
E198_IN_AA(T302, X465) → T203_IN_AA(T302, X465)
T203_IN_AA(.(lbrace, T335), X510) → U2_AA(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
T203_IN_AA(.(lbrace, T335), X510) → E1_IN_AA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_AA(T941, T943) → U110_AA(T941, T943, t234_in_aa(T941, X1569))
E1_IN_AA(T941, T943) → T234_IN_AA(T941, X1569)
T234_IN_AA(T780, X1303) → U15_AA(T780, X1303, n32_in_aa(T780, X1302))
T234_IN_AA(T780, X1303) → N32_IN_AA(T780, X1302)
T234_IN_AA(T780, X1303) → U16_AA(T780, X1303, n32_in_aa(T780, T784))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → U17_AA(T780, X1303, t234_in_aa(T784, X1303))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → T234_IN_AA(T784, X1303)
E1_IN_AA(T941, T943) → U111_AA(T941, T943, t234_in_aa(T941, T945))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → U112_AA(T941, T943, e1_in_aa(T945, T943))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → E1_IN_AA(T945, T943)
T203_IN_AA(T345, X530) → U3_AA(T345, X530, n32_in_aa(T345, X529))
T203_IN_AA(T345, X530) → N32_IN_AA(T345, X529)
T203_IN_AA(T345, X530) → U4_AA(T345, X530, n32_in_aa(T345, T349))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → U5_AA(T345, X530, t203_in_aa(T349, X530))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_AA(T357, X551) → U7_AA(T357, X551, t234_in_aa(T357, X550))
E198_IN_AA(T357, X551) → T234_IN_AA(T357, X550)
E198_IN_AA(T357, X551) → U8_AA(T357, X551, t234_in_aa(T357, T359))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → U9_AA(T357, X551, e198_in_aa(T359, X551))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_AA(T795, X1326) → U63_AA(T795, X1326, n32_in_aa(T795, X1325))
T174_IN_AA(T795, X1326) → N32_IN_AA(T795, X1325)
T174_IN_AA(T795, X1326) → U64_AA(T795, X1326, n32_in_aa(T795, T799))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → U65_AA(T795, X1326, t174_in_aa(T799, X1326))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_AA(T807, X1347) → U67_AA(T807, X1347, t234_in_aa(T807, X1346))
E169_IN_AA(T807, X1347) → T234_IN_AA(T807, X1346)
E169_IN_AA(T807, X1347) → U68_AA(T807, X1347, t234_in_aa(T807, T809))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → U69_AA(T807, X1347, e169_in_aa(T809, X1347))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_AA(T817, X1369) → U71_AA(T817, X1369, n32_in_aa(T817, X1368))
T145_IN_AA(T817, X1369) → N32_IN_AA(T817, X1368)
T145_IN_AA(T817, X1369) → U72_AA(T817, X1369, n32_in_aa(T817, T821))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → U73_AA(T817, X1369, t145_in_aa(T821, X1369))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_AA(T829, X1390) → U75_AA(T829, X1390, t234_in_aa(T829, X1389))
E140_IN_AA(T829, X1390) → T234_IN_AA(T829, X1389)
E140_IN_AA(T829, X1390) → U76_AA(T829, X1390, t234_in_aa(T829, T831))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → U77_AA(T829, X1390, e140_in_aa(T831, X1390))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_AA(T839, X1412) → U79_AA(T839, X1412, n32_in_aa(T839, X1411))
T116_IN_AA(T839, X1412) → N32_IN_AA(T839, X1411)
T116_IN_AA(T839, X1412) → U80_AA(T839, X1412, n32_in_aa(T839, T843))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → U81_AA(T839, X1412, t116_in_aa(T843, X1412))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_AA(T851, X1433) → U83_AA(T851, X1433, t234_in_aa(T851, X1432))
E111_IN_AA(T851, X1433) → T234_IN_AA(T851, X1432)
E111_IN_AA(T851, X1433) → U84_AA(T851, X1433, t234_in_aa(T851, T853))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → U85_AA(T851, X1433, e111_in_aa(T853, X1433))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_AA(T861, X1455) → U87_AA(T861, X1455, n32_in_aa(T861, X1454))
T87_IN_AA(T861, X1455) → N32_IN_AA(T861, X1454)
T87_IN_AA(T861, X1455) → U88_AA(T861, X1455, n32_in_aa(T861, T865))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → U89_AA(T861, X1455, t87_in_aa(T865, X1455))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_AA(T873, X1476) → U91_AA(T873, X1476, t234_in_aa(T873, X1475))
E82_IN_AA(T873, X1476) → T234_IN_AA(T873, X1475)
E82_IN_AA(T873, X1476) → U92_AA(T873, X1476, t234_in_aa(T873, T875))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → U93_AA(T873, X1476, e82_in_aa(T875, X1476))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_AA(T883, X1498) → U95_AA(T883, X1498, n32_in_aa(T883, X1497))
T58_IN_AA(T883, X1498) → N32_IN_AA(T883, X1497)
T58_IN_AA(T883, X1498) → U96_AA(T883, X1498, n32_in_aa(T883, T887))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → U97_AA(T883, X1498, t58_in_aa(T887, X1498))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_AA(T895, X1519) → U99_AA(T895, X1519, t234_in_aa(T895, X1518))
E53_IN_AA(T895, X1519) → T234_IN_AA(T895, X1518)
E53_IN_AA(T895, X1519) → U100_AA(T895, X1519, t234_in_aa(T895, T897))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → U101_AA(T895, X1519, e53_in_aa(T897, X1519))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_AAA(T62, T916, T918) → U104_AAA(T62, T916, T918, n32_in_aa(T62, T916))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → U105_AAA(T62, T916, T918, n7_in_aa(T916, T918))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_AAA(T62, T929, T931) → U106_AAA(T62, T929, T931, n32_in_aa(T62, T929))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → U107_AAA(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → P31_IN_AAA(T929, X1556, T931)
T409_IN_AA(T648, X1045) → U11_AA(T648, X1045, n32_in_aa(T648, X1044))
T409_IN_AA(T648, X1045) → N32_IN_AA(T648, X1044)
T409_IN_AA(T648, X1045) → U12_AA(T648, X1045, n32_in_aa(T648, T652))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → U13_AA(T648, X1045, t409_in_aa(T652, X1045))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_AA(T660, X1066) → U19_AA(T660, X1066, t234_in_aa(T660, X1065))
E404_IN_AA(T660, X1066) → T234_IN_AA(T660, X1065)
E404_IN_AA(T660, X1066) → U20_AA(T660, X1066, t234_in_aa(T660, T662))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → U21_AA(T660, X1066, e404_in_aa(T662, X1066))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_AA(T670, X1088) → U23_AA(T670, X1088, n32_in_aa(T670, X1087))
T380_IN_AA(T670, X1088) → N32_IN_AA(T670, X1087)
T380_IN_AA(T670, X1088) → U24_AA(T670, X1088, n32_in_aa(T670, T674))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → U25_AA(T670, X1088, t380_in_aa(T674, X1088))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_AA(T682, X1109) → U27_AA(T682, X1109, t234_in_aa(T682, X1108))
E375_IN_AA(T682, X1109) → T234_IN_AA(T682, X1108)
E375_IN_AA(T682, X1109) → U28_AA(T682, X1109, t234_in_aa(T682, T684))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → U29_AA(T682, X1109, e375_in_aa(T684, X1109))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_AA(T692, X1131) → U31_AA(T692, X1131, n32_in_aa(T692, X1130))
T351_IN_AA(T692, X1131) → N32_IN_AA(T692, X1130)
T351_IN_AA(T692, X1131) → U32_AA(T692, X1131, n32_in_aa(T692, T696))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → U33_AA(T692, X1131, t351_in_aa(T696, X1131))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_AA(T704, X1152) → U35_AA(T704, X1152, t234_in_aa(T704, X1151))
E346_IN_AA(T704, X1152) → T234_IN_AA(T704, X1151)
E346_IN_AA(T704, X1152) → U36_AA(T704, X1152, t234_in_aa(T704, T706))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → U37_AA(T704, X1152, e346_in_aa(T706, X1152))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_AA(T714, X1174) → U39_AA(T714, X1174, n32_in_aa(T714, X1173))
T322_IN_AA(T714, X1174) → N32_IN_AA(T714, X1173)
T322_IN_AA(T714, X1174) → U40_AA(T714, X1174, n32_in_aa(T714, T718))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → U41_AA(T714, X1174, t322_in_aa(T718, X1174))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_AA(T726, X1195) → U43_AA(T726, X1195, t234_in_aa(T726, X1194))
E317_IN_AA(T726, X1195) → T234_IN_AA(T726, X1194)
E317_IN_AA(T726, X1195) → U44_AA(T726, X1195, t234_in_aa(T726, T728))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → U45_AA(T726, X1195, e317_in_aa(T728, X1195))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_AA(T736, X1217) → U47_AA(T736, X1217, n32_in_aa(T736, X1216))
T293_IN_AA(T736, X1217) → N32_IN_AA(T736, X1216)
T293_IN_AA(T736, X1217) → U48_AA(T736, X1217, n32_in_aa(T736, T740))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → U49_AA(T736, X1217, t293_in_aa(T740, X1217))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_AA(T748, X1238) → U51_AA(T748, X1238, t234_in_aa(T748, X1237))
E288_IN_AA(T748, X1238) → T234_IN_AA(T748, X1237)
E288_IN_AA(T748, X1238) → U52_AA(T748, X1238, t234_in_aa(T748, T750))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → U53_AA(T748, X1238, e288_in_aa(T750, X1238))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_AA(T758, X1260) → U55_AA(T758, X1260, n32_in_aa(T758, X1259))
T264_IN_AA(T758, X1260) → N32_IN_AA(T758, X1259)
T264_IN_AA(T758, X1260) → U56_AA(T758, X1260, n32_in_aa(T758, T762))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → U57_AA(T758, X1260, t264_in_aa(T762, X1260))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_AA(T770, X1281) → U59_AA(T770, X1281, t234_in_aa(T770, X1280))
E259_IN_AA(T770, X1281) → T234_IN_AA(T770, X1280)
E259_IN_AA(T770, X1281) → U60_AA(T770, X1281, t234_in_aa(T770, T772))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → U61_AA(T770, X1281, e259_in_aa(T772, X1281))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → E259_IN_AA(T772, X1281)
U111_GA(T941, T943, t234_out_ga(T941, T945)) → U112_GA(T941, T943, e1_in_aa(T945, T943))
U111_GA(T941, T943, t234_out_ga(T941, T945)) → E1_IN_AA(T945, T943)
T409_IN_GA(T648, X1045) → U11_GA(T648, X1045, n32_in_ga(T648, X1044))
T409_IN_GA(T648, X1045) → N32_IN_GA(T648, X1044)
T409_IN_GA(T648, X1045) → U12_GA(T648, X1045, n32_in_ga(T648, T652))
U12_GA(T648, X1045, n32_out_ga(T648, T652)) → U13_GA(T648, X1045, t409_in_aa(T652, X1045))
U12_GA(T648, X1045, n32_out_ga(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_GA(T660, X1066) → U19_GA(T660, X1066, t234_in_ga(T660, X1065))
E404_IN_GA(T660, X1066) → T234_IN_GA(T660, X1065)
E404_IN_GA(T660, X1066) → U20_GA(T660, X1066, t234_in_ga(T660, T662))
U20_GA(T660, X1066, t234_out_ga(T660, T662)) → U21_GA(T660, X1066, e404_in_aa(T662, X1066))
U20_GA(T660, X1066, t234_out_ga(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_GA(T670, X1088) → U23_GA(T670, X1088, n32_in_ga(T670, X1087))
T380_IN_GA(T670, X1088) → N32_IN_GA(T670, X1087)
T380_IN_GA(T670, X1088) → U24_GA(T670, X1088, n32_in_ga(T670, T674))
U24_GA(T670, X1088, n32_out_ga(T670, T674)) → U25_GA(T670, X1088, t380_in_aa(T674, X1088))
U24_GA(T670, X1088, n32_out_ga(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_GA(T682, X1109) → U27_GA(T682, X1109, t234_in_ga(T682, X1108))
E375_IN_GA(T682, X1109) → T234_IN_GA(T682, X1108)
E375_IN_GA(T682, X1109) → U28_GA(T682, X1109, t234_in_ga(T682, T684))
U28_GA(T682, X1109, t234_out_ga(T682, T684)) → U29_GA(T682, X1109, e375_in_aa(T684, X1109))
U28_GA(T682, X1109, t234_out_ga(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_GA(T692, X1131) → U31_GA(T692, X1131, n32_in_ga(T692, X1130))
T351_IN_GA(T692, X1131) → N32_IN_GA(T692, X1130)
T351_IN_GA(T692, X1131) → U32_GA(T692, X1131, n32_in_ga(T692, T696))
U32_GA(T692, X1131, n32_out_ga(T692, T696)) → U33_GA(T692, X1131, t351_in_aa(T696, X1131))
U32_GA(T692, X1131, n32_out_ga(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_GA(T704, X1152) → U35_GA(T704, X1152, t234_in_ga(T704, X1151))
E346_IN_GA(T704, X1152) → T234_IN_GA(T704, X1151)
E346_IN_GA(T704, X1152) → U36_GA(T704, X1152, t234_in_ga(T704, T706))
U36_GA(T704, X1152, t234_out_ga(T704, T706)) → U37_GA(T704, X1152, e346_in_aa(T706, X1152))
U36_GA(T704, X1152, t234_out_ga(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_GA(T714, X1174) → U39_GA(T714, X1174, n32_in_ga(T714, X1173))
T322_IN_GA(T714, X1174) → N32_IN_GA(T714, X1173)
T322_IN_GA(T714, X1174) → U40_GA(T714, X1174, n32_in_ga(T714, T718))
U40_GA(T714, X1174, n32_out_ga(T714, T718)) → U41_GA(T714, X1174, t322_in_aa(T718, X1174))
U40_GA(T714, X1174, n32_out_ga(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_GA(T726, X1195) → U43_GA(T726, X1195, t234_in_ga(T726, X1194))
E317_IN_GA(T726, X1195) → T234_IN_GA(T726, X1194)
E317_IN_GA(T726, X1195) → U44_GA(T726, X1195, t234_in_ga(T726, T728))
U44_GA(T726, X1195, t234_out_ga(T726, T728)) → U45_GA(T726, X1195, e317_in_aa(T728, X1195))
U44_GA(T726, X1195, t234_out_ga(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_GA(T736, X1217) → U47_GA(T736, X1217, n32_in_ga(T736, X1216))
T293_IN_GA(T736, X1217) → N32_IN_GA(T736, X1216)
T293_IN_GA(T736, X1217) → U48_GA(T736, X1217, n32_in_ga(T736, T740))
U48_GA(T736, X1217, n32_out_ga(T736, T740)) → U49_GA(T736, X1217, t293_in_aa(T740, X1217))
U48_GA(T736, X1217, n32_out_ga(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_GA(T748, X1238) → U51_GA(T748, X1238, t234_in_ga(T748, X1237))
E288_IN_GA(T748, X1238) → T234_IN_GA(T748, X1237)
E288_IN_GA(T748, X1238) → U52_GA(T748, X1238, t234_in_ga(T748, T750))
U52_GA(T748, X1238, t234_out_ga(T748, T750)) → U53_GA(T748, X1238, e288_in_aa(T750, X1238))
U52_GA(T748, X1238, t234_out_ga(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_GA(T758, X1260) → U55_GA(T758, X1260, n32_in_ga(T758, X1259))
T264_IN_GA(T758, X1260) → N32_IN_GA(T758, X1259)
T264_IN_GA(T758, X1260) → U56_GA(T758, X1260, n32_in_ga(T758, T762))
U56_GA(T758, X1260, n32_out_ga(T758, T762)) → U57_GA(T758, X1260, t264_in_aa(T762, X1260))
U56_GA(T758, X1260, n32_out_ga(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_GA(T770, X1281) → U59_GA(T770, X1281, t234_in_ga(T770, X1280))
E259_IN_GA(T770, X1281) → T234_IN_GA(T770, X1280)
E259_IN_GA(T770, X1281) → U60_GA(T770, X1281, t234_in_ga(T770, T772))
U60_GA(T770, X1281, t234_out_ga(T770, T772)) → U61_GA(T770, X1281, e259_in_aa(T772, X1281))
U60_GA(T770, X1281, t234_out_ga(T770, T772)) → E259_IN_AA(T772, X1281)
T203_IN_GA(T345, X530) → U3_GA(T345, X530, n32_in_ga(T345, X529))
T203_IN_GA(T345, X530) → N32_IN_GA(T345, X529)
T203_IN_GA(T345, X530) → U4_GA(T345, X530, n32_in_ga(T345, T349))
U4_GA(T345, X530, n32_out_ga(T345, T349)) → U5_GA(T345, X530, t203_in_aa(T349, X530))
U4_GA(T345, X530, n32_out_ga(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_GA(T357, X551) → U7_GA(T357, X551, t234_in_ga(T357, X550))
E198_IN_GA(T357, X551) → T234_IN_GA(T357, X550)
E198_IN_GA(T357, X551) → U8_GA(T357, X551, t234_in_ga(T357, T359))
U8_GA(T357, X551, t234_out_ga(T357, T359)) → U9_GA(T357, X551, e198_in_aa(T359, X551))
U8_GA(T357, X551, t234_out_ga(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_GA(T795, X1326) → U63_GA(T795, X1326, n32_in_ga(T795, X1325))
T174_IN_GA(T795, X1326) → N32_IN_GA(T795, X1325)
T174_IN_GA(T795, X1326) → U64_GA(T795, X1326, n32_in_ga(T795, T799))
U64_GA(T795, X1326, n32_out_ga(T795, T799)) → U65_GA(T795, X1326, t174_in_aa(T799, X1326))
U64_GA(T795, X1326, n32_out_ga(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_GA(T807, X1347) → U67_GA(T807, X1347, t234_in_ga(T807, X1346))
E169_IN_GA(T807, X1347) → T234_IN_GA(T807, X1346)
E169_IN_GA(T807, X1347) → U68_GA(T807, X1347, t234_in_ga(T807, T809))
U68_GA(T807, X1347, t234_out_ga(T807, T809)) → U69_GA(T807, X1347, e169_in_aa(T809, X1347))
U68_GA(T807, X1347, t234_out_ga(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_GA(T817, X1369) → U71_GA(T817, X1369, n32_in_ga(T817, X1368))
T145_IN_GA(T817, X1369) → N32_IN_GA(T817, X1368)
T145_IN_GA(T817, X1369) → U72_GA(T817, X1369, n32_in_ga(T817, T821))
U72_GA(T817, X1369, n32_out_ga(T817, T821)) → U73_GA(T817, X1369, t145_in_aa(T821, X1369))
U72_GA(T817, X1369, n32_out_ga(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_GA(T829, X1390) → U75_GA(T829, X1390, t234_in_ga(T829, X1389))
E140_IN_GA(T829, X1390) → T234_IN_GA(T829, X1389)
E140_IN_GA(T829, X1390) → U76_GA(T829, X1390, t234_in_ga(T829, T831))
U76_GA(T829, X1390, t234_out_ga(T829, T831)) → U77_GA(T829, X1390, e140_in_aa(T831, X1390))
U76_GA(T829, X1390, t234_out_ga(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_GA(T839, X1412) → U79_GA(T839, X1412, n32_in_ga(T839, X1411))
T116_IN_GA(T839, X1412) → N32_IN_GA(T839, X1411)
T116_IN_GA(T839, X1412) → U80_GA(T839, X1412, n32_in_ga(T839, T843))
U80_GA(T839, X1412, n32_out_ga(T839, T843)) → U81_GA(T839, X1412, t116_in_aa(T843, X1412))
U80_GA(T839, X1412, n32_out_ga(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_GA(T851, X1433) → U83_GA(T851, X1433, t234_in_ga(T851, X1432))
E111_IN_GA(T851, X1433) → T234_IN_GA(T851, X1432)
E111_IN_GA(T851, X1433) → U84_GA(T851, X1433, t234_in_ga(T851, T853))
U84_GA(T851, X1433, t234_out_ga(T851, T853)) → U85_GA(T851, X1433, e111_in_aa(T853, X1433))
U84_GA(T851, X1433, t234_out_ga(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_GA(T861, X1455) → U87_GA(T861, X1455, n32_in_ga(T861, X1454))
T87_IN_GA(T861, X1455) → N32_IN_GA(T861, X1454)
T87_IN_GA(T861, X1455) → U88_GA(T861, X1455, n32_in_ga(T861, T865))
U88_GA(T861, X1455, n32_out_ga(T861, T865)) → U89_GA(T861, X1455, t87_in_aa(T865, X1455))
U88_GA(T861, X1455, n32_out_ga(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_GA(T873, X1476) → U91_GA(T873, X1476, t234_in_ga(T873, X1475))
E82_IN_GA(T873, X1476) → T234_IN_GA(T873, X1475)
E82_IN_GA(T873, X1476) → U92_GA(T873, X1476, t234_in_ga(T873, T875))
U92_GA(T873, X1476, t234_out_ga(T873, T875)) → U93_GA(T873, X1476, e82_in_aa(T875, X1476))
U92_GA(T873, X1476, t234_out_ga(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_GA(T883, X1498) → U95_GA(T883, X1498, n32_in_ga(T883, X1497))
T58_IN_GA(T883, X1498) → N32_IN_GA(T883, X1497)
T58_IN_GA(T883, X1498) → U96_GA(T883, X1498, n32_in_ga(T883, T887))
U96_GA(T883, X1498, n32_out_ga(T883, T887)) → U97_GA(T883, X1498, t58_in_aa(T887, X1498))
U96_GA(T883, X1498, n32_out_ga(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_GA(T895, X1519) → U99_GA(T895, X1519, t234_in_ga(T895, X1518))
E53_IN_GA(T895, X1519) → T234_IN_GA(T895, X1518)
E53_IN_GA(T895, X1519) → U100_GA(T895, X1519, t234_in_ga(T895, T897))
U100_GA(T895, X1519, t234_out_ga(T895, T897)) → U101_GA(T895, X1519, e53_in_aa(T897, X1519))
U100_GA(T895, X1519, t234_out_ga(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_GAA(T62, T916, T918) → U104_GAA(T62, T916, T918, n32_in_ga(T62, T916))
U104_GAA(T62, T916, T918, n32_out_ga(T62, T916)) → U105_GAA(T62, T916, T918, n7_in_aa(T916, T918))
U104_GAA(T62, T916, T918, n32_out_ga(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_GAA(T62, T929, T931) → U106_GAA(T62, T929, T931, n32_in_ga(T62, T929))
U106_GAA(T62, T929, T931, n32_out_ga(T62, T929)) → U107_GAA(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U106_GAA(T62, T929, T931, n32_out_ga(T62, T929)) → P31_IN_AAA(T929, X1556, T931)

The TRS R consists of the following rules:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x3)
U109_ga(x1, x2, x3)  =  U109_ga(x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga
U1_ga(x1, x2, x3)  =  U1_ga(x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga
U94_ga(x1, x2, x3)  =  U94_ga(x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga
U86_ga(x1, x2, x3)  =  U86_ga(x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga
U78_ga(x1, x2, x3)  =  U78_ga(x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga
U70_ga(x1, x2, x3)  =  U70_ga(x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga
U62_ga(x1, x2, x3)  =  U62_ga(x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U110_ga(x1, x2, x3)  =  U110_ga(x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga
U14_ga(x1, x2, x3)  =  U14_ga(x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga
U54_ga(x1, x2, x3)  =  U54_ga(x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga
U46_ga(x1, x2, x3)  =  U46_ga(x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga
U38_ga(x1, x2, x3)  =  U38_ga(x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga
U30_ga(x1, x2, x3)  =  U30_ga(x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga
U22_ga(x1, x2, x3)  =  U22_ga(x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U111_ga(x1, x2, x3)  =  U111_ga(x3)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U112_ga(x1, x2, x3)  =  U112_ga(x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
e404_out_ga(x1, x2)  =  e404_out_ga
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
e375_out_ga(x1, x2)  =  e375_out_ga
U27_ga(x1, x2, x3)  =  U27_ga(x3)
U28_ga(x1, x2, x3)  =  U28_ga(x3)
U29_ga(x1, x2, x3)  =  U29_ga(x3)
U31_ga(x1, x2, x3)  =  U31_ga(x3)
U32_ga(x1, x2, x3)  =  U32_ga(x3)
U33_ga(x1, x2, x3)  =  U33_ga(x3)
e346_out_ga(x1, x2)  =  e346_out_ga
U35_ga(x1, x2, x3)  =  U35_ga(x3)
U36_ga(x1, x2, x3)  =  U36_ga(x3)
U37_ga(x1, x2, x3)  =  U37_ga(x3)
U39_ga(x1, x2, x3)  =  U39_ga(x3)
U40_ga(x1, x2, x3)  =  U40_ga(x3)
U41_ga(x1, x2, x3)  =  U41_ga(x3)
e317_out_ga(x1, x2)  =  e317_out_ga
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U49_ga(x1, x2, x3)  =  U49_ga(x3)
e288_out_ga(x1, x2)  =  e288_out_ga
U51_ga(x1, x2, x3)  =  U51_ga(x3)
U52_ga(x1, x2, x3)  =  U52_ga(x3)
U53_ga(x1, x2, x3)  =  U53_ga(x3)
U55_ga(x1, x2, x3)  =  U55_ga(x3)
U56_ga(x1, x2, x3)  =  U56_ga(x3)
U57_ga(x1, x2, x3)  =  U57_ga(x3)
e259_out_ga(x1, x2)  =  e259_out_ga
U59_ga(x1, x2, x3)  =  U59_ga(x3)
U60_ga(x1, x2, x3)  =  U60_ga(x3)
U61_ga(x1, x2, x3)  =  U61_ga(x3)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
e198_out_ga(x1, x2)  =  e198_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U63_ga(x1, x2, x3)  =  U63_ga(x3)
U64_ga(x1, x2, x3)  =  U64_ga(x3)
U65_ga(x1, x2, x3)  =  U65_ga(x3)
e169_out_ga(x1, x2)  =  e169_out_ga
U67_ga(x1, x2, x3)  =  U67_ga(x3)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
U69_ga(x1, x2, x3)  =  U69_ga(x3)
U71_ga(x1, x2, x3)  =  U71_ga(x3)
U72_ga(x1, x2, x3)  =  U72_ga(x3)
U73_ga(x1, x2, x3)  =  U73_ga(x3)
e140_out_ga(x1, x2)  =  e140_out_ga
U75_ga(x1, x2, x3)  =  U75_ga(x3)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
U77_ga(x1, x2, x3)  =  U77_ga(x3)
U79_ga(x1, x2, x3)  =  U79_ga(x3)
U80_ga(x1, x2, x3)  =  U80_ga(x3)
U81_ga(x1, x2, x3)  =  U81_ga(x3)
e111_out_ga(x1, x2)  =  e111_out_ga
U83_ga(x1, x2, x3)  =  U83_ga(x3)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
U85_ga(x1, x2, x3)  =  U85_ga(x3)
U87_ga(x1, x2, x3)  =  U87_ga(x3)
U88_ga(x1, x2, x3)  =  U88_ga(x3)
U89_ga(x1, x2, x3)  =  U89_ga(x3)
e82_out_ga(x1, x2)  =  e82_out_ga
U91_ga(x1, x2, x3)  =  U91_ga(x3)
U92_ga(x1, x2, x3)  =  U92_ga(x3)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
U95_ga(x1, x2, x3)  =  U95_ga(x3)
U96_ga(x1, x2, x3)  =  U96_ga(x3)
U97_ga(x1, x2, x3)  =  U97_ga(x3)
e53_out_ga(x1, x2)  =  e53_out_ga
U99_ga(x1, x2, x3)  =  U99_ga(x3)
U100_ga(x1, x2, x3)  =  U100_ga(x3)
U101_ga(x1, x2, x3)  =  U101_ga(x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x4)
E1_IN_GA(x1, x2)  =  E1_IN_GA(x1)
U108_GA(x1, x2, x3)  =  U108_GA(x3)
N7_IN_GA(x1, x2)  =  N7_IN_GA(x1)
U102_GA(x1, x2, x3)  =  U102_GA(x3)
U109_GA(x1, x2, x3)  =  U109_GA(x3)
P31_IN_GAA(x1, x2, x3)  =  P31_IN_GAA(x1)
U103_GAA(x1, x2, x3, x4)  =  U103_GAA(x4)
N32_IN_GA(x1, x2)  =  N32_IN_GA(x1)
U1_GA(x1, x2, x3)  =  U1_GA(x3)
E53_IN_GA(x1, x2)  =  E53_IN_GA(x1)
U98_GA(x1, x2, x3)  =  U98_GA(x3)
T58_IN_GA(x1, x2)  =  T58_IN_GA(x1)
U94_GA(x1, x2, x3)  =  U94_GA(x3)
E82_IN_GA(x1, x2)  =  E82_IN_GA(x1)
U90_GA(x1, x2, x3)  =  U90_GA(x3)
T87_IN_GA(x1, x2)  =  T87_IN_GA(x1)
U86_GA(x1, x2, x3)  =  U86_GA(x3)
E111_IN_GA(x1, x2)  =  E111_IN_GA(x1)
U82_GA(x1, x2, x3)  =  U82_GA(x3)
T116_IN_GA(x1, x2)  =  T116_IN_GA(x1)
U78_GA(x1, x2, x3)  =  U78_GA(x3)
E140_IN_GA(x1, x2)  =  E140_IN_GA(x1)
U74_GA(x1, x2, x3)  =  U74_GA(x3)
T145_IN_GA(x1, x2)  =  T145_IN_GA(x1)
U70_GA(x1, x2, x3)  =  U70_GA(x3)
E169_IN_GA(x1, x2)  =  E169_IN_GA(x1)
U66_GA(x1, x2, x3)  =  U66_GA(x3)
T174_IN_GA(x1, x2)  =  T174_IN_GA(x1)
U62_GA(x1, x2, x3)  =  U62_GA(x3)
E198_IN_GA(x1, x2)  =  E198_IN_GA(x1)
U6_GA(x1, x2, x3)  =  U6_GA(x3)
T203_IN_GA(x1, x2)  =  T203_IN_GA(x1)
U2_GA(x1, x2, x3)  =  U2_GA(x3)
U110_GA(x1, x2, x3)  =  U110_GA(x3)
T234_IN_GA(x1, x2)  =  T234_IN_GA(x1)
U14_GA(x1, x2, x3)  =  U14_GA(x3)
E259_IN_GA(x1, x2)  =  E259_IN_GA(x1)
U58_GA(x1, x2, x3)  =  U58_GA(x3)
T264_IN_GA(x1, x2)  =  T264_IN_GA(x1)
U54_GA(x1, x2, x3)  =  U54_GA(x3)
E288_IN_GA(x1, x2)  =  E288_IN_GA(x1)
U50_GA(x1, x2, x3)  =  U50_GA(x3)
T293_IN_GA(x1, x2)  =  T293_IN_GA(x1)
U46_GA(x1, x2, x3)  =  U46_GA(x3)
E317_IN_GA(x1, x2)  =  E317_IN_GA(x1)
U42_GA(x1, x2, x3)  =  U42_GA(x3)
T322_IN_GA(x1, x2)  =  T322_IN_GA(x1)
U38_GA(x1, x2, x3)  =  U38_GA(x3)
E346_IN_GA(x1, x2)  =  E346_IN_GA(x1)
U34_GA(x1, x2, x3)  =  U34_GA(x3)
T351_IN_GA(x1, x2)  =  T351_IN_GA(x1)
U30_GA(x1, x2, x3)  =  U30_GA(x3)
E375_IN_GA(x1, x2)  =  E375_IN_GA(x1)
U26_GA(x1, x2, x3)  =  U26_GA(x3)
T380_IN_GA(x1, x2)  =  T380_IN_GA(x1)
U22_GA(x1, x2, x3)  =  U22_GA(x3)
E404_IN_GA(x1, x2)  =  E404_IN_GA(x1)
U18_GA(x1, x2, x3)  =  U18_GA(x3)
T409_IN_GA(x1, x2)  =  T409_IN_GA(x1)
U10_GA(x1, x2, x3)  =  U10_GA(x3)
U111_GA(x1, x2, x3)  =  U111_GA(x3)
U15_GA(x1, x2, x3)  =  U15_GA(x3)
U16_GA(x1, x2, x3)  =  U16_GA(x3)
U17_GA(x1, x2, x3)  =  U17_GA(x3)
T234_IN_AA(x1, x2)  =  T234_IN_AA
U14_AA(x1, x2, x3)  =  U14_AA(x3)
E259_IN_AA(x1, x2)  =  E259_IN_AA
U58_AA(x1, x2, x3)  =  U58_AA(x3)
T264_IN_AA(x1, x2)  =  T264_IN_AA
U54_AA(x1, x2, x3)  =  U54_AA(x3)
E288_IN_AA(x1, x2)  =  E288_IN_AA
U50_AA(x1, x2, x3)  =  U50_AA(x3)
T293_IN_AA(x1, x2)  =  T293_IN_AA
U46_AA(x1, x2, x3)  =  U46_AA(x3)
E317_IN_AA(x1, x2)  =  E317_IN_AA
U42_AA(x1, x2, x3)  =  U42_AA(x3)
T322_IN_AA(x1, x2)  =  T322_IN_AA
U38_AA(x1, x2, x3)  =  U38_AA(x3)
E346_IN_AA(x1, x2)  =  E346_IN_AA
U34_AA(x1, x2, x3)  =  U34_AA(x3)
T351_IN_AA(x1, x2)  =  T351_IN_AA
U30_AA(x1, x2, x3)  =  U30_AA(x3)
E375_IN_AA(x1, x2)  =  E375_IN_AA
U26_AA(x1, x2, x3)  =  U26_AA(x3)
T380_IN_AA(x1, x2)  =  T380_IN_AA
U22_AA(x1, x2, x3)  =  U22_AA(x3)
E404_IN_AA(x1, x2)  =  E404_IN_AA
U18_AA(x1, x2, x3)  =  U18_AA(x3)
T409_IN_AA(x1, x2)  =  T409_IN_AA
U10_AA(x1, x2, x3)  =  U10_AA(x3)
E1_IN_AA(x1, x2)  =  E1_IN_AA
U108_AA(x1, x2, x3)  =  U108_AA(x3)
N7_IN_AA(x1, x2)  =  N7_IN_AA
U102_AA(x1, x2, x3)  =  U102_AA(x3)
U109_AA(x1, x2, x3)  =  U109_AA(x3)
P31_IN_AAA(x1, x2, x3)  =  P31_IN_AAA
U103_AAA(x1, x2, x3, x4)  =  U103_AAA(x4)
N32_IN_AA(x1, x2)  =  N32_IN_AA
U1_AA(x1, x2, x3)  =  U1_AA(x3)
E53_IN_AA(x1, x2)  =  E53_IN_AA
U98_AA(x1, x2, x3)  =  U98_AA(x3)
T58_IN_AA(x1, x2)  =  T58_IN_AA
U94_AA(x1, x2, x3)  =  U94_AA(x3)
E82_IN_AA(x1, x2)  =  E82_IN_AA
U90_AA(x1, x2, x3)  =  U90_AA(x3)
T87_IN_AA(x1, x2)  =  T87_IN_AA
U86_AA(x1, x2, x3)  =  U86_AA(x3)
E111_IN_AA(x1, x2)  =  E111_IN_AA
U82_AA(x1, x2, x3)  =  U82_AA(x3)
T116_IN_AA(x1, x2)  =  T116_IN_AA
U78_AA(x1, x2, x3)  =  U78_AA(x3)
E140_IN_AA(x1, x2)  =  E140_IN_AA
U74_AA(x1, x2, x3)  =  U74_AA(x3)
T145_IN_AA(x1, x2)  =  T145_IN_AA
U70_AA(x1, x2, x3)  =  U70_AA(x3)
E169_IN_AA(x1, x2)  =  E169_IN_AA
U66_AA(x1, x2, x3)  =  U66_AA(x3)
T174_IN_AA(x1, x2)  =  T174_IN_AA
U62_AA(x1, x2, x3)  =  U62_AA(x3)
E198_IN_AA(x1, x2)  =  E198_IN_AA
U6_AA(x1, x2, x3)  =  U6_AA(x3)
T203_IN_AA(x1, x2)  =  T203_IN_AA
U2_AA(x1, x2, x3)  =  U2_AA(x3)
U110_AA(x1, x2, x3)  =  U110_AA(x3)
U15_AA(x1, x2, x3)  =  U15_AA(x3)
U16_AA(x1, x2, x3)  =  U16_AA(x3)
U17_AA(x1, x2, x3)  =  U17_AA(x3)
U111_AA(x1, x2, x3)  =  U111_AA(x3)
U112_AA(x1, x2, x3)  =  U112_AA(x3)
U3_AA(x1, x2, x3)  =  U3_AA(x3)
U4_AA(x1, x2, x3)  =  U4_AA(x3)
U5_AA(x1, x2, x3)  =  U5_AA(x3)
U7_AA(x1, x2, x3)  =  U7_AA(x3)
U8_AA(x1, x2, x3)  =  U8_AA(x3)
U9_AA(x1, x2, x3)  =  U9_AA(x3)
U63_AA(x1, x2, x3)  =  U63_AA(x3)
U64_AA(x1, x2, x3)  =  U64_AA(x3)
U65_AA(x1, x2, x3)  =  U65_AA(x3)
U67_AA(x1, x2, x3)  =  U67_AA(x3)
U68_AA(x1, x2, x3)  =  U68_AA(x3)
U69_AA(x1, x2, x3)  =  U69_AA(x3)
U71_AA(x1, x2, x3)  =  U71_AA(x3)
U72_AA(x1, x2, x3)  =  U72_AA(x3)
U73_AA(x1, x2, x3)  =  U73_AA(x3)
U75_AA(x1, x2, x3)  =  U75_AA(x3)
U76_AA(x1, x2, x3)  =  U76_AA(x3)
U77_AA(x1, x2, x3)  =  U77_AA(x3)
U79_AA(x1, x2, x3)  =  U79_AA(x3)
U80_AA(x1, x2, x3)  =  U80_AA(x3)
U81_AA(x1, x2, x3)  =  U81_AA(x3)
U83_AA(x1, x2, x3)  =  U83_AA(x3)
U84_AA(x1, x2, x3)  =  U84_AA(x3)
U85_AA(x1, x2, x3)  =  U85_AA(x3)
U87_AA(x1, x2, x3)  =  U87_AA(x3)
U88_AA(x1, x2, x3)  =  U88_AA(x3)
U89_AA(x1, x2, x3)  =  U89_AA(x3)
U91_AA(x1, x2, x3)  =  U91_AA(x3)
U92_AA(x1, x2, x3)  =  U92_AA(x3)
U93_AA(x1, x2, x3)  =  U93_AA(x3)
U95_AA(x1, x2, x3)  =  U95_AA(x3)
U96_AA(x1, x2, x3)  =  U96_AA(x3)
U97_AA(x1, x2, x3)  =  U97_AA(x3)
U99_AA(x1, x2, x3)  =  U99_AA(x3)
U100_AA(x1, x2, x3)  =  U100_AA(x3)
U101_AA(x1, x2, x3)  =  U101_AA(x3)
U104_AAA(x1, x2, x3, x4)  =  U104_AAA(x4)
U105_AAA(x1, x2, x3, x4)  =  U105_AAA(x4)
U106_AAA(x1, x2, x3, x4)  =  U106_AAA(x4)
U107_AAA(x1, x2, x3, x4)  =  U107_AAA(x4)
U11_AA(x1, x2, x3)  =  U11_AA(x3)
U12_AA(x1, x2, x3)  =  U12_AA(x3)
U13_AA(x1, x2, x3)  =  U13_AA(x3)
U19_AA(x1, x2, x3)  =  U19_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U21_AA(x1, x2, x3)  =  U21_AA(x3)
U23_AA(x1, x2, x3)  =  U23_AA(x3)
U24_AA(x1, x2, x3)  =  U24_AA(x3)
U25_AA(x1, x2, x3)  =  U25_AA(x3)
U27_AA(x1, x2, x3)  =  U27_AA(x3)
U28_AA(x1, x2, x3)  =  U28_AA(x3)
U29_AA(x1, x2, x3)  =  U29_AA(x3)
U31_AA(x1, x2, x3)  =  U31_AA(x3)
U32_AA(x1, x2, x3)  =  U32_AA(x3)
U33_AA(x1, x2, x3)  =  U33_AA(x3)
U35_AA(x1, x2, x3)  =  U35_AA(x3)
U36_AA(x1, x2, x3)  =  U36_AA(x3)
U37_AA(x1, x2, x3)  =  U37_AA(x3)
U39_AA(x1, x2, x3)  =  U39_AA(x3)
U40_AA(x1, x2, x3)  =  U40_AA(x3)
U41_AA(x1, x2, x3)  =  U41_AA(x3)
U43_AA(x1, x2, x3)  =  U43_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U45_AA(x1, x2, x3)  =  U45_AA(x3)
U47_AA(x1, x2, x3)  =  U47_AA(x3)
U48_AA(x1, x2, x3)  =  U48_AA(x3)
U49_AA(x1, x2, x3)  =  U49_AA(x3)
U51_AA(x1, x2, x3)  =  U51_AA(x3)
U52_AA(x1, x2, x3)  =  U52_AA(x3)
U53_AA(x1, x2, x3)  =  U53_AA(x3)
U55_AA(x1, x2, x3)  =  U55_AA(x3)
U56_AA(x1, x2, x3)  =  U56_AA(x3)
U57_AA(x1, x2, x3)  =  U57_AA(x3)
U59_AA(x1, x2, x3)  =  U59_AA(x3)
U60_AA(x1, x2, x3)  =  U60_AA(x3)
U61_AA(x1, x2, x3)  =  U61_AA(x3)
U112_GA(x1, x2, x3)  =  U112_GA(x3)
U11_GA(x1, x2, x3)  =  U11_GA(x3)
U12_GA(x1, x2, x3)  =  U12_GA(x3)
U13_GA(x1, x2, x3)  =  U13_GA(x3)
U19_GA(x1, x2, x3)  =  U19_GA(x3)
U20_GA(x1, x2, x3)  =  U20_GA(x3)
U21_GA(x1, x2, x3)  =  U21_GA(x3)
U23_GA(x1, x2, x3)  =  U23_GA(x3)
U24_GA(x1, x2, x3)  =  U24_GA(x3)
U25_GA(x1, x2, x3)  =  U25_GA(x3)
U27_GA(x1, x2, x3)  =  U27_GA(x3)
U28_GA(x1, x2, x3)  =  U28_GA(x3)
U29_GA(x1, x2, x3)  =  U29_GA(x3)
U31_GA(x1, x2, x3)  =  U31_GA(x3)
U32_GA(x1, x2, x3)  =  U32_GA(x3)
U33_GA(x1, x2, x3)  =  U33_GA(x3)
U35_GA(x1, x2, x3)  =  U35_GA(x3)
U36_GA(x1, x2, x3)  =  U36_GA(x3)
U37_GA(x1, x2, x3)  =  U37_GA(x3)
U39_GA(x1, x2, x3)  =  U39_GA(x3)
U40_GA(x1, x2, x3)  =  U40_GA(x3)
U41_GA(x1, x2, x3)  =  U41_GA(x3)
U43_GA(x1, x2, x3)  =  U43_GA(x3)
U44_GA(x1, x2, x3)  =  U44_GA(x3)
U45_GA(x1, x2, x3)  =  U45_GA(x3)
U47_GA(x1, x2, x3)  =  U47_GA(x3)
U48_GA(x1, x2, x3)  =  U48_GA(x3)
U49_GA(x1, x2, x3)  =  U49_GA(x3)
U51_GA(x1, x2, x3)  =  U51_GA(x3)
U52_GA(x1, x2, x3)  =  U52_GA(x3)
U53_GA(x1, x2, x3)  =  U53_GA(x3)
U55_GA(x1, x2, x3)  =  U55_GA(x3)
U56_GA(x1, x2, x3)  =  U56_GA(x3)
U57_GA(x1, x2, x3)  =  U57_GA(x3)
U59_GA(x1, x2, x3)  =  U59_GA(x3)
U60_GA(x1, x2, x3)  =  U60_GA(x3)
U61_GA(x1, x2, x3)  =  U61_GA(x3)
U3_GA(x1, x2, x3)  =  U3_GA(x3)
U4_GA(x1, x2, x3)  =  U4_GA(x3)
U5_GA(x1, x2, x3)  =  U5_GA(x3)
U7_GA(x1, x2, x3)  =  U7_GA(x3)
U8_GA(x1, x2, x3)  =  U8_GA(x3)
U9_GA(x1, x2, x3)  =  U9_GA(x3)
U63_GA(x1, x2, x3)  =  U63_GA(x3)
U64_GA(x1, x2, x3)  =  U64_GA(x3)
U65_GA(x1, x2, x3)  =  U65_GA(x3)
U67_GA(x1, x2, x3)  =  U67_GA(x3)
U68_GA(x1, x2, x3)  =  U68_GA(x3)
U69_GA(x1, x2, x3)  =  U69_GA(x3)
U71_GA(x1, x2, x3)  =  U71_GA(x3)
U72_GA(x1, x2, x3)  =  U72_GA(x3)
U73_GA(x1, x2, x3)  =  U73_GA(x3)
U75_GA(x1, x2, x3)  =  U75_GA(x3)
U76_GA(x1, x2, x3)  =  U76_GA(x3)
U77_GA(x1, x2, x3)  =  U77_GA(x3)
U79_GA(x1, x2, x3)  =  U79_GA(x3)
U80_GA(x1, x2, x3)  =  U80_GA(x3)
U81_GA(x1, x2, x3)  =  U81_GA(x3)
U83_GA(x1, x2, x3)  =  U83_GA(x3)
U84_GA(x1, x2, x3)  =  U84_GA(x3)
U85_GA(x1, x2, x3)  =  U85_GA(x3)
U87_GA(x1, x2, x3)  =  U87_GA(x3)
U88_GA(x1, x2, x3)  =  U88_GA(x3)
U89_GA(x1, x2, x3)  =  U89_GA(x3)
U91_GA(x1, x2, x3)  =  U91_GA(x3)
U92_GA(x1, x2, x3)  =  U92_GA(x3)
U93_GA(x1, x2, x3)  =  U93_GA(x3)
U95_GA(x1, x2, x3)  =  U95_GA(x3)
U96_GA(x1, x2, x3)  =  U96_GA(x3)
U97_GA(x1, x2, x3)  =  U97_GA(x3)
U99_GA(x1, x2, x3)  =  U99_GA(x3)
U100_GA(x1, x2, x3)  =  U100_GA(x3)
U101_GA(x1, x2, x3)  =  U101_GA(x3)
U104_GAA(x1, x2, x3, x4)  =  U104_GAA(x4)
U105_GAA(x1, x2, x3, x4)  =  U105_GAA(x4)
U106_GAA(x1, x2, x3, x4)  =  U106_GAA(x4)
U107_GAA(x1, x2, x3, x4)  =  U107_GAA(x4)

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

(77) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 2 SCCs with 224 less nodes.

(78) Complex Obligation (AND)

(79) Obligation:

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

T234_IN_AA(.(lbrace, T392), X599) → E259_IN_AA(T392, X599)
E259_IN_AA(T400, X625) → T264_IN_AA(T400, X625)
T264_IN_AA(.(lbrace, T433), X670) → E288_IN_AA(T433, X670)
E288_IN_AA(T441, X696) → T293_IN_AA(T441, X696)
T293_IN_AA(.(lbrace, T474), X741) → E317_IN_AA(T474, X741)
E317_IN_AA(T482, X767) → T322_IN_AA(T482, X767)
T322_IN_AA(.(lbrace, T515), X812) → E346_IN_AA(T515, X812)
E346_IN_AA(T523, X838) → T351_IN_AA(T523, X838)
T351_IN_AA(.(lbrace, T556), X883) → E375_IN_AA(T556, X883)
E375_IN_AA(T564, X909) → T380_IN_AA(T564, X909)
T380_IN_AA(.(lbrace, T597), X954) → E404_IN_AA(T597, X954)
E404_IN_AA(T605, X980) → T409_IN_AA(T605, X980)
T409_IN_AA(.(lbrace, T638), X1025) → E1_IN_AA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_AA(T22, T24) → N7_IN_AA(T22, T24)
N7_IN_AA(.(lbrace, T41), T43) → E1_IN_AA(T41, .(rbrace, T43))
E1_IN_AA(T62, T64) → P31_IN_AAA(T62, X59, T64)
P31_IN_AAA(T62, X59, T64) → N32_IN_AA(T62, X59)
N32_IN_AA(.(lbrace, T89), X84) → E53_IN_AA(T89, X84)
E53_IN_AA(T97, X110) → T58_IN_AA(T97, X110)
T58_IN_AA(.(lbrace, T130), X155) → E82_IN_AA(T130, X155)
E82_IN_AA(T138, X181) → T87_IN_AA(T138, X181)
T87_IN_AA(.(lbrace, T171), X226) → E111_IN_AA(T171, X226)
E111_IN_AA(T179, X252) → T116_IN_AA(T179, X252)
T116_IN_AA(.(lbrace, T212), X297) → E140_IN_AA(T212, X297)
E140_IN_AA(T220, X323) → T145_IN_AA(T220, X323)
T145_IN_AA(.(lbrace, T253), X368) → E169_IN_AA(T253, X368)
E169_IN_AA(T261, X394) → T174_IN_AA(T261, X394)
T174_IN_AA(.(lbrace, T294), X439) → E198_IN_AA(T294, X439)
E198_IN_AA(T302, X465) → T203_IN_AA(T302, X465)
T203_IN_AA(.(lbrace, T335), X510) → E1_IN_AA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_AA(T941, T943) → T234_IN_AA(T941, X1569)
T234_IN_AA(T780, X1303) → N32_IN_AA(T780, X1302)
T234_IN_AA(T780, X1303) → U16_AA(T780, X1303, n32_in_aa(T780, T784))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → T234_IN_AA(T784, X1303)
E1_IN_AA(T941, T943) → U111_AA(T941, T943, t234_in_aa(T941, T945))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → E1_IN_AA(T945, T943)
T203_IN_AA(T345, X530) → N32_IN_AA(T345, X529)
T203_IN_AA(T345, X530) → U4_AA(T345, X530, n32_in_aa(T345, T349))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_AA(T357, X551) → T234_IN_AA(T357, X550)
E198_IN_AA(T357, X551) → U8_AA(T357, X551, t234_in_aa(T357, T359))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_AA(T795, X1326) → N32_IN_AA(T795, X1325)
T174_IN_AA(T795, X1326) → U64_AA(T795, X1326, n32_in_aa(T795, T799))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_AA(T807, X1347) → T234_IN_AA(T807, X1346)
E169_IN_AA(T807, X1347) → U68_AA(T807, X1347, t234_in_aa(T807, T809))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_AA(T817, X1369) → N32_IN_AA(T817, X1368)
T145_IN_AA(T817, X1369) → U72_AA(T817, X1369, n32_in_aa(T817, T821))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_AA(T829, X1390) → T234_IN_AA(T829, X1389)
E140_IN_AA(T829, X1390) → U76_AA(T829, X1390, t234_in_aa(T829, T831))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_AA(T839, X1412) → N32_IN_AA(T839, X1411)
T116_IN_AA(T839, X1412) → U80_AA(T839, X1412, n32_in_aa(T839, T843))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_AA(T851, X1433) → T234_IN_AA(T851, X1432)
E111_IN_AA(T851, X1433) → U84_AA(T851, X1433, t234_in_aa(T851, T853))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_AA(T861, X1455) → N32_IN_AA(T861, X1454)
T87_IN_AA(T861, X1455) → U88_AA(T861, X1455, n32_in_aa(T861, T865))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_AA(T873, X1476) → T234_IN_AA(T873, X1475)
E82_IN_AA(T873, X1476) → U92_AA(T873, X1476, t234_in_aa(T873, T875))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_AA(T883, X1498) → N32_IN_AA(T883, X1497)
T58_IN_AA(T883, X1498) → U96_AA(T883, X1498, n32_in_aa(T883, T887))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_AA(T895, X1519) → T234_IN_AA(T895, X1518)
E53_IN_AA(T895, X1519) → U100_AA(T895, X1519, t234_in_aa(T895, T897))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_AAA(T62, T916, T918) → U104_AAA(T62, T916, T918, n32_in_aa(T62, T916))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_AAA(T62, T929, T931) → U106_AAA(T62, T929, T931, n32_in_aa(T62, T929))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → P31_IN_AAA(T929, X1556, T931)
T409_IN_AA(T648, X1045) → N32_IN_AA(T648, X1044)
T409_IN_AA(T648, X1045) → U12_AA(T648, X1045, n32_in_aa(T648, T652))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_AA(T660, X1066) → T234_IN_AA(T660, X1065)
E404_IN_AA(T660, X1066) → U20_AA(T660, X1066, t234_in_aa(T660, T662))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_AA(T670, X1088) → N32_IN_AA(T670, X1087)
T380_IN_AA(T670, X1088) → U24_AA(T670, X1088, n32_in_aa(T670, T674))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_AA(T682, X1109) → T234_IN_AA(T682, X1108)
E375_IN_AA(T682, X1109) → U28_AA(T682, X1109, t234_in_aa(T682, T684))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_AA(T692, X1131) → N32_IN_AA(T692, X1130)
T351_IN_AA(T692, X1131) → U32_AA(T692, X1131, n32_in_aa(T692, T696))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_AA(T704, X1152) → T234_IN_AA(T704, X1151)
E346_IN_AA(T704, X1152) → U36_AA(T704, X1152, t234_in_aa(T704, T706))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_AA(T714, X1174) → N32_IN_AA(T714, X1173)
T322_IN_AA(T714, X1174) → U40_AA(T714, X1174, n32_in_aa(T714, T718))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_AA(T726, X1195) → T234_IN_AA(T726, X1194)
E317_IN_AA(T726, X1195) → U44_AA(T726, X1195, t234_in_aa(T726, T728))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_AA(T736, X1217) → N32_IN_AA(T736, X1216)
T293_IN_AA(T736, X1217) → U48_AA(T736, X1217, n32_in_aa(T736, T740))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_AA(T748, X1238) → T234_IN_AA(T748, X1237)
E288_IN_AA(T748, X1238) → U52_AA(T748, X1238, t234_in_aa(T748, T750))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_AA(T758, X1260) → N32_IN_AA(T758, X1259)
T264_IN_AA(T758, X1260) → U56_AA(T758, X1260, n32_in_aa(T758, T762))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_AA(T770, X1281) → T234_IN_AA(T770, X1280)
E259_IN_AA(T770, X1281) → U60_AA(T770, X1281, t234_in_aa(T770, T772))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → E259_IN_AA(T772, X1281)

The TRS R consists of the following rules:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x3)
U109_ga(x1, x2, x3)  =  U109_ga(x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga
U1_ga(x1, x2, x3)  =  U1_ga(x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga
U94_ga(x1, x2, x3)  =  U94_ga(x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga
U86_ga(x1, x2, x3)  =  U86_ga(x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga
U78_ga(x1, x2, x3)  =  U78_ga(x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga
U70_ga(x1, x2, x3)  =  U70_ga(x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga
U62_ga(x1, x2, x3)  =  U62_ga(x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U110_ga(x1, x2, x3)  =  U110_ga(x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga
U14_ga(x1, x2, x3)  =  U14_ga(x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga
U54_ga(x1, x2, x3)  =  U54_ga(x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga
U46_ga(x1, x2, x3)  =  U46_ga(x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga
U38_ga(x1, x2, x3)  =  U38_ga(x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga
U30_ga(x1, x2, x3)  =  U30_ga(x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga
U22_ga(x1, x2, x3)  =  U22_ga(x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U111_ga(x1, x2, x3)  =  U111_ga(x3)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U112_ga(x1, x2, x3)  =  U112_ga(x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
e404_out_ga(x1, x2)  =  e404_out_ga
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
e375_out_ga(x1, x2)  =  e375_out_ga
U27_ga(x1, x2, x3)  =  U27_ga(x3)
U28_ga(x1, x2, x3)  =  U28_ga(x3)
U29_ga(x1, x2, x3)  =  U29_ga(x3)
U31_ga(x1, x2, x3)  =  U31_ga(x3)
U32_ga(x1, x2, x3)  =  U32_ga(x3)
U33_ga(x1, x2, x3)  =  U33_ga(x3)
e346_out_ga(x1, x2)  =  e346_out_ga
U35_ga(x1, x2, x3)  =  U35_ga(x3)
U36_ga(x1, x2, x3)  =  U36_ga(x3)
U37_ga(x1, x2, x3)  =  U37_ga(x3)
U39_ga(x1, x2, x3)  =  U39_ga(x3)
U40_ga(x1, x2, x3)  =  U40_ga(x3)
U41_ga(x1, x2, x3)  =  U41_ga(x3)
e317_out_ga(x1, x2)  =  e317_out_ga
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U49_ga(x1, x2, x3)  =  U49_ga(x3)
e288_out_ga(x1, x2)  =  e288_out_ga
U51_ga(x1, x2, x3)  =  U51_ga(x3)
U52_ga(x1, x2, x3)  =  U52_ga(x3)
U53_ga(x1, x2, x3)  =  U53_ga(x3)
U55_ga(x1, x2, x3)  =  U55_ga(x3)
U56_ga(x1, x2, x3)  =  U56_ga(x3)
U57_ga(x1, x2, x3)  =  U57_ga(x3)
e259_out_ga(x1, x2)  =  e259_out_ga
U59_ga(x1, x2, x3)  =  U59_ga(x3)
U60_ga(x1, x2, x3)  =  U60_ga(x3)
U61_ga(x1, x2, x3)  =  U61_ga(x3)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
e198_out_ga(x1, x2)  =  e198_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U63_ga(x1, x2, x3)  =  U63_ga(x3)
U64_ga(x1, x2, x3)  =  U64_ga(x3)
U65_ga(x1, x2, x3)  =  U65_ga(x3)
e169_out_ga(x1, x2)  =  e169_out_ga
U67_ga(x1, x2, x3)  =  U67_ga(x3)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
U69_ga(x1, x2, x3)  =  U69_ga(x3)
U71_ga(x1, x2, x3)  =  U71_ga(x3)
U72_ga(x1, x2, x3)  =  U72_ga(x3)
U73_ga(x1, x2, x3)  =  U73_ga(x3)
e140_out_ga(x1, x2)  =  e140_out_ga
U75_ga(x1, x2, x3)  =  U75_ga(x3)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
U77_ga(x1, x2, x3)  =  U77_ga(x3)
U79_ga(x1, x2, x3)  =  U79_ga(x3)
U80_ga(x1, x2, x3)  =  U80_ga(x3)
U81_ga(x1, x2, x3)  =  U81_ga(x3)
e111_out_ga(x1, x2)  =  e111_out_ga
U83_ga(x1, x2, x3)  =  U83_ga(x3)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
U85_ga(x1, x2, x3)  =  U85_ga(x3)
U87_ga(x1, x2, x3)  =  U87_ga(x3)
U88_ga(x1, x2, x3)  =  U88_ga(x3)
U89_ga(x1, x2, x3)  =  U89_ga(x3)
e82_out_ga(x1, x2)  =  e82_out_ga
U91_ga(x1, x2, x3)  =  U91_ga(x3)
U92_ga(x1, x2, x3)  =  U92_ga(x3)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
U95_ga(x1, x2, x3)  =  U95_ga(x3)
U96_ga(x1, x2, x3)  =  U96_ga(x3)
U97_ga(x1, x2, x3)  =  U97_ga(x3)
e53_out_ga(x1, x2)  =  e53_out_ga
U99_ga(x1, x2, x3)  =  U99_ga(x3)
U100_ga(x1, x2, x3)  =  U100_ga(x3)
U101_ga(x1, x2, x3)  =  U101_ga(x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x4)
T234_IN_AA(x1, x2)  =  T234_IN_AA
E259_IN_AA(x1, x2)  =  E259_IN_AA
T264_IN_AA(x1, x2)  =  T264_IN_AA
E288_IN_AA(x1, x2)  =  E288_IN_AA
T293_IN_AA(x1, x2)  =  T293_IN_AA
E317_IN_AA(x1, x2)  =  E317_IN_AA
T322_IN_AA(x1, x2)  =  T322_IN_AA
E346_IN_AA(x1, x2)  =  E346_IN_AA
T351_IN_AA(x1, x2)  =  T351_IN_AA
E375_IN_AA(x1, x2)  =  E375_IN_AA
T380_IN_AA(x1, x2)  =  T380_IN_AA
E404_IN_AA(x1, x2)  =  E404_IN_AA
T409_IN_AA(x1, x2)  =  T409_IN_AA
E1_IN_AA(x1, x2)  =  E1_IN_AA
N7_IN_AA(x1, x2)  =  N7_IN_AA
P31_IN_AAA(x1, x2, x3)  =  P31_IN_AAA
N32_IN_AA(x1, x2)  =  N32_IN_AA
E53_IN_AA(x1, x2)  =  E53_IN_AA
T58_IN_AA(x1, x2)  =  T58_IN_AA
E82_IN_AA(x1, x2)  =  E82_IN_AA
T87_IN_AA(x1, x2)  =  T87_IN_AA
E111_IN_AA(x1, x2)  =  E111_IN_AA
T116_IN_AA(x1, x2)  =  T116_IN_AA
E140_IN_AA(x1, x2)  =  E140_IN_AA
T145_IN_AA(x1, x2)  =  T145_IN_AA
E169_IN_AA(x1, x2)  =  E169_IN_AA
T174_IN_AA(x1, x2)  =  T174_IN_AA
E198_IN_AA(x1, x2)  =  E198_IN_AA
T203_IN_AA(x1, x2)  =  T203_IN_AA
U16_AA(x1, x2, x3)  =  U16_AA(x3)
U111_AA(x1, x2, x3)  =  U111_AA(x3)
U4_AA(x1, x2, x3)  =  U4_AA(x3)
U8_AA(x1, x2, x3)  =  U8_AA(x3)
U64_AA(x1, x2, x3)  =  U64_AA(x3)
U68_AA(x1, x2, x3)  =  U68_AA(x3)
U72_AA(x1, x2, x3)  =  U72_AA(x3)
U76_AA(x1, x2, x3)  =  U76_AA(x3)
U80_AA(x1, x2, x3)  =  U80_AA(x3)
U84_AA(x1, x2, x3)  =  U84_AA(x3)
U88_AA(x1, x2, x3)  =  U88_AA(x3)
U92_AA(x1, x2, x3)  =  U92_AA(x3)
U96_AA(x1, x2, x3)  =  U96_AA(x3)
U100_AA(x1, x2, x3)  =  U100_AA(x3)
U104_AAA(x1, x2, x3, x4)  =  U104_AAA(x4)
U106_AAA(x1, x2, x3, x4)  =  U106_AAA(x4)
U12_AA(x1, x2, x3)  =  U12_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U24_AA(x1, x2, x3)  =  U24_AA(x3)
U28_AA(x1, x2, x3)  =  U28_AA(x3)
U32_AA(x1, x2, x3)  =  U32_AA(x3)
U36_AA(x1, x2, x3)  =  U36_AA(x3)
U40_AA(x1, x2, x3)  =  U40_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U48_AA(x1, x2, x3)  =  U48_AA(x3)
U52_AA(x1, x2, x3)  =  U52_AA(x3)
U56_AA(x1, x2, x3)  =  U56_AA(x3)
U60_AA(x1, x2, x3)  =  U60_AA(x3)

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

(80) UsableRulesProof (EQUIVALENT transformation)

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

(81) Obligation:

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

T234_IN_AA(.(lbrace, T392), X599) → E259_IN_AA(T392, X599)
E259_IN_AA(T400, X625) → T264_IN_AA(T400, X625)
T264_IN_AA(.(lbrace, T433), X670) → E288_IN_AA(T433, X670)
E288_IN_AA(T441, X696) → T293_IN_AA(T441, X696)
T293_IN_AA(.(lbrace, T474), X741) → E317_IN_AA(T474, X741)
E317_IN_AA(T482, X767) → T322_IN_AA(T482, X767)
T322_IN_AA(.(lbrace, T515), X812) → E346_IN_AA(T515, X812)
E346_IN_AA(T523, X838) → T351_IN_AA(T523, X838)
T351_IN_AA(.(lbrace, T556), X883) → E375_IN_AA(T556, X883)
E375_IN_AA(T564, X909) → T380_IN_AA(T564, X909)
T380_IN_AA(.(lbrace, T597), X954) → E404_IN_AA(T597, X954)
E404_IN_AA(T605, X980) → T409_IN_AA(T605, X980)
T409_IN_AA(.(lbrace, T638), X1025) → E1_IN_AA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
E1_IN_AA(T22, T24) → N7_IN_AA(T22, T24)
N7_IN_AA(.(lbrace, T41), T43) → E1_IN_AA(T41, .(rbrace, T43))
E1_IN_AA(T62, T64) → P31_IN_AAA(T62, X59, T64)
P31_IN_AAA(T62, X59, T64) → N32_IN_AA(T62, X59)
N32_IN_AA(.(lbrace, T89), X84) → E53_IN_AA(T89, X84)
E53_IN_AA(T97, X110) → T58_IN_AA(T97, X110)
T58_IN_AA(.(lbrace, T130), X155) → E82_IN_AA(T130, X155)
E82_IN_AA(T138, X181) → T87_IN_AA(T138, X181)
T87_IN_AA(.(lbrace, T171), X226) → E111_IN_AA(T171, X226)
E111_IN_AA(T179, X252) → T116_IN_AA(T179, X252)
T116_IN_AA(.(lbrace, T212), X297) → E140_IN_AA(T212, X297)
E140_IN_AA(T220, X323) → T145_IN_AA(T220, X323)
T145_IN_AA(.(lbrace, T253), X368) → E169_IN_AA(T253, X368)
E169_IN_AA(T261, X394) → T174_IN_AA(T261, X394)
T174_IN_AA(.(lbrace, T294), X439) → E198_IN_AA(T294, X439)
E198_IN_AA(T302, X465) → T203_IN_AA(T302, X465)
T203_IN_AA(.(lbrace, T335), X510) → E1_IN_AA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_AA(T941, T943) → T234_IN_AA(T941, X1569)
T234_IN_AA(T780, X1303) → N32_IN_AA(T780, X1302)
T234_IN_AA(T780, X1303) → U16_AA(T780, X1303, n32_in_aa(T780, T784))
U16_AA(T780, X1303, n32_out_aa(T780, T784)) → T234_IN_AA(T784, X1303)
E1_IN_AA(T941, T943) → U111_AA(T941, T943, t234_in_aa(T941, T945))
U111_AA(T941, T943, t234_out_aa(T941, T945)) → E1_IN_AA(T945, T943)
T203_IN_AA(T345, X530) → N32_IN_AA(T345, X529)
T203_IN_AA(T345, X530) → U4_AA(T345, X530, n32_in_aa(T345, T349))
U4_AA(T345, X530, n32_out_aa(T345, T349)) → T203_IN_AA(T349, X530)
E198_IN_AA(T357, X551) → T234_IN_AA(T357, X550)
E198_IN_AA(T357, X551) → U8_AA(T357, X551, t234_in_aa(T357, T359))
U8_AA(T357, X551, t234_out_aa(T357, T359)) → E198_IN_AA(T359, X551)
T174_IN_AA(T795, X1326) → N32_IN_AA(T795, X1325)
T174_IN_AA(T795, X1326) → U64_AA(T795, X1326, n32_in_aa(T795, T799))
U64_AA(T795, X1326, n32_out_aa(T795, T799)) → T174_IN_AA(T799, X1326)
E169_IN_AA(T807, X1347) → T234_IN_AA(T807, X1346)
E169_IN_AA(T807, X1347) → U68_AA(T807, X1347, t234_in_aa(T807, T809))
U68_AA(T807, X1347, t234_out_aa(T807, T809)) → E169_IN_AA(T809, X1347)
T145_IN_AA(T817, X1369) → N32_IN_AA(T817, X1368)
T145_IN_AA(T817, X1369) → U72_AA(T817, X1369, n32_in_aa(T817, T821))
U72_AA(T817, X1369, n32_out_aa(T817, T821)) → T145_IN_AA(T821, X1369)
E140_IN_AA(T829, X1390) → T234_IN_AA(T829, X1389)
E140_IN_AA(T829, X1390) → U76_AA(T829, X1390, t234_in_aa(T829, T831))
U76_AA(T829, X1390, t234_out_aa(T829, T831)) → E140_IN_AA(T831, X1390)
T116_IN_AA(T839, X1412) → N32_IN_AA(T839, X1411)
T116_IN_AA(T839, X1412) → U80_AA(T839, X1412, n32_in_aa(T839, T843))
U80_AA(T839, X1412, n32_out_aa(T839, T843)) → T116_IN_AA(T843, X1412)
E111_IN_AA(T851, X1433) → T234_IN_AA(T851, X1432)
E111_IN_AA(T851, X1433) → U84_AA(T851, X1433, t234_in_aa(T851, T853))
U84_AA(T851, X1433, t234_out_aa(T851, T853)) → E111_IN_AA(T853, X1433)
T87_IN_AA(T861, X1455) → N32_IN_AA(T861, X1454)
T87_IN_AA(T861, X1455) → U88_AA(T861, X1455, n32_in_aa(T861, T865))
U88_AA(T861, X1455, n32_out_aa(T861, T865)) → T87_IN_AA(T865, X1455)
E82_IN_AA(T873, X1476) → T234_IN_AA(T873, X1475)
E82_IN_AA(T873, X1476) → U92_AA(T873, X1476, t234_in_aa(T873, T875))
U92_AA(T873, X1476, t234_out_aa(T873, T875)) → E82_IN_AA(T875, X1476)
T58_IN_AA(T883, X1498) → N32_IN_AA(T883, X1497)
T58_IN_AA(T883, X1498) → U96_AA(T883, X1498, n32_in_aa(T883, T887))
U96_AA(T883, X1498, n32_out_aa(T883, T887)) → T58_IN_AA(T887, X1498)
E53_IN_AA(T895, X1519) → T234_IN_AA(T895, X1518)
E53_IN_AA(T895, X1519) → U100_AA(T895, X1519, t234_in_aa(T895, T897))
U100_AA(T895, X1519, t234_out_aa(T895, T897)) → E53_IN_AA(T897, X1519)
P31_IN_AAA(T62, T916, T918) → U104_AAA(T62, T916, T918, n32_in_aa(T62, T916))
U104_AAA(T62, T916, T918, n32_out_aa(T62, T916)) → N7_IN_AA(T916, T918)
P31_IN_AAA(T62, T929, T931) → U106_AAA(T62, T929, T931, n32_in_aa(T62, T929))
U106_AAA(T62, T929, T931, n32_out_aa(T62, T929)) → P31_IN_AAA(T929, X1556, T931)
T409_IN_AA(T648, X1045) → N32_IN_AA(T648, X1044)
T409_IN_AA(T648, X1045) → U12_AA(T648, X1045, n32_in_aa(T648, T652))
U12_AA(T648, X1045, n32_out_aa(T648, T652)) → T409_IN_AA(T652, X1045)
E404_IN_AA(T660, X1066) → T234_IN_AA(T660, X1065)
E404_IN_AA(T660, X1066) → U20_AA(T660, X1066, t234_in_aa(T660, T662))
U20_AA(T660, X1066, t234_out_aa(T660, T662)) → E404_IN_AA(T662, X1066)
T380_IN_AA(T670, X1088) → N32_IN_AA(T670, X1087)
T380_IN_AA(T670, X1088) → U24_AA(T670, X1088, n32_in_aa(T670, T674))
U24_AA(T670, X1088, n32_out_aa(T670, T674)) → T380_IN_AA(T674, X1088)
E375_IN_AA(T682, X1109) → T234_IN_AA(T682, X1108)
E375_IN_AA(T682, X1109) → U28_AA(T682, X1109, t234_in_aa(T682, T684))
U28_AA(T682, X1109, t234_out_aa(T682, T684)) → E375_IN_AA(T684, X1109)
T351_IN_AA(T692, X1131) → N32_IN_AA(T692, X1130)
T351_IN_AA(T692, X1131) → U32_AA(T692, X1131, n32_in_aa(T692, T696))
U32_AA(T692, X1131, n32_out_aa(T692, T696)) → T351_IN_AA(T696, X1131)
E346_IN_AA(T704, X1152) → T234_IN_AA(T704, X1151)
E346_IN_AA(T704, X1152) → U36_AA(T704, X1152, t234_in_aa(T704, T706))
U36_AA(T704, X1152, t234_out_aa(T704, T706)) → E346_IN_AA(T706, X1152)
T322_IN_AA(T714, X1174) → N32_IN_AA(T714, X1173)
T322_IN_AA(T714, X1174) → U40_AA(T714, X1174, n32_in_aa(T714, T718))
U40_AA(T714, X1174, n32_out_aa(T714, T718)) → T322_IN_AA(T718, X1174)
E317_IN_AA(T726, X1195) → T234_IN_AA(T726, X1194)
E317_IN_AA(T726, X1195) → U44_AA(T726, X1195, t234_in_aa(T726, T728))
U44_AA(T726, X1195, t234_out_aa(T726, T728)) → E317_IN_AA(T728, X1195)
T293_IN_AA(T736, X1217) → N32_IN_AA(T736, X1216)
T293_IN_AA(T736, X1217) → U48_AA(T736, X1217, n32_in_aa(T736, T740))
U48_AA(T736, X1217, n32_out_aa(T736, T740)) → T293_IN_AA(T740, X1217)
E288_IN_AA(T748, X1238) → T234_IN_AA(T748, X1237)
E288_IN_AA(T748, X1238) → U52_AA(T748, X1238, t234_in_aa(T748, T750))
U52_AA(T748, X1238, t234_out_aa(T748, T750)) → E288_IN_AA(T750, X1238)
T264_IN_AA(T758, X1260) → N32_IN_AA(T758, X1259)
T264_IN_AA(T758, X1260) → U56_AA(T758, X1260, n32_in_aa(T758, T762))
U56_AA(T758, X1260, n32_out_aa(T758, T762)) → T264_IN_AA(T762, X1260)
E259_IN_AA(T770, X1281) → T234_IN_AA(T770, X1280)
E259_IN_AA(T770, X1281) → U60_AA(T770, X1281, t234_in_aa(T770, T772))
U60_AA(T770, X1281, t234_out_aa(T770, T772)) → E259_IN_AA(T772, X1281)

The TRS R consists of the following rules:

n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)

The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
a  =  a
b  =  b
c  =  c
lbrace  =  lbrace
star  =  star
rbrace  =  rbrace
plus  =  plus
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
T234_IN_AA(x1, x2)  =  T234_IN_AA
E259_IN_AA(x1, x2)  =  E259_IN_AA
T264_IN_AA(x1, x2)  =  T264_IN_AA
E288_IN_AA(x1, x2)  =  E288_IN_AA
T293_IN_AA(x1, x2)  =  T293_IN_AA
E317_IN_AA(x1, x2)  =  E317_IN_AA
T322_IN_AA(x1, x2)  =  T322_IN_AA
E346_IN_AA(x1, x2)  =  E346_IN_AA
T351_IN_AA(x1, x2)  =  T351_IN_AA
E375_IN_AA(x1, x2)  =  E375_IN_AA
T380_IN_AA(x1, x2)  =  T380_IN_AA
E404_IN_AA(x1, x2)  =  E404_IN_AA
T409_IN_AA(x1, x2)  =  T409_IN_AA
E1_IN_AA(x1, x2)  =  E1_IN_AA
N7_IN_AA(x1, x2)  =  N7_IN_AA
P31_IN_AAA(x1, x2, x3)  =  P31_IN_AAA
N32_IN_AA(x1, x2)  =  N32_IN_AA
E53_IN_AA(x1, x2)  =  E53_IN_AA
T58_IN_AA(x1, x2)  =  T58_IN_AA
E82_IN_AA(x1, x2)  =  E82_IN_AA
T87_IN_AA(x1, x2)  =  T87_IN_AA
E111_IN_AA(x1, x2)  =  E111_IN_AA
T116_IN_AA(x1, x2)  =  T116_IN_AA
E140_IN_AA(x1, x2)  =  E140_IN_AA
T145_IN_AA(x1, x2)  =  T145_IN_AA
E169_IN_AA(x1, x2)  =  E169_IN_AA
T174_IN_AA(x1, x2)  =  T174_IN_AA
E198_IN_AA(x1, x2)  =  E198_IN_AA
T203_IN_AA(x1, x2)  =  T203_IN_AA
U16_AA(x1, x2, x3)  =  U16_AA(x3)
U111_AA(x1, x2, x3)  =  U111_AA(x3)
U4_AA(x1, x2, x3)  =  U4_AA(x3)
U8_AA(x1, x2, x3)  =  U8_AA(x3)
U64_AA(x1, x2, x3)  =  U64_AA(x3)
U68_AA(x1, x2, x3)  =  U68_AA(x3)
U72_AA(x1, x2, x3)  =  U72_AA(x3)
U76_AA(x1, x2, x3)  =  U76_AA(x3)
U80_AA(x1, x2, x3)  =  U80_AA(x3)
U84_AA(x1, x2, x3)  =  U84_AA(x3)
U88_AA(x1, x2, x3)  =  U88_AA(x3)
U92_AA(x1, x2, x3)  =  U92_AA(x3)
U96_AA(x1, x2, x3)  =  U96_AA(x3)
U100_AA(x1, x2, x3)  =  U100_AA(x3)
U104_AAA(x1, x2, x3, x4)  =  U104_AAA(x4)
U106_AAA(x1, x2, x3, x4)  =  U106_AAA(x4)
U12_AA(x1, x2, x3)  =  U12_AA(x3)
U20_AA(x1, x2, x3)  =  U20_AA(x3)
U24_AA(x1, x2, x3)  =  U24_AA(x3)
U28_AA(x1, x2, x3)  =  U28_AA(x3)
U32_AA(x1, x2, x3)  =  U32_AA(x3)
U36_AA(x1, x2, x3)  =  U36_AA(x3)
U40_AA(x1, x2, x3)  =  U40_AA(x3)
U44_AA(x1, x2, x3)  =  U44_AA(x3)
U48_AA(x1, x2, x3)  =  U48_AA(x3)
U52_AA(x1, x2, x3)  =  U52_AA(x3)
U56_AA(x1, x2, x3)  =  U56_AA(x3)
U60_AA(x1, x2, x3)  =  U60_AA(x3)

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

(82) PiDPToQDPProof (SOUND transformation)

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

(83) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
T234_IN_AA → U16_AA(n32_in_aa)
U16_AA(n32_out_aa) → T234_IN_AA
E1_IN_AA → U111_AA(t234_in_aa)
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
T203_IN_AA → U4_AA(n32_in_aa)
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
E198_IN_AA → U8_AA(t234_in_aa)
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(84) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T234_IN_AA → U16_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))

(85) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
E1_IN_AA → U111_AA(t234_in_aa)
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
T203_IN_AA → U4_AA(n32_in_aa)
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
E198_IN_AA → U8_AA(t234_in_aa)
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(86) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E1_IN_AA → U111_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))

(87) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
T203_IN_AA → U4_AA(n32_in_aa)
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
E198_IN_AA → U8_AA(t234_in_aa)
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(88) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T203_IN_AA → U4_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))

(89) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
E198_IN_AA → U8_AA(t234_in_aa)
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(90) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E198_IN_AA → U8_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))

(91) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
T174_IN_AA → U64_AA(n32_in_aa)
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(92) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T174_IN_AA → U64_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))

(93) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
E169_IN_AA → U68_AA(t234_in_aa)
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(94) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E169_IN_AA → U68_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))

(95) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
T145_IN_AA → U72_AA(n32_in_aa)
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(96) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T145_IN_AA → U72_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))

(97) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
E140_IN_AA → U76_AA(t234_in_aa)
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(98) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E140_IN_AA → U76_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))

(99) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
T116_IN_AA → U80_AA(n32_in_aa)
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(100) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T116_IN_AA → U80_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))

(101) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
E111_IN_AA → U84_AA(t234_in_aa)
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(102) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E111_IN_AA → U84_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))

(103) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
T87_IN_AA → U88_AA(n32_in_aa)
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(104) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T87_IN_AA → U88_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))

(105) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
E82_IN_AA → U92_AA(t234_in_aa)
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(106) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E82_IN_AA → U92_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))

(107) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
T58_IN_AA → U96_AA(n32_in_aa)
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(108) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T58_IN_AA → U96_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))

(109) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
E53_IN_AA → U100_AA(t234_in_aa)
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(110) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E53_IN_AA → U100_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))

(111) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
P31_IN_AAA → U104_AAA(n32_in_aa)
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(112) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P31_IN_AAA → U104_AAA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))

(113) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
P31_IN_AAA → U106_AAA(n32_in_aa)
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(114) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule P31_IN_AAA → U106_AAA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))

(115) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
T409_IN_AA → U12_AA(n32_in_aa)
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(116) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T409_IN_AA → U12_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))

(117) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
E404_IN_AA → U20_AA(t234_in_aa)
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(118) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E404_IN_AA → U20_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))

(119) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
T380_IN_AA → U24_AA(n32_in_aa)
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(120) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T380_IN_AA → U24_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))

(121) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
E375_IN_AA → U28_AA(t234_in_aa)
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(122) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E375_IN_AA → U28_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))

(123) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
T351_IN_AA → U32_AA(n32_in_aa)
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(124) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T351_IN_AA → U32_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))

(125) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
E346_IN_AA → U36_AA(t234_in_aa)
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(126) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E346_IN_AA → U36_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))

(127) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
T322_IN_AA → U40_AA(n32_in_aa)
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(128) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T322_IN_AA → U40_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))

(129) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
E317_IN_AA → U44_AA(t234_in_aa)
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(130) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E317_IN_AA → U44_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))

(131) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
T293_IN_AA → U48_AA(n32_in_aa)
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(132) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T293_IN_AA → U48_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))

(133) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
E288_IN_AA → U52_AA(t234_in_aa)
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))
T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(134) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E288_IN_AA → U52_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E288_IN_AA → U52_AA(t234_out_aa)
E288_IN_AA → U52_AA(U14_aa(e259_in_aa))
E288_IN_AA → U52_AA(U15_aa(n32_in_aa))
E288_IN_AA → U52_AA(U16_aa(n32_in_aa))

(135) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
T264_IN_AA → U56_AA(n32_in_aa)
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))
T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))
E288_IN_AA → U52_AA(t234_out_aa)
E288_IN_AA → U52_AA(U14_aa(e259_in_aa))
E288_IN_AA → U52_AA(U15_aa(n32_in_aa))
E288_IN_AA → U52_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(136) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule T264_IN_AA → U56_AA(n32_in_aa) at position [0] we obtained the following new rules [LPAR04]:

T264_IN_AA → U56_AA(n32_out_aa)
T264_IN_AA → U56_AA(U1_aa(e53_in_aa))

(137) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
E259_IN_AA → U60_AA(t234_in_aa)
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))
T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))
E288_IN_AA → U52_AA(t234_out_aa)
E288_IN_AA → U52_AA(U14_aa(e259_in_aa))
E288_IN_AA → U52_AA(U15_aa(n32_in_aa))
E288_IN_AA → U52_AA(U16_aa(n32_in_aa))
T264_IN_AA → U56_AA(n32_out_aa)
T264_IN_AA → U56_AA(U1_aa(e53_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(138) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule E259_IN_AA → U60_AA(t234_in_aa) at position [0] we obtained the following new rules [LPAR04]:

E259_IN_AA → U60_AA(t234_out_aa)
E259_IN_AA → U60_AA(U14_aa(e259_in_aa))
E259_IN_AA → U60_AA(U15_aa(n32_in_aa))
E259_IN_AA → U60_AA(U16_aa(n32_in_aa))

(139) Obligation:

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

T234_IN_AA → E259_IN_AA
E259_IN_AA → T264_IN_AA
T264_IN_AA → E288_IN_AA
E288_IN_AA → T293_IN_AA
T293_IN_AA → E317_IN_AA
E317_IN_AA → T322_IN_AA
T322_IN_AA → E346_IN_AA
E346_IN_AA → T351_IN_AA
T351_IN_AA → E375_IN_AA
E375_IN_AA → T380_IN_AA
T380_IN_AA → E404_IN_AA
E404_IN_AA → T409_IN_AA
T409_IN_AA → E1_IN_AA
E1_IN_AA → N7_IN_AA
N7_IN_AA → E1_IN_AA
E1_IN_AA → P31_IN_AAA
P31_IN_AAA → N32_IN_AA
N32_IN_AA → E53_IN_AA
E53_IN_AA → T58_IN_AA
T58_IN_AA → E82_IN_AA
E82_IN_AA → T87_IN_AA
T87_IN_AA → E111_IN_AA
E111_IN_AA → T116_IN_AA
T116_IN_AA → E140_IN_AA
E140_IN_AA → T145_IN_AA
T145_IN_AA → E169_IN_AA
E169_IN_AA → T174_IN_AA
T174_IN_AA → E198_IN_AA
E198_IN_AA → T203_IN_AA
T203_IN_AA → E1_IN_AA
E1_IN_AA → T234_IN_AA
T234_IN_AA → N32_IN_AA
U16_AA(n32_out_aa) → T234_IN_AA
U111_AA(t234_out_aa) → E1_IN_AA
T203_IN_AA → N32_IN_AA
U4_AA(n32_out_aa) → T203_IN_AA
E198_IN_AA → T234_IN_AA
U8_AA(t234_out_aa) → E198_IN_AA
T174_IN_AA → N32_IN_AA
U64_AA(n32_out_aa) → T174_IN_AA
E169_IN_AA → T234_IN_AA
U68_AA(t234_out_aa) → E169_IN_AA
T145_IN_AA → N32_IN_AA
U72_AA(n32_out_aa) → T145_IN_AA
E140_IN_AA → T234_IN_AA
U76_AA(t234_out_aa) → E140_IN_AA
T116_IN_AA → N32_IN_AA
U80_AA(n32_out_aa) → T116_IN_AA
E111_IN_AA → T234_IN_AA
U84_AA(t234_out_aa) → E111_IN_AA
T87_IN_AA → N32_IN_AA
U88_AA(n32_out_aa) → T87_IN_AA
E82_IN_AA → T234_IN_AA
U92_AA(t234_out_aa) → E82_IN_AA
T58_IN_AA → N32_IN_AA
U96_AA(n32_out_aa) → T58_IN_AA
E53_IN_AA → T234_IN_AA
U100_AA(t234_out_aa) → E53_IN_AA
U104_AAA(n32_out_aa) → N7_IN_AA
U106_AAA(n32_out_aa) → P31_IN_AAA
T409_IN_AA → N32_IN_AA
U12_AA(n32_out_aa) → T409_IN_AA
E404_IN_AA → T234_IN_AA
U20_AA(t234_out_aa) → E404_IN_AA
T380_IN_AA → N32_IN_AA
U24_AA(n32_out_aa) → T380_IN_AA
E375_IN_AA → T234_IN_AA
U28_AA(t234_out_aa) → E375_IN_AA
T351_IN_AA → N32_IN_AA
U32_AA(n32_out_aa) → T351_IN_AA
E346_IN_AA → T234_IN_AA
U36_AA(t234_out_aa) → E346_IN_AA
T322_IN_AA → N32_IN_AA
U40_AA(n32_out_aa) → T322_IN_AA
E317_IN_AA → T234_IN_AA
U44_AA(t234_out_aa) → E317_IN_AA
T293_IN_AA → N32_IN_AA
U48_AA(n32_out_aa) → T293_IN_AA
E288_IN_AA → T234_IN_AA
U52_AA(t234_out_aa) → E288_IN_AA
T264_IN_AA → N32_IN_AA
U56_AA(n32_out_aa) → T264_IN_AA
E259_IN_AA → T234_IN_AA
U60_AA(t234_out_aa) → E259_IN_AA
T234_IN_AA → U16_AA(n32_out_aa)
T234_IN_AA → U16_AA(U1_aa(e53_in_aa))
E1_IN_AA → U111_AA(t234_out_aa)
E1_IN_AA → U111_AA(U14_aa(e259_in_aa))
E1_IN_AA → U111_AA(U15_aa(n32_in_aa))
E1_IN_AA → U111_AA(U16_aa(n32_in_aa))
T203_IN_AA → U4_AA(n32_out_aa)
T203_IN_AA → U4_AA(U1_aa(e53_in_aa))
E198_IN_AA → U8_AA(t234_out_aa)
E198_IN_AA → U8_AA(U14_aa(e259_in_aa))
E198_IN_AA → U8_AA(U15_aa(n32_in_aa))
E198_IN_AA → U8_AA(U16_aa(n32_in_aa))
T174_IN_AA → U64_AA(n32_out_aa)
T174_IN_AA → U64_AA(U1_aa(e53_in_aa))
E169_IN_AA → U68_AA(t234_out_aa)
E169_IN_AA → U68_AA(U14_aa(e259_in_aa))
E169_IN_AA → U68_AA(U15_aa(n32_in_aa))
E169_IN_AA → U68_AA(U16_aa(n32_in_aa))
T145_IN_AA → U72_AA(n32_out_aa)
T145_IN_AA → U72_AA(U1_aa(e53_in_aa))
E140_IN_AA → U76_AA(t234_out_aa)
E140_IN_AA → U76_AA(U14_aa(e259_in_aa))
E140_IN_AA → U76_AA(U15_aa(n32_in_aa))
E140_IN_AA → U76_AA(U16_aa(n32_in_aa))
T116_IN_AA → U80_AA(n32_out_aa)
T116_IN_AA → U80_AA(U1_aa(e53_in_aa))
E111_IN_AA → U84_AA(t234_out_aa)
E111_IN_AA → U84_AA(U14_aa(e259_in_aa))
E111_IN_AA → U84_AA(U15_aa(n32_in_aa))
E111_IN_AA → U84_AA(U16_aa(n32_in_aa))
T87_IN_AA → U88_AA(n32_out_aa)
T87_IN_AA → U88_AA(U1_aa(e53_in_aa))
E82_IN_AA → U92_AA(t234_out_aa)
E82_IN_AA → U92_AA(U14_aa(e259_in_aa))
E82_IN_AA → U92_AA(U15_aa(n32_in_aa))
E82_IN_AA → U92_AA(U16_aa(n32_in_aa))
T58_IN_AA → U96_AA(n32_out_aa)
T58_IN_AA → U96_AA(U1_aa(e53_in_aa))
E53_IN_AA → U100_AA(t234_out_aa)
E53_IN_AA → U100_AA(U14_aa(e259_in_aa))
E53_IN_AA → U100_AA(U15_aa(n32_in_aa))
E53_IN_AA → U100_AA(U16_aa(n32_in_aa))
P31_IN_AAA → U104_AAA(n32_out_aa)
P31_IN_AAA → U104_AAA(U1_aa(e53_in_aa))
P31_IN_AAA → U106_AAA(n32_out_aa)
P31_IN_AAA → U106_AAA(U1_aa(e53_in_aa))
T409_IN_AA → U12_AA(n32_out_aa)
T409_IN_AA → U12_AA(U1_aa(e53_in_aa))
E404_IN_AA → U20_AA(t234_out_aa)
E404_IN_AA → U20_AA(U14_aa(e259_in_aa))
E404_IN_AA → U20_AA(U15_aa(n32_in_aa))
E404_IN_AA → U20_AA(U16_aa(n32_in_aa))
T380_IN_AA → U24_AA(n32_out_aa)
T380_IN_AA → U24_AA(U1_aa(e53_in_aa))
E375_IN_AA → U28_AA(t234_out_aa)
E375_IN_AA → U28_AA(U14_aa(e259_in_aa))
E375_IN_AA → U28_AA(U15_aa(n32_in_aa))
E375_IN_AA → U28_AA(U16_aa(n32_in_aa))
T351_IN_AA → U32_AA(n32_out_aa)
T351_IN_AA → U32_AA(U1_aa(e53_in_aa))
E346_IN_AA → U36_AA(t234_out_aa)
E346_IN_AA → U36_AA(U14_aa(e259_in_aa))
E346_IN_AA → U36_AA(U15_aa(n32_in_aa))
E346_IN_AA → U36_AA(U16_aa(n32_in_aa))
T322_IN_AA → U40_AA(n32_out_aa)
T322_IN_AA → U40_AA(U1_aa(e53_in_aa))
E317_IN_AA → U44_AA(t234_out_aa)
E317_IN_AA → U44_AA(U14_aa(e259_in_aa))
E317_IN_AA → U44_AA(U15_aa(n32_in_aa))
E317_IN_AA → U44_AA(U16_aa(n32_in_aa))
T293_IN_AA → U48_AA(n32_out_aa)
T293_IN_AA → U48_AA(U1_aa(e53_in_aa))
E288_IN_AA → U52_AA(t234_out_aa)
E288_IN_AA → U52_AA(U14_aa(e259_in_aa))
E288_IN_AA → U52_AA(U15_aa(n32_in_aa))
E288_IN_AA → U52_AA(U16_aa(n32_in_aa))
T264_IN_AA → U56_AA(n32_out_aa)
T264_IN_AA → U56_AA(U1_aa(e53_in_aa))
E259_IN_AA → U60_AA(t234_out_aa)
E259_IN_AA → U60_AA(U14_aa(e259_in_aa))
E259_IN_AA → U60_AA(U15_aa(n32_in_aa))
E259_IN_AA → U60_AA(U16_aa(n32_in_aa))

The TRS R consists of the following rules:

n32_in_aa → n32_out_aa
n32_in_aa → U1_aa(e53_in_aa)
t234_in_aa → t234_out_aa
t234_in_aa → U14_aa(e259_in_aa)
t234_in_aa → U15_aa(n32_in_aa)
t234_in_aa → U16_aa(n32_in_aa)
U1_aa(e53_out_aa) → n32_out_aa
U14_aa(e259_out_aa) → t234_out_aa
U15_aa(n32_out_aa) → t234_out_aa
U16_aa(n32_out_aa) → U17_aa(t234_in_aa)
e53_in_aa → U98_aa(t58_in_aa)
e53_in_aa → U99_aa(t234_in_aa)
e53_in_aa → U100_aa(t234_in_aa)
e259_in_aa → U58_aa(t264_in_aa)
e259_in_aa → U59_aa(t234_in_aa)
e259_in_aa → U60_aa(t234_in_aa)
U17_aa(t234_out_aa) → t234_out_aa
U98_aa(t58_out_aa) → e53_out_aa
U99_aa(t234_out_aa) → e53_out_aa
U100_aa(t234_out_aa) → U101_aa(e53_in_aa)
U58_aa(t264_out_aa) → e259_out_aa
U59_aa(t234_out_aa) → e259_out_aa
U60_aa(t234_out_aa) → U61_aa(e259_in_aa)
t58_in_aa → t58_out_aa
t58_in_aa → U94_aa(e82_in_aa)
t58_in_aa → U95_aa(n32_in_aa)
t58_in_aa → U96_aa(n32_in_aa)
U101_aa(e53_out_aa) → e53_out_aa
t264_in_aa → t264_out_aa
t264_in_aa → U54_aa(e288_in_aa)
t264_in_aa → U55_aa(n32_in_aa)
t264_in_aa → U56_aa(n32_in_aa)
U61_aa(e259_out_aa) → e259_out_aa
U94_aa(e82_out_aa) → t58_out_aa
U95_aa(n32_out_aa) → t58_out_aa
U96_aa(n32_out_aa) → U97_aa(t58_in_aa)
U54_aa(e288_out_aa) → t264_out_aa
U55_aa(n32_out_aa) → t264_out_aa
U56_aa(n32_out_aa) → U57_aa(t264_in_aa)
e82_in_aa → U90_aa(t87_in_aa)
e82_in_aa → U91_aa(t234_in_aa)
e82_in_aa → U92_aa(t234_in_aa)
U97_aa(t58_out_aa) → t58_out_aa
e288_in_aa → U50_aa(t293_in_aa)
e288_in_aa → U51_aa(t234_in_aa)
e288_in_aa → U52_aa(t234_in_aa)
U57_aa(t264_out_aa) → t264_out_aa
U90_aa(t87_out_aa) → e82_out_aa
U91_aa(t234_out_aa) → e82_out_aa
U92_aa(t234_out_aa) → U93_aa(e82_in_aa)
U50_aa(t293_out_aa) → e288_out_aa
U51_aa(t234_out_aa) → e288_out_aa
U52_aa(t234_out_aa) → U53_aa(e288_in_aa)
t87_in_aa → t87_out_aa
t87_in_aa → U86_aa(e111_in_aa)
t87_in_aa → U87_aa(n32_in_aa)
t87_in_aa → U88_aa(n32_in_aa)
U93_aa(e82_out_aa) → e82_out_aa
t293_in_aa → t293_out_aa
t293_in_aa → U46_aa(e317_in_aa)
t293_in_aa → U47_aa(n32_in_aa)
t293_in_aa → U48_aa(n32_in_aa)
U53_aa(e288_out_aa) → e288_out_aa
U86_aa(e111_out_aa) → t87_out_aa
U87_aa(n32_out_aa) → t87_out_aa
U88_aa(n32_out_aa) → U89_aa(t87_in_aa)
U46_aa(e317_out_aa) → t293_out_aa
U47_aa(n32_out_aa) → t293_out_aa
U48_aa(n32_out_aa) → U49_aa(t293_in_aa)
e111_in_aa → U82_aa(t116_in_aa)
e111_in_aa → U83_aa(t234_in_aa)
e111_in_aa → U84_aa(t234_in_aa)
U89_aa(t87_out_aa) → t87_out_aa
e317_in_aa → U42_aa(t322_in_aa)
e317_in_aa → U43_aa(t234_in_aa)
e317_in_aa → U44_aa(t234_in_aa)
U49_aa(t293_out_aa) → t293_out_aa
U82_aa(t116_out_aa) → e111_out_aa
U83_aa(t234_out_aa) → e111_out_aa
U84_aa(t234_out_aa) → U85_aa(e111_in_aa)
U42_aa(t322_out_aa) → e317_out_aa
U43_aa(t234_out_aa) → e317_out_aa
U44_aa(t234_out_aa) → U45_aa(e317_in_aa)
t116_in_aa → t116_out_aa
t116_in_aa → U78_aa(e140_in_aa)
t116_in_aa → U79_aa(n32_in_aa)
t116_in_aa → U80_aa(n32_in_aa)
U85_aa(e111_out_aa) → e111_out_aa
t322_in_aa → t322_out_aa
t322_in_aa → U38_aa(e346_in_aa)
t322_in_aa → U39_aa(n32_in_aa)
t322_in_aa → U40_aa(n32_in_aa)
U45_aa(e317_out_aa) → e317_out_aa
U78_aa(e140_out_aa) → t116_out_aa
U79_aa(n32_out_aa) → t116_out_aa
U80_aa(n32_out_aa) → U81_aa(t116_in_aa)
U38_aa(e346_out_aa) → t322_out_aa
U39_aa(n32_out_aa) → t322_out_aa
U40_aa(n32_out_aa) → U41_aa(t322_in_aa)
e140_in_aa → U74_aa(t145_in_aa)
e140_in_aa → U75_aa(t234_in_aa)
e140_in_aa → U76_aa(t234_in_aa)
U81_aa(t116_out_aa) → t116_out_aa
e346_in_aa → U34_aa(t351_in_aa)
e346_in_aa → U35_aa(t234_in_aa)
e346_in_aa → U36_aa(t234_in_aa)
U41_aa(t322_out_aa) → t322_out_aa
U74_aa(t145_out_aa) → e140_out_aa
U75_aa(t234_out_aa) → e140_out_aa
U76_aa(t234_out_aa) → U77_aa(e140_in_aa)
U34_aa(t351_out_aa) → e346_out_aa
U35_aa(t234_out_aa) → e346_out_aa
U36_aa(t234_out_aa) → U37_aa(e346_in_aa)
t145_in_aa → t145_out_aa
t145_in_aa → U70_aa(e169_in_aa)
t145_in_aa → U71_aa(n32_in_aa)
t145_in_aa → U72_aa(n32_in_aa)
U77_aa(e140_out_aa) → e140_out_aa
t351_in_aa → t351_out_aa
t351_in_aa → U30_aa(e375_in_aa)
t351_in_aa → U31_aa(n32_in_aa)
t351_in_aa → U32_aa(n32_in_aa)
U37_aa(e346_out_aa) → e346_out_aa
U70_aa(e169_out_aa) → t145_out_aa
U71_aa(n32_out_aa) → t145_out_aa
U72_aa(n32_out_aa) → U73_aa(t145_in_aa)
U30_aa(e375_out_aa) → t351_out_aa
U31_aa(n32_out_aa) → t351_out_aa
U32_aa(n32_out_aa) → U33_aa(t351_in_aa)
e169_in_aa → U66_aa(t174_in_aa)
e169_in_aa → U67_aa(t234_in_aa)
e169_in_aa → U68_aa(t234_in_aa)
U73_aa(t145_out_aa) → t145_out_aa
e375_in_aa → U26_aa(t380_in_aa)
e375_in_aa → U27_aa(t234_in_aa)
e375_in_aa → U28_aa(t234_in_aa)
U33_aa(t351_out_aa) → t351_out_aa
U66_aa(t174_out_aa) → e169_out_aa
U67_aa(t234_out_aa) → e169_out_aa
U68_aa(t234_out_aa) → U69_aa(e169_in_aa)
U26_aa(t380_out_aa) → e375_out_aa
U27_aa(t234_out_aa) → e375_out_aa
U28_aa(t234_out_aa) → U29_aa(e375_in_aa)
t174_in_aa → t174_out_aa
t174_in_aa → U62_aa(e198_in_aa)
t174_in_aa → U63_aa(n32_in_aa)
t174_in_aa → U64_aa(n32_in_aa)
U69_aa(e169_out_aa) → e169_out_aa
t380_in_aa → t380_out_aa
t380_in_aa → U22_aa(e404_in_aa)
t380_in_aa → U23_aa(n32_in_aa)
t380_in_aa → U24_aa(n32_in_aa)
U29_aa(e375_out_aa) → e375_out_aa
U62_aa(e198_out_aa) → t174_out_aa
U63_aa(n32_out_aa) → t174_out_aa
U64_aa(n32_out_aa) → U65_aa(t174_in_aa)
U22_aa(e404_out_aa) → t380_out_aa
U23_aa(n32_out_aa) → t380_out_aa
U24_aa(n32_out_aa) → U25_aa(t380_in_aa)
e198_in_aa → U6_aa(t203_in_aa)
e198_in_aa → U7_aa(t234_in_aa)
e198_in_aa → U8_aa(t234_in_aa)
U65_aa(t174_out_aa) → t174_out_aa
e404_in_aa → U18_aa(t409_in_aa)
e404_in_aa → U19_aa(t234_in_aa)
e404_in_aa → U20_aa(t234_in_aa)
U25_aa(t380_out_aa) → t380_out_aa
U6_aa(t203_out_aa) → e198_out_aa
U7_aa(t234_out_aa) → e198_out_aa
U8_aa(t234_out_aa) → U9_aa(e198_in_aa)
U18_aa(t409_out_aa) → e404_out_aa
U19_aa(t234_out_aa) → e404_out_aa
U20_aa(t234_out_aa) → U21_aa(e404_in_aa)
t203_in_aa → t203_out_aa
t203_in_aa → U2_aa(e1_in_aa)
t203_in_aa → U3_aa(n32_in_aa)
t203_in_aa → U4_aa(n32_in_aa)
U9_aa(e198_out_aa) → e198_out_aa
t409_in_aa → t409_out_aa
t409_in_aa → U10_aa(e1_in_aa)
t409_in_aa → U11_aa(n32_in_aa)
t409_in_aa → U12_aa(n32_in_aa)
U21_aa(e404_out_aa) → e404_out_aa
U2_aa(e1_out_aa) → t203_out_aa
U3_aa(n32_out_aa) → t203_out_aa
U4_aa(n32_out_aa) → U5_aa(t203_in_aa)
U10_aa(e1_out_aa) → t409_out_aa
U11_aa(n32_out_aa) → t409_out_aa
U12_aa(n32_out_aa) → U13_aa(t409_in_aa)
e1_in_aa → U108_aa(n7_in_aa)
e1_in_aa → U109_aa(p31_in_aaa)
e1_in_aa → U110_aa(t234_in_aa)
e1_in_aa → U111_aa(t234_in_aa)
U5_aa(t203_out_aa) → t203_out_aa
U13_aa(t409_out_aa) → t409_out_aa
U108_aa(n7_out_aa) → e1_out_aa
U109_aa(p31_out_aaa) → e1_out_aa
U110_aa(t234_out_aa) → e1_out_aa
U111_aa(t234_out_aa) → U112_aa(e1_in_aa)
n7_in_aa → n7_out_aa
n7_in_aa → U102_aa(e1_in_aa)
p31_in_aaa → U103_aaa(n32_in_aa)
p31_in_aaa → U104_aaa(n32_in_aa)
p31_in_aaa → U106_aaa(n32_in_aa)
U112_aa(e1_out_aa) → e1_out_aa
U102_aa(e1_out_aa) → n7_out_aa
U103_aaa(n32_out_aa) → p31_out_aaa
U104_aaa(n32_out_aa) → U105_aaa(n7_in_aa)
U106_aaa(n32_out_aa) → U107_aaa(p31_in_aaa)
U105_aaa(n7_out_aa) → p31_out_aaa
U107_aaa(p31_out_aaa) → p31_out_aaa

The set Q consists of the following terms:

n32_in_aa
t234_in_aa
U1_aa(x0)
U14_aa(x0)
U15_aa(x0)
U16_aa(x0)
e53_in_aa
e259_in_aa
U17_aa(x0)
U98_aa(x0)
U99_aa(x0)
U100_aa(x0)
U58_aa(x0)
U59_aa(x0)
U60_aa(x0)
t58_in_aa
U101_aa(x0)
t264_in_aa
U61_aa(x0)
U94_aa(x0)
U95_aa(x0)
U96_aa(x0)
U54_aa(x0)
U55_aa(x0)
U56_aa(x0)
e82_in_aa
U97_aa(x0)
e288_in_aa
U57_aa(x0)
U90_aa(x0)
U91_aa(x0)
U92_aa(x0)
U50_aa(x0)
U51_aa(x0)
U52_aa(x0)
t87_in_aa
U93_aa(x0)
t293_in_aa
U53_aa(x0)
U86_aa(x0)
U87_aa(x0)
U88_aa(x0)
U46_aa(x0)
U47_aa(x0)
U48_aa(x0)
e111_in_aa
U89_aa(x0)
e317_in_aa
U49_aa(x0)
U82_aa(x0)
U83_aa(x0)
U84_aa(x0)
U42_aa(x0)
U43_aa(x0)
U44_aa(x0)
t116_in_aa
U85_aa(x0)
t322_in_aa
U45_aa(x0)
U78_aa(x0)
U79_aa(x0)
U80_aa(x0)
U38_aa(x0)
U39_aa(x0)
U40_aa(x0)
e140_in_aa
U81_aa(x0)
e346_in_aa
U41_aa(x0)
U74_aa(x0)
U75_aa(x0)
U76_aa(x0)
U34_aa(x0)
U35_aa(x0)
U36_aa(x0)
t145_in_aa
U77_aa(x0)
t351_in_aa
U37_aa(x0)
U70_aa(x0)
U71_aa(x0)
U72_aa(x0)
U30_aa(x0)
U31_aa(x0)
U32_aa(x0)
e169_in_aa
U73_aa(x0)
e375_in_aa
U33_aa(x0)
U66_aa(x0)
U67_aa(x0)
U68_aa(x0)
U26_aa(x0)
U27_aa(x0)
U28_aa(x0)
t174_in_aa
U69_aa(x0)
t380_in_aa
U29_aa(x0)
U62_aa(x0)
U63_aa(x0)
U64_aa(x0)
U22_aa(x0)
U23_aa(x0)
U24_aa(x0)
e198_in_aa
U65_aa(x0)
e404_in_aa
U25_aa(x0)
U6_aa(x0)
U7_aa(x0)
U8_aa(x0)
U18_aa(x0)
U19_aa(x0)
U20_aa(x0)
t203_in_aa
U9_aa(x0)
t409_in_aa
U21_aa(x0)
U2_aa(x0)
U3_aa(x0)
U4_aa(x0)
U10_aa(x0)
U11_aa(x0)
U12_aa(x0)
e1_in_aa
U5_aa(x0)
U13_aa(x0)
U108_aa(x0)
U109_aa(x0)
U110_aa(x0)
U111_aa(x0)
n7_in_aa
p31_in_aaa
U112_aa(x0)
U102_aa(x0)
U103_aaa(x0)
U104_aaa(x0)
U106_aaa(x0)
U105_aaa(x0)
U107_aaa(x0)

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

(140) Obligation:

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

E1_IN_GA(T22, T24) → N7_IN_GA(T22, T24)
N7_IN_GA(.(lbrace, T41), T43) → E1_IN_GA(T41, .(rbrace, T43))
E1_IN_GA(T62, T64) → P31_IN_GAA(T62, X59, T64)
P31_IN_GAA(T62, X59, T64) → N32_IN_GA(T62, X59)
N32_IN_GA(.(lbrace, T89), X84) → E53_IN_GA(T89, X84)
E53_IN_GA(T97, X110) → T58_IN_GA(T97, X110)
T58_IN_GA(.(lbrace, T130), X155) → E82_IN_GA(T130, X155)
E82_IN_GA(T138, X181) → T87_IN_GA(T138, X181)
T87_IN_GA(.(lbrace, T171), X226) → E111_IN_GA(T171, X226)
E111_IN_GA(T179, X252) → T116_IN_GA(T179, X252)
T116_IN_GA(.(lbrace, T212), X297) → E140_IN_GA(T212, X297)
E140_IN_GA(T220, X323) → T145_IN_GA(T220, X323)
T145_IN_GA(.(lbrace, T253), X368) → E169_IN_GA(T253, X368)
E169_IN_GA(T261, X394) → T174_IN_GA(T261, X394)
T174_IN_GA(.(lbrace, T294), X439) → E198_IN_GA(T294, X439)
E198_IN_GA(T302, X465) → T203_IN_GA(T302, X465)
T203_IN_GA(.(lbrace, T335), X510) → E1_IN_GA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_GA(T941, T943) → T234_IN_GA(T941, X1569)
T234_IN_GA(.(lbrace, T392), X599) → E259_IN_GA(T392, X599)
E259_IN_GA(T400, X625) → T264_IN_GA(T400, X625)
T264_IN_GA(.(lbrace, T433), X670) → E288_IN_GA(T433, X670)
E288_IN_GA(T441, X696) → T293_IN_GA(T441, X696)
T293_IN_GA(.(lbrace, T474), X741) → E317_IN_GA(T474, X741)
E317_IN_GA(T482, X767) → T322_IN_GA(T482, X767)
T322_IN_GA(.(lbrace, T515), X812) → E346_IN_GA(T515, X812)
E346_IN_GA(T523, X838) → T351_IN_GA(T523, X838)
T351_IN_GA(.(lbrace, T556), X883) → E375_IN_GA(T556, X883)
E375_IN_GA(T564, X909) → T380_IN_GA(T564, X909)
T380_IN_GA(.(lbrace, T597), X954) → E404_IN_GA(T597, X954)
E404_IN_GA(T605, X980) → T409_IN_GA(T605, X980)
T409_IN_GA(.(lbrace, T638), X1025) → E1_IN_GA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
T409_IN_GA(T648, X1045) → N32_IN_GA(T648, X1044)
E404_IN_GA(T660, X1066) → T234_IN_GA(T660, X1065)
T234_IN_GA(T780, X1303) → N32_IN_GA(T780, X1302)
T380_IN_GA(T670, X1088) → N32_IN_GA(T670, X1087)
E375_IN_GA(T682, X1109) → T234_IN_GA(T682, X1108)
T351_IN_GA(T692, X1131) → N32_IN_GA(T692, X1130)
E346_IN_GA(T704, X1152) → T234_IN_GA(T704, X1151)
T322_IN_GA(T714, X1174) → N32_IN_GA(T714, X1173)
E317_IN_GA(T726, X1195) → T234_IN_GA(T726, X1194)
T293_IN_GA(T736, X1217) → N32_IN_GA(T736, X1216)
E288_IN_GA(T748, X1238) → T234_IN_GA(T748, X1237)
T264_IN_GA(T758, X1260) → N32_IN_GA(T758, X1259)
E259_IN_GA(T770, X1281) → T234_IN_GA(T770, X1280)
T203_IN_GA(T345, X530) → N32_IN_GA(T345, X529)
E198_IN_GA(T357, X551) → T234_IN_GA(T357, X550)
T174_IN_GA(T795, X1326) → N32_IN_GA(T795, X1325)
E169_IN_GA(T807, X1347) → T234_IN_GA(T807, X1346)
T145_IN_GA(T817, X1369) → N32_IN_GA(T817, X1368)
E140_IN_GA(T829, X1390) → T234_IN_GA(T829, X1389)
T116_IN_GA(T839, X1412) → N32_IN_GA(T839, X1411)
E111_IN_GA(T851, X1433) → T234_IN_GA(T851, X1432)
T87_IN_GA(T861, X1455) → N32_IN_GA(T861, X1454)
E82_IN_GA(T873, X1476) → T234_IN_GA(T873, X1475)
T58_IN_GA(T883, X1498) → N32_IN_GA(T883, X1497)
E53_IN_GA(T895, X1519) → T234_IN_GA(T895, X1518)

The TRS R consists of the following rules:

e1_in_ga(T22, T24) → U108_ga(T22, T24, n7_in_ga(T22, T24))
n7_in_ga(.(a, T36), T36) → n7_out_ga(.(a, T36), T36)
n7_in_ga(.(b, T36), T36) → n7_out_ga(.(b, T36), T36)
n7_in_ga(.(c, T36), T36) → n7_out_ga(.(c, T36), T36)
n7_in_ga(.(lbrace, T41), T43) → U102_ga(T41, T43, e1_in_ga(T41, .(rbrace, T43)))
e1_in_ga(T62, T64) → U109_ga(T62, T64, p31_in_gaa(T62, X59, T64))
p31_in_gaa(T62, X59, T64) → U103_gaa(T62, X59, T64, n32_in_ga(T62, X59))
n32_in_ga(.(a, .(star, T86)), T86) → n32_out_ga(.(a, .(star, T86)), T86)
n32_in_ga(.(b, .(star, T86)), T86) → n32_out_ga(.(b, .(star, T86)), T86)
n32_in_ga(.(c, .(star, T86)), T86) → n32_out_ga(.(c, .(star, T86)), T86)
n32_in_ga(.(lbrace, T89), X84) → U1_ga(T89, X84, e53_in_ga(T89, X84))
e53_in_ga(T97, X110) → U98_ga(T97, X110, t58_in_ga(T97, X110))
t58_in_ga(.(a, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(a, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(b, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(b, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(c, .(rbrace, .(star, T127))), T127) → t58_out_ga(.(c, .(rbrace, .(star, T127))), T127)
t58_in_ga(.(lbrace, T130), X155) → U94_ga(T130, X155, e82_in_ga(T130, X155))
e82_in_ga(T138, X181) → U90_ga(T138, X181, t87_in_ga(T138, X181))
t87_in_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_ga(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_ga(.(lbrace, T171), X226) → U86_ga(T171, X226, e111_in_ga(T171, X226))
e111_in_ga(T179, X252) → U82_ga(T179, X252, t116_in_ga(T179, X252))
t116_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_ga(.(lbrace, T212), X297) → U78_ga(T212, X297, e140_in_ga(T212, X297))
e140_in_ga(T220, X323) → U74_ga(T220, X323, t145_in_ga(T220, X323))
t145_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_ga(.(lbrace, T253), X368) → U70_ga(T253, X368, e169_in_ga(T253, X368))
e169_in_ga(T261, X394) → U66_ga(T261, X394, t174_in_ga(T261, X394))
t174_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_ga(.(lbrace, T294), X439) → U62_ga(T294, X439, e198_in_ga(T294, X439))
e198_in_ga(T302, X465) → U6_ga(T302, X465, t203_in_ga(T302, X465))
t203_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_ga(.(lbrace, T335), X510) → U2_ga(T335, X510, e1_in_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_ga(T941, T943) → U110_ga(T941, T943, t234_in_ga(T941, X1569))
t234_in_ga(.(a, .(plus, T389)), T389) → t234_out_ga(.(a, .(plus, T389)), T389)
t234_in_ga(.(b, .(plus, T389)), T389) → t234_out_ga(.(b, .(plus, T389)), T389)
t234_in_ga(.(c, .(plus, T389)), T389) → t234_out_ga(.(c, .(plus, T389)), T389)
t234_in_ga(.(lbrace, T392), X599) → U14_ga(T392, X599, e259_in_ga(T392, X599))
e259_in_ga(T400, X625) → U58_ga(T400, X625, t264_in_ga(T400, X625))
t264_in_ga(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_ga(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_ga(.(lbrace, T433), X670) → U54_ga(T433, X670, e288_in_ga(T433, X670))
e288_in_ga(T441, X696) → U50_ga(T441, X696, t293_in_ga(T441, X696))
t293_in_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_ga(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_ga(.(lbrace, T474), X741) → U46_ga(T474, X741, e317_in_ga(T474, X741))
e317_in_ga(T482, X767) → U42_ga(T482, X767, t322_in_ga(T482, X767))
t322_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_ga(.(lbrace, T515), X812) → U38_ga(T515, X812, e346_in_ga(T515, X812))
e346_in_ga(T523, X838) → U34_ga(T523, X838, t351_in_ga(T523, X838))
t351_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_ga(.(lbrace, T556), X883) → U30_ga(T556, X883, e375_in_ga(T556, X883))
e375_in_ga(T564, X909) → U26_ga(T564, X909, t380_in_ga(T564, X909))
t380_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_ga(.(lbrace, T597), X954) → U22_ga(T597, X954, e404_in_ga(T597, X954))
e404_in_ga(T605, X980) → U18_ga(T605, X980, t409_in_ga(T605, X980))
t409_in_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_ga(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_ga(.(lbrace, T638), X1025) → U10_ga(T638, X1025, e1_in_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_ga(T941, T943) → U111_ga(T941, T943, t234_in_ga(T941, T945))
t234_in_ga(T780, X1303) → U15_ga(T780, X1303, n32_in_ga(T780, X1302))
U15_ga(T780, X1303, n32_out_ga(T780, X1302)) → t234_out_ga(T780, X1303)
t234_in_ga(T780, X1303) → U16_ga(T780, X1303, n32_in_ga(T780, T784))
U16_ga(T780, X1303, n32_out_ga(T780, T784)) → U17_ga(T780, X1303, t234_in_aa(T784, X1303))
t234_in_aa(.(a, .(plus, T389)), T389) → t234_out_aa(.(a, .(plus, T389)), T389)
t234_in_aa(.(b, .(plus, T389)), T389) → t234_out_aa(.(b, .(plus, T389)), T389)
t234_in_aa(.(c, .(plus, T389)), T389) → t234_out_aa(.(c, .(plus, T389)), T389)
t234_in_aa(.(lbrace, T392), X599) → U14_aa(T392, X599, e259_in_aa(T392, X599))
e259_in_aa(T400, X625) → U58_aa(T400, X625, t264_in_aa(T400, X625))
t264_in_aa(.(a, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(a, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(b, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(b, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(c, .(rbrace, .(plus, T430))), T430) → t264_out_aa(.(c, .(rbrace, .(plus, T430))), T430)
t264_in_aa(.(lbrace, T433), X670) → U54_aa(T433, X670, e288_in_aa(T433, X670))
e288_in_aa(T441, X696) → U50_aa(T441, X696, t293_in_aa(T441, X696))
t293_in_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(a, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(b, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471) → t293_out_aa(.(c, .(rbrace, .(rbrace, .(plus, T471)))), T471)
t293_in_aa(.(lbrace, T474), X741) → U46_aa(T474, X741, e317_in_aa(T474, X741))
e317_in_aa(T482, X767) → U42_aa(T482, X767, t322_in_aa(T482, X767))
t322_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512) → t322_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(plus, T512))))), T512)
t322_in_aa(.(lbrace, T515), X812) → U38_aa(T515, X812, e346_in_aa(T515, X812))
e346_in_aa(T523, X838) → U34_aa(T523, X838, t351_in_aa(T523, X838))
t351_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553) → t351_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T553)))))), T553)
t351_in_aa(.(lbrace, T556), X883) → U30_aa(T556, X883, e375_in_aa(T556, X883))
e375_in_aa(T564, X909) → U26_aa(T564, X909, t380_in_aa(T564, X909))
t380_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594) → t380_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T594))))))), T594)
t380_in_aa(.(lbrace, T597), X954) → U22_aa(T597, X954, e404_in_aa(T597, X954))
e404_in_aa(T605, X980) → U18_aa(T605, X980, t409_in_aa(T605, X980))
t409_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635) → t409_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, T635)))))))), T635)
t409_in_aa(.(lbrace, T638), X1025) → U10_aa(T638, X1025, e1_in_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025))))))))))
e1_in_aa(T22, T24) → U108_aa(T22, T24, n7_in_aa(T22, T24))
n7_in_aa(.(a, T36), T36) → n7_out_aa(.(a, T36), T36)
n7_in_aa(.(b, T36), T36) → n7_out_aa(.(b, T36), T36)
n7_in_aa(.(c, T36), T36) → n7_out_aa(.(c, T36), T36)
n7_in_aa(.(lbrace, T41), T43) → U102_aa(T41, T43, e1_in_aa(T41, .(rbrace, T43)))
e1_in_aa(T62, T64) → U109_aa(T62, T64, p31_in_aaa(T62, X59, T64))
p31_in_aaa(T62, X59, T64) → U103_aaa(T62, X59, T64, n32_in_aa(T62, X59))
n32_in_aa(.(a, .(star, T86)), T86) → n32_out_aa(.(a, .(star, T86)), T86)
n32_in_aa(.(b, .(star, T86)), T86) → n32_out_aa(.(b, .(star, T86)), T86)
n32_in_aa(.(c, .(star, T86)), T86) → n32_out_aa(.(c, .(star, T86)), T86)
n32_in_aa(.(lbrace, T89), X84) → U1_aa(T89, X84, e53_in_aa(T89, X84))
e53_in_aa(T97, X110) → U98_aa(T97, X110, t58_in_aa(T97, X110))
t58_in_aa(.(a, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(a, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(b, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(b, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(c, .(rbrace, .(star, T127))), T127) → t58_out_aa(.(c, .(rbrace, .(star, T127))), T127)
t58_in_aa(.(lbrace, T130), X155) → U94_aa(T130, X155, e82_in_aa(T130, X155))
e82_in_aa(T138, X181) → U90_aa(T138, X181, t87_in_aa(T138, X181))
t87_in_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(a, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(b, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168) → t87_out_aa(.(c, .(rbrace, .(rbrace, .(star, T168)))), T168)
t87_in_aa(.(lbrace, T171), X226) → U86_aa(T171, X226, e111_in_aa(T171, X226))
e111_in_aa(T179, X252) → U82_aa(T179, X252, t116_in_aa(T179, X252))
t116_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209) → t116_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(star, T209))))), T209)
t116_in_aa(.(lbrace, T212), X297) → U78_aa(T212, X297, e140_in_aa(T212, X297))
e140_in_aa(T220, X323) → U74_aa(T220, X323, t145_in_aa(T220, X323))
t145_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250) → t145_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T250)))))), T250)
t145_in_aa(.(lbrace, T253), X368) → U70_aa(T253, X368, e169_in_aa(T253, X368))
e169_in_aa(T261, X394) → U66_aa(T261, X394, t174_in_aa(T261, X394))
t174_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291) → t174_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T291))))))), T291)
t174_in_aa(.(lbrace, T294), X439) → U62_aa(T294, X439, e198_in_aa(T294, X439))
e198_in_aa(T302, X465) → U6_aa(T302, X465, t203_in_aa(T302, X465))
t203_in_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(a, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(b, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332) → t203_out_aa(.(c, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, T332)))))))), T332)
t203_in_aa(.(lbrace, T335), X510) → U2_aa(T335, X510, e1_in_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510))))))))))
e1_in_aa(T941, T943) → U110_aa(T941, T943, t234_in_aa(T941, X1569))
t234_in_aa(T780, X1303) → U15_aa(T780, X1303, n32_in_aa(T780, X1302))
U15_aa(T780, X1303, n32_out_aa(T780, X1302)) → t234_out_aa(T780, X1303)
t234_in_aa(T780, X1303) → U16_aa(T780, X1303, n32_in_aa(T780, T784))
U16_aa(T780, X1303, n32_out_aa(T780, T784)) → U17_aa(T780, X1303, t234_in_aa(T784, X1303))
U17_aa(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_aa(T780, X1303)
U110_aa(T941, T943, t234_out_aa(T941, X1569)) → e1_out_aa(T941, T943)
e1_in_aa(T941, T943) → U111_aa(T941, T943, t234_in_aa(T941, T945))
U111_aa(T941, T943, t234_out_aa(T941, T945)) → U112_aa(T941, T943, e1_in_aa(T945, T943))
U112_aa(T941, T943, e1_out_aa(T945, T943)) → e1_out_aa(T941, T943)
U2_aa(T335, X510, e1_out_aa(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_aa(.(lbrace, T335), X510)
t203_in_aa(T345, X530) → U3_aa(T345, X530, n32_in_aa(T345, X529))
U3_aa(T345, X530, n32_out_aa(T345, X529)) → t203_out_aa(T345, X530)
t203_in_aa(T345, X530) → U4_aa(T345, X530, n32_in_aa(T345, T349))
U4_aa(T345, X530, n32_out_aa(T345, T349)) → U5_aa(T345, X530, t203_in_aa(T349, X530))
U5_aa(T345, X530, t203_out_aa(T349, X530)) → t203_out_aa(T345, X530)
U6_aa(T302, X465, t203_out_aa(T302, X465)) → e198_out_aa(T302, X465)
e198_in_aa(T357, X551) → U7_aa(T357, X551, t234_in_aa(T357, X550))
U7_aa(T357, X551, t234_out_aa(T357, X550)) → e198_out_aa(T357, X551)
e198_in_aa(T357, X551) → U8_aa(T357, X551, t234_in_aa(T357, T359))
U8_aa(T357, X551, t234_out_aa(T357, T359)) → U9_aa(T357, X551, e198_in_aa(T359, X551))
U9_aa(T357, X551, e198_out_aa(T359, X551)) → e198_out_aa(T357, X551)
U62_aa(T294, X439, e198_out_aa(T294, X439)) → t174_out_aa(.(lbrace, T294), X439)
t174_in_aa(T795, X1326) → U63_aa(T795, X1326, n32_in_aa(T795, X1325))
U63_aa(T795, X1326, n32_out_aa(T795, X1325)) → t174_out_aa(T795, X1326)
t174_in_aa(T795, X1326) → U64_aa(T795, X1326, n32_in_aa(T795, T799))
U64_aa(T795, X1326, n32_out_aa(T795, T799)) → U65_aa(T795, X1326, t174_in_aa(T799, X1326))
U65_aa(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_aa(T795, X1326)
U66_aa(T261, X394, t174_out_aa(T261, X394)) → e169_out_aa(T261, X394)
e169_in_aa(T807, X1347) → U67_aa(T807, X1347, t234_in_aa(T807, X1346))
U67_aa(T807, X1347, t234_out_aa(T807, X1346)) → e169_out_aa(T807, X1347)
e169_in_aa(T807, X1347) → U68_aa(T807, X1347, t234_in_aa(T807, T809))
U68_aa(T807, X1347, t234_out_aa(T807, T809)) → U69_aa(T807, X1347, e169_in_aa(T809, X1347))
U69_aa(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_aa(T807, X1347)
U70_aa(T253, X368, e169_out_aa(T253, X368)) → t145_out_aa(.(lbrace, T253), X368)
t145_in_aa(T817, X1369) → U71_aa(T817, X1369, n32_in_aa(T817, X1368))
U71_aa(T817, X1369, n32_out_aa(T817, X1368)) → t145_out_aa(T817, X1369)
t145_in_aa(T817, X1369) → U72_aa(T817, X1369, n32_in_aa(T817, T821))
U72_aa(T817, X1369, n32_out_aa(T817, T821)) → U73_aa(T817, X1369, t145_in_aa(T821, X1369))
U73_aa(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_aa(T817, X1369)
U74_aa(T220, X323, t145_out_aa(T220, X323)) → e140_out_aa(T220, X323)
e140_in_aa(T829, X1390) → U75_aa(T829, X1390, t234_in_aa(T829, X1389))
U75_aa(T829, X1390, t234_out_aa(T829, X1389)) → e140_out_aa(T829, X1390)
e140_in_aa(T829, X1390) → U76_aa(T829, X1390, t234_in_aa(T829, T831))
U76_aa(T829, X1390, t234_out_aa(T829, T831)) → U77_aa(T829, X1390, e140_in_aa(T831, X1390))
U77_aa(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_aa(T829, X1390)
U78_aa(T212, X297, e140_out_aa(T212, X297)) → t116_out_aa(.(lbrace, T212), X297)
t116_in_aa(T839, X1412) → U79_aa(T839, X1412, n32_in_aa(T839, X1411))
U79_aa(T839, X1412, n32_out_aa(T839, X1411)) → t116_out_aa(T839, X1412)
t116_in_aa(T839, X1412) → U80_aa(T839, X1412, n32_in_aa(T839, T843))
U80_aa(T839, X1412, n32_out_aa(T839, T843)) → U81_aa(T839, X1412, t116_in_aa(T843, X1412))
U81_aa(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_aa(T839, X1412)
U82_aa(T179, X252, t116_out_aa(T179, X252)) → e111_out_aa(T179, X252)
e111_in_aa(T851, X1433) → U83_aa(T851, X1433, t234_in_aa(T851, X1432))
U83_aa(T851, X1433, t234_out_aa(T851, X1432)) → e111_out_aa(T851, X1433)
e111_in_aa(T851, X1433) → U84_aa(T851, X1433, t234_in_aa(T851, T853))
U84_aa(T851, X1433, t234_out_aa(T851, T853)) → U85_aa(T851, X1433, e111_in_aa(T853, X1433))
U85_aa(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_aa(T851, X1433)
U86_aa(T171, X226, e111_out_aa(T171, X226)) → t87_out_aa(.(lbrace, T171), X226)
t87_in_aa(T861, X1455) → U87_aa(T861, X1455, n32_in_aa(T861, X1454))
U87_aa(T861, X1455, n32_out_aa(T861, X1454)) → t87_out_aa(T861, X1455)
t87_in_aa(T861, X1455) → U88_aa(T861, X1455, n32_in_aa(T861, T865))
U88_aa(T861, X1455, n32_out_aa(T861, T865)) → U89_aa(T861, X1455, t87_in_aa(T865, X1455))
U89_aa(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_aa(T861, X1455)
U90_aa(T138, X181, t87_out_aa(T138, X181)) → e82_out_aa(T138, X181)
e82_in_aa(T873, X1476) → U91_aa(T873, X1476, t234_in_aa(T873, X1475))
U91_aa(T873, X1476, t234_out_aa(T873, X1475)) → e82_out_aa(T873, X1476)
e82_in_aa(T873, X1476) → U92_aa(T873, X1476, t234_in_aa(T873, T875))
U92_aa(T873, X1476, t234_out_aa(T873, T875)) → U93_aa(T873, X1476, e82_in_aa(T875, X1476))
U93_aa(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_aa(T873, X1476)
U94_aa(T130, X155, e82_out_aa(T130, X155)) → t58_out_aa(.(lbrace, T130), X155)
t58_in_aa(T883, X1498) → U95_aa(T883, X1498, n32_in_aa(T883, X1497))
U95_aa(T883, X1498, n32_out_aa(T883, X1497)) → t58_out_aa(T883, X1498)
t58_in_aa(T883, X1498) → U96_aa(T883, X1498, n32_in_aa(T883, T887))
U96_aa(T883, X1498, n32_out_aa(T883, T887)) → U97_aa(T883, X1498, t58_in_aa(T887, X1498))
U97_aa(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_aa(T883, X1498)
U98_aa(T97, X110, t58_out_aa(T97, X110)) → e53_out_aa(T97, X110)
e53_in_aa(T895, X1519) → U99_aa(T895, X1519, t234_in_aa(T895, X1518))
U99_aa(T895, X1519, t234_out_aa(T895, X1518)) → e53_out_aa(T895, X1519)
e53_in_aa(T895, X1519) → U100_aa(T895, X1519, t234_in_aa(T895, T897))
U100_aa(T895, X1519, t234_out_aa(T895, T897)) → U101_aa(T895, X1519, e53_in_aa(T897, X1519))
U101_aa(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_aa(T895, X1519)
U1_aa(T89, X84, e53_out_aa(T89, X84)) → n32_out_aa(.(lbrace, T89), X84)
U103_aaa(T62, X59, T64, n32_out_aa(T62, X59)) → p31_out_aaa(T62, X59, T64)
p31_in_aaa(T62, T916, T918) → U104_aaa(T62, T916, T918, n32_in_aa(T62, T916))
U104_aaa(T62, T916, T918, n32_out_aa(T62, T916)) → U105_aaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_aaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_aaa(T62, T916, T918)
p31_in_aaa(T62, T929, T931) → U106_aaa(T62, T929, T931, n32_in_aa(T62, T929))
U106_aaa(T62, T929, T931, n32_out_aa(T62, T929)) → U107_aaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_aaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_aaa(T62, T929, T931)
U109_aa(T62, T64, p31_out_aaa(T62, X59, T64)) → e1_out_aa(T62, T64)
U102_aa(T41, T43, e1_out_aa(T41, .(rbrace, T43))) → n7_out_aa(.(lbrace, T41), T43)
U108_aa(T22, T24, n7_out_aa(T22, T24)) → e1_out_aa(T22, T24)
U10_aa(T638, X1025, e1_out_aa(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_aa(.(lbrace, T638), X1025)
t409_in_aa(T648, X1045) → U11_aa(T648, X1045, n32_in_aa(T648, X1044))
U11_aa(T648, X1045, n32_out_aa(T648, X1044)) → t409_out_aa(T648, X1045)
t409_in_aa(T648, X1045) → U12_aa(T648, X1045, n32_in_aa(T648, T652))
U12_aa(T648, X1045, n32_out_aa(T648, T652)) → U13_aa(T648, X1045, t409_in_aa(T652, X1045))
U13_aa(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_aa(T648, X1045)
U18_aa(T605, X980, t409_out_aa(T605, X980)) → e404_out_aa(T605, X980)
e404_in_aa(T660, X1066) → U19_aa(T660, X1066, t234_in_aa(T660, X1065))
U19_aa(T660, X1066, t234_out_aa(T660, X1065)) → e404_out_aa(T660, X1066)
e404_in_aa(T660, X1066) → U20_aa(T660, X1066, t234_in_aa(T660, T662))
U20_aa(T660, X1066, t234_out_aa(T660, T662)) → U21_aa(T660, X1066, e404_in_aa(T662, X1066))
U21_aa(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_aa(T660, X1066)
U22_aa(T597, X954, e404_out_aa(T597, X954)) → t380_out_aa(.(lbrace, T597), X954)
t380_in_aa(T670, X1088) → U23_aa(T670, X1088, n32_in_aa(T670, X1087))
U23_aa(T670, X1088, n32_out_aa(T670, X1087)) → t380_out_aa(T670, X1088)
t380_in_aa(T670, X1088) → U24_aa(T670, X1088, n32_in_aa(T670, T674))
U24_aa(T670, X1088, n32_out_aa(T670, T674)) → U25_aa(T670, X1088, t380_in_aa(T674, X1088))
U25_aa(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_aa(T670, X1088)
U26_aa(T564, X909, t380_out_aa(T564, X909)) → e375_out_aa(T564, X909)
e375_in_aa(T682, X1109) → U27_aa(T682, X1109, t234_in_aa(T682, X1108))
U27_aa(T682, X1109, t234_out_aa(T682, X1108)) → e375_out_aa(T682, X1109)
e375_in_aa(T682, X1109) → U28_aa(T682, X1109, t234_in_aa(T682, T684))
U28_aa(T682, X1109, t234_out_aa(T682, T684)) → U29_aa(T682, X1109, e375_in_aa(T684, X1109))
U29_aa(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_aa(T682, X1109)
U30_aa(T556, X883, e375_out_aa(T556, X883)) → t351_out_aa(.(lbrace, T556), X883)
t351_in_aa(T692, X1131) → U31_aa(T692, X1131, n32_in_aa(T692, X1130))
U31_aa(T692, X1131, n32_out_aa(T692, X1130)) → t351_out_aa(T692, X1131)
t351_in_aa(T692, X1131) → U32_aa(T692, X1131, n32_in_aa(T692, T696))
U32_aa(T692, X1131, n32_out_aa(T692, T696)) → U33_aa(T692, X1131, t351_in_aa(T696, X1131))
U33_aa(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_aa(T692, X1131)
U34_aa(T523, X838, t351_out_aa(T523, X838)) → e346_out_aa(T523, X838)
e346_in_aa(T704, X1152) → U35_aa(T704, X1152, t234_in_aa(T704, X1151))
U35_aa(T704, X1152, t234_out_aa(T704, X1151)) → e346_out_aa(T704, X1152)
e346_in_aa(T704, X1152) → U36_aa(T704, X1152, t234_in_aa(T704, T706))
U36_aa(T704, X1152, t234_out_aa(T704, T706)) → U37_aa(T704, X1152, e346_in_aa(T706, X1152))
U37_aa(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_aa(T704, X1152)
U38_aa(T515, X812, e346_out_aa(T515, X812)) → t322_out_aa(.(lbrace, T515), X812)
t322_in_aa(T714, X1174) → U39_aa(T714, X1174, n32_in_aa(T714, X1173))
U39_aa(T714, X1174, n32_out_aa(T714, X1173)) → t322_out_aa(T714, X1174)
t322_in_aa(T714, X1174) → U40_aa(T714, X1174, n32_in_aa(T714, T718))
U40_aa(T714, X1174, n32_out_aa(T714, T718)) → U41_aa(T714, X1174, t322_in_aa(T718, X1174))
U41_aa(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_aa(T714, X1174)
U42_aa(T482, X767, t322_out_aa(T482, X767)) → e317_out_aa(T482, X767)
e317_in_aa(T726, X1195) → U43_aa(T726, X1195, t234_in_aa(T726, X1194))
U43_aa(T726, X1195, t234_out_aa(T726, X1194)) → e317_out_aa(T726, X1195)
e317_in_aa(T726, X1195) → U44_aa(T726, X1195, t234_in_aa(T726, T728))
U44_aa(T726, X1195, t234_out_aa(T726, T728)) → U45_aa(T726, X1195, e317_in_aa(T728, X1195))
U45_aa(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_aa(T726, X1195)
U46_aa(T474, X741, e317_out_aa(T474, X741)) → t293_out_aa(.(lbrace, T474), X741)
t293_in_aa(T736, X1217) → U47_aa(T736, X1217, n32_in_aa(T736, X1216))
U47_aa(T736, X1217, n32_out_aa(T736, X1216)) → t293_out_aa(T736, X1217)
t293_in_aa(T736, X1217) → U48_aa(T736, X1217, n32_in_aa(T736, T740))
U48_aa(T736, X1217, n32_out_aa(T736, T740)) → U49_aa(T736, X1217, t293_in_aa(T740, X1217))
U49_aa(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_aa(T736, X1217)
U50_aa(T441, X696, t293_out_aa(T441, X696)) → e288_out_aa(T441, X696)
e288_in_aa(T748, X1238) → U51_aa(T748, X1238, t234_in_aa(T748, X1237))
U51_aa(T748, X1238, t234_out_aa(T748, X1237)) → e288_out_aa(T748, X1238)
e288_in_aa(T748, X1238) → U52_aa(T748, X1238, t234_in_aa(T748, T750))
U52_aa(T748, X1238, t234_out_aa(T748, T750)) → U53_aa(T748, X1238, e288_in_aa(T750, X1238))
U53_aa(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_aa(T748, X1238)
U54_aa(T433, X670, e288_out_aa(T433, X670)) → t264_out_aa(.(lbrace, T433), X670)
t264_in_aa(T758, X1260) → U55_aa(T758, X1260, n32_in_aa(T758, X1259))
U55_aa(T758, X1260, n32_out_aa(T758, X1259)) → t264_out_aa(T758, X1260)
t264_in_aa(T758, X1260) → U56_aa(T758, X1260, n32_in_aa(T758, T762))
U56_aa(T758, X1260, n32_out_aa(T758, T762)) → U57_aa(T758, X1260, t264_in_aa(T762, X1260))
U57_aa(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_aa(T758, X1260)
U58_aa(T400, X625, t264_out_aa(T400, X625)) → e259_out_aa(T400, X625)
e259_in_aa(T770, X1281) → U59_aa(T770, X1281, t234_in_aa(T770, X1280))
U59_aa(T770, X1281, t234_out_aa(T770, X1280)) → e259_out_aa(T770, X1281)
e259_in_aa(T770, X1281) → U60_aa(T770, X1281, t234_in_aa(T770, T772))
U60_aa(T770, X1281, t234_out_aa(T770, T772)) → U61_aa(T770, X1281, e259_in_aa(T772, X1281))
U61_aa(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_aa(T770, X1281)
U14_aa(T392, X599, e259_out_aa(T392, X599)) → t234_out_aa(.(lbrace, T392), X599)
U17_ga(T780, X1303, t234_out_aa(T784, X1303)) → t234_out_ga(T780, X1303)
U111_ga(T941, T943, t234_out_ga(T941, T945)) → U112_ga(T941, T943, e1_in_aa(T945, T943))
U112_ga(T941, T943, e1_out_aa(T945, T943)) → e1_out_ga(T941, T943)
U10_ga(T638, X1025, e1_out_ga(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))) → t409_out_ga(.(lbrace, T638), X1025)
t409_in_ga(T648, X1045) → U11_ga(T648, X1045, n32_in_ga(T648, X1044))
U11_ga(T648, X1045, n32_out_ga(T648, X1044)) → t409_out_ga(T648, X1045)
t409_in_ga(T648, X1045) → U12_ga(T648, X1045, n32_in_ga(T648, T652))
U12_ga(T648, X1045, n32_out_ga(T648, T652)) → U13_ga(T648, X1045, t409_in_aa(T652, X1045))
U13_ga(T648, X1045, t409_out_aa(T652, X1045)) → t409_out_ga(T648, X1045)
U18_ga(T605, X980, t409_out_ga(T605, X980)) → e404_out_ga(T605, X980)
e404_in_ga(T660, X1066) → U19_ga(T660, X1066, t234_in_ga(T660, X1065))
U19_ga(T660, X1066, t234_out_ga(T660, X1065)) → e404_out_ga(T660, X1066)
e404_in_ga(T660, X1066) → U20_ga(T660, X1066, t234_in_ga(T660, T662))
U20_ga(T660, X1066, t234_out_ga(T660, T662)) → U21_ga(T660, X1066, e404_in_aa(T662, X1066))
U21_ga(T660, X1066, e404_out_aa(T662, X1066)) → e404_out_ga(T660, X1066)
U22_ga(T597, X954, e404_out_ga(T597, X954)) → t380_out_ga(.(lbrace, T597), X954)
t380_in_ga(T670, X1088) → U23_ga(T670, X1088, n32_in_ga(T670, X1087))
U23_ga(T670, X1088, n32_out_ga(T670, X1087)) → t380_out_ga(T670, X1088)
t380_in_ga(T670, X1088) → U24_ga(T670, X1088, n32_in_ga(T670, T674))
U24_ga(T670, X1088, n32_out_ga(T670, T674)) → U25_ga(T670, X1088, t380_in_aa(T674, X1088))
U25_ga(T670, X1088, t380_out_aa(T674, X1088)) → t380_out_ga(T670, X1088)
U26_ga(T564, X909, t380_out_ga(T564, X909)) → e375_out_ga(T564, X909)
e375_in_ga(T682, X1109) → U27_ga(T682, X1109, t234_in_ga(T682, X1108))
U27_ga(T682, X1109, t234_out_ga(T682, X1108)) → e375_out_ga(T682, X1109)
e375_in_ga(T682, X1109) → U28_ga(T682, X1109, t234_in_ga(T682, T684))
U28_ga(T682, X1109, t234_out_ga(T682, T684)) → U29_ga(T682, X1109, e375_in_aa(T684, X1109))
U29_ga(T682, X1109, e375_out_aa(T684, X1109)) → e375_out_ga(T682, X1109)
U30_ga(T556, X883, e375_out_ga(T556, X883)) → t351_out_ga(.(lbrace, T556), X883)
t351_in_ga(T692, X1131) → U31_ga(T692, X1131, n32_in_ga(T692, X1130))
U31_ga(T692, X1131, n32_out_ga(T692, X1130)) → t351_out_ga(T692, X1131)
t351_in_ga(T692, X1131) → U32_ga(T692, X1131, n32_in_ga(T692, T696))
U32_ga(T692, X1131, n32_out_ga(T692, T696)) → U33_ga(T692, X1131, t351_in_aa(T696, X1131))
U33_ga(T692, X1131, t351_out_aa(T696, X1131)) → t351_out_ga(T692, X1131)
U34_ga(T523, X838, t351_out_ga(T523, X838)) → e346_out_ga(T523, X838)
e346_in_ga(T704, X1152) → U35_ga(T704, X1152, t234_in_ga(T704, X1151))
U35_ga(T704, X1152, t234_out_ga(T704, X1151)) → e346_out_ga(T704, X1152)
e346_in_ga(T704, X1152) → U36_ga(T704, X1152, t234_in_ga(T704, T706))
U36_ga(T704, X1152, t234_out_ga(T704, T706)) → U37_ga(T704, X1152, e346_in_aa(T706, X1152))
U37_ga(T704, X1152, e346_out_aa(T706, X1152)) → e346_out_ga(T704, X1152)
U38_ga(T515, X812, e346_out_ga(T515, X812)) → t322_out_ga(.(lbrace, T515), X812)
t322_in_ga(T714, X1174) → U39_ga(T714, X1174, n32_in_ga(T714, X1173))
U39_ga(T714, X1174, n32_out_ga(T714, X1173)) → t322_out_ga(T714, X1174)
t322_in_ga(T714, X1174) → U40_ga(T714, X1174, n32_in_ga(T714, T718))
U40_ga(T714, X1174, n32_out_ga(T714, T718)) → U41_ga(T714, X1174, t322_in_aa(T718, X1174))
U41_ga(T714, X1174, t322_out_aa(T718, X1174)) → t322_out_ga(T714, X1174)
U42_ga(T482, X767, t322_out_ga(T482, X767)) → e317_out_ga(T482, X767)
e317_in_ga(T726, X1195) → U43_ga(T726, X1195, t234_in_ga(T726, X1194))
U43_ga(T726, X1195, t234_out_ga(T726, X1194)) → e317_out_ga(T726, X1195)
e317_in_ga(T726, X1195) → U44_ga(T726, X1195, t234_in_ga(T726, T728))
U44_ga(T726, X1195, t234_out_ga(T726, T728)) → U45_ga(T726, X1195, e317_in_aa(T728, X1195))
U45_ga(T726, X1195, e317_out_aa(T728, X1195)) → e317_out_ga(T726, X1195)
U46_ga(T474, X741, e317_out_ga(T474, X741)) → t293_out_ga(.(lbrace, T474), X741)
t293_in_ga(T736, X1217) → U47_ga(T736, X1217, n32_in_ga(T736, X1216))
U47_ga(T736, X1217, n32_out_ga(T736, X1216)) → t293_out_ga(T736, X1217)
t293_in_ga(T736, X1217) → U48_ga(T736, X1217, n32_in_ga(T736, T740))
U48_ga(T736, X1217, n32_out_ga(T736, T740)) → U49_ga(T736, X1217, t293_in_aa(T740, X1217))
U49_ga(T736, X1217, t293_out_aa(T740, X1217)) → t293_out_ga(T736, X1217)
U50_ga(T441, X696, t293_out_ga(T441, X696)) → e288_out_ga(T441, X696)
e288_in_ga(T748, X1238) → U51_ga(T748, X1238, t234_in_ga(T748, X1237))
U51_ga(T748, X1238, t234_out_ga(T748, X1237)) → e288_out_ga(T748, X1238)
e288_in_ga(T748, X1238) → U52_ga(T748, X1238, t234_in_ga(T748, T750))
U52_ga(T748, X1238, t234_out_ga(T748, T750)) → U53_ga(T748, X1238, e288_in_aa(T750, X1238))
U53_ga(T748, X1238, e288_out_aa(T750, X1238)) → e288_out_ga(T748, X1238)
U54_ga(T433, X670, e288_out_ga(T433, X670)) → t264_out_ga(.(lbrace, T433), X670)
t264_in_ga(T758, X1260) → U55_ga(T758, X1260, n32_in_ga(T758, X1259))
U55_ga(T758, X1260, n32_out_ga(T758, X1259)) → t264_out_ga(T758, X1260)
t264_in_ga(T758, X1260) → U56_ga(T758, X1260, n32_in_ga(T758, T762))
U56_ga(T758, X1260, n32_out_ga(T758, T762)) → U57_ga(T758, X1260, t264_in_aa(T762, X1260))
U57_ga(T758, X1260, t264_out_aa(T762, X1260)) → t264_out_ga(T758, X1260)
U58_ga(T400, X625, t264_out_ga(T400, X625)) → e259_out_ga(T400, X625)
e259_in_ga(T770, X1281) → U59_ga(T770, X1281, t234_in_ga(T770, X1280))
U59_ga(T770, X1281, t234_out_ga(T770, X1280)) → e259_out_ga(T770, X1281)
e259_in_ga(T770, X1281) → U60_ga(T770, X1281, t234_in_ga(T770, T772))
U60_ga(T770, X1281, t234_out_ga(T770, T772)) → U61_ga(T770, X1281, e259_in_aa(T772, X1281))
U61_ga(T770, X1281, e259_out_aa(T772, X1281)) → e259_out_ga(T770, X1281)
U14_ga(T392, X599, e259_out_ga(T392, X599)) → t234_out_ga(.(lbrace, T392), X599)
U110_ga(T941, T943, t234_out_ga(T941, X1569)) → e1_out_ga(T941, T943)
U2_ga(T335, X510, e1_out_ga(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))) → t203_out_ga(.(lbrace, T335), X510)
t203_in_ga(T345, X530) → U3_ga(T345, X530, n32_in_ga(T345, X529))
U3_ga(T345, X530, n32_out_ga(T345, X529)) → t203_out_ga(T345, X530)
t203_in_ga(T345, X530) → U4_ga(T345, X530, n32_in_ga(T345, T349))
U4_ga(T345, X530, n32_out_ga(T345, T349)) → U5_ga(T345, X530, t203_in_aa(T349, X530))
U5_ga(T345, X530, t203_out_aa(T349, X530)) → t203_out_ga(T345, X530)
U6_ga(T302, X465, t203_out_ga(T302, X465)) → e198_out_ga(T302, X465)
e198_in_ga(T357, X551) → U7_ga(T357, X551, t234_in_ga(T357, X550))
U7_ga(T357, X551, t234_out_ga(T357, X550)) → e198_out_ga(T357, X551)
e198_in_ga(T357, X551) → U8_ga(T357, X551, t234_in_ga(T357, T359))
U8_ga(T357, X551, t234_out_ga(T357, T359)) → U9_ga(T357, X551, e198_in_aa(T359, X551))
U9_ga(T357, X551, e198_out_aa(T359, X551)) → e198_out_ga(T357, X551)
U62_ga(T294, X439, e198_out_ga(T294, X439)) → t174_out_ga(.(lbrace, T294), X439)
t174_in_ga(T795, X1326) → U63_ga(T795, X1326, n32_in_ga(T795, X1325))
U63_ga(T795, X1326, n32_out_ga(T795, X1325)) → t174_out_ga(T795, X1326)
t174_in_ga(T795, X1326) → U64_ga(T795, X1326, n32_in_ga(T795, T799))
U64_ga(T795, X1326, n32_out_ga(T795, T799)) → U65_ga(T795, X1326, t174_in_aa(T799, X1326))
U65_ga(T795, X1326, t174_out_aa(T799, X1326)) → t174_out_ga(T795, X1326)
U66_ga(T261, X394, t174_out_ga(T261, X394)) → e169_out_ga(T261, X394)
e169_in_ga(T807, X1347) → U67_ga(T807, X1347, t234_in_ga(T807, X1346))
U67_ga(T807, X1347, t234_out_ga(T807, X1346)) → e169_out_ga(T807, X1347)
e169_in_ga(T807, X1347) → U68_ga(T807, X1347, t234_in_ga(T807, T809))
U68_ga(T807, X1347, t234_out_ga(T807, T809)) → U69_ga(T807, X1347, e169_in_aa(T809, X1347))
U69_ga(T807, X1347, e169_out_aa(T809, X1347)) → e169_out_ga(T807, X1347)
U70_ga(T253, X368, e169_out_ga(T253, X368)) → t145_out_ga(.(lbrace, T253), X368)
t145_in_ga(T817, X1369) → U71_ga(T817, X1369, n32_in_ga(T817, X1368))
U71_ga(T817, X1369, n32_out_ga(T817, X1368)) → t145_out_ga(T817, X1369)
t145_in_ga(T817, X1369) → U72_ga(T817, X1369, n32_in_ga(T817, T821))
U72_ga(T817, X1369, n32_out_ga(T817, T821)) → U73_ga(T817, X1369, t145_in_aa(T821, X1369))
U73_ga(T817, X1369, t145_out_aa(T821, X1369)) → t145_out_ga(T817, X1369)
U74_ga(T220, X323, t145_out_ga(T220, X323)) → e140_out_ga(T220, X323)
e140_in_ga(T829, X1390) → U75_ga(T829, X1390, t234_in_ga(T829, X1389))
U75_ga(T829, X1390, t234_out_ga(T829, X1389)) → e140_out_ga(T829, X1390)
e140_in_ga(T829, X1390) → U76_ga(T829, X1390, t234_in_ga(T829, T831))
U76_ga(T829, X1390, t234_out_ga(T829, T831)) → U77_ga(T829, X1390, e140_in_aa(T831, X1390))
U77_ga(T829, X1390, e140_out_aa(T831, X1390)) → e140_out_ga(T829, X1390)
U78_ga(T212, X297, e140_out_ga(T212, X297)) → t116_out_ga(.(lbrace, T212), X297)
t116_in_ga(T839, X1412) → U79_ga(T839, X1412, n32_in_ga(T839, X1411))
U79_ga(T839, X1412, n32_out_ga(T839, X1411)) → t116_out_ga(T839, X1412)
t116_in_ga(T839, X1412) → U80_ga(T839, X1412, n32_in_ga(T839, T843))
U80_ga(T839, X1412, n32_out_ga(T839, T843)) → U81_ga(T839, X1412, t116_in_aa(T843, X1412))
U81_ga(T839, X1412, t116_out_aa(T843, X1412)) → t116_out_ga(T839, X1412)
U82_ga(T179, X252, t116_out_ga(T179, X252)) → e111_out_ga(T179, X252)
e111_in_ga(T851, X1433) → U83_ga(T851, X1433, t234_in_ga(T851, X1432))
U83_ga(T851, X1433, t234_out_ga(T851, X1432)) → e111_out_ga(T851, X1433)
e111_in_ga(T851, X1433) → U84_ga(T851, X1433, t234_in_ga(T851, T853))
U84_ga(T851, X1433, t234_out_ga(T851, T853)) → U85_ga(T851, X1433, e111_in_aa(T853, X1433))
U85_ga(T851, X1433, e111_out_aa(T853, X1433)) → e111_out_ga(T851, X1433)
U86_ga(T171, X226, e111_out_ga(T171, X226)) → t87_out_ga(.(lbrace, T171), X226)
t87_in_ga(T861, X1455) → U87_ga(T861, X1455, n32_in_ga(T861, X1454))
U87_ga(T861, X1455, n32_out_ga(T861, X1454)) → t87_out_ga(T861, X1455)
t87_in_ga(T861, X1455) → U88_ga(T861, X1455, n32_in_ga(T861, T865))
U88_ga(T861, X1455, n32_out_ga(T861, T865)) → U89_ga(T861, X1455, t87_in_aa(T865, X1455))
U89_ga(T861, X1455, t87_out_aa(T865, X1455)) → t87_out_ga(T861, X1455)
U90_ga(T138, X181, t87_out_ga(T138, X181)) → e82_out_ga(T138, X181)
e82_in_ga(T873, X1476) → U91_ga(T873, X1476, t234_in_ga(T873, X1475))
U91_ga(T873, X1476, t234_out_ga(T873, X1475)) → e82_out_ga(T873, X1476)
e82_in_ga(T873, X1476) → U92_ga(T873, X1476, t234_in_ga(T873, T875))
U92_ga(T873, X1476, t234_out_ga(T873, T875)) → U93_ga(T873, X1476, e82_in_aa(T875, X1476))
U93_ga(T873, X1476, e82_out_aa(T875, X1476)) → e82_out_ga(T873, X1476)
U94_ga(T130, X155, e82_out_ga(T130, X155)) → t58_out_ga(.(lbrace, T130), X155)
t58_in_ga(T883, X1498) → U95_ga(T883, X1498, n32_in_ga(T883, X1497))
U95_ga(T883, X1498, n32_out_ga(T883, X1497)) → t58_out_ga(T883, X1498)
t58_in_ga(T883, X1498) → U96_ga(T883, X1498, n32_in_ga(T883, T887))
U96_ga(T883, X1498, n32_out_ga(T883, T887)) → U97_ga(T883, X1498, t58_in_aa(T887, X1498))
U97_ga(T883, X1498, t58_out_aa(T887, X1498)) → t58_out_ga(T883, X1498)
U98_ga(T97, X110, t58_out_ga(T97, X110)) → e53_out_ga(T97, X110)
e53_in_ga(T895, X1519) → U99_ga(T895, X1519, t234_in_ga(T895, X1518))
U99_ga(T895, X1519, t234_out_ga(T895, X1518)) → e53_out_ga(T895, X1519)
e53_in_ga(T895, X1519) → U100_ga(T895, X1519, t234_in_ga(T895, T897))
U100_ga(T895, X1519, t234_out_ga(T895, T897)) → U101_ga(T895, X1519, e53_in_aa(T897, X1519))
U101_ga(T895, X1519, e53_out_aa(T897, X1519)) → e53_out_ga(T895, X1519)
U1_ga(T89, X84, e53_out_ga(T89, X84)) → n32_out_ga(.(lbrace, T89), X84)
U103_gaa(T62, X59, T64, n32_out_ga(T62, X59)) → p31_out_gaa(T62, X59, T64)
p31_in_gaa(T62, T916, T918) → U104_gaa(T62, T916, T918, n32_in_ga(T62, T916))
U104_gaa(T62, T916, T918, n32_out_ga(T62, T916)) → U105_gaa(T62, T916, T918, n7_in_aa(T916, T918))
U105_gaa(T62, T916, T918, n7_out_aa(T916, T918)) → p31_out_gaa(T62, T916, T918)
p31_in_gaa(T62, T929, T931) → U106_gaa(T62, T929, T931, n32_in_ga(T62, T929))
U106_gaa(T62, T929, T931, n32_out_ga(T62, T929)) → U107_gaa(T62, T929, T931, p31_in_aaa(T929, X1556, T931))
U107_gaa(T62, T929, T931, p31_out_aaa(T929, X1556, T931)) → p31_out_gaa(T62, T929, T931)
U109_ga(T62, T64, p31_out_gaa(T62, X59, T64)) → e1_out_ga(T62, T64)
U102_ga(T41, T43, e1_out_ga(T41, .(rbrace, T43))) → n7_out_ga(.(lbrace, T41), T43)
U108_ga(T22, T24, n7_out_ga(T22, T24)) → e1_out_ga(T22, T24)

The argument filtering Pi contains the following mapping:
e1_in_ga(x1, x2)  =  e1_in_ga(x1)
U108_ga(x1, x2, x3)  =  U108_ga(x3)
n7_in_ga(x1, x2)  =  n7_in_ga(x1)
.(x1, x2)  =  .(x1, x2)
a  =  a
n7_out_ga(x1, x2)  =  n7_out_ga
b  =  b
c  =  c
lbrace  =  lbrace
U102_ga(x1, x2, x3)  =  U102_ga(x3)
U109_ga(x1, x2, x3)  =  U109_ga(x3)
p31_in_gaa(x1, x2, x3)  =  p31_in_gaa(x1)
U103_gaa(x1, x2, x3, x4)  =  U103_gaa(x4)
n32_in_ga(x1, x2)  =  n32_in_ga(x1)
star  =  star
n32_out_ga(x1, x2)  =  n32_out_ga
U1_ga(x1, x2, x3)  =  U1_ga(x3)
e53_in_ga(x1, x2)  =  e53_in_ga(x1)
U98_ga(x1, x2, x3)  =  U98_ga(x3)
t58_in_ga(x1, x2)  =  t58_in_ga(x1)
rbrace  =  rbrace
t58_out_ga(x1, x2)  =  t58_out_ga
U94_ga(x1, x2, x3)  =  U94_ga(x3)
e82_in_ga(x1, x2)  =  e82_in_ga(x1)
U90_ga(x1, x2, x3)  =  U90_ga(x3)
t87_in_ga(x1, x2)  =  t87_in_ga(x1)
t87_out_ga(x1, x2)  =  t87_out_ga
U86_ga(x1, x2, x3)  =  U86_ga(x3)
e111_in_ga(x1, x2)  =  e111_in_ga(x1)
U82_ga(x1, x2, x3)  =  U82_ga(x3)
t116_in_ga(x1, x2)  =  t116_in_ga(x1)
t116_out_ga(x1, x2)  =  t116_out_ga
U78_ga(x1, x2, x3)  =  U78_ga(x3)
e140_in_ga(x1, x2)  =  e140_in_ga(x1)
U74_ga(x1, x2, x3)  =  U74_ga(x3)
t145_in_ga(x1, x2)  =  t145_in_ga(x1)
t145_out_ga(x1, x2)  =  t145_out_ga
U70_ga(x1, x2, x3)  =  U70_ga(x3)
e169_in_ga(x1, x2)  =  e169_in_ga(x1)
U66_ga(x1, x2, x3)  =  U66_ga(x3)
t174_in_ga(x1, x2)  =  t174_in_ga(x1)
t174_out_ga(x1, x2)  =  t174_out_ga
U62_ga(x1, x2, x3)  =  U62_ga(x3)
e198_in_ga(x1, x2)  =  e198_in_ga(x1)
U6_ga(x1, x2, x3)  =  U6_ga(x3)
t203_in_ga(x1, x2)  =  t203_in_ga(x1)
t203_out_ga(x1, x2)  =  t203_out_ga
U2_ga(x1, x2, x3)  =  U2_ga(x3)
U110_ga(x1, x2, x3)  =  U110_ga(x3)
t234_in_ga(x1, x2)  =  t234_in_ga(x1)
plus  =  plus
t234_out_ga(x1, x2)  =  t234_out_ga
U14_ga(x1, x2, x3)  =  U14_ga(x3)
e259_in_ga(x1, x2)  =  e259_in_ga(x1)
U58_ga(x1, x2, x3)  =  U58_ga(x3)
t264_in_ga(x1, x2)  =  t264_in_ga(x1)
t264_out_ga(x1, x2)  =  t264_out_ga
U54_ga(x1, x2, x3)  =  U54_ga(x3)
e288_in_ga(x1, x2)  =  e288_in_ga(x1)
U50_ga(x1, x2, x3)  =  U50_ga(x3)
t293_in_ga(x1, x2)  =  t293_in_ga(x1)
t293_out_ga(x1, x2)  =  t293_out_ga
U46_ga(x1, x2, x3)  =  U46_ga(x3)
e317_in_ga(x1, x2)  =  e317_in_ga(x1)
U42_ga(x1, x2, x3)  =  U42_ga(x3)
t322_in_ga(x1, x2)  =  t322_in_ga(x1)
t322_out_ga(x1, x2)  =  t322_out_ga
U38_ga(x1, x2, x3)  =  U38_ga(x3)
e346_in_ga(x1, x2)  =  e346_in_ga(x1)
U34_ga(x1, x2, x3)  =  U34_ga(x3)
t351_in_ga(x1, x2)  =  t351_in_ga(x1)
t351_out_ga(x1, x2)  =  t351_out_ga
U30_ga(x1, x2, x3)  =  U30_ga(x3)
e375_in_ga(x1, x2)  =  e375_in_ga(x1)
U26_ga(x1, x2, x3)  =  U26_ga(x3)
t380_in_ga(x1, x2)  =  t380_in_ga(x1)
t380_out_ga(x1, x2)  =  t380_out_ga
U22_ga(x1, x2, x3)  =  U22_ga(x3)
e404_in_ga(x1, x2)  =  e404_in_ga(x1)
U18_ga(x1, x2, x3)  =  U18_ga(x3)
t409_in_ga(x1, x2)  =  t409_in_ga(x1)
t409_out_ga(x1, x2)  =  t409_out_ga
U10_ga(x1, x2, x3)  =  U10_ga(x3)
U111_ga(x1, x2, x3)  =  U111_ga(x3)
U15_ga(x1, x2, x3)  =  U15_ga(x3)
U16_ga(x1, x2, x3)  =  U16_ga(x3)
U17_ga(x1, x2, x3)  =  U17_ga(x3)
U112_ga(x1, x2, x3)  =  U112_ga(x3)
e1_in_aa(x1, x2)  =  e1_in_aa
U108_aa(x1, x2, x3)  =  U108_aa(x3)
n7_in_aa(x1, x2)  =  n7_in_aa
n7_out_aa(x1, x2)  =  n7_out_aa
U102_aa(x1, x2, x3)  =  U102_aa(x3)
U109_aa(x1, x2, x3)  =  U109_aa(x3)
p31_in_aaa(x1, x2, x3)  =  p31_in_aaa
U103_aaa(x1, x2, x3, x4)  =  U103_aaa(x4)
n32_in_aa(x1, x2)  =  n32_in_aa
n32_out_aa(x1, x2)  =  n32_out_aa
U1_aa(x1, x2, x3)  =  U1_aa(x3)
e53_in_aa(x1, x2)  =  e53_in_aa
U98_aa(x1, x2, x3)  =  U98_aa(x3)
t58_in_aa(x1, x2)  =  t58_in_aa
t58_out_aa(x1, x2)  =  t58_out_aa
U94_aa(x1, x2, x3)  =  U94_aa(x3)
e82_in_aa(x1, x2)  =  e82_in_aa
U90_aa(x1, x2, x3)  =  U90_aa(x3)
t87_in_aa(x1, x2)  =  t87_in_aa
t87_out_aa(x1, x2)  =  t87_out_aa
U86_aa(x1, x2, x3)  =  U86_aa(x3)
e111_in_aa(x1, x2)  =  e111_in_aa
U82_aa(x1, x2, x3)  =  U82_aa(x3)
t116_in_aa(x1, x2)  =  t116_in_aa
t116_out_aa(x1, x2)  =  t116_out_aa
U78_aa(x1, x2, x3)  =  U78_aa(x3)
e140_in_aa(x1, x2)  =  e140_in_aa
U74_aa(x1, x2, x3)  =  U74_aa(x3)
t145_in_aa(x1, x2)  =  t145_in_aa
t145_out_aa(x1, x2)  =  t145_out_aa
U70_aa(x1, x2, x3)  =  U70_aa(x3)
e169_in_aa(x1, x2)  =  e169_in_aa
U66_aa(x1, x2, x3)  =  U66_aa(x3)
t174_in_aa(x1, x2)  =  t174_in_aa
t174_out_aa(x1, x2)  =  t174_out_aa
U62_aa(x1, x2, x3)  =  U62_aa(x3)
e198_in_aa(x1, x2)  =  e198_in_aa
U6_aa(x1, x2, x3)  =  U6_aa(x3)
t203_in_aa(x1, x2)  =  t203_in_aa
t203_out_aa(x1, x2)  =  t203_out_aa
U2_aa(x1, x2, x3)  =  U2_aa(x3)
U110_aa(x1, x2, x3)  =  U110_aa(x3)
t234_in_aa(x1, x2)  =  t234_in_aa
t234_out_aa(x1, x2)  =  t234_out_aa
U14_aa(x1, x2, x3)  =  U14_aa(x3)
e259_in_aa(x1, x2)  =  e259_in_aa
U58_aa(x1, x2, x3)  =  U58_aa(x3)
t264_in_aa(x1, x2)  =  t264_in_aa
t264_out_aa(x1, x2)  =  t264_out_aa
U54_aa(x1, x2, x3)  =  U54_aa(x3)
e288_in_aa(x1, x2)  =  e288_in_aa
U50_aa(x1, x2, x3)  =  U50_aa(x3)
t293_in_aa(x1, x2)  =  t293_in_aa
t293_out_aa(x1, x2)  =  t293_out_aa
U46_aa(x1, x2, x3)  =  U46_aa(x3)
e317_in_aa(x1, x2)  =  e317_in_aa
U42_aa(x1, x2, x3)  =  U42_aa(x3)
t322_in_aa(x1, x2)  =  t322_in_aa
t322_out_aa(x1, x2)  =  t322_out_aa
U38_aa(x1, x2, x3)  =  U38_aa(x3)
e346_in_aa(x1, x2)  =  e346_in_aa
U34_aa(x1, x2, x3)  =  U34_aa(x3)
t351_in_aa(x1, x2)  =  t351_in_aa
t351_out_aa(x1, x2)  =  t351_out_aa
U30_aa(x1, x2, x3)  =  U30_aa(x3)
e375_in_aa(x1, x2)  =  e375_in_aa
U26_aa(x1, x2, x3)  =  U26_aa(x3)
t380_in_aa(x1, x2)  =  t380_in_aa
t380_out_aa(x1, x2)  =  t380_out_aa
U22_aa(x1, x2, x3)  =  U22_aa(x3)
e404_in_aa(x1, x2)  =  e404_in_aa
U18_aa(x1, x2, x3)  =  U18_aa(x3)
t409_in_aa(x1, x2)  =  t409_in_aa
t409_out_aa(x1, x2)  =  t409_out_aa
U10_aa(x1, x2, x3)  =  U10_aa(x3)
U111_aa(x1, x2, x3)  =  U111_aa(x3)
U15_aa(x1, x2, x3)  =  U15_aa(x3)
U16_aa(x1, x2, x3)  =  U16_aa(x3)
U17_aa(x1, x2, x3)  =  U17_aa(x3)
U112_aa(x1, x2, x3)  =  U112_aa(x3)
e1_out_aa(x1, x2)  =  e1_out_aa
U11_aa(x1, x2, x3)  =  U11_aa(x3)
U12_aa(x1, x2, x3)  =  U12_aa(x3)
U13_aa(x1, x2, x3)  =  U13_aa(x3)
e404_out_aa(x1, x2)  =  e404_out_aa
U19_aa(x1, x2, x3)  =  U19_aa(x3)
U20_aa(x1, x2, x3)  =  U20_aa(x3)
U21_aa(x1, x2, x3)  =  U21_aa(x3)
U23_aa(x1, x2, x3)  =  U23_aa(x3)
U24_aa(x1, x2, x3)  =  U24_aa(x3)
U25_aa(x1, x2, x3)  =  U25_aa(x3)
e375_out_aa(x1, x2)  =  e375_out_aa
U27_aa(x1, x2, x3)  =  U27_aa(x3)
U28_aa(x1, x2, x3)  =  U28_aa(x3)
U29_aa(x1, x2, x3)  =  U29_aa(x3)
U31_aa(x1, x2, x3)  =  U31_aa(x3)
U32_aa(x1, x2, x3)  =  U32_aa(x3)
U33_aa(x1, x2, x3)  =  U33_aa(x3)
e346_out_aa(x1, x2)  =  e346_out_aa
U35_aa(x1, x2, x3)  =  U35_aa(x3)
U36_aa(x1, x2, x3)  =  U36_aa(x3)
U37_aa(x1, x2, x3)  =  U37_aa(x3)
U39_aa(x1, x2, x3)  =  U39_aa(x3)
U40_aa(x1, x2, x3)  =  U40_aa(x3)
U41_aa(x1, x2, x3)  =  U41_aa(x3)
e317_out_aa(x1, x2)  =  e317_out_aa
U43_aa(x1, x2, x3)  =  U43_aa(x3)
U44_aa(x1, x2, x3)  =  U44_aa(x3)
U45_aa(x1, x2, x3)  =  U45_aa(x3)
U47_aa(x1, x2, x3)  =  U47_aa(x3)
U48_aa(x1, x2, x3)  =  U48_aa(x3)
U49_aa(x1, x2, x3)  =  U49_aa(x3)
e288_out_aa(x1, x2)  =  e288_out_aa
U51_aa(x1, x2, x3)  =  U51_aa(x3)
U52_aa(x1, x2, x3)  =  U52_aa(x3)
U53_aa(x1, x2, x3)  =  U53_aa(x3)
U55_aa(x1, x2, x3)  =  U55_aa(x3)
U56_aa(x1, x2, x3)  =  U56_aa(x3)
U57_aa(x1, x2, x3)  =  U57_aa(x3)
e259_out_aa(x1, x2)  =  e259_out_aa
U59_aa(x1, x2, x3)  =  U59_aa(x3)
U60_aa(x1, x2, x3)  =  U60_aa(x3)
U61_aa(x1, x2, x3)  =  U61_aa(x3)
U3_aa(x1, x2, x3)  =  U3_aa(x3)
U4_aa(x1, x2, x3)  =  U4_aa(x3)
U5_aa(x1, x2, x3)  =  U5_aa(x3)
e198_out_aa(x1, x2)  =  e198_out_aa
U7_aa(x1, x2, x3)  =  U7_aa(x3)
U8_aa(x1, x2, x3)  =  U8_aa(x3)
U9_aa(x1, x2, x3)  =  U9_aa(x3)
U63_aa(x1, x2, x3)  =  U63_aa(x3)
U64_aa(x1, x2, x3)  =  U64_aa(x3)
U65_aa(x1, x2, x3)  =  U65_aa(x3)
e169_out_aa(x1, x2)  =  e169_out_aa
U67_aa(x1, x2, x3)  =  U67_aa(x3)
U68_aa(x1, x2, x3)  =  U68_aa(x3)
U69_aa(x1, x2, x3)  =  U69_aa(x3)
U71_aa(x1, x2, x3)  =  U71_aa(x3)
U72_aa(x1, x2, x3)  =  U72_aa(x3)
U73_aa(x1, x2, x3)  =  U73_aa(x3)
e140_out_aa(x1, x2)  =  e140_out_aa
U75_aa(x1, x2, x3)  =  U75_aa(x3)
U76_aa(x1, x2, x3)  =  U76_aa(x3)
U77_aa(x1, x2, x3)  =  U77_aa(x3)
U79_aa(x1, x2, x3)  =  U79_aa(x3)
U80_aa(x1, x2, x3)  =  U80_aa(x3)
U81_aa(x1, x2, x3)  =  U81_aa(x3)
e111_out_aa(x1, x2)  =  e111_out_aa
U83_aa(x1, x2, x3)  =  U83_aa(x3)
U84_aa(x1, x2, x3)  =  U84_aa(x3)
U85_aa(x1, x2, x3)  =  U85_aa(x3)
U87_aa(x1, x2, x3)  =  U87_aa(x3)
U88_aa(x1, x2, x3)  =  U88_aa(x3)
U89_aa(x1, x2, x3)  =  U89_aa(x3)
e82_out_aa(x1, x2)  =  e82_out_aa
U91_aa(x1, x2, x3)  =  U91_aa(x3)
U92_aa(x1, x2, x3)  =  U92_aa(x3)
U93_aa(x1, x2, x3)  =  U93_aa(x3)
U95_aa(x1, x2, x3)  =  U95_aa(x3)
U96_aa(x1, x2, x3)  =  U96_aa(x3)
U97_aa(x1, x2, x3)  =  U97_aa(x3)
e53_out_aa(x1, x2)  =  e53_out_aa
U99_aa(x1, x2, x3)  =  U99_aa(x3)
U100_aa(x1, x2, x3)  =  U100_aa(x3)
U101_aa(x1, x2, x3)  =  U101_aa(x3)
p31_out_aaa(x1, x2, x3)  =  p31_out_aaa
U104_aaa(x1, x2, x3, x4)  =  U104_aaa(x4)
U105_aaa(x1, x2, x3, x4)  =  U105_aaa(x4)
U106_aaa(x1, x2, x3, x4)  =  U106_aaa(x4)
U107_aaa(x1, x2, x3, x4)  =  U107_aaa(x4)
e1_out_ga(x1, x2)  =  e1_out_ga
U11_ga(x1, x2, x3)  =  U11_ga(x3)
U12_ga(x1, x2, x3)  =  U12_ga(x3)
U13_ga(x1, x2, x3)  =  U13_ga(x3)
e404_out_ga(x1, x2)  =  e404_out_ga
U19_ga(x1, x2, x3)  =  U19_ga(x3)
U20_ga(x1, x2, x3)  =  U20_ga(x3)
U21_ga(x1, x2, x3)  =  U21_ga(x3)
U23_ga(x1, x2, x3)  =  U23_ga(x3)
U24_ga(x1, x2, x3)  =  U24_ga(x3)
U25_ga(x1, x2, x3)  =  U25_ga(x3)
e375_out_ga(x1, x2)  =  e375_out_ga
U27_ga(x1, x2, x3)  =  U27_ga(x3)
U28_ga(x1, x2, x3)  =  U28_ga(x3)
U29_ga(x1, x2, x3)  =  U29_ga(x3)
U31_ga(x1, x2, x3)  =  U31_ga(x3)
U32_ga(x1, x2, x3)  =  U32_ga(x3)
U33_ga(x1, x2, x3)  =  U33_ga(x3)
e346_out_ga(x1, x2)  =  e346_out_ga
U35_ga(x1, x2, x3)  =  U35_ga(x3)
U36_ga(x1, x2, x3)  =  U36_ga(x3)
U37_ga(x1, x2, x3)  =  U37_ga(x3)
U39_ga(x1, x2, x3)  =  U39_ga(x3)
U40_ga(x1, x2, x3)  =  U40_ga(x3)
U41_ga(x1, x2, x3)  =  U41_ga(x3)
e317_out_ga(x1, x2)  =  e317_out_ga
U43_ga(x1, x2, x3)  =  U43_ga(x3)
U44_ga(x1, x2, x3)  =  U44_ga(x3)
U45_ga(x1, x2, x3)  =  U45_ga(x3)
U47_ga(x1, x2, x3)  =  U47_ga(x3)
U48_ga(x1, x2, x3)  =  U48_ga(x3)
U49_ga(x1, x2, x3)  =  U49_ga(x3)
e288_out_ga(x1, x2)  =  e288_out_ga
U51_ga(x1, x2, x3)  =  U51_ga(x3)
U52_ga(x1, x2, x3)  =  U52_ga(x3)
U53_ga(x1, x2, x3)  =  U53_ga(x3)
U55_ga(x1, x2, x3)  =  U55_ga(x3)
U56_ga(x1, x2, x3)  =  U56_ga(x3)
U57_ga(x1, x2, x3)  =  U57_ga(x3)
e259_out_ga(x1, x2)  =  e259_out_ga
U59_ga(x1, x2, x3)  =  U59_ga(x3)
U60_ga(x1, x2, x3)  =  U60_ga(x3)
U61_ga(x1, x2, x3)  =  U61_ga(x3)
U3_ga(x1, x2, x3)  =  U3_ga(x3)
U4_ga(x1, x2, x3)  =  U4_ga(x3)
U5_ga(x1, x2, x3)  =  U5_ga(x3)
e198_out_ga(x1, x2)  =  e198_out_ga
U7_ga(x1, x2, x3)  =  U7_ga(x3)
U8_ga(x1, x2, x3)  =  U8_ga(x3)
U9_ga(x1, x2, x3)  =  U9_ga(x3)
U63_ga(x1, x2, x3)  =  U63_ga(x3)
U64_ga(x1, x2, x3)  =  U64_ga(x3)
U65_ga(x1, x2, x3)  =  U65_ga(x3)
e169_out_ga(x1, x2)  =  e169_out_ga
U67_ga(x1, x2, x3)  =  U67_ga(x3)
U68_ga(x1, x2, x3)  =  U68_ga(x3)
U69_ga(x1, x2, x3)  =  U69_ga(x3)
U71_ga(x1, x2, x3)  =  U71_ga(x3)
U72_ga(x1, x2, x3)  =  U72_ga(x3)
U73_ga(x1, x2, x3)  =  U73_ga(x3)
e140_out_ga(x1, x2)  =  e140_out_ga
U75_ga(x1, x2, x3)  =  U75_ga(x3)
U76_ga(x1, x2, x3)  =  U76_ga(x3)
U77_ga(x1, x2, x3)  =  U77_ga(x3)
U79_ga(x1, x2, x3)  =  U79_ga(x3)
U80_ga(x1, x2, x3)  =  U80_ga(x3)
U81_ga(x1, x2, x3)  =  U81_ga(x3)
e111_out_ga(x1, x2)  =  e111_out_ga
U83_ga(x1, x2, x3)  =  U83_ga(x3)
U84_ga(x1, x2, x3)  =  U84_ga(x3)
U85_ga(x1, x2, x3)  =  U85_ga(x3)
U87_ga(x1, x2, x3)  =  U87_ga(x3)
U88_ga(x1, x2, x3)  =  U88_ga(x3)
U89_ga(x1, x2, x3)  =  U89_ga(x3)
e82_out_ga(x1, x2)  =  e82_out_ga
U91_ga(x1, x2, x3)  =  U91_ga(x3)
U92_ga(x1, x2, x3)  =  U92_ga(x3)
U93_ga(x1, x2, x3)  =  U93_ga(x3)
U95_ga(x1, x2, x3)  =  U95_ga(x3)
U96_ga(x1, x2, x3)  =  U96_ga(x3)
U97_ga(x1, x2, x3)  =  U97_ga(x3)
e53_out_ga(x1, x2)  =  e53_out_ga
U99_ga(x1, x2, x3)  =  U99_ga(x3)
U100_ga(x1, x2, x3)  =  U100_ga(x3)
U101_ga(x1, x2, x3)  =  U101_ga(x3)
p31_out_gaa(x1, x2, x3)  =  p31_out_gaa
U104_gaa(x1, x2, x3, x4)  =  U104_gaa(x4)
U105_gaa(x1, x2, x3, x4)  =  U105_gaa(x4)
U106_gaa(x1, x2, x3, x4)  =  U106_gaa(x4)
U107_gaa(x1, x2, x3, x4)  =  U107_gaa(x4)
E1_IN_GA(x1, x2)  =  E1_IN_GA(x1)
N7_IN_GA(x1, x2)  =  N7_IN_GA(x1)
P31_IN_GAA(x1, x2, x3)  =  P31_IN_GAA(x1)
N32_IN_GA(x1, x2)  =  N32_IN_GA(x1)
E53_IN_GA(x1, x2)  =  E53_IN_GA(x1)
T58_IN_GA(x1, x2)  =  T58_IN_GA(x1)
E82_IN_GA(x1, x2)  =  E82_IN_GA(x1)
T87_IN_GA(x1, x2)  =  T87_IN_GA(x1)
E111_IN_GA(x1, x2)  =  E111_IN_GA(x1)
T116_IN_GA(x1, x2)  =  T116_IN_GA(x1)
E140_IN_GA(x1, x2)  =  E140_IN_GA(x1)
T145_IN_GA(x1, x2)  =  T145_IN_GA(x1)
E169_IN_GA(x1, x2)  =  E169_IN_GA(x1)
T174_IN_GA(x1, x2)  =  T174_IN_GA(x1)
E198_IN_GA(x1, x2)  =  E198_IN_GA(x1)
T203_IN_GA(x1, x2)  =  T203_IN_GA(x1)
T234_IN_GA(x1, x2)  =  T234_IN_GA(x1)
E259_IN_GA(x1, x2)  =  E259_IN_GA(x1)
T264_IN_GA(x1, x2)  =  T264_IN_GA(x1)
E288_IN_GA(x1, x2)  =  E288_IN_GA(x1)
T293_IN_GA(x1, x2)  =  T293_IN_GA(x1)
E317_IN_GA(x1, x2)  =  E317_IN_GA(x1)
T322_IN_GA(x1, x2)  =  T322_IN_GA(x1)
E346_IN_GA(x1, x2)  =  E346_IN_GA(x1)
T351_IN_GA(x1, x2)  =  T351_IN_GA(x1)
E375_IN_GA(x1, x2)  =  E375_IN_GA(x1)
T380_IN_GA(x1, x2)  =  T380_IN_GA(x1)
E404_IN_GA(x1, x2)  =  E404_IN_GA(x1)
T409_IN_GA(x1, x2)  =  T409_IN_GA(x1)

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

(141) UsableRulesProof (EQUIVALENT transformation)

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

(142) Obligation:

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

E1_IN_GA(T22, T24) → N7_IN_GA(T22, T24)
N7_IN_GA(.(lbrace, T41), T43) → E1_IN_GA(T41, .(rbrace, T43))
E1_IN_GA(T62, T64) → P31_IN_GAA(T62, X59, T64)
P31_IN_GAA(T62, X59, T64) → N32_IN_GA(T62, X59)
N32_IN_GA(.(lbrace, T89), X84) → E53_IN_GA(T89, X84)
E53_IN_GA(T97, X110) → T58_IN_GA(T97, X110)
T58_IN_GA(.(lbrace, T130), X155) → E82_IN_GA(T130, X155)
E82_IN_GA(T138, X181) → T87_IN_GA(T138, X181)
T87_IN_GA(.(lbrace, T171), X226) → E111_IN_GA(T171, X226)
E111_IN_GA(T179, X252) → T116_IN_GA(T179, X252)
T116_IN_GA(.(lbrace, T212), X297) → E140_IN_GA(T212, X297)
E140_IN_GA(T220, X323) → T145_IN_GA(T220, X323)
T145_IN_GA(.(lbrace, T253), X368) → E169_IN_GA(T253, X368)
E169_IN_GA(T261, X394) → T174_IN_GA(T261, X394)
T174_IN_GA(.(lbrace, T294), X439) → E198_IN_GA(T294, X439)
E198_IN_GA(T302, X465) → T203_IN_GA(T302, X465)
T203_IN_GA(.(lbrace, T335), X510) → E1_IN_GA(T335, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(star, X510)))))))))
E1_IN_GA(T941, T943) → T234_IN_GA(T941, X1569)
T234_IN_GA(.(lbrace, T392), X599) → E259_IN_GA(T392, X599)
E259_IN_GA(T400, X625) → T264_IN_GA(T400, X625)
T264_IN_GA(.(lbrace, T433), X670) → E288_IN_GA(T433, X670)
E288_IN_GA(T441, X696) → T293_IN_GA(T441, X696)
T293_IN_GA(.(lbrace, T474), X741) → E317_IN_GA(T474, X741)
E317_IN_GA(T482, X767) → T322_IN_GA(T482, X767)
T322_IN_GA(.(lbrace, T515), X812) → E346_IN_GA(T515, X812)
E346_IN_GA(T523, X838) → T351_IN_GA(T523, X838)
T351_IN_GA(.(lbrace, T556), X883) → E375_IN_GA(T556, X883)
E375_IN_GA(T564, X909) → T380_IN_GA(T564, X909)
T380_IN_GA(.(lbrace, T597), X954) → E404_IN_GA(T597, X954)
E404_IN_GA(T605, X980) → T409_IN_GA(T605, X980)
T409_IN_GA(.(lbrace, T638), X1025) → E1_IN_GA(T638, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(rbrace, .(plus, X1025)))))))))
T409_IN_GA(T648, X1045) → N32_IN_GA(T648, X1044)
E404_IN_GA(T660, X1066) → T234_IN_GA(T660, X1065)
T234_IN_GA(T780, X1303) → N32_IN_GA(T780, X1302)
T380_IN_GA(T670, X1088) → N32_IN_GA(T670, X1087)
E375_IN_GA(T682, X1109) → T234_IN_GA(T682, X1108)
T351_IN_GA(T692, X1131) → N32_IN_GA(T692, X1130)
E346_IN_GA(T704, X1152) → T234_IN_GA(T704, X1151)
T322_IN_GA(T714, X1174) → N32_IN_GA(T714, X1173)
E317_IN_GA(T726, X1195) → T234_IN_GA(T726, X1194)
T293_IN_GA(T736, X1217) → N32_IN_GA(T736, X1216)
E288_IN_GA(T748, X1238) → T234_IN_GA(T748, X1237)
T264_IN_GA(T758, X1260) → N32_IN_GA(T758, X1259)
E259_IN_GA(T770, X1281) → T234_IN_GA(T770, X1280)
T203_IN_GA(T345, X530) → N32_IN_GA(T345, X529)
E198_IN_GA(T357, X551) → T234_IN_GA(T357, X550)
T174_IN_GA(T795, X1326) → N32_IN_GA(T795, X1325)
E169_IN_GA(T807, X1347) → T234_IN_GA(T807, X1346)
T145_IN_GA(T817, X1369) → N32_IN_GA(T817, X1368)
E140_IN_GA(T829, X1390) → T234_IN_GA(T829, X1389)
T116_IN_GA(T839, X1412) → N32_IN_GA(T839, X1411)
E111_IN_GA(T851, X1433) → T234_IN_GA(T851, X1432)
T87_IN_GA(T861, X1455) → N32_IN_GA(T861, X1454)
E82_IN_GA(T873, X1476) → T234_IN_GA(T873, X1475)
T58_IN_GA(T883, X1498) → N32_IN_GA(T883, X1497)
E53_IN_GA(T895, X1519) → T234_IN_GA(T895, X1518)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2)  =  .(x1, x2)
lbrace  =  lbrace
star  =  star
rbrace  =  rbrace
plus  =  plus
E1_IN_GA(x1, x2)  =  E1_IN_GA(x1)
N7_IN_GA(x1, x2)  =  N7_IN_GA(x1)
P31_IN_GAA(x1, x2, x3)  =  P31_IN_GAA(x1)
N32_IN_GA(x1, x2)  =  N32_IN_GA(x1)
E53_IN_GA(x1, x2)  =  E53_IN_GA(x1)
T58_IN_GA(x1, x2)  =  T58_IN_GA(x1)
E82_IN_GA(x1, x2)  =  E82_IN_GA(x1)
T87_IN_GA(x1, x2)  =  T87_IN_GA(x1)
E111_IN_GA(x1, x2)  =  E111_IN_GA(x1)
T116_IN_GA(x1, x2)  =  T116_IN_GA(x1)
E140_IN_GA(x1, x2)  =  E140_IN_GA(x1)
T145_IN_GA(x1, x2)  =  T145_IN_GA(x1)
E169_IN_GA(x1, x2)  =  E169_IN_GA(x1)
T174_IN_GA(x1, x2)  =  T174_IN_GA(x1)
E198_IN_GA(x1, x2)  =  E198_IN_GA(x1)
T203_IN_GA(x1, x2)  =  T203_IN_GA(x1)
T234_IN_GA(x1, x2)  =  T234_IN_GA(x1)
E259_IN_GA(x1, x2)  =  E259_IN_GA(x1)
T264_IN_GA(x1, x2)  =  T264_IN_GA(x1)
E288_IN_GA(x1, x2)  =  E288_IN_GA(x1)
T293_IN_GA(x1, x2)  =  T293_IN_GA(x1)
E317_IN_GA(x1, x2)  =  E317_IN_GA(x1)
T322_IN_GA(x1, x2)  =  T322_IN_GA(x1)
E346_IN_GA(x1, x2)  =  E346_IN_GA(x1)
T351_IN_GA(x1, x2)  =  T351_IN_GA(x1)
E375_IN_GA(x1, x2)  =  E375_IN_GA(x1)
T380_IN_GA(x1, x2)  =  T380_IN_GA(x1)
E404_IN_GA(x1, x2)  =  E404_IN_GA(x1)
T409_IN_GA(x1, x2)  =  T409_IN_GA(x1)

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