Left Termination proof of /tmp/tmp8VvAy2/vangelder.pl

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

0 Prolog

↳1 PrologToPiTRSViaGraphTransformerProof (⇒, 1109 ms)

↳2 PiTRS

↳3 DependencyPairsProof (⇔, 2790 ms)

↳4 PiDP

↳5 DependencyGraphProof (⇔, 0 ms)

↳6 PiDP

↳7 PiDPToQDPProof (⇔, 408 ms)

↳8 QDP

↳9 Instantiation (⇔, 0 ms)

↳10 QDP

↳11 QDPOrderProof (⇔, 1371 ms)

↳12 QDP

↳13 DependencyGraphProof (⇔, 0 ms)

↳14 TRUE

(0) Obligation:

Clauses:

e(a, b).
q(X, Y) :- e(X, Y).
q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X))).
q(X, f(f(Y))) :- p(X, f(Y)).
p(X, Y) :- e(X, Y).
p(X, f(Y)) :- ','(r(X, f(Y)), p(X, Y)).
r(X, Y) :- e(X, Y).
r(X, f(Y)) :- ','(q(X, Y), r(X, Y)).
r(f(X), f(X)) :- t(f(X), f(X)).
t(X, Y) :- e(X, Y).
t(f(X), f(Y)) :- ','(q(f(X), f(Y)), t(X, Y)).

Query: q(g,g)

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

Transformed Prolog program to (Pi-)TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
3 [label="A: q(T1, T2)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
5 [label="5: q(T1, T2), SCOPE: 1, CLAUSE: 1 | q(T1, T2), SCOPE: 1, CLAUSE: 2 | q(T1, T2), SCOPE: 1, CLAUSE: 3\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: e(T5, T6) | q(T5, T6), SCOPE: 1, CLAUSE: 2 | q(T5, T6), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: e(T5, T6), SCOPE: 2, CLAUSE: 0 | ?_2 | q(T5, T6), SCOPE: 1, CLAUSE: 2 | q(T5, T6), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: e(T5, T6), SCOPE: 2, CLAUSE: 0\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ?_2 | q(T5, T6), SCOPE: 1, CLAUSE: 2 | q(T5, T6), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: q(T5, T6), SCOPE: 1, CLAUSE: 2 | q(T5, T6), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: q(T5, T6), SCOPE: 1, CLAUSE: 2\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: q(T5, T6), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="B: ','(p(T11, f(f(T11))), q(T11, f(T11)))\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="N3: p(T11, f(f(T11)))\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="D: q(T11, f(T11))\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: p(T11, f(f(T11))), SCOPE: 3, CLAUSE: 4 | p(T11, f(f(T11))), SCOPE: 3, CLAUSE: 5\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: p(T11, f(f(T11))), SCOPE: 3, CLAUSE: 4\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: p(T11, f(f(T11))), SCOPE: 3, CLAUSE: 5\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: e(T18, f(f(T18)))\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: e(T18, f(f(T18))), SCOPE: 4, CLAUSE: 0\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="N4: ','(r(T22, f(f(T22))), p(T22, f(T22)))\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="N5: r(T22, f(f(T22)))\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="N7: p(T22, f(T22))\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 6 | r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 7 | r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 8\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 6\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 7 | r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 8\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: e(T29, f(f(T29)))\n\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: e(T29, f(f(T29))), SCOPE: 6, CLAUSE: 0\n\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 7\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 8\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="N6: ','(q(T36, f(T36)), r(T36, f(T36)))\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: q(T36, f(T36))\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="X: r(T36, f(T36))\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: r(T36, f(T36)), SCOPE: 7, CLAUSE: 6 | r(T36, f(T36)), SCOPE: 7, CLAUSE: 7 | r(T36, f(T36)), SCOPE: 7, CLAUSE: 8\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: r(T36, f(T36)), SCOPE: 7, CLAUSE: 6\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: r(T36, f(T36)), SCOPE: 7, CLAUSE: 7 | r(T36, f(T36)), SCOPE: 7, CLAUSE: 8\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: e(T44, f(T44))\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: e(T44, f(T44)), SCOPE: 8, CLAUSE: 0\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: r(T36, f(T36)), SCOPE: 7, CLAUSE: 7\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: r(T36, f(T36)), SCOPE: 7, CLAUSE: 8\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="Y: ','(q(T51, T51), r(T51, T51))\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="H: q(T51, T51)\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="Z: r(T51, T51)\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: q(T51, T51), SCOPE: 9, CLAUSE: 1 | q(T51, T51), SCOPE: 9, CLAUSE: 2 | q(T51, T51), SCOPE: 9, CLAUSE: 3\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: q(T51, T51), SCOPE: 9, CLAUSE: 1\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: q(T51, T51), SCOPE: 9, CLAUSE: 2 | q(T51, T51), SCOPE: 9, CLAUSE: 3\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: e(T58, T58)\n\nT58 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: e(T58, T58), SCOPE: 10, CLAUSE: 0\n\nT58 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: q(T51, T51), SCOPE: 9, CLAUSE: 3\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: p(f(f(T65)), f(T65))\n\nT65 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: p(f(f(T65)), f(T65)), SCOPE: 11, CLAUSE: 4 | p(f(f(T65)), f(T65)), SCOPE: 11, CLAUSE: 5\n\nT65 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: p(f(f(T65)), f(T65)), SCOPE: 11, CLAUSE: 4\n\nT65 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: p(f(f(T65)), f(T65)), SCOPE: 11, CLAUSE: 5\n\nT65 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: e(f(f(T71)), f(T71))\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: e(f(f(T71)), f(T71)), SCOPE: 12, CLAUSE: 0\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="I: ','(r(f(f(T75)), f(T75)), p(f(f(T75)), T75))\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="N9: r(f(f(T75)), f(T75))\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="V: p(f(f(T75)), T75)\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 6 | r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 7 | r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 8\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 6\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 7 | r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 8\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: e(f(f(T82)), f(T82))\n\nT82 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: e(f(f(T82)), f(T82)), SCOPE: 14, CLAUSE: 0\n\nT82 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 7\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 8\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="N10: ','(q(f(f(T89)), T89), r(f(f(T89)), T89))\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="N11: q(f(f(T89)), T89)\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="T: r(f(f(T89)), T89)\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 1 | q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 2 | q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 3\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 1\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 2 | q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 3\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: e(f(f(T96)), T96)\n\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: e(f(f(T96)), T96), SCOPE: 16, CLAUSE: 0\n\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 3\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: p(f(f(f(f(T103)))), f(T103))\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: p(f(f(f(f(T103)))), f(T103)), SCOPE: 17, CLAUSE: 4 | p(f(f(f(f(T103)))), f(T103)), SCOPE: 17, CLAUSE: 5\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: p(f(f(f(f(T103)))), f(T103)), SCOPE: 17, CLAUSE: 4\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
235 [label="235: p(f(f(f(f(T103)))), f(T103)), SCOPE: 17, CLAUSE: 5\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: e(f(f(f(f(T109)))), f(T109))\n\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: e(f(f(f(f(T109)))), f(T109)), SCOPE: 18, CLAUSE: 0\n\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
241 [label="N12: ','(r(f(f(f(f(T113)))), f(T113)), p(f(f(f(f(T113)))), T113))\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="N13: r(f(f(f(f(T113)))), f(T113))\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="R: p(f(f(f(f(T113)))), T113)\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 6 | r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 7 | r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 8\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 6\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
260 [label="260: r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 7 | r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 8\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
262 [label="262: e(f(f(f(f(T120)))), f(T120))\n\nT120 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: e(f(f(f(f(T120)))), f(T120)), SCOPE: 20, CLAUSE: 0\n\nT120 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 7\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 8\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="N14: ','(q(f(f(f(f(T127)))), T127), r(f(f(f(f(T127)))), T127))\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="N15: q(f(f(f(f(T127)))), T127)\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="P: r(f(f(f(f(T127)))), T127)\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 1 | q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 2 | q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 3\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 1\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 2 | q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 3\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: e(f(f(f(f(T134)))), T134)\n\nT134 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: e(f(f(f(f(T134)))), T134), SCOPE: 22, CLAUSE: 0\n\nT134 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
294 [label="294: q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 3\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: p(f(f(f(f(f(f(T141)))))), f(T141))\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
300 [label="300: p(f(f(f(f(f(f(T141)))))), f(T141)), SCOPE: 23, CLAUSE: 4 | p(f(f(f(f(f(f(T141)))))), f(T141)), SCOPE: 23, CLAUSE: 5\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: p(f(f(f(f(f(f(T141)))))), f(T141)), SCOPE: 23, CLAUSE: 4\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
304 [label="304: p(f(f(f(f(f(f(T141)))))), f(T141)), SCOPE: 23, CLAUSE: 5\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: e(f(f(f(f(f(f(T147)))))), f(T147))\n\nT147 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: e(f(f(f(f(f(f(T147)))))), f(T147)), SCOPE: 24, CLAUSE: 0\n\nT147 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
310 [label="310: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
312 [label="N16: ','(r(f(f(f(f(f(f(T151)))))), f(T151)), p(f(f(f(f(f(f(T151)))))), T151))\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="N17: r(f(f(f(f(f(f(T151)))))), f(T151))\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="N: p(f(f(f(f(f(f(T151)))))), T151)\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 6 | r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 7 | r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 8\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
324 [label="324: r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 6\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 7 | r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 8\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
331 [label="331: e(f(f(f(f(f(f(T158)))))), f(T158))\n\nT158 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: e(f(f(f(f(f(f(T158)))))), f(T158)), SCOPE: 26, CLAUSE: 0\n\nT158 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
338 [label="338: r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 7\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 8\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="N18: ','(q(f(f(f(f(f(f(T165)))))), T165), r(f(f(f(f(f(f(T165)))))), T165))\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
350 [label="N19: q(f(f(f(f(f(f(T165)))))), T165)\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
351 [label="L: r(f(f(f(f(f(f(T165)))))), T165)\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
359 [label="359: q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 1 | q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 2 | q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 3\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 1\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
362 [label="362: q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 2 | q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 3\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
377 [label="377: e(f(f(f(f(f(f(T172)))))), T172)\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
378 [label="378: e(f(f(f(f(f(f(T172)))))), T172), SCOPE: 28, CLAUSE: 0\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
379 [label="379: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
380 [label="380: q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 3\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: p(f(f(f(f(f(f(f(f(T179)))))))), f(T179))\n\nT179 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
382 [label="382: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
384 [label="F: p(f(T181), f(T179))\n\nT179 is ground\nT181 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
413 [label="413: p(f(T181), f(T179)), SCOPE: 29, CLAUSE: 4 | p(f(T181), f(T179)), SCOPE: 29, CLAUSE: 5\n\nT179 is ground\nT181 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
416 [label="416: p(f(T181), f(T179)), SCOPE: 29, CLAUSE: 4\n\nT179 is ground\nT181 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
417 [label="417: p(f(T181), f(T179)), SCOPE: 29, CLAUSE: 5\n\nT179 is ground\nT181 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
420 [label="420: e(f(T192), f(T193))\n\nT192 is ground\nT193 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
421 [label="421: e(f(T192), f(T193)), SCOPE: 30, CLAUSE: 0\n\nT192 is ground\nT193 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
422 [label="422: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
424 [label="G: ','(r(f(T200), f(T201)), p(f(T200), T201))\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
429 [label="N20: r(f(T200), f(T201))\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
430 [label="N22: p(f(T200), T201)\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
437 [label="437: r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 6 | r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 7 | r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 8\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
438 [label="438: r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 6\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 7 | r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 8\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
443 [label="443: e(f(T214), f(T215))\n\nT214 is ground\nT215 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
444 [label="444: e(f(T214), f(T215)), SCOPE: 32, CLAUSE: 0\n\nT214 is ground\nT215 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
445 [label="445: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
448 [label="448: r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 7\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
449 [label="449: r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 8\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
454 [label="N21: ','(q(f(T228), T229), r(f(T228), T229))\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
458 [label="458: q(f(T228), T229)\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
460 [label="N23: r(f(T228), T229)\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
463 [label="463: r(f(T228), T229), SCOPE: 33, CLAUSE: 6 | r(f(T228), T229), SCOPE: 33, CLAUSE: 7 | r(f(T228), T229), SCOPE: 33, CLAUSE: 8\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
464 [label="464: r(f(T228), T229), SCOPE: 33, CLAUSE: 6\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
465 [label="465: r(f(T228), T229), SCOPE: 33, CLAUSE: 7 | r(f(T228), T229), SCOPE: 33, CLAUSE: 8\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
466 [label="466: e(f(T244), T245)\n\nT244 is ground\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
467 [label="467: e(f(T244), T245), SCOPE: 34, CLAUSE: 0\n\nT244 is ground\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
468 [label="468: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
470 [label="470: r(f(T228), T229), SCOPE: 33, CLAUSE: 7\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
471 [label="471: r(f(T228), T229), SCOPE: 33, CLAUSE: 8\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
474 [label="474: ','(q(f(T254), T255), r(f(T254), T255))\n\nT254 is ground\nT255 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
482 [label="J: t(f(T260), f(T260))\n\nT260 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
484 [label="484: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
492 [label="492: t(f(T260), f(T260)), SCOPE: 35, CLAUSE: 9 | t(f(T260), f(T260)), SCOPE: 35, CLAUSE: 10\n\nT260 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
494 [label="494: t(f(T260), f(T260)), SCOPE: 35, CLAUSE: 9\n\nT260 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
495 [label="495: t(f(T260), f(T260)), SCOPE: 35, CLAUSE: 10\n\nT260 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
496 [label="496: e(f(T266), f(T266))\n\nT266 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
497 [label="497: e(f(T266), f(T266)), SCOPE: 36, CLAUSE: 0\n\nT266 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
498 [label="498: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
500 [label="K: ','(q(f(T270), f(T270)), t(T270, T270))\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
508 [label="508: q(f(T270), f(T270))\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
509 [label="N24: t(T270, T270)\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
510 [label="510: t(T270, T270), SCOPE: 37, CLAUSE: 9 | t(T270, T270), SCOPE: 37, CLAUSE: 10\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
515 [label="515: t(T270, T270), SCOPE: 37, CLAUSE: 9\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
516 [label="516: t(T270, T270), SCOPE: 37, CLAUSE: 10\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
518 [label="518: e(T278, T278)\n\nT278 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
519 [label="519: e(T278, T278), SCOPE: 38, CLAUSE: 0\n\nT278 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
520 [label="520: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
525 [label="525: ','(q(f(T281), f(T281)), t(T281, T281))\n\nT281 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
528 [label="528: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
537 [label="537: t(f(T285), f(T285))\n\nT285 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
538 [label="538: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
541 [label="541: p(f(T200), T201), SCOPE: 39, CLAUSE: 4 | p(f(T200), T201), SCOPE: 39, CLAUSE: 5\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
542 [label="542: p(f(T200), T201), SCOPE: 39, CLAUSE: 4\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
543 [label="543: p(f(T200), T201), SCOPE: 39, CLAUSE: 5\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
545 [label="545: e(f(T297), T298)\n\nT297 is ground\nT298 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
547 [label="547: e(f(T297), T298), SCOPE: 40, CLAUSE: 0\n\nT297 is ground\nT298 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
549 [label="549: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
553 [label="553: ','(r(f(T303), f(T304)), p(f(T303), T304))\n\nT303 is ground\nT304 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
554 [label="554: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
562 [label="562: r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 6 | r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 7 | r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 8\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
564 [label="564: r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 6\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
565 [label="565: r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 7 | r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 8\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
571 [label="571: e(f(f(f(f(f(f(T312)))))), T312)\n\nT312 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
572 [label="572: e(f(f(f(f(f(f(T312)))))), T312), SCOPE: 42, CLAUSE: 0\n\nT312 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
573 [label="573: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
576 [label="576: r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 7\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
577 [label="577: r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 8\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
580 [label="M: ','(q(f(f(f(f(f(f(f(T322))))))), T322), r(f(f(f(f(f(f(f(T322))))))), T322))\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
581 [label="581: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
587 [label="N25: q(f(f(f(f(f(f(f(T322))))))), T322)\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
588 [label="N26: r(f(f(f(f(f(f(f(T322))))))), T322)\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
590 [label="590: q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 1 | q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 2 | q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 3\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
592 [label="592: q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 1\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
593 [label="593: q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 2 | q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 3\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
594 [label="594: e(f(f(f(f(f(f(f(T329))))))), T329)\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
597 [label="597: e(f(f(f(f(f(f(f(T329))))))), T329), SCOPE: 44, CLAUSE: 0\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
598 [label="598: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
599 [label="599: q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 3\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
602 [label="602: p(f(f(f(f(f(f(f(f(f(T336))))))))), f(T336))\n\nT336 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
603 [label="603: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
614 [label="614: p(f(T338), f(T336))\n\nT336 is ground\nT338 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
619 [label="619: r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 6 | r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 7 | r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 8\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
620 [label="620: r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 6\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
621 [label="621: r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 7 | r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 8\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
622 [label="622: e(f(f(f(f(f(f(f(T346))))))), T346)\n\nT346 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
623 [label="623: e(f(f(f(f(f(f(f(T346))))))), T346), SCOPE: 46, CLAUSE: 0\n\nT346 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
624 [label="624: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
626 [label="626: r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 7\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
629 [label="629: r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 8\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
632 [label="632: ','(q(f(f(f(f(f(f(f(f(T356)))))))), T356), r(f(f(f(f(f(f(f(f(T356)))))))), T356))\n\nT356 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
633 [label="633: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
641 [label="641: ','(q(f(T358), T356), r(f(T358), T356))\n\nT356 is ground\nT358 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
645 [label="645: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
646 [label="646: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
649 [label="649: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
650 [label="650: p(f(f(f(f(f(f(T151)))))), T151), SCOPE: 47, CLAUSE: 4 | p(f(f(f(f(f(f(T151)))))), T151), SCOPE: 47, CLAUSE: 5\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
651 [label="651: p(f(f(f(f(f(f(T151)))))), T151), SCOPE: 47, CLAUSE: 4\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
652 [label="652: p(f(f(f(f(f(f(T151)))))), T151), SCOPE: 47, CLAUSE: 5\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
655 [label="655: e(f(f(f(f(f(f(T369)))))), T369)\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
656 [label="656: e(f(f(f(f(f(f(T369)))))), T369), SCOPE: 48, CLAUSE: 0\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
657 [label="657: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
659 [label="O: ','(r(f(f(f(f(f(f(f(T375))))))), f(T375)), p(f(f(f(f(f(f(f(T375))))))), T375))\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
660 [label="660: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
669 [label="669: r(f(f(f(f(f(f(f(T375))))))), f(T375))\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
670 [label="N27: p(f(f(f(f(f(f(f(T375))))))), T375)\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
677 [label="677: p(f(f(f(f(f(f(f(T375))))))), T375), SCOPE: 49, CLAUSE: 4 | p(f(f(f(f(f(f(f(T375))))))), T375), SCOPE: 49, CLAUSE: 5\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
682 [label="682: p(f(f(f(f(f(f(f(T375))))))), T375), SCOPE: 49, CLAUSE: 4\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
683 [label="683: p(f(f(f(f(f(f(f(T375))))))), T375), SCOPE: 49, CLAUSE: 5\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
690 [label="690: e(f(f(f(f(f(f(f(T383))))))), T383)\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
692 [label="692: e(f(f(f(f(f(f(f(T383))))))), T383), SCOPE: 50, CLAUSE: 0\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
693 [label="693: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
695 [label="695: ','(r(f(f(f(f(f(f(f(f(T389)))))))), f(T389)), p(f(f(f(f(f(f(f(f(T389)))))))), T389))\n\nT389 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
696 [label="696: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
701 [label="701: ','(r(f(T391), f(T389)), p(f(T391), T389))\n\nT389 is ground\nT391 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
727 [label="727: r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 6 | r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 7 | r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 8\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
733 [label="733: r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 6\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
734 [label="734: r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 7 | r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 8\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
738 [label="738: e(f(f(f(f(T399)))), T399)\n\nT399 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
739 [label="739: e(f(f(f(f(T399)))), T399), SCOPE: 52, CLAUSE: 0\n\nT399 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
740 [label="740: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
743 [label="743: r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 7\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
744 [label="744: r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 8\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
747 [label="Q: ','(q(f(f(f(f(f(T409))))), T409), r(f(f(f(f(f(T409))))), T409))\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
748 [label="748: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
763 [label="N28: q(f(f(f(f(f(T409))))), T409)\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
764 [label="N29: r(f(f(f(f(f(T409))))), T409)\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
767 [label="767: q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 1 | q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 2 | q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 3\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
769 [label="769: q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 1\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
770 [label="770: q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 2 | q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 3\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
771 [label="771: e(f(f(f(f(f(T416))))), T416)\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
772 [label="772: e(f(f(f(f(f(T416))))), T416), SCOPE: 54, CLAUSE: 0\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
773 [label="773: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
774 [label="774: q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 3\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
793 [label="793: p(f(f(f(f(f(f(f(T423))))))), f(T423))\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
794 [label="794: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
798 [label="798: r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 6 | r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 7 | r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 8\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
800 [label="800: r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 6\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
801 [label="801: r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 7 | r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 8\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
816 [label="816: e(f(f(f(f(f(T430))))), T430)\n\nT430 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
817 [label="817: e(f(f(f(f(f(T430))))), T430), SCOPE: 56, CLAUSE: 0\n\nT430 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
818 [label="818: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
821 [label="821: r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 7\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
822 [label="822: r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 8\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
824 [label="824: ','(q(f(f(f(f(f(f(T440)))))), T440), r(f(f(f(f(f(f(T440)))))), T440))\n\nT440 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
825 [label="825: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
830 [label="830: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
834 [label="834: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
835 [label="835: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
836 [label="836: p(f(f(f(f(T113)))), T113), SCOPE: 57, CLAUSE: 4 | p(f(f(f(f(T113)))), T113), SCOPE: 57, CLAUSE: 5\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
839 [label="839: p(f(f(f(f(T113)))), T113), SCOPE: 57, CLAUSE: 4\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
840 [label="840: p(f(f(f(f(T113)))), T113), SCOPE: 57, CLAUSE: 5\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
842 [label="842: e(f(f(f(f(T450)))), T450)\n\nT450 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
843 [label="843: e(f(f(f(f(T450)))), T450), SCOPE: 58, CLAUSE: 0\n\nT450 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
844 [label="844: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
848 [label="S: ','(r(f(f(f(f(f(T456))))), f(T456)), p(f(f(f(f(f(T456))))), T456))\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
849 [label="849: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
856 [label="856: r(f(f(f(f(f(T456))))), f(T456))\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
857 [label="N30: p(f(f(f(f(f(T456))))), T456)\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
863 [label="863: p(f(f(f(f(f(T456))))), T456), SCOPE: 59, CLAUSE: 4 | p(f(f(f(f(f(T456))))), T456), SCOPE: 59, CLAUSE: 5\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
864 [label="864: p(f(f(f(f(f(T456))))), T456), SCOPE: 59, CLAUSE: 4\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
865 [label="865: p(f(f(f(f(f(T456))))), T456), SCOPE: 59, CLAUSE: 5\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
868 [label="868: e(f(f(f(f(f(T464))))), T464)\n\nT464 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
869 [label="869: e(f(f(f(f(f(T464))))), T464), SCOPE: 60, CLAUSE: 0\n\nT464 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
870 [label="870: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
873 [label="873: ','(r(f(f(f(f(f(f(T470)))))), f(T470)), p(f(f(f(f(f(f(T470)))))), T470))\n\nT470 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
875 [label="875: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
883 [label="883: r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 6 | r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 7 | r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 8\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
888 [label="888: r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 6\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
889 [label="889: r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 7 | r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 8\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
892 [label="892: e(f(f(T477)), T477)\n\nT477 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
893 [label="893: e(f(f(T477)), T477), SCOPE: 62, CLAUSE: 0\n\nT477 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
894 [label="894: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
895 [label="895: r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 7\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
896 [label="896: r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 8\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
900 [label="U: ','(q(f(f(f(T487))), T487), r(f(f(f(T487))), T487))\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
901 [label="901: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
907 [label="N31: q(f(f(f(T487))), T487)\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
908 [label="N32: r(f(f(f(T487))), T487)\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
914 [label="914: q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 1 | q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 2 | q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 3\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
917 [label="917: q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 1\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
918 [label="918: q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 2 | q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 3\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
922 [label="922: e(f(f(f(T494))), T494)\n\nT494 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
923 [label="923: e(f(f(f(T494))), T494), SCOPE: 64, CLAUSE: 0\n\nT494 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
924 [label="924: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
926 [label="926: q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 3\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
930 [label="930: p(f(f(f(f(f(T501))))), f(T501))\n\nT501 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
931 [label="931: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
934 [label="934: r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 6 | r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 7 | r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 8\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
935 [label="935: r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 6\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
936 [label="936: r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 7 | r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 8\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
947 [label="947: e(f(f(f(T508))), T508)\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
948 [label="948: e(f(f(f(T508))), T508), SCOPE: 66, CLAUSE: 0\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
949 [label="949: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
952 [label="952: r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 7\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
953 [label="953: r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 8\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
955 [label="955: ','(q(f(f(f(f(T518)))), T518), r(f(f(f(f(T518)))), T518))\n\nT518 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
956 [label="956: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
959 [label="959: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
970 [label="970: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
971 [label="971: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
973 [label="973: p(f(f(T75)), T75), SCOPE: 67, CLAUSE: 4 | p(f(f(T75)), T75), SCOPE: 67, CLAUSE: 5\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
983 [label="983: p(f(f(T75)), T75), SCOPE: 67, CLAUSE: 4\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
984 [label="984: p(f(f(T75)), T75), SCOPE: 67, CLAUSE: 5\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
997 [label="997: e(f(f(T528)), T528)\n\nT528 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
998 [label="998: e(f(f(T528)), T528), SCOPE: 68, CLAUSE: 0\n\nT528 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
999 [label="999: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1004 [label="W: ','(r(f(f(f(T534))), f(T534)), p(f(f(f(T534))), T534))\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1005 [label="1005: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1012 [label="1012: r(f(f(f(T534))), f(T534))\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1013 [label="N33: p(f(f(f(T534))), T534)\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1019 [label="1019: p(f(f(f(T534))), T534), SCOPE: 69, CLAUSE: 4 | p(f(f(f(T534))), T534), SCOPE: 69, CLAUSE: 5\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1027 [label="1027: p(f(f(f(T534))), T534), SCOPE: 69, CLAUSE: 4\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1028 [label="1028: p(f(f(f(T534))), T534), SCOPE: 69, CLAUSE: 5\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1032 [label="1032: e(f(f(f(T542))), T542)\n\nT542 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1033 [label="1033: e(f(f(f(T542))), T542), SCOPE: 70, CLAUSE: 0\n\nT542 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1034 [label="1034: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1039 [label="1039: ','(r(f(f(f(f(T548)))), f(T548)), p(f(f(f(f(T548)))), T548))\n\nT548 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1040 [label="1040: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1049 [label="1049: r(T51, T51), SCOPE: 71, CLAUSE: 6 | r(T51, T51), SCOPE: 71, CLAUSE: 7 | r(T51, T51), SCOPE: 71, CLAUSE: 8\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1052 [label="1052: r(T51, T51), SCOPE: 71, CLAUSE: 6\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1053 [label="1053: r(T51, T51), SCOPE: 71, CLAUSE: 7 | r(T51, T51), SCOPE: 71, CLAUSE: 8\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1056 [label="1056: e(T555, T555)\n\nT555 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1057 [label="1057: e(T555, T555), SCOPE: 72, CLAUSE: 0\n\nT555 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1058 [label="1058: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1059 [label="1059: r(T51, T51), SCOPE: 71, CLAUSE: 7\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1060 [label="1060: r(T51, T51), SCOPE: 71, CLAUSE: 8\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1062 [label="N1: ','(q(f(T565), T565), r(f(T565), T565))\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1063 [label="1063: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1073 [label="N34: q(f(T565), T565)\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1074 [label="N35: r(f(T565), T565)\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1076 [label="1076: q(f(T565), T565), SCOPE: 73, CLAUSE: 1 | q(f(T565), T565), SCOPE: 73, CLAUSE: 2 | q(f(T565), T565), SCOPE: 73, CLAUSE: 3\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1081 [label="1081: q(f(T565), T565), SCOPE: 73, CLAUSE: 1\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1082 [label="1082: q(f(T565), T565), SCOPE: 73, CLAUSE: 2 | q(f(T565), T565), SCOPE: 73, CLAUSE: 3\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1083 [label="1083: e(f(T572), T572)\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1084 [label="1084: e(f(T572), T572), SCOPE: 74, CLAUSE: 0\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1085 [label="1085: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1087 [label="1087: q(f(T565), T565), SCOPE: 73, CLAUSE: 3\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1090 [label="1090: p(f(f(f(T579))), f(T579))\n\nT579 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1091 [label="1091: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1097 [label="1097: r(f(T565), T565), SCOPE: 75, CLAUSE: 6 | r(f(T565), T565), SCOPE: 75, CLAUSE: 7 | r(f(T565), T565), SCOPE: 75, CLAUSE: 8\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1100 [label="1100: r(f(T565), T565), SCOPE: 75, CLAUSE: 6\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1101 [label="1101: r(f(T565), T565), SCOPE: 75, CLAUSE: 7 | r(f(T565), T565), SCOPE: 75, CLAUSE: 8\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1103 [label="1103: e(f(T586), T586)\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1104 [label="1104: e(f(T586), T586), SCOPE: 76, CLAUSE: 0\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1105 [label="1105: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1110 [label="1110: r(f(T565), T565), SCOPE: 75, CLAUSE: 7\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1111 [label="1111: r(f(T565), T565), SCOPE: 75, CLAUSE: 8\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1118 [label="1118: ','(q(f(f(T596)), T596), r(f(f(T596)), T596))\n\nT596 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1119 [label="1119: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1124 [label="1124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1125 [label="1125: t(f(T601), f(T601))\n\nT601 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1126 [label="1126: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1129 [label="1129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1130 [label="1130: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1134 [label="1134: p(T22, f(T22)), SCOPE: 77, CLAUSE: 4 | p(T22, f(T22)), SCOPE: 77, CLAUSE: 5\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1139 [label="1139: p(T22, f(T22)), SCOPE: 77, CLAUSE: 4\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1140 [label="1140: p(T22, f(T22)), SCOPE: 77, CLAUSE: 5\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1144 [label="1144: e(T610, f(T610))\n\nT610 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1145 [label="1145: e(T610, f(T610)), SCOPE: 78, CLAUSE: 0\n\nT610 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1146 [label="1146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1149 [label="N8: ','(r(T614, f(T614)), p(T614, T614))\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1153 [label="1153: r(T614, f(T614))\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1154 [label="E: p(T614, T614)\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1161 [label="1161: p(T614, T614), SCOPE: 79, CLAUSE: 4 | p(T614, T614), SCOPE: 79, CLAUSE: 5\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1166 [label="1166: p(T614, T614), SCOPE: 79, CLAUSE: 4\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1167 [label="1167: p(T614, T614), SCOPE: 79, CLAUSE: 5\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1172 [label="1172: e(T622, T622)\n\nT622 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1174 [label="1174: e(T622, T622), SCOPE: 80, CLAUSE: 0\n\nT622 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1175 [label="1175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1179 [label="N2: ','(r(f(T628), f(T628)), p(f(T628), T628))\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1180 [label="1180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1182 [label="1182: r(f(T628), f(T628))\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1183 [label="N36: p(f(T628), T628)\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1186 [label="1186: p(f(T628), T628), SCOPE: 81, CLAUSE: 4 | p(f(T628), T628), SCOPE: 81, CLAUSE: 5\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1189 [label="1189: p(f(T628), T628), SCOPE: 81, CLAUSE: 4\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1190 [label="1190: p(f(T628), T628), SCOPE: 81, CLAUSE: 5\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1195 [label="1195: e(f(T636), T636)\n\nT636 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1196 [label="1196: e(f(T636), T636), SCOPE: 82, CLAUSE: 0\n\nT636 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1197 [label="1197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1204 [label="1204: ','(r(f(f(T642)), f(T642)), p(f(f(T642)), T642))\n\nT642 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1205 [label="1205: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1208 [label="1208: q(T11, f(T11)), SCOPE: 83, CLAUSE: 1 | q(T11, f(T11)), SCOPE: 83, CLAUSE: 2 | q(T11, f(T11)), SCOPE: 83, CLAUSE: 3\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1211 [label="1211: q(T11, f(T11)), SCOPE: 83, CLAUSE: 1\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1212 [label="1212: q(T11, f(T11)), SCOPE: 83, CLAUSE: 2 | q(T11, f(T11)), SCOPE: 83, CLAUSE: 3\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1216 [label="1216: e(T649, f(T649))\n\nT649 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1217 [label="1217: e(T649, f(T649)), SCOPE: 84, CLAUSE: 0\n\nT649 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1218 [label="1218: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1221 [label="1221: q(T11, f(T11)), SCOPE: 83, CLAUSE: 3\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1229 [label="1229: p(f(T656), f(T656))\n\nT656 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1230 [label="1230: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1233 [label="1233: p(T662, f(T663))\n\nT662 is ground\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1234 [label="1234: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1236 [label="1236: p(T662, f(T663)), SCOPE: 85, CLAUSE: 4 | p(T662, f(T663)), SCOPE: 85, CLAUSE: 5\n\nT662 is ground\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1240 [label="1240: p(T662, f(T663)), SCOPE: 85, CLAUSE: 4\n\nT662 is ground\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1241 [label="1241: p(T662, f(T663)), SCOPE: 85, CLAUSE: 5\n\nT662 is ground\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1248 [label="1248: e(T674, f(T675))\n\nT674 is ground\nT675 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1249 [label="1249: e(T674, f(T675)), SCOPE: 86, CLAUSE: 0\n\nT674 is ground\nT675 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1250 [label="1250: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1259 [label="C: ','(r(T682, f(T683)), p(T682, T683))\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1263 [label="N37: r(T682, f(T683))\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1264 [label="N39: p(T682, T683)\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1268 [label="1268: r(T682, f(T683)), SCOPE: 87, CLAUSE: 6 | r(T682, f(T683)), SCOPE: 87, CLAUSE: 7 | r(T682, f(T683)), SCOPE: 87, CLAUSE: 8\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1276 [label="1276: r(T682, f(T683)), SCOPE: 87, CLAUSE: 6\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1277 [label="1277: r(T682, f(T683)), SCOPE: 87, CLAUSE: 7 | r(T682, f(T683)), SCOPE: 87, CLAUSE: 8\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1283 [label="1283: e(T696, f(T697))\n\nT696 is ground\nT697 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1284 [label="1284: e(T696, f(T697)), SCOPE: 88, CLAUSE: 0\n\nT696 is ground\nT697 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1285 [label="1285: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1290 [label="1290: r(T682, f(T683)), SCOPE: 87, CLAUSE: 7\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1291 [label="1291: r(T682, f(T683)), SCOPE: 87, CLAUSE: 8\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1297 [label="N38: ','(q(T710, T711), r(T710, T711))\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1301 [label="1301: q(T710, T711)\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1302 [label="N40: r(T710, T711)\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1310 [label="1310: r(T710, T711), SCOPE: 89, CLAUSE: 6 | r(T710, T711), SCOPE: 89, CLAUSE: 7 | r(T710, T711), SCOPE: 89, CLAUSE: 8\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1315 [label="1315: r(T710, T711), SCOPE: 89, CLAUSE: 6\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1316 [label="1316: r(T710, T711), SCOPE: 89, CLAUSE: 7 | r(T710, T711), SCOPE: 89, CLAUSE: 8\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1320 [label="1320: e(T726, T727)\n\nT726 is ground\nT727 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1321 [label="1321: e(T726, T727), SCOPE: 90, CLAUSE: 0\n\nT726 is ground\nT727 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1322 [label="1322: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1323 [label="1323: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1324 [label="1324: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1328 [label="1328: r(T710, T711), SCOPE: 89, CLAUSE: 7\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1329 [label="1329: r(T710, T711), SCOPE: 89, CLAUSE: 8\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1335 [label="1335: ','(q(T736, T737), r(T736, T737))\n\nT736 is ground\nT737 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1336 [label="1336: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1341 [label="1341: t(f(T742), f(T742))\n\nT742 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1342 [label="1342: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1347 [label="1347: t(f(T746), f(T746))\n\nT746 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1348 [label="1348: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1359 [label="1359: p(T682, T683), SCOPE: 91, CLAUSE: 4 | p(T682, T683), SCOPE: 91, CLAUSE: 5\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1364 [label="1364: p(T682, T683), SCOPE: 91, CLAUSE: 4\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1365 [label="1365: p(T682, T683), SCOPE: 91, CLAUSE: 5\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1369 [label="1369: e(T758, T759)\n\nT758 is ground\nT759 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1370 [label="1370: e(T758, T759), SCOPE: 92, CLAUSE: 0\n\nT758 is ground\nT759 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1371 [label="1371: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1372 [label="1372: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1373 [label="1373: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1379 [label="1379: ','(r(T764, f(T765)), p(T764, T765))\n\nT764 is ground\nT765 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
1381 [label="1381: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
1382 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 1382 [arrowhead = none ];
1382 -> 5;

1383 [label="ONLY EVAL with clause\nq(X3, X4) :- e(X3, X4).\nand substitutionT1 -> T5,\nX3 -> T5,\nT2 -> T6,\nX4 -> T6", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 1383 [arrowhead = none ];
1383 -> 8;

1384 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
8 -> 1384 [arrowhead = none ];
1384 -> 12;

1385 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
12 -> 1385 [arrowhead = none ];
1385 -> 14;

1386 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
12 -> 1386 [arrowhead = none ];
1386 -> 16;

1387 [label="EVAL with clause\ne(a, b).\nand substitutionT5 -> a,\nT6 -> b", fontsize=14, style = filled, fillcolor = lightblue];
14 -> 1387 [arrowhead = none ];
1387 -> 20;

1388 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 1388 [arrowhead = none ];
1388 -> 22;

1389 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 1389 [arrowhead = none ];
1389 -> 26;

1390 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 1390 [arrowhead = none ];
1390 -> 24;

1391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 1391 [arrowhead = none ];
1391 -> 31;

1392 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 1392 [arrowhead = none ];
1392 -> 33;

1393 [label="EVAL with clause\nq(X9, f(f(X9))) :- ','(p(X9, f(f(X9))), q(X9, f(X9))).\nand substitutionT5 -> T11,\nX9 -> T11,\nT6 -> f(f(T11))", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 1393 [arrowhead = none ];
1393 -> 40;

1394 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 1394 [arrowhead = none ];
1394 -> 41;

1395 [label="EVAL with clause\nq(X984, f(f(X985))) :- p(X984, f(X985)).\nand substitutionT5 -> T662,\nX984 -> T662,\nX985 -> T663,\nT6 -> f(f(T663))", fontsize=14, style = filled, fillcolor = lightblue];
33 -> 1395 [arrowhead = none ];
1395 -> 1233;

1396 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 1396 [arrowhead = none ];
1396 -> 1234;

1397 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
40 -> 1397 [arrowhead = none ];
1397 -> 44;

1398 [label="SPLIT 2\nnew knowledge:\nT11 is ground", fontsize=14, style = filled, fillcolor = violet];
40 -> 1398 [arrowhead = none ];
1398 -> 45;

1399 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
44 -> 1399 [arrowhead = none ];
1399 -> 51;

1400 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
45 -> 1400 [arrowhead = none ];
1400 -> 1208;

1401 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
51 -> 1401 [arrowhead = none ];
1401 -> 57;

1402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
51 -> 1402 [arrowhead = none ];
1402 -> 58;

1403 [label="ONLY EVAL with clause\np(X22, X23) :- e(X22, X23).\nand substitutionT11 -> T18,\nX22 -> T18,\nX23 -> f(f(T18))", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 1403 [arrowhead = none ];
1403 -> 66;

1404 [label="ONLY EVAL with clause\np(X30, f(X31)) :- ','(r(X30, f(X31)), p(X30, X31)).\nand substitutionT11 -> T22,\nX30 -> T22,\nX31 -> f(T22)", fontsize=14, style = filled, fillcolor = lightblue];
58 -> 1404 [arrowhead = none ];
1404 -> 78;

1405 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
66 -> 1405 [arrowhead = none ];
1405 -> 67;

1406 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
67 -> 1406 [arrowhead = none ];
1406 -> 68;

1407 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
78 -> 1407 [arrowhead = none ];
1407 -> 82;

1408 [label="SPLIT 2\nnew knowledge:\nT22 is ground", fontsize=14, style = filled, fillcolor = violet];
78 -> 1408 [arrowhead = none ];
1408 -> 83;

1409 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
82 -> 1409 [arrowhead = none ];
1409 -> 86;

1410 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
83 -> 1410 [arrowhead = none ];
1410 -> 1134;

1411 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 1411 [arrowhead = none ];
1411 -> 88;

1412 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 1412 [arrowhead = none ];
1412 -> 89;

1413 [label="ONLY EVAL with clause\nr(X44, X45) :- e(X44, X45).\nand substitutionT22 -> T29,\nX44 -> T29,\nX45 -> f(f(T29))", fontsize=14, style = filled, fillcolor = lightblue];
88 -> 1413 [arrowhead = none ];
1413 -> 90;

1414 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
89 -> 1414 [arrowhead = none ];
1414 -> 98;

1415 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
89 -> 1415 [arrowhead = none ];
1415 -> 99;

1416 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
90 -> 1416 [arrowhead = none ];
1416 -> 91;

1417 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
91 -> 1417 [arrowhead = none ];
1417 -> 94;

1418 [label="ONLY EVAL with clause\nr(X58, f(X59)) :- ','(q(X58, X59), r(X58, X59)).\nand substitutionT22 -> T36,\nX58 -> T36,\nX59 -> f(T36)", fontsize=14, style = filled, fillcolor = lightblue];
98 -> 1418 [arrowhead = none ];
1418 -> 103;

1419 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 1419 [arrowhead = none ];
1419 -> 1130;

1420 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
103 -> 1420 [arrowhead = none ];
1420 -> 106;

1421 [label="SPLIT 2\nnew knowledge:\nT36 is ground", fontsize=14, style = filled, fillcolor = violet];
103 -> 1421 [arrowhead = none ];
1421 -> 107;

1422 [label="INSTANCE with matching:\nT11 -> T36", fontsize=14, style = filled, fillcolor = lightgrey];
106 -> 1422 [arrowhead = none , style=dashed];
1422 -> 45[style=dashed];

1423 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
107 -> 1423 [arrowhead = none ];
1423 -> 111;

1424 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
111 -> 1424 [arrowhead = none ];
1424 -> 115;

1425 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
111 -> 1425 [arrowhead = none ];
1425 -> 116;

1426 [label="ONLY EVAL with clause\nr(X74, X75) :- e(X74, X75).\nand substitutionT36 -> T44,\nX74 -> T44,\nX75 -> f(T44)", fontsize=14, style = filled, fillcolor = lightblue];
115 -> 1426 [arrowhead = none ];
1426 -> 118;

1427 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 1427 [arrowhead = none ];
1427 -> 123;

1428 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
116 -> 1428 [arrowhead = none ];
1428 -> 124;

1429 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
118 -> 1429 [arrowhead = none ];
1429 -> 119;

1430 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
119 -> 1430 [arrowhead = none ];
1430 -> 120;

1431 [label="ONLY EVAL with clause\nr(X88, f(X89)) :- ','(q(X88, X89), r(X88, X89)).\nand substitutionT36 -> T51,\nX88 -> T51,\nX89 -> T51", fontsize=14, style = filled, fillcolor = lightblue];
123 -> 1431 [arrowhead = none ];
1431 -> 128;

1432 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 1432 [arrowhead = none ];
1432 -> 1129;

1433 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
128 -> 1433 [arrowhead = none ];
1433 -> 133;

1434 [label="SPLIT 2\nnew knowledge:\nT51 is ground", fontsize=14, style = filled, fillcolor = violet];
128 -> 1434 [arrowhead = none ];
1434 -> 134;

1435 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 1435 [arrowhead = none ];
1435 -> 137;

1436 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
134 -> 1436 [arrowhead = none ];
1436 -> 1049;

1437 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
137 -> 1437 [arrowhead = none ];
1437 -> 139;

1438 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
137 -> 1438 [arrowhead = none ];
1438 -> 140;

1439 [label="ONLY EVAL with clause\nq(X102, X103) :- e(X102, X103).\nand substitutionT51 -> T58,\nX102 -> T58,\nX103 -> T58", fontsize=14, style = filled, fillcolor = lightblue];
139 -> 1439 [arrowhead = none ];
1439 -> 143;

1440 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
140 -> 1440 [arrowhead = none ];
1440 -> 148;

1441 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
143 -> 1441 [arrowhead = none ];
1441 -> 144;

1442 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
144 -> 1442 [arrowhead = none ];
1442 -> 146;

1443 [label="EVAL with clause\nq(X109, f(f(X110))) :- p(X109, f(X110)).\nand substitutionT51 -> f(f(T65)),\nX109 -> f(f(T65)),\nX110 -> T65,\nT64 -> f(f(T65))", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 1443 [arrowhead = none ];
1443 -> 152;

1444 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
148 -> 1444 [arrowhead = none ];
1444 -> 153;

1445 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
152 -> 1445 [arrowhead = none ];
1445 -> 158;

1446 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
158 -> 1446 [arrowhead = none ];
1446 -> 159;

1447 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
158 -> 1447 [arrowhead = none ];
1447 -> 161;

1448 [label="ONLY EVAL with clause\np(X121, X122) :- e(X121, X122).\nand substitutionT65 -> T71,\nX121 -> f(f(T71)),\nX122 -> f(T71)", fontsize=14, style = filled, fillcolor = lightblue];
159 -> 1448 [arrowhead = none ];
1448 -> 164;

1449 [label="ONLY EVAL with clause\np(X129, f(X130)) :- ','(r(X129, f(X130)), p(X129, X130)).\nand substitutionT65 -> T75,\nX129 -> f(f(T75)),\nX130 -> T75", fontsize=14, style = filled, fillcolor = lightblue];
161 -> 1449 [arrowhead = none ];
1449 -> 172;

1450 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
164 -> 1450 [arrowhead = none ];
1450 -> 167;

1451 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
167 -> 1451 [arrowhead = none ];
1451 -> 169;

1452 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
172 -> 1452 [arrowhead = none ];
1452 -> 178;

1453 [label="SPLIT 2\nnew knowledge:\nT75 is ground", fontsize=14, style = filled, fillcolor = violet];
172 -> 1453 [arrowhead = none ];
1453 -> 179;

1454 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
178 -> 1454 [arrowhead = none ];
1454 -> 182;

1455 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
179 -> 1455 [arrowhead = none ];
1455 -> 973;

1456 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
182 -> 1456 [arrowhead = none ];
1456 -> 183;

1457 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
182 -> 1457 [arrowhead = none ];
1457 -> 184;

1458 [label="ONLY EVAL with clause\nr(X143, X144) :- e(X143, X144).\nand substitutionT75 -> T82,\nX143 -> f(f(T82)),\nX144 -> f(T82)", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 1458 [arrowhead = none ];
1458 -> 186;

1459 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
184 -> 1459 [arrowhead = none ];
1459 -> 192;

1460 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
184 -> 1460 [arrowhead = none ];
1460 -> 193;

1461 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
186 -> 1461 [arrowhead = none ];
1461 -> 187;

1462 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
187 -> 1462 [arrowhead = none ];
1462 -> 189;

1463 [label="ONLY EVAL with clause\nr(X157, f(X158)) :- ','(q(X157, X158), r(X157, X158)).\nand substitutionT75 -> T89,\nX157 -> f(f(T89)),\nX158 -> T89", fontsize=14, style = filled, fillcolor = lightblue];
192 -> 1463 [arrowhead = none ];
1463 -> 197;

1464 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
193 -> 1464 [arrowhead = none ];
1464 -> 971;

1465 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
197 -> 1465 [arrowhead = none ];
1465 -> 207;

1466 [label="SPLIT 2\nnew knowledge:\nT89 is ground", fontsize=14, style = filled, fillcolor = violet];
197 -> 1466 [arrowhead = none ];
1466 -> 208;

1467 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
207 -> 1467 [arrowhead = none ];
1467 -> 211;

1468 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
208 -> 1468 [arrowhead = none ];
1468 -> 883;

1469 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
211 -> 1469 [arrowhead = none ];
1469 -> 212;

1470 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
211 -> 1470 [arrowhead = none ];
1470 -> 213;

1471 [label="ONLY EVAL with clause\nq(X171, X172) :- e(X171, X172).\nand substitutionT89 -> T96,\nX171 -> f(f(T96)),\nX172 -> T96", fontsize=14, style = filled, fillcolor = lightblue];
212 -> 1471 [arrowhead = none ];
1471 -> 218;

1472 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
213 -> 1472 [arrowhead = none ];
1472 -> 224;

1473 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
218 -> 1473 [arrowhead = none ];
1473 -> 220;

1474 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
220 -> 1474 [arrowhead = none ];
1474 -> 221;

1475 [label="EVAL with clause\nq(X178, f(f(X179))) :- p(X178, f(X179)).\nand substitutionT89 -> f(f(T103)),\nX178 -> f(f(f(f(T103)))),\nX179 -> T103,\nT102 -> f(f(T103))", fontsize=14, style = filled, fillcolor = lightblue];
224 -> 1475 [arrowhead = none ];
1475 -> 228;

1476 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
224 -> 1476 [arrowhead = none ];
1476 -> 231;

1477 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
228 -> 1477 [arrowhead = none ];
1477 -> 232;

1478 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
232 -> 1478 [arrowhead = none ];
1478 -> 234;

1479 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
232 -> 1479 [arrowhead = none ];
1479 -> 235;

1480 [label="ONLY EVAL with clause\np(X190, X191) :- e(X190, X191).\nand substitutionT103 -> T109,\nX190 -> f(f(f(f(T109)))),\nX191 -> f(T109)", fontsize=14, style = filled, fillcolor = lightblue];
234 -> 1480 [arrowhead = none ];
1480 -> 236;

1481 [label="ONLY EVAL with clause\np(X198, f(X199)) :- ','(r(X198, f(X199)), p(X198, X199)).\nand substitutionT103 -> T113,\nX198 -> f(f(f(f(T113)))),\nX199 -> T113", fontsize=14, style = filled, fillcolor = lightblue];
235 -> 1481 [arrowhead = none ];
1481 -> 241;

1482 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
236 -> 1482 [arrowhead = none ];
1482 -> 237;

1483 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
237 -> 1483 [arrowhead = none ];
1483 -> 238;

1484 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
241 -> 1484 [arrowhead = none ];
1484 -> 248;

1485 [label="SPLIT 2\nnew knowledge:\nT113 is ground", fontsize=14, style = filled, fillcolor = violet];
241 -> 1485 [arrowhead = none ];
1485 -> 250;

1486 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
248 -> 1486 [arrowhead = none ];
1486 -> 258;

1487 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
250 -> 1487 [arrowhead = none ];
1487 -> 836;

1488 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
258 -> 1488 [arrowhead = none ];
1488 -> 259;

1489 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
258 -> 1489 [arrowhead = none ];
1489 -> 260;

1490 [label="ONLY EVAL with clause\nr(X212, X213) :- e(X212, X213).\nand substitutionT113 -> T120,\nX212 -> f(f(f(f(T120)))),\nX213 -> f(T120)", fontsize=14, style = filled, fillcolor = lightblue];
259 -> 1490 [arrowhead = none ];
1490 -> 262;

1491 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
260 -> 1491 [arrowhead = none ];
1491 -> 266;

1492 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
260 -> 1492 [arrowhead = none ];
1492 -> 267;

1493 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
262 -> 1493 [arrowhead = none ];
1493 -> 263;

1494 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
263 -> 1494 [arrowhead = none ];
1494 -> 264;

1495 [label="ONLY EVAL with clause\nr(X226, f(X227)) :- ','(q(X226, X227), r(X226, X227)).\nand substitutionT113 -> T127,\nX226 -> f(f(f(f(T127)))),\nX227 -> T127", fontsize=14, style = filled, fillcolor = lightblue];
266 -> 1495 [arrowhead = none ];
1495 -> 270;

1496 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
267 -> 1496 [arrowhead = none ];
1496 -> 835;

1497 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
270 -> 1497 [arrowhead = none ];
1497 -> 277;

1498 [label="SPLIT 2\nnew knowledge:\nT127 is ground", fontsize=14, style = filled, fillcolor = violet];
270 -> 1498 [arrowhead = none ];
1498 -> 279;

1499 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
277 -> 1499 [arrowhead = none ];
1499 -> 282;

1500 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
279 -> 1500 [arrowhead = none ];
1500 -> 727;

1501 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
282 -> 1501 [arrowhead = none ];
1501 -> 284;

1502 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
282 -> 1502 [arrowhead = none ];
1502 -> 285;

1503 [label="ONLY EVAL with clause\nq(X240, X241) :- e(X240, X241).\nand substitutionT127 -> T134,\nX240 -> f(f(f(f(T134)))),\nX241 -> T134", fontsize=14, style = filled, fillcolor = lightblue];
284 -> 1503 [arrowhead = none ];
1503 -> 290;

1504 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
285 -> 1504 [arrowhead = none ];
1504 -> 294;

1505 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
290 -> 1505 [arrowhead = none ];
1505 -> 292;

1506 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
292 -> 1506 [arrowhead = none ];
1506 -> 293;

1507 [label="EVAL with clause\nq(X247, f(f(X248))) :- p(X247, f(X248)).\nand substitutionT127 -> f(f(T141)),\nX247 -> f(f(f(f(f(f(T141)))))),\nX248 -> T141,\nT140 -> f(f(T141))", fontsize=14, style = filled, fillcolor = lightblue];
294 -> 1507 [arrowhead = none ];
1507 -> 297;

1508 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
294 -> 1508 [arrowhead = none ];
1508 -> 298;

1509 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
297 -> 1509 [arrowhead = none ];
1509 -> 300;

1510 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
300 -> 1510 [arrowhead = none ];
1510 -> 303;

1511 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
300 -> 1511 [arrowhead = none ];
1511 -> 304;

1512 [label="ONLY EVAL with clause\np(X259, X260) :- e(X259, X260).\nand substitutionT141 -> T147,\nX259 -> f(f(f(f(f(f(T147)))))),\nX260 -> f(T147)", fontsize=14, style = filled, fillcolor = lightblue];
303 -> 1512 [arrowhead = none ];
1512 -> 308;

1513 [label="ONLY EVAL with clause\np(X267, f(X268)) :- ','(r(X267, f(X268)), p(X267, X268)).\nand substitutionT141 -> T151,\nX267 -> f(f(f(f(f(f(T151)))))),\nX268 -> T151", fontsize=14, style = filled, fillcolor = lightblue];
304 -> 1513 [arrowhead = none ];
1513 -> 312;

1514 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
308 -> 1514 [arrowhead = none ];
1514 -> 309;

1515 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
309 -> 1515 [arrowhead = none ];
1515 -> 310;

1516 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
312 -> 1516 [arrowhead = none ];
1516 -> 317;

1517 [label="SPLIT 2\nnew knowledge:\nT151 is ground", fontsize=14, style = filled, fillcolor = violet];
312 -> 1517 [arrowhead = none ];
1517 -> 318;

1518 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
317 -> 1518 [arrowhead = none ];
1518 -> 320;

1519 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
318 -> 1519 [arrowhead = none ];
1519 -> 650;

1520 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
320 -> 1520 [arrowhead = none ];
1520 -> 324;

1521 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
320 -> 1521 [arrowhead = none ];
1521 -> 325;

1522 [label="ONLY EVAL with clause\nr(X281, X282) :- e(X281, X282).\nand substitutionT151 -> T158,\nX281 -> f(f(f(f(f(f(T158)))))),\nX282 -> f(T158)", fontsize=14, style = filled, fillcolor = lightblue];
324 -> 1522 [arrowhead = none ];
1522 -> 331;

1523 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
325 -> 1523 [arrowhead = none ];
1523 -> 338;

1524 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
325 -> 1524 [arrowhead = none ];
1524 -> 340;

1525 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
331 -> 1525 [arrowhead = none ];
1525 -> 332;

1526 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
332 -> 1526 [arrowhead = none ];
1526 -> 334;

1527 [label="ONLY EVAL with clause\nr(X295, f(X296)) :- ','(q(X295, X296), r(X295, X296)).\nand substitutionT151 -> T165,\nX295 -> f(f(f(f(f(f(T165)))))),\nX296 -> T165", fontsize=14, style = filled, fillcolor = lightblue];
338 -> 1527 [arrowhead = none ];
1527 -> 344;

1528 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
340 -> 1528 [arrowhead = none ];
1528 -> 649;

1529 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
344 -> 1529 [arrowhead = none ];
1529 -> 350;

1530 [label="SPLIT 2\nnew knowledge:\nT165 is ground", fontsize=14, style = filled, fillcolor = violet];
344 -> 1530 [arrowhead = none ];
1530 -> 351;

1531 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
350 -> 1531 [arrowhead = none ];
1531 -> 359;

1532 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
351 -> 1532 [arrowhead = none ];
1532 -> 562;

1533 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
359 -> 1533 [arrowhead = none ];
1533 -> 361;

1534 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
359 -> 1534 [arrowhead = none ];
1534 -> 362;

1535 [label="ONLY EVAL with clause\nq(X309, X310) :- e(X309, X310).\nand substitutionT165 -> T172,\nX309 -> f(f(f(f(f(f(T172)))))),\nX310 -> T172", fontsize=14, style = filled, fillcolor = lightblue];
361 -> 1535 [arrowhead = none ];
1535 -> 377;

1536 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
362 -> 1536 [arrowhead = none ];
1536 -> 380;

1537 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
377 -> 1537 [arrowhead = none ];
1537 -> 378;

1538 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
378 -> 1538 [arrowhead = none ];
1538 -> 379;

1539 [label="EVAL with clause\nq(X316, f(f(X317))) :- p(X316, f(X317)).\nand substitutionT165 -> f(f(T179)),\nX316 -> f(f(f(f(f(f(f(f(T179)))))))),\nX317 -> T179,\nT178 -> f(f(T179))", fontsize=14, style = filled, fillcolor = lightblue];
380 -> 1539 [arrowhead = none ];
1539 -> 381;

1540 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
380 -> 1540 [arrowhead = none ];
1540 -> 382;

1541 [label="GENERALIZATION\nT181 <-- f(f(f(f(f(f(f(T179)))))))\n\nNew Knowledge:\nT181 is ground", fontsize=14, style = filled, fillcolor = violet];
381 -> 1541 [arrowhead = none ];
1541 -> 384;

1542 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
384 -> 1542 [arrowhead = none ];
1542 -> 413;

1543 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
413 -> 1543 [arrowhead = none ];
1543 -> 416;

1544 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
413 -> 1544 [arrowhead = none ];
1544 -> 417;

1545 [label="ONLY EVAL with clause\np(X330, X331) :- e(X330, X331).\nand substitutionT181 -> T192,\nX330 -> f(T192),\nT179 -> T193,\nX331 -> f(T193)", fontsize=14, style = filled, fillcolor = lightblue];
416 -> 1545 [arrowhead = none ];
1545 -> 420;

1546 [label="ONLY EVAL with clause\np(X338, f(X339)) :- ','(r(X338, f(X339)), p(X338, X339)).\nand substitutionT181 -> T200,\nX338 -> f(T200),\nT179 -> T201,\nX339 -> T201", fontsize=14, style = filled, fillcolor = lightblue];
417 -> 1546 [arrowhead = none ];
1546 -> 424;

1547 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
420 -> 1547 [arrowhead = none ];
1547 -> 421;

1548 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
421 -> 1548 [arrowhead = none ];
1548 -> 422;

1549 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
424 -> 1549 [arrowhead = none ];
1549 -> 429;

1550 [label="SPLIT 2\nnew knowledge:\nT200 is ground\nT201 is ground", fontsize=14, style = filled, fillcolor = violet];
424 -> 1550 [arrowhead = none ];
1550 -> 430;

1551 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
429 -> 1551 [arrowhead = none ];
1551 -> 437;

1552 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
430 -> 1552 [arrowhead = none ];
1552 -> 541;

1553 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
437 -> 1553 [arrowhead = none ];
1553 -> 438;

1554 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
437 -> 1554 [arrowhead = none ];
1554 -> 439;

1555 [label="ONLY EVAL with clause\nr(X352, X353) :- e(X352, X353).\nand substitutionT200 -> T214,\nX352 -> f(T214),\nT201 -> T215,\nX353 -> f(T215)", fontsize=14, style = filled, fillcolor = lightblue];
438 -> 1555 [arrowhead = none ];
1555 -> 443;

1556 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
439 -> 1556 [arrowhead = none ];
1556 -> 448;

1557 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
439 -> 1557 [arrowhead = none ];
1557 -> 449;

1558 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
443 -> 1558 [arrowhead = none ];
1558 -> 444;

1559 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
444 -> 1559 [arrowhead = none ];
1559 -> 445;

1560 [label="ONLY EVAL with clause\nr(X366, f(X367)) :- ','(q(X366, X367), r(X366, X367)).\nand substitutionT200 -> T228,\nX366 -> f(T228),\nT201 -> T229,\nX367 -> T229", fontsize=14, style = filled, fillcolor = lightblue];
448 -> 1560 [arrowhead = none ];
1560 -> 454;

1561 [label="EVAL with clause\nr(f(X445), f(X445)) :- t(f(X445), f(X445)).\nand substitutionT200 -> T285,\nX445 -> T285,\nT201 -> T285", fontsize=14, style = filled, fillcolor = lightblue];
449 -> 1561 [arrowhead = none ];
1561 -> 537;

1562 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
449 -> 1562 [arrowhead = none ];
1562 -> 538;

1563 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
454 -> 1563 [arrowhead = none ];
1563 -> 458;

1564 [label="SPLIT 2\nnew knowledge:\nT228 is ground\nT229 is ground", fontsize=14, style = filled, fillcolor = violet];
454 -> 1564 [arrowhead = none ];
1564 -> 460;

1565 [label="INSTANCE with matching:\nT1 -> f(T228)\nT2 -> T229", fontsize=14, style = filled, fillcolor = lightgrey];
458 -> 1565 [arrowhead = none , style=dashed];
1565 -> 3[style=dashed];

1566 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
460 -> 1566 [arrowhead = none ];
1566 -> 463;

1567 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
463 -> 1567 [arrowhead = none ];
1567 -> 464;

1568 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
463 -> 1568 [arrowhead = none ];
1568 -> 465;

1569 [label="ONLY EVAL with clause\nr(X382, X383) :- e(X382, X383).\nand substitutionT228 -> T244,\nX382 -> f(T244),\nT229 -> T245,\nX383 -> T245", fontsize=14, style = filled, fillcolor = lightblue];
464 -> 1569 [arrowhead = none ];
1569 -> 466;

1570 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
465 -> 1570 [arrowhead = none ];
1570 -> 470;

1571 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
465 -> 1571 [arrowhead = none ];
1571 -> 471;

1572 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
466 -> 1572 [arrowhead = none ];
1572 -> 467;

1573 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
467 -> 1573 [arrowhead = none ];
1573 -> 468;

1574 [label="EVAL with clause\nr(X392, f(X393)) :- ','(q(X392, X393), r(X392, X393)).\nand substitutionT228 -> T254,\nX392 -> f(T254),\nX393 -> T255,\nT229 -> f(T255)", fontsize=14, style = filled, fillcolor = lightblue];
470 -> 1574 [arrowhead = none ];
1574 -> 474;

1575 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
470 -> 1575 [arrowhead = none ];
1575 -> 475;

1576 [label="EVAL with clause\nr(f(X398), f(X398)) :- t(f(X398), f(X398)).\nand substitutionT228 -> T260,\nX398 -> T260,\nT229 -> f(T260)", fontsize=14, style = filled, fillcolor = lightblue];
471 -> 1576 [arrowhead = none ];
1576 -> 482;

1577 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
471 -> 1577 [arrowhead = none ];
1577 -> 484;

1578 [label="INSTANCE with matching:\nT228 -> T254\nT229 -> T255", fontsize=14, style = filled, fillcolor = lightgrey];
474 -> 1578 [arrowhead = none , style=dashed];
1578 -> 454[style=dashed];

1579 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
482 -> 1579 [arrowhead = none ];
1579 -> 492;

1580 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
492 -> 1580 [arrowhead = none ];
1580 -> 494;

1581 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
492 -> 1581 [arrowhead = none ];
1581 -> 495;

1582 [label="ONLY EVAL with clause\nt(X409, X410) :- e(X409, X410).\nand substitutionT260 -> T266,\nX409 -> f(T266),\nX410 -> f(T266)", fontsize=14, style = filled, fillcolor = lightblue];
494 -> 1582 [arrowhead = none ];
1582 -> 496;

1583 [label="ONLY EVAL with clause\nt(f(X417), f(X418)) :- ','(q(f(X417), f(X418)), t(X417, X418)).\nand substitutionT260 -> T270,\nX417 -> T270,\nX418 -> T270", fontsize=14, style = filled, fillcolor = lightblue];
495 -> 1583 [arrowhead = none ];
1583 -> 500;

1584 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
496 -> 1584 [arrowhead = none ];
1584 -> 497;

1585 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
497 -> 1585 [arrowhead = none ];
1585 -> 498;

1586 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
500 -> 1586 [arrowhead = none ];
1586 -> 508;

1587 [label="SPLIT 2\nnew knowledge:\nT270 is ground", fontsize=14, style = filled, fillcolor = violet];
500 -> 1587 [arrowhead = none ];
1587 -> 509;

1588 [label="INSTANCE with matching:\nT51 -> f(T270)", fontsize=14, style = filled, fillcolor = lightgrey];
508 -> 1588 [arrowhead = none , style=dashed];
1588 -> 133[style=dashed];

1589 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
509 -> 1589 [arrowhead = none ];
1589 -> 510;

1590 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
510 -> 1590 [arrowhead = none ];
1590 -> 515;

1591 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
510 -> 1591 [arrowhead = none ];
1591 -> 516;

1592 [label="ONLY EVAL with clause\nt(X433, X434) :- e(X433, X434).\nand substitutionT270 -> T278,\nX433 -> T278,\nX434 -> T278", fontsize=14, style = filled, fillcolor = lightblue];
515 -> 1592 [arrowhead = none ];
1592 -> 518;

1593 [label="EVAL with clause\nt(f(X439), f(X440)) :- ','(q(f(X439), f(X440)), t(X439, X440)).\nand substitutionX439 -> T281,\nT270 -> f(T281),\nX440 -> T281", fontsize=14, style = filled, fillcolor = lightblue];
516 -> 1593 [arrowhead = none ];
1593 -> 525;

1594 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
516 -> 1594 [arrowhead = none ];
1594 -> 528;

1595 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
518 -> 1595 [arrowhead = none ];
1595 -> 519;

1596 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
519 -> 1596 [arrowhead = none ];
1596 -> 520;

1597 [label="INSTANCE with matching:\nT270 -> T281", fontsize=14, style = filled, fillcolor = lightgrey];
525 -> 1597 [arrowhead = none , style=dashed];
1597 -> 500[style=dashed];

1598 [label="INSTANCE with matching:\nT260 -> T285", fontsize=14, style = filled, fillcolor = lightgrey];
537 -> 1598 [arrowhead = none , style=dashed];
1598 -> 482[style=dashed];

1599 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
541 -> 1599 [arrowhead = none ];
1599 -> 542;

1600 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
541 -> 1600 [arrowhead = none ];
1600 -> 543;

1601 [label="ONLY EVAL with clause\np(X458, X459) :- e(X458, X459).\nand substitutionT200 -> T297,\nX458 -> f(T297),\nT201 -> T298,\nX459 -> T298", fontsize=14, style = filled, fillcolor = lightblue];
542 -> 1601 [arrowhead = none ];
1601 -> 545;

1602 [label="EVAL with clause\np(X464, f(X465)) :- ','(r(X464, f(X465)), p(X464, X465)).\nand substitutionT200 -> T303,\nX464 -> f(T303),\nX465 -> T304,\nT201 -> f(T304)", fontsize=14, style = filled, fillcolor = lightblue];
543 -> 1602 [arrowhead = none ];
1602 -> 553;

1603 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
543 -> 1603 [arrowhead = none ];
1603 -> 554;

1604 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
545 -> 1604 [arrowhead = none ];
1604 -> 547;

1605 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
547 -> 1605 [arrowhead = none ];
1605 -> 549;

1606 [label="INSTANCE with matching:\nT200 -> T303\nT201 -> T304", fontsize=14, style = filled, fillcolor = lightgrey];
553 -> 1606 [arrowhead = none , style=dashed];
1606 -> 424[style=dashed];

1607 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
562 -> 1607 [arrowhead = none ];
1607 -> 564;

1608 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
562 -> 1608 [arrowhead = none ];
1608 -> 565;

1609 [label="ONLY EVAL with clause\nr(X478, X479) :- e(X478, X479).\nand substitutionT165 -> T312,\nX478 -> f(f(f(f(f(f(T312)))))),\nX479 -> T312", fontsize=14, style = filled, fillcolor = lightblue];
564 -> 1609 [arrowhead = none ];
1609 -> 571;

1610 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
565 -> 1610 [arrowhead = none ];
1610 -> 576;

1611 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
565 -> 1611 [arrowhead = none ];
1611 -> 577;

1612 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
571 -> 1612 [arrowhead = none ];
1612 -> 572;

1613 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
572 -> 1613 [arrowhead = none ];
1613 -> 573;

1614 [label="EVAL with clause\nr(X488, f(X489)) :- ','(q(X488, X489), r(X488, X489)).\nand substitutionT165 -> f(T322),\nX488 -> f(f(f(f(f(f(f(T322))))))),\nX489 -> T322,\nT321 -> f(T322)", fontsize=14, style = filled, fillcolor = lightblue];
576 -> 1614 [arrowhead = none ];
1614 -> 580;

1615 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
576 -> 1615 [arrowhead = none ];
1615 -> 581;

1616 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
577 -> 1616 [arrowhead = none ];
1616 -> 646;

1617 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
580 -> 1617 [arrowhead = none ];
1617 -> 587;

1618 [label="SPLIT 2\nnew knowledge:\nT322 is ground", fontsize=14, style = filled, fillcolor = violet];
580 -> 1618 [arrowhead = none ];
1618 -> 588;

1619 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
587 -> 1619 [arrowhead = none ];
1619 -> 590;

1620 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
588 -> 1620 [arrowhead = none ];
1620 -> 619;

1621 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
590 -> 1621 [arrowhead = none ];
1621 -> 592;

1622 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
590 -> 1622 [arrowhead = none ];
1622 -> 593;

1623 [label="ONLY EVAL with clause\nq(X502, X503) :- e(X502, X503).\nand substitutionT322 -> T329,\nX502 -> f(f(f(f(f(f(f(T329))))))),\nX503 -> T329", fontsize=14, style = filled, fillcolor = lightblue];
592 -> 1623 [arrowhead = none ];
1623 -> 594;

1624 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
593 -> 1624 [arrowhead = none ];
1624 -> 599;

1625 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
594 -> 1625 [arrowhead = none ];
1625 -> 597;

1626 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
597 -> 1626 [arrowhead = none ];
1626 -> 598;

1627 [label="EVAL with clause\nq(X509, f(f(X510))) :- p(X509, f(X510)).\nand substitutionT322 -> f(f(T336)),\nX509 -> f(f(f(f(f(f(f(f(f(T336))))))))),\nX510 -> T336,\nT335 -> f(f(T336))", fontsize=14, style = filled, fillcolor = lightblue];
599 -> 1627 [arrowhead = none ];
1627 -> 602;

1628 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
599 -> 1628 [arrowhead = none ];
1628 -> 603;

1629 [label="GENERALIZATION\nT338 <-- f(f(f(f(f(f(f(f(T336))))))))\n\nNew Knowledge:\nT338 is ground", fontsize=14, style = filled, fillcolor = violet];
602 -> 1629 [arrowhead = none ];
1629 -> 614;

1630 [label="INSTANCE with matching:\nT181 -> T338\nT179 -> T336", fontsize=14, style = filled, fillcolor = lightgrey];
614 -> 1630 [arrowhead = none , style=dashed];
1630 -> 384[style=dashed];

1631 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
619 -> 1631 [arrowhead = none ];
1631 -> 620;

1632 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
619 -> 1632 [arrowhead = none ];
1632 -> 621;

1633 [label="ONLY EVAL with clause\nr(X525, X526) :- e(X525, X526).\nand substitutionT322 -> T346,\nX525 -> f(f(f(f(f(f(f(T346))))))),\nX526 -> T346", fontsize=14, style = filled, fillcolor = lightblue];
620 -> 1633 [arrowhead = none ];
1633 -> 622;

1634 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
621 -> 1634 [arrowhead = none ];
1634 -> 626;

1635 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
621 -> 1635 [arrowhead = none ];
1635 -> 629;

1636 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
622 -> 1636 [arrowhead = none ];
1636 -> 623;

1637 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
623 -> 1637 [arrowhead = none ];
1637 -> 624;

1638 [label="EVAL with clause\nr(X535, f(X536)) :- ','(q(X535, X536), r(X535, X536)).\nand substitutionT322 -> f(T356),\nX535 -> f(f(f(f(f(f(f(f(T356)))))))),\nX536 -> T356,\nT355 -> f(T356)", fontsize=14, style = filled, fillcolor = lightblue];
626 -> 1638 [arrowhead = none ];
1638 -> 632;

1639 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
626 -> 1639 [arrowhead = none ];
1639 -> 633;

1640 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
629 -> 1640 [arrowhead = none ];
1640 -> 645;

1641 [label="GENERALIZATION\nT358 <-- f(f(f(f(f(f(f(T356)))))))\n\nNew Knowledge:\nT358 is ground", fontsize=14, style = filled, fillcolor = violet];
632 -> 1641 [arrowhead = none ];
1641 -> 641;

1642 [label="INSTANCE with matching:\nT228 -> T358\nT229 -> T356", fontsize=14, style = filled, fillcolor = lightgrey];
641 -> 1642 [arrowhead = none , style=dashed];
1642 -> 454[style=dashed];

1643 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
650 -> 1643 [arrowhead = none ];
1643 -> 651;

1644 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
650 -> 1644 [arrowhead = none ];
1644 -> 652;

1645 [label="ONLY EVAL with clause\np(X554, X555) :- e(X554, X555).\nand substitutionT151 -> T369,\nX554 -> f(f(f(f(f(f(T369)))))),\nX555 -> T369", fontsize=14, style = filled, fillcolor = lightblue];
651 -> 1645 [arrowhead = none ];
1645 -> 655;

1646 [label="EVAL with clause\np(X560, f(X561)) :- ','(r(X560, f(X561)), p(X560, X561)).\nand substitutionT151 -> f(T375),\nX560 -> f(f(f(f(f(f(f(T375))))))),\nX561 -> T375,\nT374 -> f(T375)", fontsize=14, style = filled, fillcolor = lightblue];
652 -> 1646 [arrowhead = none ];
1646 -> 659;

1647 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
652 -> 1647 [arrowhead = none ];
1647 -> 660;

1648 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
655 -> 1648 [arrowhead = none ];
1648 -> 656;

1649 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
656 -> 1649 [arrowhead = none ];
1649 -> 657;

1650 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
659 -> 1650 [arrowhead = none ];
1650 -> 669;

1651 [label="SPLIT 2\nnew knowledge:\nT375 is ground", fontsize=14, style = filled, fillcolor = violet];
659 -> 1651 [arrowhead = none ];
1651 -> 670;

1652 [label="INSTANCE with matching:\nT165 -> f(T375)", fontsize=14, style = filled, fillcolor = lightgrey];
669 -> 1652 [arrowhead = none , style=dashed];
1652 -> 351[style=dashed];

1653 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
670 -> 1653 [arrowhead = none ];
1653 -> 677;

1654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
677 -> 1654 [arrowhead = none ];
1654 -> 682;

1655 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
677 -> 1655 [arrowhead = none ];
1655 -> 683;

1656 [label="ONLY EVAL with clause\np(X576, X577) :- e(X576, X577).\nand substitutionT375 -> T383,\nX576 -> f(f(f(f(f(f(f(T383))))))),\nX577 -> T383", fontsize=14, style = filled, fillcolor = lightblue];
682 -> 1656 [arrowhead = none ];
1656 -> 690;

1657 [label="EVAL with clause\np(X582, f(X583)) :- ','(r(X582, f(X583)), p(X582, X583)).\nand substitutionT375 -> f(T389),\nX582 -> f(f(f(f(f(f(f(f(T389)))))))),\nX583 -> T389,\nT388 -> f(T389)", fontsize=14, style = filled, fillcolor = lightblue];
683 -> 1657 [arrowhead = none ];
1657 -> 695;

1658 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
683 -> 1658 [arrowhead = none ];
1658 -> 696;

1659 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
690 -> 1659 [arrowhead = none ];
1659 -> 692;

1660 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
692 -> 1660 [arrowhead = none ];
1660 -> 693;

1661 [label="GENERALIZATION\nT391 <-- f(f(f(f(f(f(f(T389)))))))\n\nNew Knowledge:\nT391 is ground", fontsize=14, style = filled, fillcolor = violet];
695 -> 1661 [arrowhead = none ];
1661 -> 701;

1662 [label="INSTANCE with matching:\nT200 -> T391\nT201 -> T389", fontsize=14, style = filled, fillcolor = lightgrey];
701 -> 1662 [arrowhead = none , style=dashed];
1662 -> 424[style=dashed];

1663 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
727 -> 1663 [arrowhead = none ];
1663 -> 733;

1664 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
727 -> 1664 [arrowhead = none ];
1664 -> 734;

1665 [label="ONLY EVAL with clause\nr(X598, X599) :- e(X598, X599).\nand substitutionT127 -> T399,\nX598 -> f(f(f(f(T399)))),\nX599 -> T399", fontsize=14, style = filled, fillcolor = lightblue];
733 -> 1665 [arrowhead = none ];
1665 -> 738;

1666 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
734 -> 1666 [arrowhead = none ];
1666 -> 743;

1667 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
734 -> 1667 [arrowhead = none ];
1667 -> 744;

1668 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
738 -> 1668 [arrowhead = none ];
1668 -> 739;

1669 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
739 -> 1669 [arrowhead = none ];
1669 -> 740;

1670 [label="EVAL with clause\nr(X608, f(X609)) :- ','(q(X608, X609), r(X608, X609)).\nand substitutionT127 -> f(T409),\nX608 -> f(f(f(f(f(T409))))),\nX609 -> T409,\nT408 -> f(T409)", fontsize=14, style = filled, fillcolor = lightblue];
743 -> 1670 [arrowhead = none ];
1670 -> 747;

1671 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
743 -> 1671 [arrowhead = none ];
1671 -> 748;

1672 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
744 -> 1672 [arrowhead = none ];
1672 -> 834;

1673 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
747 -> 1673 [arrowhead = none ];
1673 -> 763;

1674 [label="SPLIT 2\nnew knowledge:\nT409 is ground", fontsize=14, style = filled, fillcolor = violet];
747 -> 1674 [arrowhead = none ];
1674 -> 764;

1675 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
763 -> 1675 [arrowhead = none ];
1675 -> 767;

1676 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
764 -> 1676 [arrowhead = none ];
1676 -> 798;

1677 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
767 -> 1677 [arrowhead = none ];
1677 -> 769;

1678 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
767 -> 1678 [arrowhead = none ];
1678 -> 770;

1679 [label="ONLY EVAL with clause\nq(X622, X623) :- e(X622, X623).\nand substitutionT409 -> T416,\nX622 -> f(f(f(f(f(T416))))),\nX623 -> T416", fontsize=14, style = filled, fillcolor = lightblue];
769 -> 1679 [arrowhead = none ];
1679 -> 771;

1680 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
770 -> 1680 [arrowhead = none ];
1680 -> 774;

1681 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
771 -> 1681 [arrowhead = none ];
1681 -> 772;

1682 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
772 -> 1682 [arrowhead = none ];
1682 -> 773;

1683 [label="EVAL with clause\nq(X629, f(f(X630))) :- p(X629, f(X630)).\nand substitutionT409 -> f(f(T423)),\nX629 -> f(f(f(f(f(f(f(T423))))))),\nX630 -> T423,\nT422 -> f(f(T423))", fontsize=14, style = filled, fillcolor = lightblue];
774 -> 1683 [arrowhead = none ];
1683 -> 793;

1684 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
774 -> 1684 [arrowhead = none ];
1684 -> 794;

1685 [label="INSTANCE with matching:\nT151 -> f(T423)", fontsize=14, style = filled, fillcolor = lightgrey];
793 -> 1685 [arrowhead = none , style=dashed];
1685 -> 318[style=dashed];

1686 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
798 -> 1686 [arrowhead = none ];
1686 -> 800;

1687 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
798 -> 1687 [arrowhead = none ];
1687 -> 801;

1688 [label="ONLY EVAL with clause\nr(X643, X644) :- e(X643, X644).\nand substitutionT409 -> T430,\nX643 -> f(f(f(f(f(T430))))),\nX644 -> T430", fontsize=14, style = filled, fillcolor = lightblue];
800 -> 1688 [arrowhead = none ];
1688 -> 816;

1689 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
801 -> 1689 [arrowhead = none ];
1689 -> 821;

1690 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
801 -> 1690 [arrowhead = none ];
1690 -> 822;

1691 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
816 -> 1691 [arrowhead = none ];
1691 -> 817;

1692 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
817 -> 1692 [arrowhead = none ];
1692 -> 818;

1693 [label="EVAL with clause\nr(X653, f(X654)) :- ','(q(X653, X654), r(X653, X654)).\nand substitutionT409 -> f(T440),\nX653 -> f(f(f(f(f(f(T440)))))),\nX654 -> T440,\nT439 -> f(T440)", fontsize=14, style = filled, fillcolor = lightblue];
821 -> 1693 [arrowhead = none ];
1693 -> 824;

1694 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
821 -> 1694 [arrowhead = none ];
1694 -> 825;

1695 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
822 -> 1695 [arrowhead = none ];
1695 -> 830;

1696 [label="INSTANCE with matching:\nT165 -> T440", fontsize=14, style = filled, fillcolor = lightgrey];
824 -> 1696 [arrowhead = none , style=dashed];
1696 -> 344[style=dashed];

1697 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
836 -> 1697 [arrowhead = none ];
1697 -> 839;

1698 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
836 -> 1698 [arrowhead = none ];
1698 -> 840;

1699 [label="ONLY EVAL with clause\np(X670, X671) :- e(X670, X671).\nand substitutionT113 -> T450,\nX670 -> f(f(f(f(T450)))),\nX671 -> T450", fontsize=14, style = filled, fillcolor = lightblue];
839 -> 1699 [arrowhead = none ];
1699 -> 842;

1700 [label="EVAL with clause\np(X676, f(X677)) :- ','(r(X676, f(X677)), p(X676, X677)).\nand substitutionT113 -> f(T456),\nX676 -> f(f(f(f(f(T456))))),\nX677 -> T456,\nT455 -> f(T456)", fontsize=14, style = filled, fillcolor = lightblue];
840 -> 1700 [arrowhead = none ];
1700 -> 848;

1701 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
840 -> 1701 [arrowhead = none ];
1701 -> 849;

1702 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
842 -> 1702 [arrowhead = none ];
1702 -> 843;

1703 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
843 -> 1703 [arrowhead = none ];
1703 -> 844;

1704 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
848 -> 1704 [arrowhead = none ];
1704 -> 856;

1705 [label="SPLIT 2\nnew knowledge:\nT456 is ground", fontsize=14, style = filled, fillcolor = violet];
848 -> 1705 [arrowhead = none ];
1705 -> 857;

1706 [label="INSTANCE with matching:\nT127 -> f(T456)", fontsize=14, style = filled, fillcolor = lightgrey];
856 -> 1706 [arrowhead = none , style=dashed];
1706 -> 279[style=dashed];

1707 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
857 -> 1707 [arrowhead = none ];
1707 -> 863;

1708 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
863 -> 1708 [arrowhead = none ];
1708 -> 864;

1709 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
863 -> 1709 [arrowhead = none ];
1709 -> 865;

1710 [label="ONLY EVAL with clause\np(X692, X693) :- e(X692, X693).\nand substitutionT456 -> T464,\nX692 -> f(f(f(f(f(T464))))),\nX693 -> T464", fontsize=14, style = filled, fillcolor = lightblue];
864 -> 1710 [arrowhead = none ];
1710 -> 868;

1711 [label="EVAL with clause\np(X698, f(X699)) :- ','(r(X698, f(X699)), p(X698, X699)).\nand substitutionT456 -> f(T470),\nX698 -> f(f(f(f(f(f(T470)))))),\nX699 -> T470,\nT469 -> f(T470)", fontsize=14, style = filled, fillcolor = lightblue];
865 -> 1711 [arrowhead = none ];
1711 -> 873;

1712 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
865 -> 1712 [arrowhead = none ];
1712 -> 875;

1713 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
868 -> 1713 [arrowhead = none ];
1713 -> 869;

1714 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
869 -> 1714 [arrowhead = none ];
1714 -> 870;

1715 [label="INSTANCE with matching:\nT151 -> T470", fontsize=14, style = filled, fillcolor = lightgrey];
873 -> 1715 [arrowhead = none , style=dashed];
1715 -> 312[style=dashed];

1716 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
883 -> 1716 [arrowhead = none ];
1716 -> 888;

1717 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
883 -> 1717 [arrowhead = none ];
1717 -> 889;

1718 [label="ONLY EVAL with clause\nr(X712, X713) :- e(X712, X713).\nand substitutionT89 -> T477,\nX712 -> f(f(T477)),\nX713 -> T477", fontsize=14, style = filled, fillcolor = lightblue];
888 -> 1718 [arrowhead = none ];
1718 -> 892;

1719 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
889 -> 1719 [arrowhead = none ];
1719 -> 895;

1720 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
889 -> 1720 [arrowhead = none ];
1720 -> 896;

1721 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
892 -> 1721 [arrowhead = none ];
1721 -> 893;

1722 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
893 -> 1722 [arrowhead = none ];
1722 -> 894;

1723 [label="EVAL with clause\nr(X722, f(X723)) :- ','(q(X722, X723), r(X722, X723)).\nand substitutionT89 -> f(T487),\nX722 -> f(f(f(T487))),\nX723 -> T487,\nT486 -> f(T487)", fontsize=14, style = filled, fillcolor = lightblue];
895 -> 1723 [arrowhead = none ];
1723 -> 900;

1724 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
895 -> 1724 [arrowhead = none ];
1724 -> 901;

1725 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
896 -> 1725 [arrowhead = none ];
1725 -> 970;

1726 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
900 -> 1726 [arrowhead = none ];
1726 -> 907;

1727 [label="SPLIT 2\nnew knowledge:\nT487 is ground", fontsize=14, style = filled, fillcolor = violet];
900 -> 1727 [arrowhead = none ];
1727 -> 908;

1728 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
907 -> 1728 [arrowhead = none ];
1728 -> 914;

1729 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
908 -> 1729 [arrowhead = none ];
1729 -> 934;

1730 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
914 -> 1730 [arrowhead = none ];
1730 -> 917;

1731 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
914 -> 1731 [arrowhead = none ];
1731 -> 918;

1732 [label="ONLY EVAL with clause\nq(X736, X737) :- e(X736, X737).\nand substitutionT487 -> T494,\nX736 -> f(f(f(T494))),\nX737 -> T494", fontsize=14, style = filled, fillcolor = lightblue];
917 -> 1732 [arrowhead = none ];
1732 -> 922;

1733 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
918 -> 1733 [arrowhead = none ];
1733 -> 926;

1734 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
922 -> 1734 [arrowhead = none ];
1734 -> 923;

1735 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
923 -> 1735 [arrowhead = none ];
1735 -> 924;

1736 [label="EVAL with clause\nq(X743, f(f(X744))) :- p(X743, f(X744)).\nand substitutionT487 -> f(f(T501)),\nX743 -> f(f(f(f(f(T501))))),\nX744 -> T501,\nT500 -> f(f(T501))", fontsize=14, style = filled, fillcolor = lightblue];
926 -> 1736 [arrowhead = none ];
1736 -> 930;

1737 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
926 -> 1737 [arrowhead = none ];
1737 -> 931;

1738 [label="INSTANCE with matching:\nT113 -> f(T501)", fontsize=14, style = filled, fillcolor = lightgrey];
930 -> 1738 [arrowhead = none , style=dashed];
1738 -> 250[style=dashed];

1739 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
934 -> 1739 [arrowhead = none ];
1739 -> 935;

1740 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
934 -> 1740 [arrowhead = none ];
1740 -> 936;

1741 [label="ONLY EVAL with clause\nr(X757, X758) :- e(X757, X758).\nand substitutionT487 -> T508,\nX757 -> f(f(f(T508))),\nX758 -> T508", fontsize=14, style = filled, fillcolor = lightblue];
935 -> 1741 [arrowhead = none ];
1741 -> 947;

1742 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
936 -> 1742 [arrowhead = none ];
1742 -> 952;

1743 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
936 -> 1743 [arrowhead = none ];
1743 -> 953;

1744 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
947 -> 1744 [arrowhead = none ];
1744 -> 948;

1745 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
948 -> 1745 [arrowhead = none ];
1745 -> 949;

1746 [label="EVAL with clause\nr(X767, f(X768)) :- ','(q(X767, X768), r(X767, X768)).\nand substitutionT487 -> f(T518),\nX767 -> f(f(f(f(T518)))),\nX768 -> T518,\nT517 -> f(T518)", fontsize=14, style = filled, fillcolor = lightblue];
952 -> 1746 [arrowhead = none ];
1746 -> 955;

1747 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
952 -> 1747 [arrowhead = none ];
1747 -> 956;

1748 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
953 -> 1748 [arrowhead = none ];
1748 -> 959;

1749 [label="INSTANCE with matching:\nT127 -> T518", fontsize=14, style = filled, fillcolor = lightgrey];
955 -> 1749 [arrowhead = none , style=dashed];
1749 -> 270[style=dashed];

1750 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
973 -> 1750 [arrowhead = none ];
1750 -> 983;

1751 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
973 -> 1751 [arrowhead = none ];
1751 -> 984;

1752 [label="ONLY EVAL with clause\np(X784, X785) :- e(X784, X785).\nand substitutionT75 -> T528,\nX784 -> f(f(T528)),\nX785 -> T528", fontsize=14, style = filled, fillcolor = lightblue];
983 -> 1752 [arrowhead = none ];
1752 -> 997;

1753 [label="EVAL with clause\np(X790, f(X791)) :- ','(r(X790, f(X791)), p(X790, X791)).\nand substitutionT75 -> f(T534),\nX790 -> f(f(f(T534))),\nX791 -> T534,\nT533 -> f(T534)", fontsize=14, style = filled, fillcolor = lightblue];
984 -> 1753 [arrowhead = none ];
1753 -> 1004;

1754 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
984 -> 1754 [arrowhead = none ];
1754 -> 1005;

1755 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
997 -> 1755 [arrowhead = none ];
1755 -> 998;

1756 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
998 -> 1756 [arrowhead = none ];
1756 -> 999;

1757 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1004 -> 1757 [arrowhead = none ];
1757 -> 1012;

1758 [label="SPLIT 2\nnew knowledge:\nT534 is ground", fontsize=14, style = filled, fillcolor = violet];
1004 -> 1758 [arrowhead = none ];
1758 -> 1013;

1759 [label="INSTANCE with matching:\nT89 -> f(T534)", fontsize=14, style = filled, fillcolor = lightgrey];
1012 -> 1759 [arrowhead = none , style=dashed];
1759 -> 208[style=dashed];

1760 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1013 -> 1760 [arrowhead = none ];
1760 -> 1019;

1761 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1019 -> 1761 [arrowhead = none ];
1761 -> 1027;

1762 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1019 -> 1762 [arrowhead = none ];
1762 -> 1028;

1763 [label="ONLY EVAL with clause\np(X806, X807) :- e(X806, X807).\nand substitutionT534 -> T542,\nX806 -> f(f(f(T542))),\nX807 -> T542", fontsize=14, style = filled, fillcolor = lightblue];
1027 -> 1763 [arrowhead = none ];
1763 -> 1032;

1764 [label="EVAL with clause\np(X812, f(X813)) :- ','(r(X812, f(X813)), p(X812, X813)).\nand substitutionT534 -> f(T548),\nX812 -> f(f(f(f(T548)))),\nX813 -> T548,\nT547 -> f(T548)", fontsize=14, style = filled, fillcolor = lightblue];
1028 -> 1764 [arrowhead = none ];
1764 -> 1039;

1765 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1028 -> 1765 [arrowhead = none ];
1765 -> 1040;

1766 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1032 -> 1766 [arrowhead = none ];
1766 -> 1033;

1767 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1033 -> 1767 [arrowhead = none ];
1767 -> 1034;

1768 [label="INSTANCE with matching:\nT113 -> T548", fontsize=14, style = filled, fillcolor = lightgrey];
1039 -> 1768 [arrowhead = none , style=dashed];
1768 -> 241[style=dashed];

1769 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1049 -> 1769 [arrowhead = none ];
1769 -> 1052;

1770 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1049 -> 1770 [arrowhead = none ];
1770 -> 1053;

1771 [label="ONLY EVAL with clause\nr(X826, X827) :- e(X826, X827).\nand substitutionT51 -> T555,\nX826 -> T555,\nX827 -> T555", fontsize=14, style = filled, fillcolor = lightblue];
1052 -> 1771 [arrowhead = none ];
1771 -> 1056;

1772 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1053 -> 1772 [arrowhead = none ];
1772 -> 1059;

1773 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1053 -> 1773 [arrowhead = none ];
1773 -> 1060;

1774 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1056 -> 1774 [arrowhead = none ];
1774 -> 1057;

1775 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1057 -> 1775 [arrowhead = none ];
1775 -> 1058;

1776 [label="EVAL with clause\nr(X836, f(X837)) :- ','(q(X836, X837), r(X836, X837)).\nand substitutionT51 -> f(T565),\nX836 -> f(T565),\nX837 -> T565,\nT564 -> f(T565)", fontsize=14, style = filled, fillcolor = lightblue];
1059 -> 1776 [arrowhead = none ];
1776 -> 1062;

1777 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1059 -> 1777 [arrowhead = none ];
1777 -> 1063;

1778 [label="EVAL with clause\nr(f(X888), f(X888)) :- t(f(X888), f(X888)).\nand substitutionX888 -> T601,\nT51 -> f(T601)", fontsize=14, style = filled, fillcolor = lightblue];
1060 -> 1778 [arrowhead = none ];
1778 -> 1125;

1779 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1060 -> 1779 [arrowhead = none ];
1779 -> 1126;

1780 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1062 -> 1780 [arrowhead = none ];
1780 -> 1073;

1781 [label="SPLIT 2\nnew knowledge:\nT565 is ground", fontsize=14, style = filled, fillcolor = violet];
1062 -> 1781 [arrowhead = none ];
1781 -> 1074;

1782 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1073 -> 1782 [arrowhead = none ];
1782 -> 1076;

1783 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1074 -> 1783 [arrowhead = none ];
1783 -> 1097;

1784 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1076 -> 1784 [arrowhead = none ];
1784 -> 1081;

1785 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1076 -> 1785 [arrowhead = none ];
1785 -> 1082;

1786 [label="ONLY EVAL with clause\nq(X850, X851) :- e(X850, X851).\nand substitutionT565 -> T572,\nX850 -> f(T572),\nX851 -> T572", fontsize=14, style = filled, fillcolor = lightblue];
1081 -> 1786 [arrowhead = none ];
1786 -> 1083;

1787 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1082 -> 1787 [arrowhead = none ];
1787 -> 1087;

1788 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1083 -> 1788 [arrowhead = none ];
1788 -> 1084;

1789 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1084 -> 1789 [arrowhead = none ];
1789 -> 1085;

1790 [label="EVAL with clause\nq(X857, f(f(X858))) :- p(X857, f(X858)).\nand substitutionT565 -> f(f(T579)),\nX857 -> f(f(f(T579))),\nX858 -> T579,\nT578 -> f(f(T579))", fontsize=14, style = filled, fillcolor = lightblue];
1087 -> 1790 [arrowhead = none ];
1790 -> 1090;

1791 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1087 -> 1791 [arrowhead = none ];
1791 -> 1091;

1792 [label="INSTANCE with matching:\nT75 -> f(T579)", fontsize=14, style = filled, fillcolor = lightgrey];
1090 -> 1792 [arrowhead = none , style=dashed];
1792 -> 179[style=dashed];

1793 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1097 -> 1793 [arrowhead = none ];
1793 -> 1100;

1794 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1097 -> 1794 [arrowhead = none ];
1794 -> 1101;

1795 [label="ONLY EVAL with clause\nr(X871, X872) :- e(X871, X872).\nand substitutionT565 -> T586,\nX871 -> f(T586),\nX872 -> T586", fontsize=14, style = filled, fillcolor = lightblue];
1100 -> 1795 [arrowhead = none ];
1795 -> 1103;

1796 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1101 -> 1796 [arrowhead = none ];
1796 -> 1110;

1797 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1101 -> 1797 [arrowhead = none ];
1797 -> 1111;

1798 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1103 -> 1798 [arrowhead = none ];
1798 -> 1104;

1799 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1104 -> 1799 [arrowhead = none ];
1799 -> 1105;

1800 [label="EVAL with clause\nr(X881, f(X882)) :- ','(q(X881, X882), r(X881, X882)).\nand substitutionT565 -> f(T596),\nX881 -> f(f(T596)),\nX882 -> T596,\nT595 -> f(T596)", fontsize=14, style = filled, fillcolor = lightblue];
1110 -> 1800 [arrowhead = none ];
1800 -> 1118;

1801 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1110 -> 1801 [arrowhead = none ];
1801 -> 1119;

1802 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1111 -> 1802 [arrowhead = none ];
1802 -> 1124;

1803 [label="INSTANCE with matching:\nT89 -> T596", fontsize=14, style = filled, fillcolor = lightgrey];
1118 -> 1803 [arrowhead = none , style=dashed];
1803 -> 197[style=dashed];

1804 [label="INSTANCE with matching:\nT260 -> T601", fontsize=14, style = filled, fillcolor = lightgrey];
1125 -> 1804 [arrowhead = none , style=dashed];
1804 -> 482[style=dashed];

1805 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1134 -> 1805 [arrowhead = none ];
1805 -> 1139;

1806 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1134 -> 1806 [arrowhead = none ];
1806 -> 1140;

1807 [label="ONLY EVAL with clause\np(X903, X904) :- e(X903, X904).\nand substitutionT22 -> T610,\nX903 -> T610,\nX904 -> f(T610)", fontsize=14, style = filled, fillcolor = lightblue];
1139 -> 1807 [arrowhead = none ];
1807 -> 1144;

1808 [label="ONLY EVAL with clause\np(X911, f(X912)) :- ','(r(X911, f(X912)), p(X911, X912)).\nand substitutionT22 -> T614,\nX911 -> T614,\nX912 -> T614", fontsize=14, style = filled, fillcolor = lightblue];
1140 -> 1808 [arrowhead = none ];
1808 -> 1149;

1809 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1144 -> 1809 [arrowhead = none ];
1809 -> 1145;

1810 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1145 -> 1810 [arrowhead = none ];
1810 -> 1146;

1811 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1149 -> 1811 [arrowhead = none ];
1811 -> 1153;

1812 [label="SPLIT 2\nnew knowledge:\nT614 is ground", fontsize=14, style = filled, fillcolor = violet];
1149 -> 1812 [arrowhead = none ];
1812 -> 1154;

1813 [label="INSTANCE with matching:\nT36 -> T614", fontsize=14, style = filled, fillcolor = lightgrey];
1153 -> 1813 [arrowhead = none , style=dashed];
1813 -> 107[style=dashed];

1814 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1154 -> 1814 [arrowhead = none ];
1814 -> 1161;

1815 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1161 -> 1815 [arrowhead = none ];
1815 -> 1166;

1816 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1161 -> 1816 [arrowhead = none ];
1816 -> 1167;

1817 [label="ONLY EVAL with clause\np(X927, X928) :- e(X927, X928).\nand substitutionT614 -> T622,\nX927 -> T622,\nX928 -> T622", fontsize=14, style = filled, fillcolor = lightblue];
1166 -> 1817 [arrowhead = none ];
1817 -> 1172;

1818 [label="EVAL with clause\np(X933, f(X934)) :- ','(r(X933, f(X934)), p(X933, X934)).\nand substitutionT614 -> f(T628),\nX933 -> f(T628),\nX934 -> T628,\nT627 -> f(T628)", fontsize=14, style = filled, fillcolor = lightblue];
1167 -> 1818 [arrowhead = none ];
1818 -> 1179;

1819 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1167 -> 1819 [arrowhead = none ];
1819 -> 1180;

1820 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1172 -> 1820 [arrowhead = none ];
1820 -> 1174;

1821 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1174 -> 1821 [arrowhead = none ];
1821 -> 1175;

1822 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1179 -> 1822 [arrowhead = none ];
1822 -> 1182;

1823 [label="SPLIT 2\nnew knowledge:\nT628 is ground", fontsize=14, style = filled, fillcolor = violet];
1179 -> 1823 [arrowhead = none ];
1823 -> 1183;

1824 [label="INSTANCE with matching:\nT51 -> f(T628)", fontsize=14, style = filled, fillcolor = lightgrey];
1182 -> 1824 [arrowhead = none , style=dashed];
1824 -> 134[style=dashed];

1825 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1183 -> 1825 [arrowhead = none ];
1825 -> 1186;

1826 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1186 -> 1826 [arrowhead = none ];
1826 -> 1189;

1827 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1186 -> 1827 [arrowhead = none ];
1827 -> 1190;

1828 [label="ONLY EVAL with clause\np(X949, X950) :- e(X949, X950).\nand substitutionT628 -> T636,\nX949 -> f(T636),\nX950 -> T636", fontsize=14, style = filled, fillcolor = lightblue];
1189 -> 1828 [arrowhead = none ];
1828 -> 1195;

1829 [label="EVAL with clause\np(X955, f(X956)) :- ','(r(X955, f(X956)), p(X955, X956)).\nand substitutionT628 -> f(T642),\nX955 -> f(f(T642)),\nX956 -> T642,\nT641 -> f(T642)", fontsize=14, style = filled, fillcolor = lightblue];
1190 -> 1829 [arrowhead = none ];
1829 -> 1204;

1830 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1190 -> 1830 [arrowhead = none ];
1830 -> 1205;

1831 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1195 -> 1831 [arrowhead = none ];
1831 -> 1196;

1832 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1196 -> 1832 [arrowhead = none ];
1832 -> 1197;

1833 [label="INSTANCE with matching:\nT75 -> T642", fontsize=14, style = filled, fillcolor = lightgrey];
1204 -> 1833 [arrowhead = none , style=dashed];
1833 -> 172[style=dashed];

1834 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1208 -> 1834 [arrowhead = none ];
1834 -> 1211;

1835 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1208 -> 1835 [arrowhead = none ];
1835 -> 1212;

1836 [label="ONLY EVAL with clause\nq(X969, X970) :- e(X969, X970).\nand substitutionT11 -> T649,\nX969 -> T649,\nX970 -> f(T649)", fontsize=14, style = filled, fillcolor = lightblue];
1211 -> 1836 [arrowhead = none ];
1836 -> 1216;

1837 [label="BACKTRACK\nfor clause: q(X, f(f(X))) :- ','(p(X, f(f(X))), q(X, f(X)))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1212 -> 1837 [arrowhead = none ];
1837 -> 1221;

1838 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1216 -> 1838 [arrowhead = none ];
1838 -> 1217;

1839 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1217 -> 1839 [arrowhead = none ];
1839 -> 1218;

1840 [label="EVAL with clause\nq(X976, f(f(X977))) :- p(X976, f(X977)).\nand substitutionT11 -> f(T656),\nX976 -> f(T656),\nX977 -> T656,\nT655 -> f(T656)", fontsize=14, style = filled, fillcolor = lightblue];
1221 -> 1840 [arrowhead = none ];
1840 -> 1229;

1841 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1221 -> 1841 [arrowhead = none ];
1841 -> 1230;

1842 [label="INSTANCE with matching:\nT614 -> f(T656)", fontsize=14, style = filled, fillcolor = lightgrey];
1229 -> 1842 [arrowhead = none , style=dashed];
1842 -> 1154[style=dashed];

1843 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1233 -> 1843 [arrowhead = none ];
1843 -> 1236;

1844 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1236 -> 1844 [arrowhead = none ];
1844 -> 1240;

1845 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1236 -> 1845 [arrowhead = none ];
1845 -> 1241;

1846 [label="ONLY EVAL with clause\np(X996, X997) :- e(X996, X997).\nand substitutionT662 -> T674,\nX996 -> T674,\nT663 -> T675,\nX997 -> f(T675)", fontsize=14, style = filled, fillcolor = lightblue];
1240 -> 1846 [arrowhead = none ];
1846 -> 1248;

1847 [label="ONLY EVAL with clause\np(X1004, f(X1005)) :- ','(r(X1004, f(X1005)), p(X1004, X1005)).\nand substitutionT662 -> T682,\nX1004 -> T682,\nT663 -> T683,\nX1005 -> T683", fontsize=14, style = filled, fillcolor = lightblue];
1241 -> 1847 [arrowhead = none ];
1847 -> 1259;

1848 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1248 -> 1848 [arrowhead = none ];
1848 -> 1249;

1849 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1249 -> 1849 [arrowhead = none ];
1849 -> 1250;

1850 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1259 -> 1850 [arrowhead = none ];
1850 -> 1263;

1851 [label="SPLIT 2\nnew knowledge:\nT682 is ground\nT683 is ground", fontsize=14, style = filled, fillcolor = violet];
1259 -> 1851 [arrowhead = none ];
1851 -> 1264;

1852 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1263 -> 1852 [arrowhead = none ];
1852 -> 1268;

1853 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1264 -> 1853 [arrowhead = none ];
1853 -> 1359;

1854 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1268 -> 1854 [arrowhead = none ];
1854 -> 1276;

1855 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1268 -> 1855 [arrowhead = none ];
1855 -> 1277;

1856 [label="ONLY EVAL with clause\nr(X1018, X1019) :- e(X1018, X1019).\nand substitutionT682 -> T696,\nX1018 -> T696,\nT683 -> T697,\nX1019 -> f(T697)", fontsize=14, style = filled, fillcolor = lightblue];
1276 -> 1856 [arrowhead = none ];
1856 -> 1283;

1857 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1277 -> 1857 [arrowhead = none ];
1857 -> 1290;

1858 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1277 -> 1858 [arrowhead = none ];
1858 -> 1291;

1859 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1283 -> 1859 [arrowhead = none ];
1859 -> 1284;

1860 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
1284 -> 1860 [arrowhead = none ];
1860 -> 1285;

1861 [label="ONLY EVAL with clause\nr(X1032, f(X1033)) :- ','(q(X1032, X1033), r(X1032, X1033)).\nand substitutionT682 -> T710,\nX1032 -> T710,\nT683 -> T711,\nX1033 -> T711", fontsize=14, style = filled, fillcolor = lightblue];
1290 -> 1861 [arrowhead = none ];
1861 -> 1297;

1862 [label="EVAL with clause\nr(f(X1069), f(X1069)) :- t(f(X1069), f(X1069)).\nand substitutionX1069 -> T746,\nT682 -> f(T746),\nT683 -> T746", fontsize=14, style = filled, fillcolor = lightblue];
1291 -> 1862 [arrowhead = none ];
1862 -> 1347;

1863 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1291 -> 1863 [arrowhead = none ];
1863 -> 1348;

1864 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
1297 -> 1864 [arrowhead = none ];
1864 -> 1301;

1865 [label="SPLIT 2\nnew knowledge:\nT710 is ground\nT711 is ground", fontsize=14, style = filled, fillcolor = violet];
1297 -> 1865 [arrowhead = none ];
1865 -> 1302;

1866 [label="INSTANCE with matching:\nT1 -> T710\nT2 -> T711", fontsize=14, style = filled, fillcolor = lightgrey];
1301 -> 1866 [arrowhead = none , style=dashed];
1866 -> 3[style=dashed];

1867 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1302 -> 1867 [arrowhead = none ];
1867 -> 1310;

1868 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1310 -> 1868 [arrowhead = none ];
1868 -> 1315;

1869 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1310 -> 1869 [arrowhead = none ];
1869 -> 1316;

1870 [label="ONLY EVAL with clause\nr(X1048, X1049) :- e(X1048, X1049).\nand substitutionT710 -> T726,\nX1048 -> T726,\nT711 -> T727,\nX1049 -> T727", fontsize=14, style = filled, fillcolor = lightblue];
1315 -> 1870 [arrowhead = none ];
1870 -> 1320;

1871 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1316 -> 1871 [arrowhead = none ];
1871 -> 1328;

1872 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1316 -> 1872 [arrowhead = none ];
1872 -> 1329;

1873 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1320 -> 1873 [arrowhead = none ];
1873 -> 1321;

1874 [label="EVAL with clause\ne(a, b).\nand substitutionT726 -> a,\nT727 -> b", fontsize=14, style = filled, fillcolor = lightblue];
1321 -> 1874 [arrowhead = none ];
1874 -> 1322;

1875 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1321 -> 1875 [arrowhead = none ];
1875 -> 1323;

1876 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1322 -> 1876 [arrowhead = none ];
1876 -> 1324;

1877 [label="EVAL with clause\nr(X1058, f(X1059)) :- ','(q(X1058, X1059), r(X1058, X1059)).\nand substitutionT710 -> T736,\nX1058 -> T736,\nX1059 -> T737,\nT711 -> f(T737)", fontsize=14, style = filled, fillcolor = lightblue];
1328 -> 1877 [arrowhead = none ];
1877 -> 1335;

1878 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1328 -> 1878 [arrowhead = none ];
1878 -> 1336;

1879 [label="EVAL with clause\nr(f(X1064), f(X1064)) :- t(f(X1064), f(X1064)).\nand substitutionX1064 -> T742,\nT710 -> f(T742),\nT711 -> f(T742)", fontsize=14, style = filled, fillcolor = lightblue];
1329 -> 1879 [arrowhead = none ];
1879 -> 1341;

1880 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1329 -> 1880 [arrowhead = none ];
1880 -> 1342;

1881 [label="INSTANCE with matching:\nT710 -> T736\nT711 -> T737", fontsize=14, style = filled, fillcolor = lightgrey];
1335 -> 1881 [arrowhead = none , style=dashed];
1881 -> 1297[style=dashed];

1882 [label="INSTANCE with matching:\nT260 -> T742", fontsize=14, style = filled, fillcolor = lightgrey];
1341 -> 1882 [arrowhead = none , style=dashed];
1882 -> 482[style=dashed];

1883 [label="INSTANCE with matching:\nT260 -> T746", fontsize=14, style = filled, fillcolor = lightgrey];
1347 -> 1883 [arrowhead = none , style=dashed];
1883 -> 482[style=dashed];

1884 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1359 -> 1884 [arrowhead = none ];
1884 -> 1364;

1885 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
1359 -> 1885 [arrowhead = none ];
1885 -> 1365;

1886 [label="ONLY EVAL with clause\np(X1082, X1083) :- e(X1082, X1083).\nand substitutionT682 -> T758,\nX1082 -> T758,\nT683 -> T759,\nX1083 -> T759", fontsize=14, style = filled, fillcolor = lightblue];
1364 -> 1886 [arrowhead = none ];
1886 -> 1369;

1887 [label="EVAL with clause\np(X1088, f(X1089)) :- ','(r(X1088, f(X1089)), p(X1088, X1089)).\nand substitutionT682 -> T764,\nX1088 -> T764,\nX1089 -> T765,\nT683 -> f(T765)", fontsize=14, style = filled, fillcolor = lightblue];
1365 -> 1887 [arrowhead = none ];
1887 -> 1379;

1888 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1365 -> 1888 [arrowhead = none ];
1888 -> 1381;

1889 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1369 -> 1889 [arrowhead = none ];
1889 -> 1370;

1890 [label="EVAL with clause\ne(a, b).\nand substitutionT758 -> a,\nT759 -> b", fontsize=14, style = filled, fillcolor = lightblue];
1370 -> 1890 [arrowhead = none ];
1890 -> 1371;

1891 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
1370 -> 1891 [arrowhead = none ];
1891 -> 1372;

1892 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
1371 -> 1892 [arrowhead = none ];
1892 -> 1373;

1893 [label="INSTANCE with matching:\nT682 -> T764\nT683 -> T765", fontsize=14, style = filled, fillcolor = lightgrey];
1379 -> 1893 [arrowhead = none , style=dashed];
1893 -> 1259[style=dashed];

}

(2) Obligation:

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

qA_in_gg(a, b) → qA_out_gg(a, b)
qA_in_gg(T11, f(f(T11))) → U1_gg(T11, pB_in_g(T11))
pB_in_g(T11) → U49_g(T11, pN3_in_g(T11))
pN3_in_g(T22) → U17_g(T22, pN4_in_g(T22))
pN4_in_g(T22) → U51_g(T22, rN5_in_g(T22))
rN5_in_g(T36) → U18_g(T36, pN6_in_g(T36))
pN6_in_g(T36) → U53_g(T36, qD_in_g(T36))
qD_in_g(f(T656)) → U3_g(T656, pE_in_g(f(T656)))
pE_in_g(f(T628)) → U16_g(T628, pN2_in_g(T628))
pN2_in_g(T628) → U91_g(T628, rZ_in_g(f(T628)))
rZ_in_g(f(T565)) → U14_g(T565, pN1_in_g(T565))
pN1_in_g(T565) → U87_g(T565, qN34_in_g(T565))
qN34_in_g(f(f(T579))) → U41_g(T579, pV_in_g(f(T579)))
pV_in_g(f(T534)) → U12_g(T534, pW_in_g(T534))
pW_in_g(T534) → U85_g(T534, rT_in_g(f(T534)))
rT_in_g(f(T487)) → U11_g(T487, pU_in_g(T487))
pU_in_g(T487) → U83_g(T487, qN31_in_g(T487))
qN31_in_g(f(f(T501))) → U38_g(T501, pR_in_g(f(T501)))
pR_in_g(f(T456)) → U10_g(T456, pS_in_g(T456))
pS_in_g(T456) → U81_g(T456, rP_in_g(f(T456)))
rP_in_g(f(T409)) → U9_g(T409, pQ_in_g(T409))
pQ_in_g(T409) → U79_g(T409, qN28_in_g(T409))
qN28_in_g(f(f(T423))) → U35_g(T423, pN_in_g(f(T423)))
pN_in_g(f(T375)) → U8_g(T375, pO_in_g(T375))
pO_in_g(T375) → U77_g(T375, rL_in_g(f(T375)))
rL_in_g(f(T322)) → U7_g(T322, pM_in_g(T322))
pM_in_g(T322) → U75_g(T322, qN25_in_g(T322))
qN25_in_g(f(f(T336))) → U32_g(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
pF_in_gg(T200, T201) → U4_gg(T200, T201, pG_in_gg(T200, T201))
pG_in_gg(T200, T201) → U69_gg(T200, T201, rN20_in_gg(T200, T201))
rN20_in_gg(T228, T229) → U26_gg(T228, T229, pN21_in_gg(T228, T229))
pN21_in_gg(T228, T229) → U71_gg(T228, T229, qA_in_gg(f(T228), T229))
qA_in_gg(T682, f(f(T683))) → U2_gg(T682, T683, pC_in_gg(T682, T683))
pC_in_gg(T682, T683) → U93_gg(T682, T683, rN37_in_gg(T682, T683))
rN37_in_gg(T710, T711) → U44_gg(T710, T711, pN38_in_gg(T710, T711))
pN38_in_gg(T710, T711) → U95_gg(T710, T711, qA_in_gg(T710, T711))
U95_gg(T710, T711, qA_out_gg(T710, T711)) → U96_gg(T710, T711, rN40_in_gg(T710, T711))
rN40_in_gg(a, b) → rN40_out_gg(a, b)
rN40_in_gg(T736, f(T737)) → U47_gg(T736, T737, pN38_in_gg(T736, T737))
U47_gg(T736, T737, pN38_out_gg(T736, T737)) → rN40_out_gg(T736, f(T737))
rN40_in_gg(f(T742), f(T742)) → U48_gg(T742, tJ_in_g(T742))
tJ_in_g(T270) → U6_g(T270, pK_in_g(T270))
pK_in_g(T270) → U73_g(T270, qH_in_g(f(T270)))
qH_in_g(f(f(T75))) → U5_g(T75, pI_in_g(T75))
pI_in_g(T75) → U57_g(T75, rN9_in_g(T75))
rN9_in_g(T89) → U20_g(T89, pN10_in_g(T89))
pN10_in_g(T89) → U59_g(T89, qN11_in_g(T89))
qN11_in_g(f(f(T113))) → U21_g(T113, pN12_in_g(T113))
pN12_in_g(T113) → U61_g(T113, rN13_in_g(T113))
rN13_in_g(T127) → U22_g(T127, pN14_in_g(T127))
pN14_in_g(T127) → U63_g(T127, qN15_in_g(T127))
qN15_in_g(f(f(T151))) → U23_g(T151, pN16_in_g(T151))
pN16_in_g(T151) → U65_g(T151, rN17_in_g(T151))
rN17_in_g(T165) → U24_g(T165, pN18_in_g(T165))
pN18_in_g(T165) → U67_g(T165, qN19_in_g(T165))
qN19_in_g(f(f(T179))) → U25_g(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
U25_g(T179, pF_out_gg(f(f(f(f(f(f(f(T179))))))), T179)) → qN19_out_g(f(f(T179)))
U67_g(T165, qN19_out_g(T165)) → U68_g(T165, rL_in_g(T165))
U68_g(T165, rL_out_g(T165)) → pN18_out_g(T165)
U24_g(T165, pN18_out_g(T165)) → rN17_out_g(T165)
U65_g(T151, rN17_out_g(T151)) → U66_g(T151, pN_in_g(T151))
U66_g(T151, pN_out_g(T151)) → pN16_out_g(T151)
U23_g(T151, pN16_out_g(T151)) → qN15_out_g(f(f(T151)))
U63_g(T127, qN15_out_g(T127)) → U64_g(T127, rP_in_g(T127))
U64_g(T127, rP_out_g(T127)) → pN14_out_g(T127)
U22_g(T127, pN14_out_g(T127)) → rN13_out_g(T127)
U61_g(T113, rN13_out_g(T113)) → U62_g(T113, pR_in_g(T113))
U62_g(T113, pR_out_g(T113)) → pN12_out_g(T113)
U21_g(T113, pN12_out_g(T113)) → qN11_out_g(f(f(T113)))
U59_g(T89, qN11_out_g(T89)) → U60_g(T89, rT_in_g(T89))
U60_g(T89, rT_out_g(T89)) → pN10_out_g(T89)
U20_g(T89, pN10_out_g(T89)) → rN9_out_g(T89)
U57_g(T75, rN9_out_g(T75)) → U58_g(T75, pV_in_g(T75))
U58_g(T75, pV_out_g(T75)) → pI_out_g(T75)
U5_g(T75, pI_out_g(T75)) → qH_out_g(f(f(T75)))
U73_g(T270, qH_out_g(f(T270))) → U74_g(T270, tN24_in_g(T270))
tN24_in_g(f(T281)) → U31_g(T281, pK_in_g(T281))
U31_g(T281, pK_out_g(T281)) → tN24_out_g(f(T281))
U74_g(T270, tN24_out_g(T270)) → pK_out_g(T270)
U6_g(T270, pK_out_g(T270)) → tJ_out_g(T270)
U48_gg(T742, tJ_out_g(T742)) → rN40_out_gg(f(T742), f(T742))
U96_gg(T710, T711, rN40_out_gg(T710, T711)) → pN38_out_gg(T710, T711)
U44_gg(T710, T711, pN38_out_gg(T710, T711)) → rN37_out_gg(T710, T711)
rN37_in_gg(f(T746), T746) → U45_gg(T746, tJ_in_g(T746))
U45_gg(T746, tJ_out_g(T746)) → rN37_out_gg(f(T746), T746)
U93_gg(T682, T683, rN37_out_gg(T682, T683)) → U94_gg(T682, T683, pN39_in_gg(T682, T683))
pN39_in_gg(a, b) → pN39_out_gg(a, b)
pN39_in_gg(T764, f(T765)) → U46_gg(T764, T765, pC_in_gg(T764, T765))
U46_gg(T764, T765, pC_out_gg(T764, T765)) → pN39_out_gg(T764, f(T765))
U94_gg(T682, T683, pN39_out_gg(T682, T683)) → pC_out_gg(T682, T683)
U2_gg(T682, T683, pC_out_gg(T682, T683)) → qA_out_gg(T682, f(f(T683)))
U71_gg(T228, T229, qA_out_gg(f(T228), T229)) → U72_gg(T228, T229, rN23_in_gg(T228, T229))
rN23_in_gg(T254, f(T255)) → U29_gg(T254, T255, pN21_in_gg(T254, T255))
U29_gg(T254, T255, pN21_out_gg(T254, T255)) → rN23_out_gg(T254, f(T255))
rN23_in_gg(T260, f(T260)) → U30_gg(T260, tJ_in_g(T260))
U30_gg(T260, tJ_out_g(T260)) → rN23_out_gg(T260, f(T260))
U72_gg(T228, T229, rN23_out_gg(T228, T229)) → pN21_out_gg(T228, T229)
U26_gg(T228, T229, pN21_out_gg(T228, T229)) → rN20_out_gg(T228, T229)
rN20_in_gg(T285, T285) → U27_gg(T285, tJ_in_g(T285))
U27_gg(T285, tJ_out_g(T285)) → rN20_out_gg(T285, T285)
U69_gg(T200, T201, rN20_out_gg(T200, T201)) → U70_gg(T200, T201, pN22_in_gg(T200, T201))
pN22_in_gg(T303, f(T304)) → U28_gg(T303, T304, pG_in_gg(T303, T304))
U28_gg(T303, T304, pG_out_gg(T303, T304)) → pN22_out_gg(T303, f(T304))
U70_gg(T200, T201, pN22_out_gg(T200, T201)) → pG_out_gg(T200, T201)
U4_gg(T200, T201, pG_out_gg(T200, T201)) → pF_out_gg(T200, T201)
U32_g(T336, pF_out_gg(f(f(f(f(f(f(f(f(T336)))))))), T336)) → qN25_out_g(f(f(T336)))
U75_g(T322, qN25_out_g(T322)) → U76_g(T322, rN26_in_g(T322))
rN26_in_g(f(T356)) → U33_g(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
U33_g(T356, pN21_out_gg(f(f(f(f(f(f(f(T356))))))), T356)) → rN26_out_g(f(T356))
U76_g(T322, rN26_out_g(T322)) → pM_out_g(T322)
U7_g(T322, pM_out_g(T322)) → rL_out_g(f(T322))
U77_g(T375, rL_out_g(f(T375))) → U78_g(T375, pN27_in_g(T375))
pN27_in_g(f(T389)) → U34_g(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
U34_g(T389, pG_out_gg(f(f(f(f(f(f(f(T389))))))), T389)) → pN27_out_g(f(T389))
U78_g(T375, pN27_out_g(T375)) → pO_out_g(T375)
U8_g(T375, pO_out_g(T375)) → pN_out_g(f(T375))
U35_g(T423, pN_out_g(f(T423))) → qN28_out_g(f(f(T423)))
U79_g(T409, qN28_out_g(T409)) → U80_g(T409, rN29_in_g(T409))
rN29_in_g(f(T440)) → U36_g(T440, pN18_in_g(T440))
U36_g(T440, pN18_out_g(T440)) → rN29_out_g(f(T440))
U80_g(T409, rN29_out_g(T409)) → pQ_out_g(T409)
U9_g(T409, pQ_out_g(T409)) → rP_out_g(f(T409))
U81_g(T456, rP_out_g(f(T456))) → U82_g(T456, pN30_in_g(T456))
pN30_in_g(f(T470)) → U37_g(T470, pN16_in_g(T470))
U37_g(T470, pN16_out_g(T470)) → pN30_out_g(f(T470))
U82_g(T456, pN30_out_g(T456)) → pS_out_g(T456)
U10_g(T456, pS_out_g(T456)) → pR_out_g(f(T456))
U38_g(T501, pR_out_g(f(T501))) → qN31_out_g(f(f(T501)))
U83_g(T487, qN31_out_g(T487)) → U84_g(T487, rN32_in_g(T487))
rN32_in_g(f(T518)) → U39_g(T518, pN14_in_g(T518))
U39_g(T518, pN14_out_g(T518)) → rN32_out_g(f(T518))
U84_g(T487, rN32_out_g(T487)) → pU_out_g(T487)
U11_g(T487, pU_out_g(T487)) → rT_out_g(f(T487))
U85_g(T534, rT_out_g(f(T534))) → U86_g(T534, pN33_in_g(T534))
pN33_in_g(f(T548)) → U40_g(T548, pN12_in_g(T548))
U40_g(T548, pN12_out_g(T548)) → pN33_out_g(f(T548))
U86_g(T534, pN33_out_g(T534)) → pW_out_g(T534)
U12_g(T534, pW_out_g(T534)) → pV_out_g(f(T534))
U41_g(T579, pV_out_g(f(T579))) → qN34_out_g(f(f(T579)))
U87_g(T565, qN34_out_g(T565)) → U88_g(T565, rN35_in_g(T565))
rN35_in_g(f(T596)) → U42_g(T596, pN10_in_g(T596))
U42_g(T596, pN10_out_g(T596)) → rN35_out_g(f(T596))
U88_g(T565, rN35_out_g(T565)) → pN1_out_g(T565)
U14_g(T565, pN1_out_g(T565)) → rZ_out_g(f(T565))
rZ_in_g(f(T601)) → U15_g(T601, tJ_in_g(T601))
U15_g(T601, tJ_out_g(T601)) → rZ_out_g(f(T601))
U91_g(T628, rZ_out_g(f(T628))) → U92_g(T628, pN36_in_g(T628))
pN36_in_g(f(T642)) → U43_g(T642, pI_in_g(T642))
U43_g(T642, pI_out_g(T642)) → pN36_out_g(f(T642))
U92_g(T628, pN36_out_g(T628)) → pN2_out_g(T628)
U16_g(T628, pN2_out_g(T628)) → pE_out_g(f(T628))
U3_g(T656, pE_out_g(f(T656))) → qD_out_g(f(T656))
U53_g(T36, qD_out_g(T36)) → U54_g(T36, rX_in_g(T36))
rX_in_g(T51) → U13_g(T51, pY_in_g(T51))
pY_in_g(T51) → U55_g(T51, qH_in_g(T51))
U55_g(T51, qH_out_g(T51)) → U56_g(T51, rZ_in_g(T51))
U56_g(T51, rZ_out_g(T51)) → pY_out_g(T51)
U13_g(T51, pY_out_g(T51)) → rX_out_g(T51)
U54_g(T36, rX_out_g(T36)) → pN6_out_g(T36)
U18_g(T36, pN6_out_g(T36)) → rN5_out_g(T36)
U51_g(T22, rN5_out_g(T22)) → U52_g(T22, pN7_in_g(T22))
pN7_in_g(T614) → U19_g(T614, pN8_in_g(T614))
pN8_in_g(T614) → U89_g(T614, rX_in_g(T614))
U89_g(T614, rX_out_g(T614)) → U90_g(T614, pE_in_g(T614))
U90_g(T614, pE_out_g(T614)) → pN8_out_g(T614)
U19_g(T614, pN8_out_g(T614)) → pN7_out_g(T614)
U52_g(T22, pN7_out_g(T22)) → pN4_out_g(T22)
U17_g(T22, pN4_out_g(T22)) → pN3_out_g(T22)
U49_g(T11, pN3_out_g(T11)) → U50_g(T11, qD_in_g(T11))
U50_g(T11, qD_out_g(T11)) → pB_out_g(T11)
U1_gg(T11, pB_out_g(T11)) → qA_out_gg(T11, f(f(T11)))

Pi is empty.

(3) 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:

QA_IN_GG(T11, f(f(T11))) → U1_GG(T11, pB_in_g(T11))
QA_IN_GG(T11, f(f(T11))) → PB_IN_G(T11)
PB_IN_G(T11) → U49_G(T11, pN3_in_g(T11))
PB_IN_G(T11) → PN3_IN_G(T11)
PN3_IN_G(T22) → U17_G(T22, pN4_in_g(T22))
PN3_IN_G(T22) → PN4_IN_G(T22)
PN4_IN_G(T22) → U51_G(T22, rN5_in_g(T22))
PN4_IN_G(T22) → RN5_IN_G(T22)
RN5_IN_G(T36) → U18_G(T36, pN6_in_g(T36))
RN5_IN_G(T36) → PN6_IN_G(T36)
PN6_IN_G(T36) → U53_G(T36, qD_in_g(T36))
PN6_IN_G(T36) → QD_IN_G(T36)
QD_IN_G(f(T656)) → U3_G(T656, pE_in_g(f(T656)))
QD_IN_G(f(T656)) → PE_IN_G(f(T656))
PE_IN_G(f(T628)) → U16_G(T628, pN2_in_g(T628))
PE_IN_G(f(T628)) → PN2_IN_G(T628)
PN2_IN_G(T628) → U91_G(T628, rZ_in_g(f(T628)))
PN2_IN_G(T628) → RZ_IN_G(f(T628))
RZ_IN_G(f(T565)) → U14_G(T565, pN1_in_g(T565))
RZ_IN_G(f(T565)) → PN1_IN_G(T565)
PN1_IN_G(T565) → U87_G(T565, qN34_in_g(T565))
PN1_IN_G(T565) → QN34_IN_G(T565)
QN34_IN_G(f(f(T579))) → U41_G(T579, pV_in_g(f(T579)))
QN34_IN_G(f(f(T579))) → PV_IN_G(f(T579))
PV_IN_G(f(T534)) → U12_G(T534, pW_in_g(T534))
PV_IN_G(f(T534)) → PW_IN_G(T534)
PW_IN_G(T534) → U85_G(T534, rT_in_g(f(T534)))
PW_IN_G(T534) → RT_IN_G(f(T534))
RT_IN_G(f(T487)) → U11_G(T487, pU_in_g(T487))
RT_IN_G(f(T487)) → PU_IN_G(T487)
PU_IN_G(T487) → U83_G(T487, qN31_in_g(T487))
PU_IN_G(T487) → QN31_IN_G(T487)
QN31_IN_G(f(f(T501))) → U38_G(T501, pR_in_g(f(T501)))
QN31_IN_G(f(f(T501))) → PR_IN_G(f(T501))
PR_IN_G(f(T456)) → U10_G(T456, pS_in_g(T456))
PR_IN_G(f(T456)) → PS_IN_G(T456)
PS_IN_G(T456) → U81_G(T456, rP_in_g(f(T456)))
PS_IN_G(T456) → RP_IN_G(f(T456))
RP_IN_G(f(T409)) → U9_G(T409, pQ_in_g(T409))
RP_IN_G(f(T409)) → PQ_IN_G(T409)
PQ_IN_G(T409) → U79_G(T409, qN28_in_g(T409))
PQ_IN_G(T409) → QN28_IN_G(T409)
QN28_IN_G(f(f(T423))) → U35_G(T423, pN_in_g(f(T423)))
QN28_IN_G(f(f(T423))) → PN_IN_G(f(T423))
PN_IN_G(f(T375)) → U8_G(T375, pO_in_g(T375))
PN_IN_G(f(T375)) → PO_IN_G(T375)
PO_IN_G(T375) → U77_G(T375, rL_in_g(f(T375)))
PO_IN_G(T375) → RL_IN_G(f(T375))
RL_IN_G(f(T322)) → U7_G(T322, pM_in_g(T322))
RL_IN_G(f(T322)) → PM_IN_G(T322)
PM_IN_G(T322) → U75_G(T322, qN25_in_g(T322))
PM_IN_G(T322) → QN25_IN_G(T322)
QN25_IN_G(f(f(T336))) → U32_G(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
QN25_IN_G(f(f(T336))) → PF_IN_GG(f(f(f(f(f(f(f(f(T336)))))))), T336)
PF_IN_GG(T200, T201) → U4_GG(T200, T201, pG_in_gg(T200, T201))
PF_IN_GG(T200, T201) → PG_IN_GG(T200, T201)
PG_IN_GG(T200, T201) → U69_GG(T200, T201, rN20_in_gg(T200, T201))
PG_IN_GG(T200, T201) → RN20_IN_GG(T200, T201)
RN20_IN_GG(T228, T229) → U26_GG(T228, T229, pN21_in_gg(T228, T229))
RN20_IN_GG(T228, T229) → PN21_IN_GG(T228, T229)
PN21_IN_GG(T228, T229) → U71_GG(T228, T229, qA_in_gg(f(T228), T229))
PN21_IN_GG(T228, T229) → QA_IN_GG(f(T228), T229)
QA_IN_GG(T682, f(f(T683))) → U2_GG(T682, T683, pC_in_gg(T682, T683))
QA_IN_GG(T682, f(f(T683))) → PC_IN_GG(T682, T683)
PC_IN_GG(T682, T683) → U93_GG(T682, T683, rN37_in_gg(T682, T683))
PC_IN_GG(T682, T683) → RN37_IN_GG(T682, T683)
RN37_IN_GG(T710, T711) → U44_GG(T710, T711, pN38_in_gg(T710, T711))
RN37_IN_GG(T710, T711) → PN38_IN_GG(T710, T711)
PN38_IN_GG(T710, T711) → U95_GG(T710, T711, qA_in_gg(T710, T711))
PN38_IN_GG(T710, T711) → QA_IN_GG(T710, T711)
U95_GG(T710, T711, qA_out_gg(T710, T711)) → U96_GG(T710, T711, rN40_in_gg(T710, T711))
U95_GG(T710, T711, qA_out_gg(T710, T711)) → RN40_IN_GG(T710, T711)
RN40_IN_GG(T736, f(T737)) → U47_GG(T736, T737, pN38_in_gg(T736, T737))
RN40_IN_GG(T736, f(T737)) → PN38_IN_GG(T736, T737)
RN40_IN_GG(f(T742), f(T742)) → U48_GG(T742, tJ_in_g(T742))
RN40_IN_GG(f(T742), f(T742)) → TJ_IN_G(T742)
TJ_IN_G(T270) → U6_G(T270, pK_in_g(T270))
TJ_IN_G(T270) → PK_IN_G(T270)
PK_IN_G(T270) → U73_G(T270, qH_in_g(f(T270)))
PK_IN_G(T270) → QH_IN_G(f(T270))
QH_IN_G(f(f(T75))) → U5_G(T75, pI_in_g(T75))
QH_IN_G(f(f(T75))) → PI_IN_G(T75)
PI_IN_G(T75) → U57_G(T75, rN9_in_g(T75))
PI_IN_G(T75) → RN9_IN_G(T75)
RN9_IN_G(T89) → U20_G(T89, pN10_in_g(T89))
RN9_IN_G(T89) → PN10_IN_G(T89)
PN10_IN_G(T89) → U59_G(T89, qN11_in_g(T89))
PN10_IN_G(T89) → QN11_IN_G(T89)
QN11_IN_G(f(f(T113))) → U21_G(T113, pN12_in_g(T113))
QN11_IN_G(f(f(T113))) → PN12_IN_G(T113)
PN12_IN_G(T113) → U61_G(T113, rN13_in_g(T113))
PN12_IN_G(T113) → RN13_IN_G(T113)
RN13_IN_G(T127) → U22_G(T127, pN14_in_g(T127))
RN13_IN_G(T127) → PN14_IN_G(T127)
PN14_IN_G(T127) → U63_G(T127, qN15_in_g(T127))
PN14_IN_G(T127) → QN15_IN_G(T127)
QN15_IN_G(f(f(T151))) → U23_G(T151, pN16_in_g(T151))
QN15_IN_G(f(f(T151))) → PN16_IN_G(T151)
PN16_IN_G(T151) → U65_G(T151, rN17_in_g(T151))
PN16_IN_G(T151) → RN17_IN_G(T151)
RN17_IN_G(T165) → U24_G(T165, pN18_in_g(T165))
RN17_IN_G(T165) → PN18_IN_G(T165)
PN18_IN_G(T165) → U67_G(T165, qN19_in_g(T165))
PN18_IN_G(T165) → QN19_IN_G(T165)
QN19_IN_G(f(f(T179))) → U25_G(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
QN19_IN_G(f(f(T179))) → PF_IN_GG(f(f(f(f(f(f(f(T179))))))), T179)
U67_G(T165, qN19_out_g(T165)) → U68_G(T165, rL_in_g(T165))
U67_G(T165, qN19_out_g(T165)) → RL_IN_G(T165)
U65_G(T151, rN17_out_g(T151)) → U66_G(T151, pN_in_g(T151))
U65_G(T151, rN17_out_g(T151)) → PN_IN_G(T151)
U63_G(T127, qN15_out_g(T127)) → U64_G(T127, rP_in_g(T127))
U63_G(T127, qN15_out_g(T127)) → RP_IN_G(T127)
U61_G(T113, rN13_out_g(T113)) → U62_G(T113, pR_in_g(T113))
U61_G(T113, rN13_out_g(T113)) → PR_IN_G(T113)
U59_G(T89, qN11_out_g(T89)) → U60_G(T89, rT_in_g(T89))
U59_G(T89, qN11_out_g(T89)) → RT_IN_G(T89)
U57_G(T75, rN9_out_g(T75)) → U58_G(T75, pV_in_g(T75))
U57_G(T75, rN9_out_g(T75)) → PV_IN_G(T75)
U73_G(T270, qH_out_g(f(T270))) → U74_G(T270, tN24_in_g(T270))
U73_G(T270, qH_out_g(f(T270))) → TN24_IN_G(T270)
TN24_IN_G(f(T281)) → U31_G(T281, pK_in_g(T281))
TN24_IN_G(f(T281)) → PK_IN_G(T281)
RN37_IN_GG(f(T746), T746) → U45_GG(T746, tJ_in_g(T746))
RN37_IN_GG(f(T746), T746) → TJ_IN_G(T746)
U93_GG(T682, T683, rN37_out_gg(T682, T683)) → U94_GG(T682, T683, pN39_in_gg(T682, T683))
U93_GG(T682, T683, rN37_out_gg(T682, T683)) → PN39_IN_GG(T682, T683)
PN39_IN_GG(T764, f(T765)) → U46_GG(T764, T765, pC_in_gg(T764, T765))
PN39_IN_GG(T764, f(T765)) → PC_IN_GG(T764, T765)
U71_GG(T228, T229, qA_out_gg(f(T228), T229)) → U72_GG(T228, T229, rN23_in_gg(T228, T229))
U71_GG(T228, T229, qA_out_gg(f(T228), T229)) → RN23_IN_GG(T228, T229)
RN23_IN_GG(T254, f(T255)) → U29_GG(T254, T255, pN21_in_gg(T254, T255))
RN23_IN_GG(T254, f(T255)) → PN21_IN_GG(T254, T255)
RN23_IN_GG(T260, f(T260)) → U30_GG(T260, tJ_in_g(T260))
RN23_IN_GG(T260, f(T260)) → TJ_IN_G(T260)
RN20_IN_GG(T285, T285) → U27_GG(T285, tJ_in_g(T285))
RN20_IN_GG(T285, T285) → TJ_IN_G(T285)
U69_GG(T200, T201, rN20_out_gg(T200, T201)) → U70_GG(T200, T201, pN22_in_gg(T200, T201))
U69_GG(T200, T201, rN20_out_gg(T200, T201)) → PN22_IN_GG(T200, T201)
PN22_IN_GG(T303, f(T304)) → U28_GG(T303, T304, pG_in_gg(T303, T304))
PN22_IN_GG(T303, f(T304)) → PG_IN_GG(T303, T304)
U75_G(T322, qN25_out_g(T322)) → U76_G(T322, rN26_in_g(T322))
U75_G(T322, qN25_out_g(T322)) → RN26_IN_G(T322)
RN26_IN_G(f(T356)) → U33_G(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
RN26_IN_G(f(T356)) → PN21_IN_GG(f(f(f(f(f(f(f(T356))))))), T356)
U77_G(T375, rL_out_g(f(T375))) → U78_G(T375, pN27_in_g(T375))
U77_G(T375, rL_out_g(f(T375))) → PN27_IN_G(T375)
PN27_IN_G(f(T389)) → U34_G(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
PN27_IN_G(f(T389)) → PG_IN_GG(f(f(f(f(f(f(f(T389))))))), T389)
U79_G(T409, qN28_out_g(T409)) → U80_G(T409, rN29_in_g(T409))
U79_G(T409, qN28_out_g(T409)) → RN29_IN_G(T409)
RN29_IN_G(f(T440)) → U36_G(T440, pN18_in_g(T440))
RN29_IN_G(f(T440)) → PN18_IN_G(T440)
U81_G(T456, rP_out_g(f(T456))) → U82_G(T456, pN30_in_g(T456))
U81_G(T456, rP_out_g(f(T456))) → PN30_IN_G(T456)
PN30_IN_G(f(T470)) → U37_G(T470, pN16_in_g(T470))
PN30_IN_G(f(T470)) → PN16_IN_G(T470)
U83_G(T487, qN31_out_g(T487)) → U84_G(T487, rN32_in_g(T487))
U83_G(T487, qN31_out_g(T487)) → RN32_IN_G(T487)
RN32_IN_G(f(T518)) → U39_G(T518, pN14_in_g(T518))
RN32_IN_G(f(T518)) → PN14_IN_G(T518)
U85_G(T534, rT_out_g(f(T534))) → U86_G(T534, pN33_in_g(T534))
U85_G(T534, rT_out_g(f(T534))) → PN33_IN_G(T534)
PN33_IN_G(f(T548)) → U40_G(T548, pN12_in_g(T548))
PN33_IN_G(f(T548)) → PN12_IN_G(T548)
U87_G(T565, qN34_out_g(T565)) → U88_G(T565, rN35_in_g(T565))
U87_G(T565, qN34_out_g(T565)) → RN35_IN_G(T565)
RN35_IN_G(f(T596)) → U42_G(T596, pN10_in_g(T596))
RN35_IN_G(f(T596)) → PN10_IN_G(T596)
RZ_IN_G(f(T601)) → U15_G(T601, tJ_in_g(T601))
RZ_IN_G(f(T601)) → TJ_IN_G(T601)
U91_G(T628, rZ_out_g(f(T628))) → U92_G(T628, pN36_in_g(T628))
U91_G(T628, rZ_out_g(f(T628))) → PN36_IN_G(T628)
PN36_IN_G(f(T642)) → U43_G(T642, pI_in_g(T642))
PN36_IN_G(f(T642)) → PI_IN_G(T642)
U53_G(T36, qD_out_g(T36)) → U54_G(T36, rX_in_g(T36))
U53_G(T36, qD_out_g(T36)) → RX_IN_G(T36)
RX_IN_G(T51) → U13_G(T51, pY_in_g(T51))
RX_IN_G(T51) → PY_IN_G(T51)
PY_IN_G(T51) → U55_G(T51, qH_in_g(T51))
PY_IN_G(T51) → QH_IN_G(T51)
U55_G(T51, qH_out_g(T51)) → U56_G(T51, rZ_in_g(T51))
U55_G(T51, qH_out_g(T51)) → RZ_IN_G(T51)
U51_G(T22, rN5_out_g(T22)) → U52_G(T22, pN7_in_g(T22))
U51_G(T22, rN5_out_g(T22)) → PN7_IN_G(T22)
PN7_IN_G(T614) → U19_G(T614, pN8_in_g(T614))
PN7_IN_G(T614) → PN8_IN_G(T614)
PN8_IN_G(T614) → U89_G(T614, rX_in_g(T614))
PN8_IN_G(T614) → RX_IN_G(T614)
U89_G(T614, rX_out_g(T614)) → U90_G(T614, pE_in_g(T614))
U89_G(T614, rX_out_g(T614)) → PE_IN_G(T614)
U49_G(T11, pN3_out_g(T11)) → U50_G(T11, qD_in_g(T11))
U49_G(T11, pN3_out_g(T11)) → QD_IN_G(T11)

The TRS R consists of the following rules:

qA_in_gg(a, b) → qA_out_gg(a, b)
qA_in_gg(T11, f(f(T11))) → U1_gg(T11, pB_in_g(T11))
pB_in_g(T11) → U49_g(T11, pN3_in_g(T11))
pN3_in_g(T22) → U17_g(T22, pN4_in_g(T22))
pN4_in_g(T22) → U51_g(T22, rN5_in_g(T22))
rN5_in_g(T36) → U18_g(T36, pN6_in_g(T36))
pN6_in_g(T36) → U53_g(T36, qD_in_g(T36))
qD_in_g(f(T656)) → U3_g(T656, pE_in_g(f(T656)))
pE_in_g(f(T628)) → U16_g(T628, pN2_in_g(T628))
pN2_in_g(T628) → U91_g(T628, rZ_in_g(f(T628)))
rZ_in_g(f(T565)) → U14_g(T565, pN1_in_g(T565))
pN1_in_g(T565) → U87_g(T565, qN34_in_g(T565))
qN34_in_g(f(f(T579))) → U41_g(T579, pV_in_g(f(T579)))
pV_in_g(f(T534)) → U12_g(T534, pW_in_g(T534))
pW_in_g(T534) → U85_g(T534, rT_in_g(f(T534)))
rT_in_g(f(T487)) → U11_g(T487, pU_in_g(T487))
pU_in_g(T487) → U83_g(T487, qN31_in_g(T487))
qN31_in_g(f(f(T501))) → U38_g(T501, pR_in_g(f(T501)))
pR_in_g(f(T456)) → U10_g(T456, pS_in_g(T456))
pS_in_g(T456) → U81_g(T456, rP_in_g(f(T456)))
rP_in_g(f(T409)) → U9_g(T409, pQ_in_g(T409))
pQ_in_g(T409) → U79_g(T409, qN28_in_g(T409))
qN28_in_g(f(f(T423))) → U35_g(T423, pN_in_g(f(T423)))
pN_in_g(f(T375)) → U8_g(T375, pO_in_g(T375))
pO_in_g(T375) → U77_g(T375, rL_in_g(f(T375)))
rL_in_g(f(T322)) → U7_g(T322, pM_in_g(T322))
pM_in_g(T322) → U75_g(T322, qN25_in_g(T322))
qN25_in_g(f(f(T336))) → U32_g(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
pF_in_gg(T200, T201) → U4_gg(T200, T201, pG_in_gg(T200, T201))
pG_in_gg(T200, T201) → U69_gg(T200, T201, rN20_in_gg(T200, T201))
rN20_in_gg(T228, T229) → U26_gg(T228, T229, pN21_in_gg(T228, T229))
pN21_in_gg(T228, T229) → U71_gg(T228, T229, qA_in_gg(f(T228), T229))
qA_in_gg(T682, f(f(T683))) → U2_gg(T682, T683, pC_in_gg(T682, T683))
pC_in_gg(T682, T683) → U93_gg(T682, T683, rN37_in_gg(T682, T683))
rN37_in_gg(T710, T711) → U44_gg(T710, T711, pN38_in_gg(T710, T711))
pN38_in_gg(T710, T711) → U95_gg(T710, T711, qA_in_gg(T710, T711))
U95_gg(T710, T711, qA_out_gg(T710, T711)) → U96_gg(T710, T711, rN40_in_gg(T710, T711))
rN40_in_gg(a, b) → rN40_out_gg(a, b)
rN40_in_gg(T736, f(T737)) → U47_gg(T736, T737, pN38_in_gg(T736, T737))
U47_gg(T736, T737, pN38_out_gg(T736, T737)) → rN40_out_gg(T736, f(T737))
rN40_in_gg(f(T742), f(T742)) → U48_gg(T742, tJ_in_g(T742))
tJ_in_g(T270) → U6_g(T270, pK_in_g(T270))
pK_in_g(T270) → U73_g(T270, qH_in_g(f(T270)))
qH_in_g(f(f(T75))) → U5_g(T75, pI_in_g(T75))
pI_in_g(T75) → U57_g(T75, rN9_in_g(T75))
rN9_in_g(T89) → U20_g(T89, pN10_in_g(T89))
pN10_in_g(T89) → U59_g(T89, qN11_in_g(T89))
qN11_in_g(f(f(T113))) → U21_g(T113, pN12_in_g(T113))
pN12_in_g(T113) → U61_g(T113, rN13_in_g(T113))
rN13_in_g(T127) → U22_g(T127, pN14_in_g(T127))
pN14_in_g(T127) → U63_g(T127, qN15_in_g(T127))
qN15_in_g(f(f(T151))) → U23_g(T151, pN16_in_g(T151))
pN16_in_g(T151) → U65_g(T151, rN17_in_g(T151))
rN17_in_g(T165) → U24_g(T165, pN18_in_g(T165))
pN18_in_g(T165) → U67_g(T165, qN19_in_g(T165))
qN19_in_g(f(f(T179))) → U25_g(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
U25_g(T179, pF_out_gg(f(f(f(f(f(f(f(T179))))))), T179)) → qN19_out_g(f(f(T179)))
U67_g(T165, qN19_out_g(T165)) → U68_g(T165, rL_in_g(T165))
U68_g(T165, rL_out_g(T165)) → pN18_out_g(T165)
U24_g(T165, pN18_out_g(T165)) → rN17_out_g(T165)
U65_g(T151, rN17_out_g(T151)) → U66_g(T151, pN_in_g(T151))
U66_g(T151, pN_out_g(T151)) → pN16_out_g(T151)
U23_g(T151, pN16_out_g(T151)) → qN15_out_g(f(f(T151)))
U63_g(T127, qN15_out_g(T127)) → U64_g(T127, rP_in_g(T127))
U64_g(T127, rP_out_g(T127)) → pN14_out_g(T127)
U22_g(T127, pN14_out_g(T127)) → rN13_out_g(T127)
U61_g(T113, rN13_out_g(T113)) → U62_g(T113, pR_in_g(T113))
U62_g(T113, pR_out_g(T113)) → pN12_out_g(T113)
U21_g(T113, pN12_out_g(T113)) → qN11_out_g(f(f(T113)))
U59_g(T89, qN11_out_g(T89)) → U60_g(T89, rT_in_g(T89))
U60_g(T89, rT_out_g(T89)) → pN10_out_g(T89)
U20_g(T89, pN10_out_g(T89)) → rN9_out_g(T89)
U57_g(T75, rN9_out_g(T75)) → U58_g(T75, pV_in_g(T75))
U58_g(T75, pV_out_g(T75)) → pI_out_g(T75)
U5_g(T75, pI_out_g(T75)) → qH_out_g(f(f(T75)))
U73_g(T270, qH_out_g(f(T270))) → U74_g(T270, tN24_in_g(T270))
tN24_in_g(f(T281)) → U31_g(T281, pK_in_g(T281))
U31_g(T281, pK_out_g(T281)) → tN24_out_g(f(T281))
U74_g(T270, tN24_out_g(T270)) → pK_out_g(T270)
U6_g(T270, pK_out_g(T270)) → tJ_out_g(T270)
U48_gg(T742, tJ_out_g(T742)) → rN40_out_gg(f(T742), f(T742))
U96_gg(T710, T711, rN40_out_gg(T710, T711)) → pN38_out_gg(T710, T711)
U44_gg(T710, T711, pN38_out_gg(T710, T711)) → rN37_out_gg(T710, T711)
rN37_in_gg(f(T746), T746) → U45_gg(T746, tJ_in_g(T746))
U45_gg(T746, tJ_out_g(T746)) → rN37_out_gg(f(T746), T746)
U93_gg(T682, T683, rN37_out_gg(T682, T683)) → U94_gg(T682, T683, pN39_in_gg(T682, T683))
pN39_in_gg(a, b) → pN39_out_gg(a, b)
pN39_in_gg(T764, f(T765)) → U46_gg(T764, T765, pC_in_gg(T764, T765))
U46_gg(T764, T765, pC_out_gg(T764, T765)) → pN39_out_gg(T764, f(T765))
U94_gg(T682, T683, pN39_out_gg(T682, T683)) → pC_out_gg(T682, T683)
U2_gg(T682, T683, pC_out_gg(T682, T683)) → qA_out_gg(T682, f(f(T683)))
U71_gg(T228, T229, qA_out_gg(f(T228), T229)) → U72_gg(T228, T229, rN23_in_gg(T228, T229))
rN23_in_gg(T254, f(T255)) → U29_gg(T254, T255, pN21_in_gg(T254, T255))
U29_gg(T254, T255, pN21_out_gg(T254, T255)) → rN23_out_gg(T254, f(T255))
rN23_in_gg(T260, f(T260)) → U30_gg(T260, tJ_in_g(T260))
U30_gg(T260, tJ_out_g(T260)) → rN23_out_gg(T260, f(T260))
U72_gg(T228, T229, rN23_out_gg(T228, T229)) → pN21_out_gg(T228, T229)
U26_gg(T228, T229, pN21_out_gg(T228, T229)) → rN20_out_gg(T228, T229)
rN20_in_gg(T285, T285) → U27_gg(T285, tJ_in_g(T285))
U27_gg(T285, tJ_out_g(T285)) → rN20_out_gg(T285, T285)
U69_gg(T200, T201, rN20_out_gg(T200, T201)) → U70_gg(T200, T201, pN22_in_gg(T200, T201))
pN22_in_gg(T303, f(T304)) → U28_gg(T303, T304, pG_in_gg(T303, T304))
U28_gg(T303, T304, pG_out_gg(T303, T304)) → pN22_out_gg(T303, f(T304))
U70_gg(T200, T201, pN22_out_gg(T200, T201)) → pG_out_gg(T200, T201)
U4_gg(T200, T201, pG_out_gg(T200, T201)) → pF_out_gg(T200, T201)
U32_g(T336, pF_out_gg(f(f(f(f(f(f(f(f(T336)))))))), T336)) → qN25_out_g(f(f(T336)))
U75_g(T322, qN25_out_g(T322)) → U76_g(T322, rN26_in_g(T322))
rN26_in_g(f(T356)) → U33_g(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
U33_g(T356, pN21_out_gg(f(f(f(f(f(f(f(T356))))))), T356)) → rN26_out_g(f(T356))
U76_g(T322, rN26_out_g(T322)) → pM_out_g(T322)
U7_g(T322, pM_out_g(T322)) → rL_out_g(f(T322))
U77_g(T375, rL_out_g(f(T375))) → U78_g(T375, pN27_in_g(T375))
pN27_in_g(f(T389)) → U34_g(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
U34_g(T389, pG_out_gg(f(f(f(f(f(f(f(T389))))))), T389)) → pN27_out_g(f(T389))
U78_g(T375, pN27_out_g(T375)) → pO_out_g(T375)
U8_g(T375, pO_out_g(T375)) → pN_out_g(f(T375))
U35_g(T423, pN_out_g(f(T423))) → qN28_out_g(f(f(T423)))
U79_g(T409, qN28_out_g(T409)) → U80_g(T409, rN29_in_g(T409))
rN29_in_g(f(T440)) → U36_g(T440, pN18_in_g(T440))
U36_g(T440, pN18_out_g(T440)) → rN29_out_g(f(T440))
U80_g(T409, rN29_out_g(T409)) → pQ_out_g(T409)
U9_g(T409, pQ_out_g(T409)) → rP_out_g(f(T409))
U81_g(T456, rP_out_g(f(T456))) → U82_g(T456, pN30_in_g(T456))
pN30_in_g(f(T470)) → U37_g(T470, pN16_in_g(T470))
U37_g(T470, pN16_out_g(T470)) → pN30_out_g(f(T470))
U82_g(T456, pN30_out_g(T456)) → pS_out_g(T456)
U10_g(T456, pS_out_g(T456)) → pR_out_g(f(T456))
U38_g(T501, pR_out_g(f(T501))) → qN31_out_g(f(f(T501)))
U83_g(T487, qN31_out_g(T487)) → U84_g(T487, rN32_in_g(T487))
rN32_in_g(f(T518)) → U39_g(T518, pN14_in_g(T518))
U39_g(T518, pN14_out_g(T518)) → rN32_out_g(f(T518))
U84_g(T487, rN32_out_g(T487)) → pU_out_g(T487)
U11_g(T487, pU_out_g(T487)) → rT_out_g(f(T487))
U85_g(T534, rT_out_g(f(T534))) → U86_g(T534, pN33_in_g(T534))
pN33_in_g(f(T548)) → U40_g(T548, pN12_in_g(T548))
U40_g(T548, pN12_out_g(T548)) → pN33_out_g(f(T548))
U86_g(T534, pN33_out_g(T534)) → pW_out_g(T534)
U12_g(T534, pW_out_g(T534)) → pV_out_g(f(T534))
U41_g(T579, pV_out_g(f(T579))) → qN34_out_g(f(f(T579)))
U87_g(T565, qN34_out_g(T565)) → U88_g(T565, rN35_in_g(T565))
rN35_in_g(f(T596)) → U42_g(T596, pN10_in_g(T596))
U42_g(T596, pN10_out_g(T596)) → rN35_out_g(f(T596))
U88_g(T565, rN35_out_g(T565)) → pN1_out_g(T565)
U14_g(T565, pN1_out_g(T565)) → rZ_out_g(f(T565))
rZ_in_g(f(T601)) → U15_g(T601, tJ_in_g(T601))
U15_g(T601, tJ_out_g(T601)) → rZ_out_g(f(T601))
U91_g(T628, rZ_out_g(f(T628))) → U92_g(T628, pN36_in_g(T628))
pN36_in_g(f(T642)) → U43_g(T642, pI_in_g(T642))
U43_g(T642, pI_out_g(T642)) → pN36_out_g(f(T642))
U92_g(T628, pN36_out_g(T628)) → pN2_out_g(T628)
U16_g(T628, pN2_out_g(T628)) → pE_out_g(f(T628))
U3_g(T656, pE_out_g(f(T656))) → qD_out_g(f(T656))
U53_g(T36, qD_out_g(T36)) → U54_g(T36, rX_in_g(T36))
rX_in_g(T51) → U13_g(T51, pY_in_g(T51))
pY_in_g(T51) → U55_g(T51, qH_in_g(T51))
U55_g(T51, qH_out_g(T51)) → U56_g(T51, rZ_in_g(T51))
U56_g(T51, rZ_out_g(T51)) → pY_out_g(T51)
U13_g(T51, pY_out_g(T51)) → rX_out_g(T51)
U54_g(T36, rX_out_g(T36)) → pN6_out_g(T36)
U18_g(T36, pN6_out_g(T36)) → rN5_out_g(T36)
U51_g(T22, rN5_out_g(T22)) → U52_g(T22, pN7_in_g(T22))
pN7_in_g(T614) → U19_g(T614, pN8_in_g(T614))
pN8_in_g(T614) → U89_g(T614, rX_in_g(T614))
U89_g(T614, rX_out_g(T614)) → U90_g(T614, pE_in_g(T614))
U90_g(T614, pE_out_g(T614)) → pN8_out_g(T614)
U19_g(T614, pN8_out_g(T614)) → pN7_out_g(T614)
U52_g(T22, pN7_out_g(T22)) → pN4_out_g(T22)
U17_g(T22, pN4_out_g(T22)) → pN3_out_g(T22)
U49_g(T11, pN3_out_g(T11)) → U50_g(T11, qD_in_g(T11))
U50_g(T11, qD_out_g(T11)) → pB_out_g(T11)
U1_gg(T11, pB_out_g(T11)) → qA_out_gg(T11, f(f(T11)))

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

(4) Obligation:

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

QA_IN_GG(T11, f(f(T11))) → U1_GG(T11, pB_in_g(T11))
QA_IN_GG(T11, f(f(T11))) → PB_IN_G(T11)
PB_IN_G(T11) → U49_G(T11, pN3_in_g(T11))
PB_IN_G(T11) → PN3_IN_G(T11)
PN3_IN_G(T22) → U17_G(T22, pN4_in_g(T22))
PN3_IN_G(T22) → PN4_IN_G(T22)
PN4_IN_G(T22) → U51_G(T22, rN5_in_g(T22))
PN4_IN_G(T22) → RN5_IN_G(T22)
RN5_IN_G(T36) → U18_G(T36, pN6_in_g(T36))
RN5_IN_G(T36) → PN6_IN_G(T36)
PN6_IN_G(T36) → U53_G(T36, qD_in_g(T36))
PN6_IN_G(T36) → QD_IN_G(T36)
QD_IN_G(f(T656)) → U3_G(T656, pE_in_g(f(T656)))
QD_IN_G(f(T656)) → PE_IN_G(f(T656))
PE_IN_G(f(T628)) → U16_G(T628, pN2_in_g(T628))
PE_IN_G(f(T628)) → PN2_IN_G(T628)
PN2_IN_G(T628) → U91_G(T628, rZ_in_g(f(T628)))
PN2_IN_G(T628) → RZ_IN_G(f(T628))
RZ_IN_G(f(T565)) → U14_G(T565, pN1_in_g(T565))
RZ_IN_G(f(T565)) → PN1_IN_G(T565)
PN1_IN_G(T565) → U87_G(T565, qN34_in_g(T565))
PN1_IN_G(T565) → QN34_IN_G(T565)
QN34_IN_G(f(f(T579))) → U41_G(T579, pV_in_g(f(T579)))
QN34_IN_G(f(f(T579))) → PV_IN_G(f(T579))
PV_IN_G(f(T534)) → U12_G(T534, pW_in_g(T534))
PV_IN_G(f(T534)) → PW_IN_G(T534)
PW_IN_G(T534) → U85_G(T534, rT_in_g(f(T534)))
PW_IN_G(T534) → RT_IN_G(f(T534))
RT_IN_G(f(T487)) → U11_G(T487, pU_in_g(T487))
RT_IN_G(f(T487)) → PU_IN_G(T487)
PU_IN_G(T487) → U83_G(T487, qN31_in_g(T487))
PU_IN_G(T487) → QN31_IN_G(T487)
QN31_IN_G(f(f(T501))) → U38_G(T501, pR_in_g(f(T501)))
QN31_IN_G(f(f(T501))) → PR_IN_G(f(T501))
PR_IN_G(f(T456)) → U10_G(T456, pS_in_g(T456))
PR_IN_G(f(T456)) → PS_IN_G(T456)
PS_IN_G(T456) → U81_G(T456, rP_in_g(f(T456)))
PS_IN_G(T456) → RP_IN_G(f(T456))
RP_IN_G(f(T409)) → U9_G(T409, pQ_in_g(T409))
RP_IN_G(f(T409)) → PQ_IN_G(T409)
PQ_IN_G(T409) → U79_G(T409, qN28_in_g(T409))
PQ_IN_G(T409) → QN28_IN_G(T409)
QN28_IN_G(f(f(T423))) → U35_G(T423, pN_in_g(f(T423)))
QN28_IN_G(f(f(T423))) → PN_IN_G(f(T423))
PN_IN_G(f(T375)) → U8_G(T375, pO_in_g(T375))
PN_IN_G(f(T375)) → PO_IN_G(T375)
PO_IN_G(T375) → U77_G(T375, rL_in_g(f(T375)))
PO_IN_G(T375) → RL_IN_G(f(T375))
RL_IN_G(f(T322)) → U7_G(T322, pM_in_g(T322))
RL_IN_G(f(T322)) → PM_IN_G(T322)
PM_IN_G(T322) → U75_G(T322, qN25_in_g(T322))
PM_IN_G(T322) → QN25_IN_G(T322)
QN25_IN_G(f(f(T336))) → U32_G(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
QN25_IN_G(f(f(T336))) → PF_IN_GG(f(f(f(f(f(f(f(f(T336)))))))), T336)
PF_IN_GG(T200, T201) → U4_GG(T200, T201, pG_in_gg(T200, T201))
PF_IN_GG(T200, T201) → PG_IN_GG(T200, T201)
PG_IN_GG(T200, T201) → U69_GG(T200, T201, rN20_in_gg(T200, T201))
PG_IN_GG(T200, T201) → RN20_IN_GG(T200, T201)
RN20_IN_GG(T228, T229) → U26_GG(T228, T229, pN21_in_gg(T228, T229))
RN20_IN_GG(T228, T229) → PN21_IN_GG(T228, T229)
PN21_IN_GG(T228, T229) → U71_GG(T228, T229, qA_in_gg(f(T228), T229))
PN21_IN_GG(T228, T229) → QA_IN_GG(f(T228), T229)
QA_IN_GG(T682, f(f(T683))) → U2_GG(T682, T683, pC_in_gg(T682, T683))
QA_IN_GG(T682, f(f(T683))) → PC_IN_GG(T682, T683)
PC_IN_GG(T682, T683) → U93_GG(T682, T683, rN37_in_gg(T682, T683))
PC_IN_GG(T682, T683) → RN37_IN_GG(T682, T683)
RN37_IN_GG(T710, T711) → U44_GG(T710, T711, pN38_in_gg(T710, T711))
RN37_IN_GG(T710, T711) → PN38_IN_GG(T710, T711)
PN38_IN_GG(T710, T711) → U95_GG(T710, T711, qA_in_gg(T710, T711))
PN38_IN_GG(T710, T711) → QA_IN_GG(T710, T711)
U95_GG(T710, T711, qA_out_gg(T710, T711)) → U96_GG(T710, T711, rN40_in_gg(T710, T711))
U95_GG(T710, T711, qA_out_gg(T710, T711)) → RN40_IN_GG(T710, T711)
RN40_IN_GG(T736, f(T737)) → U47_GG(T736, T737, pN38_in_gg(T736, T737))
RN40_IN_GG(T736, f(T737)) → PN38_IN_GG(T736, T737)
RN40_IN_GG(f(T742), f(T742)) → U48_GG(T742, tJ_in_g(T742))
RN40_IN_GG(f(T742), f(T742)) → TJ_IN_G(T742)
TJ_IN_G(T270) → U6_G(T270, pK_in_g(T270))
TJ_IN_G(T270) → PK_IN_G(T270)
PK_IN_G(T270) → U73_G(T270, qH_in_g(f(T270)))
PK_IN_G(T270) → QH_IN_G(f(T270))
QH_IN_G(f(f(T75))) → U5_G(T75, pI_in_g(T75))
QH_IN_G(f(f(T75))) → PI_IN_G(T75)
PI_IN_G(T75) → U57_G(T75, rN9_in_g(T75))
PI_IN_G(T75) → RN9_IN_G(T75)
RN9_IN_G(T89) → U20_G(T89, pN10_in_g(T89))
RN9_IN_G(T89) → PN10_IN_G(T89)
PN10_IN_G(T89) → U59_G(T89, qN11_in_g(T89))
PN10_IN_G(T89) → QN11_IN_G(T89)
QN11_IN_G(f(f(T113))) → U21_G(T113, pN12_in_g(T113))
QN11_IN_G(f(f(T113))) → PN12_IN_G(T113)
PN12_IN_G(T113) → U61_G(T113, rN13_in_g(T113))
PN12_IN_G(T113) → RN13_IN_G(T113)
RN13_IN_G(T127) → U22_G(T127, pN14_in_g(T127))
RN13_IN_G(T127) → PN14_IN_G(T127)
PN14_IN_G(T127) → U63_G(T127, qN15_in_g(T127))
PN14_IN_G(T127) → QN15_IN_G(T127)
QN15_IN_G(f(f(T151))) → U23_G(T151, pN16_in_g(T151))
QN15_IN_G(f(f(T151))) → PN16_IN_G(T151)
PN16_IN_G(T151) → U65_G(T151, rN17_in_g(T151))
PN16_IN_G(T151) → RN17_IN_G(T151)
RN17_IN_G(T165) → U24_G(T165, pN18_in_g(T165))
RN17_IN_G(T165) → PN18_IN_G(T165)
PN18_IN_G(T165) → U67_G(T165, qN19_in_g(T165))
PN18_IN_G(T165) → QN19_IN_G(T165)
QN19_IN_G(f(f(T179))) → U25_G(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
QN19_IN_G(f(f(T179))) → PF_IN_GG(f(f(f(f(f(f(f(T179))))))), T179)
U67_G(T165, qN19_out_g(T165)) → U68_G(T165, rL_in_g(T165))
U67_G(T165, qN19_out_g(T165)) → RL_IN_G(T165)
U65_G(T151, rN17_out_g(T151)) → U66_G(T151, pN_in_g(T151))
U65_G(T151, rN17_out_g(T151)) → PN_IN_G(T151)
U63_G(T127, qN15_out_g(T127)) → U64_G(T127, rP_in_g(T127))
U63_G(T127, qN15_out_g(T127)) → RP_IN_G(T127)
U61_G(T113, rN13_out_g(T113)) → U62_G(T113, pR_in_g(T113))
U61_G(T113, rN13_out_g(T113)) → PR_IN_G(T113)
U59_G(T89, qN11_out_g(T89)) → U60_G(T89, rT_in_g(T89))
U59_G(T89, qN11_out_g(T89)) → RT_IN_G(T89)
U57_G(T75, rN9_out_g(T75)) → U58_G(T75, pV_in_g(T75))
U57_G(T75, rN9_out_g(T75)) → PV_IN_G(T75)
U73_G(T270, qH_out_g(f(T270))) → U74_G(T270, tN24_in_g(T270))
U73_G(T270, qH_out_g(f(T270))) → TN24_IN_G(T270)
TN24_IN_G(f(T281)) → U31_G(T281, pK_in_g(T281))
TN24_IN_G(f(T281)) → PK_IN_G(T281)
RN37_IN_GG(f(T746), T746) → U45_GG(T746, tJ_in_g(T746))
RN37_IN_GG(f(T746), T746) → TJ_IN_G(T746)
U93_GG(T682, T683, rN37_out_gg(T682, T683)) → U94_GG(T682, T683, pN39_in_gg(T682, T683))
U93_GG(T682, T683, rN37_out_gg(T682, T683)) → PN39_IN_GG(T682, T683)
PN39_IN_GG(T764, f(T765)) → U46_GG(T764, T765, pC_in_gg(T764, T765))
PN39_IN_GG(T764, f(T765)) → PC_IN_GG(T764, T765)
U71_GG(T228, T229, qA_out_gg(f(T228), T229)) → U72_GG(T228, T229, rN23_in_gg(T228, T229))
U71_GG(T228, T229, qA_out_gg(f(T228), T229)) → RN23_IN_GG(T228, T229)
RN23_IN_GG(T254, f(T255)) → U29_GG(T254, T255, pN21_in_gg(T254, T255))
RN23_IN_GG(T254, f(T255)) → PN21_IN_GG(T254, T255)
RN23_IN_GG(T260, f(T260)) → U30_GG(T260, tJ_in_g(T260))
RN23_IN_GG(T260, f(T260)) → TJ_IN_G(T260)
RN20_IN_GG(T285, T285) → U27_GG(T285, tJ_in_g(T285))
RN20_IN_GG(T285, T285) → TJ_IN_G(T285)
U69_GG(T200, T201, rN20_out_gg(T200, T201)) → U70_GG(T200, T201, pN22_in_gg(T200, T201))
U69_GG(T200, T201, rN20_out_gg(T200, T201)) → PN22_IN_GG(T200, T201)
PN22_IN_GG(T303, f(T304)) → U28_GG(T303, T304, pG_in_gg(T303, T304))
PN22_IN_GG(T303, f(T304)) → PG_IN_GG(T303, T304)
U75_G(T322, qN25_out_g(T322)) → U76_G(T322, rN26_in_g(T322))
U75_G(T322, qN25_out_g(T322)) → RN26_IN_G(T322)
RN26_IN_G(f(T356)) → U33_G(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
RN26_IN_G(f(T356)) → PN21_IN_GG(f(f(f(f(f(f(f(T356))))))), T356)
U77_G(T375, rL_out_g(f(T375))) → U78_G(T375, pN27_in_g(T375))
U77_G(T375, rL_out_g(f(T375))) → PN27_IN_G(T375)
PN27_IN_G(f(T389)) → U34_G(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
PN27_IN_G(f(T389)) → PG_IN_GG(f(f(f(f(f(f(f(T389))))))), T389)
U79_G(T409, qN28_out_g(T409)) → U80_G(T409, rN29_in_g(T409))
U79_G(T409, qN28_out_g(T409)) → RN29_IN_G(T409)
RN29_IN_G(f(T440)) → U36_G(T440, pN18_in_g(T440))
RN29_IN_G(f(T440)) → PN18_IN_G(T440)
U81_G(T456, rP_out_g(f(T456))) → U82_G(T456, pN30_in_g(T456))
U81_G(T456, rP_out_g(f(T456))) → PN30_IN_G(T456)
PN30_IN_G(f(T470)) → U37_G(T470, pN16_in_g(T470))
PN30_IN_G(f(T470)) → PN16_IN_G(T470)
U83_G(T487, qN31_out_g(T487)) → U84_G(T487, rN32_in_g(T487))
U83_G(T487, qN31_out_g(T487)) → RN32_IN_G(T487)
RN32_IN_G(f(T518)) → U39_G(T518, pN14_in_g(T518))
RN32_IN_G(f(T518)) → PN14_IN_G(T518)
U85_G(T534, rT_out_g(f(T534))) → U86_G(T534, pN33_in_g(T534))
U85_G(T534, rT_out_g(f(T534))) → PN33_IN_G(T534)
PN33_IN_G(f(T548)) → U40_G(T548, pN12_in_g(T548))
PN33_IN_G(f(T548)) → PN12_IN_G(T548)
U87_G(T565, qN34_out_g(T565)) → U88_G(T565, rN35_in_g(T565))
U87_G(T565, qN34_out_g(T565)) → RN35_IN_G(T565)
RN35_IN_G(f(T596)) → U42_G(T596, pN10_in_g(T596))
RN35_IN_G(f(T596)) → PN10_IN_G(T596)
RZ_IN_G(f(T601)) → U15_G(T601, tJ_in_g(T601))
RZ_IN_G(f(T601)) → TJ_IN_G(T601)
U91_G(T628, rZ_out_g(f(T628))) → U92_G(T628, pN36_in_g(T628))
U91_G(T628, rZ_out_g(f(T628))) → PN36_IN_G(T628)
PN36_IN_G(f(T642)) → U43_G(T642, pI_in_g(T642))
PN36_IN_G(f(T642)) → PI_IN_G(T642)
U53_G(T36, qD_out_g(T36)) → U54_G(T36, rX_in_g(T36))
U53_G(T36, qD_out_g(T36)) → RX_IN_G(T36)
RX_IN_G(T51) → U13_G(T51, pY_in_g(T51))
RX_IN_G(T51) → PY_IN_G(T51)
PY_IN_G(T51) → U55_G(T51, qH_in_g(T51))
PY_IN_G(T51) → QH_IN_G(T51)
U55_G(T51, qH_out_g(T51)) → U56_G(T51, rZ_in_g(T51))
U55_G(T51, qH_out_g(T51)) → RZ_IN_G(T51)
U51_G(T22, rN5_out_g(T22)) → U52_G(T22, pN7_in_g(T22))
U51_G(T22, rN5_out_g(T22)) → PN7_IN_G(T22)
PN7_IN_G(T614) → U19_G(T614, pN8_in_g(T614))
PN7_IN_G(T614) → PN8_IN_G(T614)
PN8_IN_G(T614) → U89_G(T614, rX_in_g(T614))
PN8_IN_G(T614) → RX_IN_G(T614)
U89_G(T614, rX_out_g(T614)) → U90_G(T614, pE_in_g(T614))
U89_G(T614, rX_out_g(T614)) → PE_IN_G(T614)
U49_G(T11, pN3_out_g(T11)) → U50_G(T11, qD_in_g(T11))
U49_G(T11, pN3_out_g(T11)) → QD_IN_G(T11)

The TRS R consists of the following rules:

qA_in_gg(a, b) → qA_out_gg(a, b)
qA_in_gg(T11, f(f(T11))) → U1_gg(T11, pB_in_g(T11))
pB_in_g(T11) → U49_g(T11, pN3_in_g(T11))
pN3_in_g(T22) → U17_g(T22, pN4_in_g(T22))
pN4_in_g(T22) → U51_g(T22, rN5_in_g(T22))
rN5_in_g(T36) → U18_g(T36, pN6_in_g(T36))
pN6_in_g(T36) → U53_g(T36, qD_in_g(T36))
qD_in_g(f(T656)) → U3_g(T656, pE_in_g(f(T656)))
pE_in_g(f(T628)) → U16_g(T628, pN2_in_g(T628))
pN2_in_g(T628) → U91_g(T628, rZ_in_g(f(T628)))
rZ_in_g(f(T565)) → U14_g(T565, pN1_in_g(T565))
pN1_in_g(T565) → U87_g(T565, qN34_in_g(T565))
qN34_in_g(f(f(T579))) → U41_g(T579, pV_in_g(f(T579)))
pV_in_g(f(T534)) → U12_g(T534, pW_in_g(T534))
pW_in_g(T534) → U85_g(T534, rT_in_g(f(T534)))
rT_in_g(f(T487)) → U11_g(T487, pU_in_g(T487))
pU_in_g(T487) → U83_g(T487, qN31_in_g(T487))
qN31_in_g(f(f(T501))) → U38_g(T501, pR_in_g(f(T501)))
pR_in_g(f(T456)) → U10_g(T456, pS_in_g(T456))
pS_in_g(T456) → U81_g(T456, rP_in_g(f(T456)))
rP_in_g(f(T409)) → U9_g(T409, pQ_in_g(T409))
pQ_in_g(T409) → U79_g(T409, qN28_in_g(T409))
qN28_in_g(f(f(T423))) → U35_g(T423, pN_in_g(f(T423)))
pN_in_g(f(T375)) → U8_g(T375, pO_in_g(T375))
pO_in_g(T375) → U77_g(T375, rL_in_g(f(T375)))
rL_in_g(f(T322)) → U7_g(T322, pM_in_g(T322))
pM_in_g(T322) → U75_g(T322, qN25_in_g(T322))
qN25_in_g(f(f(T336))) → U32_g(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
pF_in_gg(T200, T201) → U4_gg(T200, T201, pG_in_gg(T200, T201))
pG_in_gg(T200, T201) → U69_gg(T200, T201, rN20_in_gg(T200, T201))
rN20_in_gg(T228, T229) → U26_gg(T228, T229, pN21_in_gg(T228, T229))
pN21_in_gg(T228, T229) → U71_gg(T228, T229, qA_in_gg(f(T228), T229))
qA_in_gg(T682, f(f(T683))) → U2_gg(T682, T683, pC_in_gg(T682, T683))
pC_in_gg(T682, T683) → U93_gg(T682, T683, rN37_in_gg(T682, T683))
rN37_in_gg(T710, T711) → U44_gg(T710, T711, pN38_in_gg(T710, T711))
pN38_in_gg(T710, T711) → U95_gg(T710, T711, qA_in_gg(T710, T711))
U95_gg(T710, T711, qA_out_gg(T710, T711)) → U96_gg(T710, T711, rN40_in_gg(T710, T711))
rN40_in_gg(a, b) → rN40_out_gg(a, b)
rN40_in_gg(T736, f(T737)) → U47_gg(T736, T737, pN38_in_gg(T736, T737))
U47_gg(T736, T737, pN38_out_gg(T736, T737)) → rN40_out_gg(T736, f(T737))
rN40_in_gg(f(T742), f(T742)) → U48_gg(T742, tJ_in_g(T742))
tJ_in_g(T270) → U6_g(T270, pK_in_g(T270))
pK_in_g(T270) → U73_g(T270, qH_in_g(f(T270)))
qH_in_g(f(f(T75))) → U5_g(T75, pI_in_g(T75))
pI_in_g(T75) → U57_g(T75, rN9_in_g(T75))
rN9_in_g(T89) → U20_g(T89, pN10_in_g(T89))
pN10_in_g(T89) → U59_g(T89, qN11_in_g(T89))
qN11_in_g(f(f(T113))) → U21_g(T113, pN12_in_g(T113))
pN12_in_g(T113) → U61_g(T113, rN13_in_g(T113))
rN13_in_g(T127) → U22_g(T127, pN14_in_g(T127))
pN14_in_g(T127) → U63_g(T127, qN15_in_g(T127))
qN15_in_g(f(f(T151))) → U23_g(T151, pN16_in_g(T151))
pN16_in_g(T151) → U65_g(T151, rN17_in_g(T151))
rN17_in_g(T165) → U24_g(T165, pN18_in_g(T165))
pN18_in_g(T165) → U67_g(T165, qN19_in_g(T165))
qN19_in_g(f(f(T179))) → U25_g(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
U25_g(T179, pF_out_gg(f(f(f(f(f(f(f(T179))))))), T179)) → qN19_out_g(f(f(T179)))
U67_g(T165, qN19_out_g(T165)) → U68_g(T165, rL_in_g(T165))
U68_g(T165, rL_out_g(T165)) → pN18_out_g(T165)
U24_g(T165, pN18_out_g(T165)) → rN17_out_g(T165)
U65_g(T151, rN17_out_g(T151)) → U66_g(T151, pN_in_g(T151))
U66_g(T151, pN_out_g(T151)) → pN16_out_g(T151)
U23_g(T151, pN16_out_g(T151)) → qN15_out_g(f(f(T151)))
U63_g(T127, qN15_out_g(T127)) → U64_g(T127, rP_in_g(T127))
U64_g(T127, rP_out_g(T127)) → pN14_out_g(T127)
U22_g(T127, pN14_out_g(T127)) → rN13_out_g(T127)
U61_g(T113, rN13_out_g(T113)) → U62_g(T113, pR_in_g(T113))
U62_g(T113, pR_out_g(T113)) → pN12_out_g(T113)
U21_g(T113, pN12_out_g(T113)) → qN11_out_g(f(f(T113)))
U59_g(T89, qN11_out_g(T89)) → U60_g(T89, rT_in_g(T89))
U60_g(T89, rT_out_g(T89)) → pN10_out_g(T89)
U20_g(T89, pN10_out_g(T89)) → rN9_out_g(T89)
U57_g(T75, rN9_out_g(T75)) → U58_g(T75, pV_in_g(T75))
U58_g(T75, pV_out_g(T75)) → pI_out_g(T75)
U5_g(T75, pI_out_g(T75)) → qH_out_g(f(f(T75)))
U73_g(T270, qH_out_g(f(T270))) → U74_g(T270, tN24_in_g(T270))
tN24_in_g(f(T281)) → U31_g(T281, pK_in_g(T281))
U31_g(T281, pK_out_g(T281)) → tN24_out_g(f(T281))
U74_g(T270, tN24_out_g(T270)) → pK_out_g(T270)
U6_g(T270, pK_out_g(T270)) → tJ_out_g(T270)
U48_gg(T742, tJ_out_g(T742)) → rN40_out_gg(f(T742), f(T742))
U96_gg(T710, T711, rN40_out_gg(T710, T711)) → pN38_out_gg(T710, T711)
U44_gg(T710, T711, pN38_out_gg(T710, T711)) → rN37_out_gg(T710, T711)
rN37_in_gg(f(T746), T746) → U45_gg(T746, tJ_in_g(T746))
U45_gg(T746, tJ_out_g(T746)) → rN37_out_gg(f(T746), T746)
U93_gg(T682, T683, rN37_out_gg(T682, T683)) → U94_gg(T682, T683, pN39_in_gg(T682, T683))
pN39_in_gg(a, b) → pN39_out_gg(a, b)
pN39_in_gg(T764, f(T765)) → U46_gg(T764, T765, pC_in_gg(T764, T765))
U46_gg(T764, T765, pC_out_gg(T764, T765)) → pN39_out_gg(T764, f(T765))
U94_gg(T682, T683, pN39_out_gg(T682, T683)) → pC_out_gg(T682, T683)
U2_gg(T682, T683, pC_out_gg(T682, T683)) → qA_out_gg(T682, f(f(T683)))
U71_gg(T228, T229, qA_out_gg(f(T228), T229)) → U72_gg(T228, T229, rN23_in_gg(T228, T229))
rN23_in_gg(T254, f(T255)) → U29_gg(T254, T255, pN21_in_gg(T254, T255))
U29_gg(T254, T255, pN21_out_gg(T254, T255)) → rN23_out_gg(T254, f(T255))
rN23_in_gg(T260, f(T260)) → U30_gg(T260, tJ_in_g(T260))
U30_gg(T260, tJ_out_g(T260)) → rN23_out_gg(T260, f(T260))
U72_gg(T228, T229, rN23_out_gg(T228, T229)) → pN21_out_gg(T228, T229)
U26_gg(T228, T229, pN21_out_gg(T228, T229)) → rN20_out_gg(T228, T229)
rN20_in_gg(T285, T285) → U27_gg(T285, tJ_in_g(T285))
U27_gg(T285, tJ_out_g(T285)) → rN20_out_gg(T285, T285)
U69_gg(T200, T201, rN20_out_gg(T200, T201)) → U70_gg(T200, T201, pN22_in_gg(T200, T201))
pN22_in_gg(T303, f(T304)) → U28_gg(T303, T304, pG_in_gg(T303, T304))
U28_gg(T303, T304, pG_out_gg(T303, T304)) → pN22_out_gg(T303, f(T304))
U70_gg(T200, T201, pN22_out_gg(T200, T201)) → pG_out_gg(T200, T201)
U4_gg(T200, T201, pG_out_gg(T200, T201)) → pF_out_gg(T200, T201)
U32_g(T336, pF_out_gg(f(f(f(f(f(f(f(f(T336)))))))), T336)) → qN25_out_g(f(f(T336)))
U75_g(T322, qN25_out_g(T322)) → U76_g(T322, rN26_in_g(T322))
rN26_in_g(f(T356)) → U33_g(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
U33_g(T356, pN21_out_gg(f(f(f(f(f(f(f(T356))))))), T356)) → rN26_out_g(f(T356))
U76_g(T322, rN26_out_g(T322)) → pM_out_g(T322)
U7_g(T322, pM_out_g(T322)) → rL_out_g(f(T322))
U77_g(T375, rL_out_g(f(T375))) → U78_g(T375, pN27_in_g(T375))
pN27_in_g(f(T389)) → U34_g(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
U34_g(T389, pG_out_gg(f(f(f(f(f(f(f(T389))))))), T389)) → pN27_out_g(f(T389))
U78_g(T375, pN27_out_g(T375)) → pO_out_g(T375)
U8_g(T375, pO_out_g(T375)) → pN_out_g(f(T375))
U35_g(T423, pN_out_g(f(T423))) → qN28_out_g(f(f(T423)))
U79_g(T409, qN28_out_g(T409)) → U80_g(T409, rN29_in_g(T409))
rN29_in_g(f(T440)) → U36_g(T440, pN18_in_g(T440))
U36_g(T440, pN18_out_g(T440)) → rN29_out_g(f(T440))
U80_g(T409, rN29_out_g(T409)) → pQ_out_g(T409)
U9_g(T409, pQ_out_g(T409)) → rP_out_g(f(T409))
U81_g(T456, rP_out_g(f(T456))) → U82_g(T456, pN30_in_g(T456))
pN30_in_g(f(T470)) → U37_g(T470, pN16_in_g(T470))
U37_g(T470, pN16_out_g(T470)) → pN30_out_g(f(T470))
U82_g(T456, pN30_out_g(T456)) → pS_out_g(T456)
U10_g(T456, pS_out_g(T456)) → pR_out_g(f(T456))
U38_g(T501, pR_out_g(f(T501))) → qN31_out_g(f(f(T501)))
U83_g(T487, qN31_out_g(T487)) → U84_g(T487, rN32_in_g(T487))
rN32_in_g(f(T518)) → U39_g(T518, pN14_in_g(T518))
U39_g(T518, pN14_out_g(T518)) → rN32_out_g(f(T518))
U84_g(T487, rN32_out_g(T487)) → pU_out_g(T487)
U11_g(T487, pU_out_g(T487)) → rT_out_g(f(T487))
U85_g(T534, rT_out_g(f(T534))) → U86_g(T534, pN33_in_g(T534))
pN33_in_g(f(T548)) → U40_g(T548, pN12_in_g(T548))
U40_g(T548, pN12_out_g(T548)) → pN33_out_g(f(T548))
U86_g(T534, pN33_out_g(T534)) → pW_out_g(T534)
U12_g(T534, pW_out_g(T534)) → pV_out_g(f(T534))
U41_g(T579, pV_out_g(f(T579))) → qN34_out_g(f(f(T579)))
U87_g(T565, qN34_out_g(T565)) → U88_g(T565, rN35_in_g(T565))
rN35_in_g(f(T596)) → U42_g(T596, pN10_in_g(T596))
U42_g(T596, pN10_out_g(T596)) → rN35_out_g(f(T596))
U88_g(T565, rN35_out_g(T565)) → pN1_out_g(T565)
U14_g(T565, pN1_out_g(T565)) → rZ_out_g(f(T565))
rZ_in_g(f(T601)) → U15_g(T601, tJ_in_g(T601))
U15_g(T601, tJ_out_g(T601)) → rZ_out_g(f(T601))
U91_g(T628, rZ_out_g(f(T628))) → U92_g(T628, pN36_in_g(T628))
pN36_in_g(f(T642)) → U43_g(T642, pI_in_g(T642))
U43_g(T642, pI_out_g(T642)) → pN36_out_g(f(T642))
U92_g(T628, pN36_out_g(T628)) → pN2_out_g(T628)
U16_g(T628, pN2_out_g(T628)) → pE_out_g(f(T628))
U3_g(T656, pE_out_g(f(T656))) → qD_out_g(f(T656))
U53_g(T36, qD_out_g(T36)) → U54_g(T36, rX_in_g(T36))
rX_in_g(T51) → U13_g(T51, pY_in_g(T51))
pY_in_g(T51) → U55_g(T51, qH_in_g(T51))
U55_g(T51, qH_out_g(T51)) → U56_g(T51, rZ_in_g(T51))
U56_g(T51, rZ_out_g(T51)) → pY_out_g(T51)
U13_g(T51, pY_out_g(T51)) → rX_out_g(T51)
U54_g(T36, rX_out_g(T36)) → pN6_out_g(T36)
U18_g(T36, pN6_out_g(T36)) → rN5_out_g(T36)
U51_g(T22, rN5_out_g(T22)) → U52_g(T22, pN7_in_g(T22))
pN7_in_g(T614) → U19_g(T614, pN8_in_g(T614))
pN8_in_g(T614) → U89_g(T614, rX_in_g(T614))
U89_g(T614, rX_out_g(T614)) → U90_g(T614, pE_in_g(T614))
U90_g(T614, pE_out_g(T614)) → pN8_out_g(T614)
U19_g(T614, pN8_out_g(T614)) → pN7_out_g(T614)
U52_g(T22, pN7_out_g(T22)) → pN4_out_g(T22)
U17_g(T22, pN4_out_g(T22)) → pN3_out_g(T22)
U49_g(T11, pN3_out_g(T11)) → U50_g(T11, qD_in_g(T11))
U50_g(T11, qD_out_g(T11)) → pB_out_g(T11)
U1_gg(T11, pB_out_g(T11)) → qA_out_gg(T11, f(f(T11)))

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

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 72 less nodes.

(6) Obligation:

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

QA_IN_GG(T11, f(f(T11))) → PB_IN_G(T11)
PB_IN_G(T11) → U49_G(T11, pN3_in_g(T11))
U49_G(T11, pN3_out_g(T11)) → QD_IN_G(T11)
QD_IN_G(f(T656)) → PE_IN_G(f(T656))
PE_IN_G(f(T628)) → PN2_IN_G(T628)
PN2_IN_G(T628) → U91_G(T628, rZ_in_g(f(T628)))
U91_G(T628, rZ_out_g(f(T628))) → PN36_IN_G(T628)
PN36_IN_G(f(T642)) → PI_IN_G(T642)
PI_IN_G(T75) → U57_G(T75, rN9_in_g(T75))
U57_G(T75, rN9_out_g(T75)) → PV_IN_G(T75)
PV_IN_G(f(T534)) → PW_IN_G(T534)
PW_IN_G(T534) → U85_G(T534, rT_in_g(f(T534)))
U85_G(T534, rT_out_g(f(T534))) → PN33_IN_G(T534)
PN33_IN_G(f(T548)) → PN12_IN_G(T548)
PN12_IN_G(T113) → U61_G(T113, rN13_in_g(T113))
U61_G(T113, rN13_out_g(T113)) → PR_IN_G(T113)
PR_IN_G(f(T456)) → PS_IN_G(T456)
PS_IN_G(T456) → U81_G(T456, rP_in_g(f(T456)))
U81_G(T456, rP_out_g(f(T456))) → PN30_IN_G(T456)
PN30_IN_G(f(T470)) → PN16_IN_G(T470)
PN16_IN_G(T151) → U65_G(T151, rN17_in_g(T151))
U65_G(T151, rN17_out_g(T151)) → PN_IN_G(T151)
PN_IN_G(f(T375)) → PO_IN_G(T375)
PO_IN_G(T375) → U77_G(T375, rL_in_g(f(T375)))
U77_G(T375, rL_out_g(f(T375))) → PN27_IN_G(T375)
PN27_IN_G(f(T389)) → PG_IN_GG(f(f(f(f(f(f(f(T389))))))), T389)
PG_IN_GG(T200, T201) → U69_GG(T200, T201, rN20_in_gg(T200, T201))
U69_GG(T200, T201, rN20_out_gg(T200, T201)) → PN22_IN_GG(T200, T201)
PN22_IN_GG(T303, f(T304)) → PG_IN_GG(T303, T304)
PG_IN_GG(T200, T201) → RN20_IN_GG(T200, T201)
RN20_IN_GG(T228, T229) → PN21_IN_GG(T228, T229)
PN21_IN_GG(T228, T229) → U71_GG(T228, T229, qA_in_gg(f(T228), T229))
U71_GG(T228, T229, qA_out_gg(f(T228), T229)) → RN23_IN_GG(T228, T229)
RN23_IN_GG(T254, f(T255)) → PN21_IN_GG(T254, T255)
PN21_IN_GG(T228, T229) → QA_IN_GG(f(T228), T229)
QA_IN_GG(T682, f(f(T683))) → PC_IN_GG(T682, T683)
PC_IN_GG(T682, T683) → U93_GG(T682, T683, rN37_in_gg(T682, T683))
U93_GG(T682, T683, rN37_out_gg(T682, T683)) → PN39_IN_GG(T682, T683)
PN39_IN_GG(T764, f(T765)) → PC_IN_GG(T764, T765)
PC_IN_GG(T682, T683) → RN37_IN_GG(T682, T683)
RN37_IN_GG(T710, T711) → PN38_IN_GG(T710, T711)
PN38_IN_GG(T710, T711) → U95_GG(T710, T711, qA_in_gg(T710, T711))
U95_GG(T710, T711, qA_out_gg(T710, T711)) → RN40_IN_GG(T710, T711)
RN40_IN_GG(T736, f(T737)) → PN38_IN_GG(T736, T737)
PN38_IN_GG(T710, T711) → QA_IN_GG(T710, T711)
RN40_IN_GG(f(T742), f(T742)) → TJ_IN_G(T742)
TJ_IN_G(T270) → PK_IN_G(T270)
PK_IN_G(T270) → U73_G(T270, qH_in_g(f(T270)))
U73_G(T270, qH_out_g(f(T270))) → TN24_IN_G(T270)
TN24_IN_G(f(T281)) → PK_IN_G(T281)
PK_IN_G(T270) → QH_IN_G(f(T270))
QH_IN_G(f(f(T75))) → PI_IN_G(T75)
PI_IN_G(T75) → RN9_IN_G(T75)
RN9_IN_G(T89) → PN10_IN_G(T89)
PN10_IN_G(T89) → U59_G(T89, qN11_in_g(T89))
U59_G(T89, qN11_out_g(T89)) → RT_IN_G(T89)
RT_IN_G(f(T487)) → PU_IN_G(T487)
PU_IN_G(T487) → U83_G(T487, qN31_in_g(T487))
U83_G(T487, qN31_out_g(T487)) → RN32_IN_G(T487)
RN32_IN_G(f(T518)) → PN14_IN_G(T518)
PN14_IN_G(T127) → U63_G(T127, qN15_in_g(T127))
U63_G(T127, qN15_out_g(T127)) → RP_IN_G(T127)
RP_IN_G(f(T409)) → PQ_IN_G(T409)
PQ_IN_G(T409) → U79_G(T409, qN28_in_g(T409))
U79_G(T409, qN28_out_g(T409)) → RN29_IN_G(T409)
RN29_IN_G(f(T440)) → PN18_IN_G(T440)
PN18_IN_G(T165) → U67_G(T165, qN19_in_g(T165))
U67_G(T165, qN19_out_g(T165)) → RL_IN_G(T165)
RL_IN_G(f(T322)) → PM_IN_G(T322)
PM_IN_G(T322) → U75_G(T322, qN25_in_g(T322))
U75_G(T322, qN25_out_g(T322)) → RN26_IN_G(T322)
RN26_IN_G(f(T356)) → PN21_IN_GG(f(f(f(f(f(f(f(T356))))))), T356)
PM_IN_G(T322) → QN25_IN_G(T322)
QN25_IN_G(f(f(T336))) → PF_IN_GG(f(f(f(f(f(f(f(f(T336)))))))), T336)
PF_IN_GG(T200, T201) → PG_IN_GG(T200, T201)
PN18_IN_G(T165) → QN19_IN_G(T165)
QN19_IN_G(f(f(T179))) → PF_IN_GG(f(f(f(f(f(f(f(T179))))))), T179)
PQ_IN_G(T409) → QN28_IN_G(T409)
QN28_IN_G(f(f(T423))) → PN_IN_G(f(T423))
PN14_IN_G(T127) → QN15_IN_G(T127)
QN15_IN_G(f(f(T151))) → PN16_IN_G(T151)
PN16_IN_G(T151) → RN17_IN_G(T151)
RN17_IN_G(T165) → PN18_IN_G(T165)
PU_IN_G(T487) → QN31_IN_G(T487)
QN31_IN_G(f(f(T501))) → PR_IN_G(f(T501))
PN10_IN_G(T89) → QN11_IN_G(T89)
QN11_IN_G(f(f(T113))) → PN12_IN_G(T113)
PN12_IN_G(T113) → RN13_IN_G(T113)
RN13_IN_G(T127) → PN14_IN_G(T127)
RN37_IN_GG(f(T746), T746) → TJ_IN_G(T746)
RN23_IN_GG(T260, f(T260)) → TJ_IN_G(T260)
RN20_IN_GG(T285, T285) → TJ_IN_G(T285)
PO_IN_G(T375) → RL_IN_G(f(T375))
PS_IN_G(T456) → RP_IN_G(f(T456))
PW_IN_G(T534) → RT_IN_G(f(T534))
PN2_IN_G(T628) → RZ_IN_G(f(T628))
RZ_IN_G(f(T565)) → PN1_IN_G(T565)
PN1_IN_G(T565) → U87_G(T565, qN34_in_g(T565))
U87_G(T565, qN34_out_g(T565)) → RN35_IN_G(T565)
RN35_IN_G(f(T596)) → PN10_IN_G(T596)
PN1_IN_G(T565) → QN34_IN_G(T565)
QN34_IN_G(f(f(T579))) → PV_IN_G(f(T579))
RZ_IN_G(f(T601)) → TJ_IN_G(T601)
PB_IN_G(T11) → PN3_IN_G(T11)
PN3_IN_G(T22) → PN4_IN_G(T22)
PN4_IN_G(T22) → U51_G(T22, rN5_in_g(T22))
U51_G(T22, rN5_out_g(T22)) → PN7_IN_G(T22)
PN7_IN_G(T614) → PN8_IN_G(T614)
PN8_IN_G(T614) → U89_G(T614, rX_in_g(T614))
U89_G(T614, rX_out_g(T614)) → PE_IN_G(T614)
PN8_IN_G(T614) → RX_IN_G(T614)
RX_IN_G(T51) → PY_IN_G(T51)
PY_IN_G(T51) → U55_G(T51, qH_in_g(T51))
U55_G(T51, qH_out_g(T51)) → RZ_IN_G(T51)
PY_IN_G(T51) → QH_IN_G(T51)
PN4_IN_G(T22) → RN5_IN_G(T22)
RN5_IN_G(T36) → PN6_IN_G(T36)
PN6_IN_G(T36) → U53_G(T36, qD_in_g(T36))
U53_G(T36, qD_out_g(T36)) → RX_IN_G(T36)
PN6_IN_G(T36) → QD_IN_G(T36)

The TRS R consists of the following rules:

qA_in_gg(a, b) → qA_out_gg(a, b)
qA_in_gg(T11, f(f(T11))) → U1_gg(T11, pB_in_g(T11))
pB_in_g(T11) → U49_g(T11, pN3_in_g(T11))
pN3_in_g(T22) → U17_g(T22, pN4_in_g(T22))
pN4_in_g(T22) → U51_g(T22, rN5_in_g(T22))
rN5_in_g(T36) → U18_g(T36, pN6_in_g(T36))
pN6_in_g(T36) → U53_g(T36, qD_in_g(T36))
qD_in_g(f(T656)) → U3_g(T656, pE_in_g(f(T656)))
pE_in_g(f(T628)) → U16_g(T628, pN2_in_g(T628))
pN2_in_g(T628) → U91_g(T628, rZ_in_g(f(T628)))
rZ_in_g(f(T565)) → U14_g(T565, pN1_in_g(T565))
pN1_in_g(T565) → U87_g(T565, qN34_in_g(T565))
qN34_in_g(f(f(T579))) → U41_g(T579, pV_in_g(f(T579)))
pV_in_g(f(T534)) → U12_g(T534, pW_in_g(T534))
pW_in_g(T534) → U85_g(T534, rT_in_g(f(T534)))
rT_in_g(f(T487)) → U11_g(T487, pU_in_g(T487))
pU_in_g(T487) → U83_g(T487, qN31_in_g(T487))
qN31_in_g(f(f(T501))) → U38_g(T501, pR_in_g(f(T501)))
pR_in_g(f(T456)) → U10_g(T456, pS_in_g(T456))
pS_in_g(T456) → U81_g(T456, rP_in_g(f(T456)))
rP_in_g(f(T409)) → U9_g(T409, pQ_in_g(T409))
pQ_in_g(T409) → U79_g(T409, qN28_in_g(T409))
qN28_in_g(f(f(T423))) → U35_g(T423, pN_in_g(f(T423)))
pN_in_g(f(T375)) → U8_g(T375, pO_in_g(T375))
pO_in_g(T375) → U77_g(T375, rL_in_g(f(T375)))
rL_in_g(f(T322)) → U7_g(T322, pM_in_g(T322))
pM_in_g(T322) → U75_g(T322, qN25_in_g(T322))
qN25_in_g(f(f(T336))) → U32_g(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
pF_in_gg(T200, T201) → U4_gg(T200, T201, pG_in_gg(T200, T201))
pG_in_gg(T200, T201) → U69_gg(T200, T201, rN20_in_gg(T200, T201))
rN20_in_gg(T228, T229) → U26_gg(T228, T229, pN21_in_gg(T228, T229))
pN21_in_gg(T228, T229) → U71_gg(T228, T229, qA_in_gg(f(T228), T229))
qA_in_gg(T682, f(f(T683))) → U2_gg(T682, T683, pC_in_gg(T682, T683))
pC_in_gg(T682, T683) → U93_gg(T682, T683, rN37_in_gg(T682, T683))
rN37_in_gg(T710, T711) → U44_gg(T710, T711, pN38_in_gg(T710, T711))
pN38_in_gg(T710, T711) → U95_gg(T710, T711, qA_in_gg(T710, T711))
U95_gg(T710, T711, qA_out_gg(T710, T711)) → U96_gg(T710, T711, rN40_in_gg(T710, T711))
rN40_in_gg(a, b) → rN40_out_gg(a, b)
rN40_in_gg(T736, f(T737)) → U47_gg(T736, T737, pN38_in_gg(T736, T737))
U47_gg(T736, T737, pN38_out_gg(T736, T737)) → rN40_out_gg(T736, f(T737))
rN40_in_gg(f(T742), f(T742)) → U48_gg(T742, tJ_in_g(T742))
tJ_in_g(T270) → U6_g(T270, pK_in_g(T270))
pK_in_g(T270) → U73_g(T270, qH_in_g(f(T270)))
qH_in_g(f(f(T75))) → U5_g(T75, pI_in_g(T75))
pI_in_g(T75) → U57_g(T75, rN9_in_g(T75))
rN9_in_g(T89) → U20_g(T89, pN10_in_g(T89))
pN10_in_g(T89) → U59_g(T89, qN11_in_g(T89))
qN11_in_g(f(f(T113))) → U21_g(T113, pN12_in_g(T113))
pN12_in_g(T113) → U61_g(T113, rN13_in_g(T113))
rN13_in_g(T127) → U22_g(T127, pN14_in_g(T127))
pN14_in_g(T127) → U63_g(T127, qN15_in_g(T127))
qN15_in_g(f(f(T151))) → U23_g(T151, pN16_in_g(T151))
pN16_in_g(T151) → U65_g(T151, rN17_in_g(T151))
rN17_in_g(T165) → U24_g(T165, pN18_in_g(T165))
pN18_in_g(T165) → U67_g(T165, qN19_in_g(T165))
qN19_in_g(f(f(T179))) → U25_g(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
U25_g(T179, pF_out_gg(f(f(f(f(f(f(f(T179))))))), T179)) → qN19_out_g(f(f(T179)))
U67_g(T165, qN19_out_g(T165)) → U68_g(T165, rL_in_g(T165))
U68_g(T165, rL_out_g(T165)) → pN18_out_g(T165)
U24_g(T165, pN18_out_g(T165)) → rN17_out_g(T165)
U65_g(T151, rN17_out_g(T151)) → U66_g(T151, pN_in_g(T151))
U66_g(T151, pN_out_g(T151)) → pN16_out_g(T151)
U23_g(T151, pN16_out_g(T151)) → qN15_out_g(f(f(T151)))
U63_g(T127, qN15_out_g(T127)) → U64_g(T127, rP_in_g(T127))
U64_g(T127, rP_out_g(T127)) → pN14_out_g(T127)
U22_g(T127, pN14_out_g(T127)) → rN13_out_g(T127)
U61_g(T113, rN13_out_g(T113)) → U62_g(T113, pR_in_g(T113))
U62_g(T113, pR_out_g(T113)) → pN12_out_g(T113)
U21_g(T113, pN12_out_g(T113)) → qN11_out_g(f(f(T113)))
U59_g(T89, qN11_out_g(T89)) → U60_g(T89, rT_in_g(T89))
U60_g(T89, rT_out_g(T89)) → pN10_out_g(T89)
U20_g(T89, pN10_out_g(T89)) → rN9_out_g(T89)
U57_g(T75, rN9_out_g(T75)) → U58_g(T75, pV_in_g(T75))
U58_g(T75, pV_out_g(T75)) → pI_out_g(T75)
U5_g(T75, pI_out_g(T75)) → qH_out_g(f(f(T75)))
U73_g(T270, qH_out_g(f(T270))) → U74_g(T270, tN24_in_g(T270))
tN24_in_g(f(T281)) → U31_g(T281, pK_in_g(T281))
U31_g(T281, pK_out_g(T281)) → tN24_out_g(f(T281))
U74_g(T270, tN24_out_g(T270)) → pK_out_g(T270)
U6_g(T270, pK_out_g(T270)) → tJ_out_g(T270)
U48_gg(T742, tJ_out_g(T742)) → rN40_out_gg(f(T742), f(T742))
U96_gg(T710, T711, rN40_out_gg(T710, T711)) → pN38_out_gg(T710, T711)
U44_gg(T710, T711, pN38_out_gg(T710, T711)) → rN37_out_gg(T710, T711)
rN37_in_gg(f(T746), T746) → U45_gg(T746, tJ_in_g(T746))
U45_gg(T746, tJ_out_g(T746)) → rN37_out_gg(f(T746), T746)
U93_gg(T682, T683, rN37_out_gg(T682, T683)) → U94_gg(T682, T683, pN39_in_gg(T682, T683))
pN39_in_gg(a, b) → pN39_out_gg(a, b)
pN39_in_gg(T764, f(T765)) → U46_gg(T764, T765, pC_in_gg(T764, T765))
U46_gg(T764, T765, pC_out_gg(T764, T765)) → pN39_out_gg(T764, f(T765))
U94_gg(T682, T683, pN39_out_gg(T682, T683)) → pC_out_gg(T682, T683)
U2_gg(T682, T683, pC_out_gg(T682, T683)) → qA_out_gg(T682, f(f(T683)))
U71_gg(T228, T229, qA_out_gg(f(T228), T229)) → U72_gg(T228, T229, rN23_in_gg(T228, T229))
rN23_in_gg(T254, f(T255)) → U29_gg(T254, T255, pN21_in_gg(T254, T255))
U29_gg(T254, T255, pN21_out_gg(T254, T255)) → rN23_out_gg(T254, f(T255))
rN23_in_gg(T260, f(T260)) → U30_gg(T260, tJ_in_g(T260))
U30_gg(T260, tJ_out_g(T260)) → rN23_out_gg(T260, f(T260))
U72_gg(T228, T229, rN23_out_gg(T228, T229)) → pN21_out_gg(T228, T229)
U26_gg(T228, T229, pN21_out_gg(T228, T229)) → rN20_out_gg(T228, T229)
rN20_in_gg(T285, T285) → U27_gg(T285, tJ_in_g(T285))
U27_gg(T285, tJ_out_g(T285)) → rN20_out_gg(T285, T285)
U69_gg(T200, T201, rN20_out_gg(T200, T201)) → U70_gg(T200, T201, pN22_in_gg(T200, T201))
pN22_in_gg(T303, f(T304)) → U28_gg(T303, T304, pG_in_gg(T303, T304))
U28_gg(T303, T304, pG_out_gg(T303, T304)) → pN22_out_gg(T303, f(T304))
U70_gg(T200, T201, pN22_out_gg(T200, T201)) → pG_out_gg(T200, T201)
U4_gg(T200, T201, pG_out_gg(T200, T201)) → pF_out_gg(T200, T201)
U32_g(T336, pF_out_gg(f(f(f(f(f(f(f(f(T336)))))))), T336)) → qN25_out_g(f(f(T336)))
U75_g(T322, qN25_out_g(T322)) → U76_g(T322, rN26_in_g(T322))
rN26_in_g(f(T356)) → U33_g(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
U33_g(T356, pN21_out_gg(f(f(f(f(f(f(f(T356))))))), T356)) → rN26_out_g(f(T356))
U76_g(T322, rN26_out_g(T322)) → pM_out_g(T322)
U7_g(T322, pM_out_g(T322)) → rL_out_g(f(T322))
U77_g(T375, rL_out_g(f(T375))) → U78_g(T375, pN27_in_g(T375))
pN27_in_g(f(T389)) → U34_g(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
U34_g(T389, pG_out_gg(f(f(f(f(f(f(f(T389))))))), T389)) → pN27_out_g(f(T389))
U78_g(T375, pN27_out_g(T375)) → pO_out_g(T375)
U8_g(T375, pO_out_g(T375)) → pN_out_g(f(T375))
U35_g(T423, pN_out_g(f(T423))) → qN28_out_g(f(f(T423)))
U79_g(T409, qN28_out_g(T409)) → U80_g(T409, rN29_in_g(T409))
rN29_in_g(f(T440)) → U36_g(T440, pN18_in_g(T440))
U36_g(T440, pN18_out_g(T440)) → rN29_out_g(f(T440))
U80_g(T409, rN29_out_g(T409)) → pQ_out_g(T409)
U9_g(T409, pQ_out_g(T409)) → rP_out_g(f(T409))
U81_g(T456, rP_out_g(f(T456))) → U82_g(T456, pN30_in_g(T456))
pN30_in_g(f(T470)) → U37_g(T470, pN16_in_g(T470))
U37_g(T470, pN16_out_g(T470)) → pN30_out_g(f(T470))
U82_g(T456, pN30_out_g(T456)) → pS_out_g(T456)
U10_g(T456, pS_out_g(T456)) → pR_out_g(f(T456))
U38_g(T501, pR_out_g(f(T501))) → qN31_out_g(f(f(T501)))
U83_g(T487, qN31_out_g(T487)) → U84_g(T487, rN32_in_g(T487))
rN32_in_g(f(T518)) → U39_g(T518, pN14_in_g(T518))
U39_g(T518, pN14_out_g(T518)) → rN32_out_g(f(T518))
U84_g(T487, rN32_out_g(T487)) → pU_out_g(T487)
U11_g(T487, pU_out_g(T487)) → rT_out_g(f(T487))
U85_g(T534, rT_out_g(f(T534))) → U86_g(T534, pN33_in_g(T534))
pN33_in_g(f(T548)) → U40_g(T548, pN12_in_g(T548))
U40_g(T548, pN12_out_g(T548)) → pN33_out_g(f(T548))
U86_g(T534, pN33_out_g(T534)) → pW_out_g(T534)
U12_g(T534, pW_out_g(T534)) → pV_out_g(f(T534))
U41_g(T579, pV_out_g(f(T579))) → qN34_out_g(f(f(T579)))
U87_g(T565, qN34_out_g(T565)) → U88_g(T565, rN35_in_g(T565))
rN35_in_g(f(T596)) → U42_g(T596, pN10_in_g(T596))
U42_g(T596, pN10_out_g(T596)) → rN35_out_g(f(T596))
U88_g(T565, rN35_out_g(T565)) → pN1_out_g(T565)
U14_g(T565, pN1_out_g(T565)) → rZ_out_g(f(T565))
rZ_in_g(f(T601)) → U15_g(T601, tJ_in_g(T601))
U15_g(T601, tJ_out_g(T601)) → rZ_out_g(f(T601))
U91_g(T628, rZ_out_g(f(T628))) → U92_g(T628, pN36_in_g(T628))
pN36_in_g(f(T642)) → U43_g(T642, pI_in_g(T642))
U43_g(T642, pI_out_g(T642)) → pN36_out_g(f(T642))
U92_g(T628, pN36_out_g(T628)) → pN2_out_g(T628)
U16_g(T628, pN2_out_g(T628)) → pE_out_g(f(T628))
U3_g(T656, pE_out_g(f(T656))) → qD_out_g(f(T656))
U53_g(T36, qD_out_g(T36)) → U54_g(T36, rX_in_g(T36))
rX_in_g(T51) → U13_g(T51, pY_in_g(T51))
pY_in_g(T51) → U55_g(T51, qH_in_g(T51))
U55_g(T51, qH_out_g(T51)) → U56_g(T51, rZ_in_g(T51))
U56_g(T51, rZ_out_g(T51)) → pY_out_g(T51)
U13_g(T51, pY_out_g(T51)) → rX_out_g(T51)
U54_g(T36, rX_out_g(T36)) → pN6_out_g(T36)
U18_g(T36, pN6_out_g(T36)) → rN5_out_g(T36)
U51_g(T22, rN5_out_g(T22)) → U52_g(T22, pN7_in_g(T22))
pN7_in_g(T614) → U19_g(T614, pN8_in_g(T614))
pN8_in_g(T614) → U89_g(T614, rX_in_g(T614))
U89_g(T614, rX_out_g(T614)) → U90_g(T614, pE_in_g(T614))
U90_g(T614, pE_out_g(T614)) → pN8_out_g(T614)
U19_g(T614, pN8_out_g(T614)) → pN7_out_g(T614)
U52_g(T22, pN7_out_g(T22)) → pN4_out_g(T22)
U17_g(T22, pN4_out_g(T22)) → pN3_out_g(T22)
U49_g(T11, pN3_out_g(T11)) → U50_g(T11, qD_in_g(T11))
U50_g(T11, qD_out_g(T11)) → pB_out_g(T11)
U1_gg(T11, pB_out_g(T11)) → qA_out_gg(T11, f(f(T11)))

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

(7) PiDPToQDPProof (EQUIVALENT transformation)

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

(8) Obligation:

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

QA_IN_GG(T11, f(f(T11))) → PB_IN_G(T11)
PB_IN_G(T11) → U49_G(T11, pN3_in_g(T11))
U49_G(T11, pN3_out_g(T11)) → QD_IN_G(T11)
QD_IN_G(f(T656)) → PE_IN_G(f(T656))
PE_IN_G(f(T628)) → PN2_IN_G(T628)
PN2_IN_G(T628) → U91_G(T628, rZ_in_g(f(T628)))
U91_G(T628, rZ_out_g(f(T628))) → PN36_IN_G(T628)
PN36_IN_G(f(T642)) → PI_IN_G(T642)
PI_IN_G(T75) → U57_G(T75, rN9_in_g(T75))
U57_G(T75, rN9_out_g(T75)) → PV_IN_G(T75)
PV_IN_G(f(T534)) → PW_IN_G(T534)
PW_IN_G(T534) → U85_G(T534, rT_in_g(f(T534)))
U85_G(T534, rT_out_g(f(T534))) → PN33_IN_G(T534)
PN33_IN_G(f(T548)) → PN12_IN_G(T548)
PN12_IN_G(T113) → U61_G(T113, rN13_in_g(T113))
U61_G(T113, rN13_out_g(T113)) → PR_IN_G(T113)
PR_IN_G(f(T456)) → PS_IN_G(T456)
PS_IN_G(T456) → U81_G(T456, rP_in_g(f(T456)))
U81_G(T456, rP_out_g(f(T456))) → PN30_IN_G(T456)
PN30_IN_G(f(T470)) → PN16_IN_G(T470)
PN16_IN_G(T151) → U65_G(T151, rN17_in_g(T151))
U65_G(T151, rN17_out_g(T151)) → PN_IN_G(T151)
PN_IN_G(f(T375)) → PO_IN_G(T375)
PO_IN_G(T375) → U77_G(T375, rL_in_g(f(T375)))
U77_G(T375, rL_out_g(f(T375))) → PN27_IN_G(T375)
PN27_IN_G(f(T389)) → PG_IN_GG(f(f(f(f(f(f(f(T389))))))), T389)
PG_IN_GG(T200, T201) → U69_GG(T200, T201, rN20_in_gg(T200, T201))
U69_GG(T200, T201, rN20_out_gg(T200, T201)) → PN22_IN_GG(T200, T201)
PN22_IN_GG(T303, f(T304)) → PG_IN_GG(T303, T304)
PG_IN_GG(T200, T201) → RN20_IN_GG(T200, T201)
RN20_IN_GG(T228, T229) → PN21_IN_GG(T228, T229)
PN21_IN_GG(T228, T229) → U71_GG(T228, T229, qA_in_gg(f(T228), T229))
U71_GG(T228, T229, qA_out_gg(f(T228), T229)) → RN23_IN_GG(T228, T229)
RN23_IN_GG(T254, f(T255)) → PN21_IN_GG(T254, T255)
PN21_IN_GG(T228, T229) → QA_IN_GG(f(T228), T229)
QA_IN_GG(T682, f(f(T683))) → PC_IN_GG(T682, T683)
PC_IN_GG(T682, T683) → U93_GG(T682, T683, rN37_in_gg(T682, T683))
U93_GG(T682, T683, rN37_out_gg(T682, T683)) → PN39_IN_GG(T682, T683)
PN39_IN_GG(T764, f(T765)) → PC_IN_GG(T764, T765)
PC_IN_GG(T682, T683) → RN37_IN_GG(T682, T683)
RN37_IN_GG(T710, T711) → PN38_IN_GG(T710, T711)
PN38_IN_GG(T710, T711) → U95_GG(T710, T711, qA_in_gg(T710, T711))
U95_GG(T710, T711, qA_out_gg(T710, T711)) → RN40_IN_GG(T710, T711)
RN40_IN_GG(T736, f(T737)) → PN38_IN_GG(T736, T737)
PN38_IN_GG(T710, T711) → QA_IN_GG(T710, T711)
RN40_IN_GG(f(T742), f(T742)) → TJ_IN_G(T742)
TJ_IN_G(T270) → PK_IN_G(T270)
PK_IN_G(T270) → U73_G(T270, qH_in_g(f(T270)))
U73_G(T270, qH_out_g(f(T270))) → TN24_IN_G(T270)
TN24_IN_G(f(T281)) → PK_IN_G(T281)
PK_IN_G(T270) → QH_IN_G(f(T270))
QH_IN_G(f(f(T75))) → PI_IN_G(T75)
PI_IN_G(T75) → RN9_IN_G(T75)
RN9_IN_G(T89) → PN10_IN_G(T89)
PN10_IN_G(T89) → U59_G(T89, qN11_in_g(T89))
U59_G(T89, qN11_out_g(T89)) → RT_IN_G(T89)
RT_IN_G(f(T487)) → PU_IN_G(T487)
PU_IN_G(T487) → U83_G(T487, qN31_in_g(T487))
U83_G(T487, qN31_out_g(T487)) → RN32_IN_G(T487)
RN32_IN_G(f(T518)) → PN14_IN_G(T518)
PN14_IN_G(T127) → U63_G(T127, qN15_in_g(T127))
U63_G(T127, qN15_out_g(T127)) → RP_IN_G(T127)
RP_IN_G(f(T409)) → PQ_IN_G(T409)
PQ_IN_G(T409) → U79_G(T409, qN28_in_g(T409))
U79_G(T409, qN28_out_g(T409)) → RN29_IN_G(T409)
RN29_IN_G(f(T440)) → PN18_IN_G(T440)
PN18_IN_G(T165) → U67_G(T165, qN19_in_g(T165))
U67_G(T165, qN19_out_g(T165)) → RL_IN_G(T165)
RL_IN_G(f(T322)) → PM_IN_G(T322)
PM_IN_G(T322) → U75_G(T322, qN25_in_g(T322))
U75_G(T322, qN25_out_g(T322)) → RN26_IN_G(T322)
RN26_IN_G(f(T356)) → PN21_IN_GG(f(f(f(f(f(f(f(T356))))))), T356)
PM_IN_G(T322) → QN25_IN_G(T322)
QN25_IN_G(f(f(T336))) → PF_IN_GG(f(f(f(f(f(f(f(f(T336)))))))), T336)
PF_IN_GG(T200, T201) → PG_IN_GG(T200, T201)
PN18_IN_G(T165) → QN19_IN_G(T165)
QN19_IN_G(f(f(T179))) → PF_IN_GG(f(f(f(f(f(f(f(T179))))))), T179)
PQ_IN_G(T409) → QN28_IN_G(T409)
QN28_IN_G(f(f(T423))) → PN_IN_G(f(T423))
PN14_IN_G(T127) → QN15_IN_G(T127)
QN15_IN_G(f(f(T151))) → PN16_IN_G(T151)
PN16_IN_G(T151) → RN17_IN_G(T151)
RN17_IN_G(T165) → PN18_IN_G(T165)
PU_IN_G(T487) → QN31_IN_G(T487)
QN31_IN_G(f(f(T501))) → PR_IN_G(f(T501))
PN10_IN_G(T89) → QN11_IN_G(T89)
QN11_IN_G(f(f(T113))) → PN12_IN_G(T113)
PN12_IN_G(T113) → RN13_IN_G(T113)
RN13_IN_G(T127) → PN14_IN_G(T127)
RN37_IN_GG(f(T746), T746) → TJ_IN_G(T746)
RN23_IN_GG(T260, f(T260)) → TJ_IN_G(T260)
RN20_IN_GG(T285, T285) → TJ_IN_G(T285)
PO_IN_G(T375) → RL_IN_G(f(T375))
PS_IN_G(T456) → RP_IN_G(f(T456))
PW_IN_G(T534) → RT_IN_G(f(T534))
PN2_IN_G(T628) → RZ_IN_G(f(T628))
RZ_IN_G(f(T565)) → PN1_IN_G(T565)
PN1_IN_G(T565) → U87_G(T565, qN34_in_g(T565))
U87_G(T565, qN34_out_g(T565)) → RN35_IN_G(T565)
RN35_IN_G(f(T596)) → PN10_IN_G(T596)
PN1_IN_G(T565) → QN34_IN_G(T565)
QN34_IN_G(f(f(T579))) → PV_IN_G(f(T579))
RZ_IN_G(f(T601)) → TJ_IN_G(T601)
PB_IN_G(T11) → PN3_IN_G(T11)
PN3_IN_G(T22) → PN4_IN_G(T22)
PN4_IN_G(T22) → U51_G(T22, rN5_in_g(T22))
U51_G(T22, rN5_out_g(T22)) → PN7_IN_G(T22)
PN7_IN_G(T614) → PN8_IN_G(T614)
PN8_IN_G(T614) → U89_G(T614, rX_in_g(T614))
U89_G(T614, rX_out_g(T614)) → PE_IN_G(T614)
PN8_IN_G(T614) → RX_IN_G(T614)
RX_IN_G(T51) → PY_IN_G(T51)
PY_IN_G(T51) → U55_G(T51, qH_in_g(T51))
U55_G(T51, qH_out_g(T51)) → RZ_IN_G(T51)
PY_IN_G(T51) → QH_IN_G(T51)
PN4_IN_G(T22) → RN5_IN_G(T22)
RN5_IN_G(T36) → PN6_IN_G(T36)
PN6_IN_G(T36) → U53_G(T36, qD_in_g(T36))
U53_G(T36, qD_out_g(T36)) → RX_IN_G(T36)
PN6_IN_G(T36) → QD_IN_G(T36)

The TRS R consists of the following rules:

qA_in_gg(a, b) → qA_out_gg(a, b)
qA_in_gg(T11, f(f(T11))) → U1_gg(T11, pB_in_g(T11))
pB_in_g(T11) → U49_g(T11, pN3_in_g(T11))
pN3_in_g(T22) → U17_g(T22, pN4_in_g(T22))
pN4_in_g(T22) → U51_g(T22, rN5_in_g(T22))
rN5_in_g(T36) → U18_g(T36, pN6_in_g(T36))
pN6_in_g(T36) → U53_g(T36, qD_in_g(T36))
qD_in_g(f(T656)) → U3_g(T656, pE_in_g(f(T656)))
pE_in_g(f(T628)) → U16_g(T628, pN2_in_g(T628))
pN2_in_g(T628) → U91_g(T628, rZ_in_g(f(T628)))
rZ_in_g(f(T565)) → U14_g(T565, pN1_in_g(T565))
pN1_in_g(T565) → U87_g(T565, qN34_in_g(T565))
qN34_in_g(f(f(T579))) → U41_g(T579, pV_in_g(f(T579)))
pV_in_g(f(T534)) → U12_g(T534, pW_in_g(T534))
pW_in_g(T534) → U85_g(T534, rT_in_g(f(T534)))
rT_in_g(f(T487)) → U11_g(T487, pU_in_g(T487))
pU_in_g(T487) → U83_g(T487, qN31_in_g(T487))
qN31_in_g(f(f(T501))) → U38_g(T501, pR_in_g(f(T501)))
pR_in_g(f(T456)) → U10_g(T456, pS_in_g(T456))
pS_in_g(T456) → U81_g(T456, rP_in_g(f(T456)))
rP_in_g(f(T409)) → U9_g(T409, pQ_in_g(T409))
pQ_in_g(T409) → U79_g(T409, qN28_in_g(T409))
qN28_in_g(f(f(T423))) → U35_g(T423, pN_in_g(f(T423)))
pN_in_g(f(T375)) → U8_g(T375, pO_in_g(T375))
pO_in_g(T375) → U77_g(T375, rL_in_g(f(T375)))
rL_in_g(f(T322)) → U7_g(T322, pM_in_g(T322))
pM_in_g(T322) → U75_g(T322, qN25_in_g(T322))
qN25_in_g(f(f(T336))) → U32_g(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
pF_in_gg(T200, T201) → U4_gg(T200, T201, pG_in_gg(T200, T201))
pG_in_gg(T200, T201) → U69_gg(T200, T201, rN20_in_gg(T200, T201))
rN20_in_gg(T228, T229) → U26_gg(T228, T229, pN21_in_gg(T228, T229))
pN21_in_gg(T228, T229) → U71_gg(T228, T229, qA_in_gg(f(T228), T229))
qA_in_gg(T682, f(f(T683))) → U2_gg(T682, T683, pC_in_gg(T682, T683))
pC_in_gg(T682, T683) → U93_gg(T682, T683, rN37_in_gg(T682, T683))
rN37_in_gg(T710, T711) → U44_gg(T710, T711, pN38_in_gg(T710, T711))
pN38_in_gg(T710, T711) → U95_gg(T710, T711, qA_in_gg(T710, T711))
U95_gg(T710, T711, qA_out_gg(T710, T711)) → U96_gg(T710, T711, rN40_in_gg(T710, T711))
rN40_in_gg(a, b) → rN40_out_gg(a, b)
rN40_in_gg(T736, f(T737)) → U47_gg(T736, T737, pN38_in_gg(T736, T737))
U47_gg(T736, T737, pN38_out_gg(T736, T737)) → rN40_out_gg(T736, f(T737))
rN40_in_gg(f(T742), f(T742)) → U48_gg(T742, tJ_in_g(T742))
tJ_in_g(T270) → U6_g(T270, pK_in_g(T270))
pK_in_g(T270) → U73_g(T270, qH_in_g(f(T270)))
qH_in_g(f(f(T75))) → U5_g(T75, pI_in_g(T75))
pI_in_g(T75) → U57_g(T75, rN9_in_g(T75))
rN9_in_g(T89) → U20_g(T89, pN10_in_g(T89))
pN10_in_g(T89) → U59_g(T89, qN11_in_g(T89))
qN11_in_g(f(f(T113))) → U21_g(T113, pN12_in_g(T113))
pN12_in_g(T113) → U61_g(T113, rN13_in_g(T113))
rN13_in_g(T127) → U22_g(T127, pN14_in_g(T127))
pN14_in_g(T127) → U63_g(T127, qN15_in_g(T127))
qN15_in_g(f(f(T151))) → U23_g(T151, pN16_in_g(T151))
pN16_in_g(T151) → U65_g(T151, rN17_in_g(T151))
rN17_in_g(T165) → U24_g(T165, pN18_in_g(T165))
pN18_in_g(T165) → U67_g(T165, qN19_in_g(T165))
qN19_in_g(f(f(T179))) → U25_g(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
U25_g(T179, pF_out_gg(f(f(f(f(f(f(f(T179))))))), T179)) → qN19_out_g(f(f(T179)))
U67_g(T165, qN19_out_g(T165)) → U68_g(T165, rL_in_g(T165))
U68_g(T165, rL_out_g(T165)) → pN18_out_g(T165)
U24_g(T165, pN18_out_g(T165)) → rN17_out_g(T165)
U65_g(T151, rN17_out_g(T151)) → U66_g(T151, pN_in_g(T151))
U66_g(T151, pN_out_g(T151)) → pN16_out_g(T151)
U23_g(T151, pN16_out_g(T151)) → qN15_out_g(f(f(T151)))
U63_g(T127, qN15_out_g(T127)) → U64_g(T127, rP_in_g(T127))
U64_g(T127, rP_out_g(T127)) → pN14_out_g(T127)
U22_g(T127, pN14_out_g(T127)) → rN13_out_g(T127)
U61_g(T113, rN13_out_g(T113)) → U62_g(T113, pR_in_g(T113))
U62_g(T113, pR_out_g(T113)) → pN12_out_g(T113)
U21_g(T113, pN12_out_g(T113)) → qN11_out_g(f(f(T113)))
U59_g(T89, qN11_out_g(T89)) → U60_g(T89, rT_in_g(T89))
U60_g(T89, rT_out_g(T89)) → pN10_out_g(T89)
U20_g(T89, pN10_out_g(T89)) → rN9_out_g(T89)
U57_g(T75, rN9_out_g(T75)) → U58_g(T75, pV_in_g(T75))
U58_g(T75, pV_out_g(T75)) → pI_out_g(T75)
U5_g(T75, pI_out_g(T75)) → qH_out_g(f(f(T75)))
U73_g(T270, qH_out_g(f(T270))) → U74_g(T270, tN24_in_g(T270))
tN24_in_g(f(T281)) → U31_g(T281, pK_in_g(T281))
U31_g(T281, pK_out_g(T281)) → tN24_out_g(f(T281))
U74_g(T270, tN24_out_g(T270)) → pK_out_g(T270)
U6_g(T270, pK_out_g(T270)) → tJ_out_g(T270)
U48_gg(T742, tJ_out_g(T742)) → rN40_out_gg(f(T742), f(T742))
U96_gg(T710, T711, rN40_out_gg(T710, T711)) → pN38_out_gg(T710, T711)
U44_gg(T710, T711, pN38_out_gg(T710, T711)) → rN37_out_gg(T710, T711)
rN37_in_gg(f(T746), T746) → U45_gg(T746, tJ_in_g(T746))
U45_gg(T746, tJ_out_g(T746)) → rN37_out_gg(f(T746), T746)
U93_gg(T682, T683, rN37_out_gg(T682, T683)) → U94_gg(T682, T683, pN39_in_gg(T682, T683))
pN39_in_gg(a, b) → pN39_out_gg(a, b)
pN39_in_gg(T764, f(T765)) → U46_gg(T764, T765, pC_in_gg(T764, T765))
U46_gg(T764, T765, pC_out_gg(T764, T765)) → pN39_out_gg(T764, f(T765))
U94_gg(T682, T683, pN39_out_gg(T682, T683)) → pC_out_gg(T682, T683)
U2_gg(T682, T683, pC_out_gg(T682, T683)) → qA_out_gg(T682, f(f(T683)))
U71_gg(T228, T229, qA_out_gg(f(T228), T229)) → U72_gg(T228, T229, rN23_in_gg(T228, T229))
rN23_in_gg(T254, f(T255)) → U29_gg(T254, T255, pN21_in_gg(T254, T255))
U29_gg(T254, T255, pN21_out_gg(T254, T255)) → rN23_out_gg(T254, f(T255))
rN23_in_gg(T260, f(T260)) → U30_gg(T260, tJ_in_g(T260))
U30_gg(T260, tJ_out_g(T260)) → rN23_out_gg(T260, f(T260))
U72_gg(T228, T229, rN23_out_gg(T228, T229)) → pN21_out_gg(T228, T229)
U26_gg(T228, T229, pN21_out_gg(T228, T229)) → rN20_out_gg(T228, T229)
rN20_in_gg(T285, T285) → U27_gg(T285, tJ_in_g(T285))
U27_gg(T285, tJ_out_g(T285)) → rN20_out_gg(T285, T285)
U69_gg(T200, T201, rN20_out_gg(T200, T201)) → U70_gg(T200, T201, pN22_in_gg(T200, T201))
pN22_in_gg(T303, f(T304)) → U28_gg(T303, T304, pG_in_gg(T303, T304))
U28_gg(T303, T304, pG_out_gg(T303, T304)) → pN22_out_gg(T303, f(T304))
U70_gg(T200, T201, pN22_out_gg(T200, T201)) → pG_out_gg(T200, T201)
U4_gg(T200, T201, pG_out_gg(T200, T201)) → pF_out_gg(T200, T201)
U32_g(T336, pF_out_gg(f(f(f(f(f(f(f(f(T336)))))))), T336)) → qN25_out_g(f(f(T336)))
U75_g(T322, qN25_out_g(T322)) → U76_g(T322, rN26_in_g(T322))
rN26_in_g(f(T356)) → U33_g(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
U33_g(T356, pN21_out_gg(f(f(f(f(f(f(f(T356))))))), T356)) → rN26_out_g(f(T356))
U76_g(T322, rN26_out_g(T322)) → pM_out_g(T322)
U7_g(T322, pM_out_g(T322)) → rL_out_g(f(T322))
U77_g(T375, rL_out_g(f(T375))) → U78_g(T375, pN27_in_g(T375))
pN27_in_g(f(T389)) → U34_g(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
U34_g(T389, pG_out_gg(f(f(f(f(f(f(f(T389))))))), T389)) → pN27_out_g(f(T389))
U78_g(T375, pN27_out_g(T375)) → pO_out_g(T375)
U8_g(T375, pO_out_g(T375)) → pN_out_g(f(T375))
U35_g(T423, pN_out_g(f(T423))) → qN28_out_g(f(f(T423)))
U79_g(T409, qN28_out_g(T409)) → U80_g(T409, rN29_in_g(T409))
rN29_in_g(f(T440)) → U36_g(T440, pN18_in_g(T440))
U36_g(T440, pN18_out_g(T440)) → rN29_out_g(f(T440))
U80_g(T409, rN29_out_g(T409)) → pQ_out_g(T409)
U9_g(T409, pQ_out_g(T409)) → rP_out_g(f(T409))
U81_g(T456, rP_out_g(f(T456))) → U82_g(T456, pN30_in_g(T456))
pN30_in_g(f(T470)) → U37_g(T470, pN16_in_g(T470))
U37_g(T470, pN16_out_g(T470)) → pN30_out_g(f(T470))
U82_g(T456, pN30_out_g(T456)) → pS_out_g(T456)
U10_g(T456, pS_out_g(T456)) → pR_out_g(f(T456))
U38_g(T501, pR_out_g(f(T501))) → qN31_out_g(f(f(T501)))
U83_g(T487, qN31_out_g(T487)) → U84_g(T487, rN32_in_g(T487))
rN32_in_g(f(T518)) → U39_g(T518, pN14_in_g(T518))
U39_g(T518, pN14_out_g(T518)) → rN32_out_g(f(T518))
U84_g(T487, rN32_out_g(T487)) → pU_out_g(T487)
U11_g(T487, pU_out_g(T487)) → rT_out_g(f(T487))
U85_g(T534, rT_out_g(f(T534))) → U86_g(T534, pN33_in_g(T534))
pN33_in_g(f(T548)) → U40_g(T548, pN12_in_g(T548))
U40_g(T548, pN12_out_g(T548)) → pN33_out_g(f(T548))
U86_g(T534, pN33_out_g(T534)) → pW_out_g(T534)
U12_g(T534, pW_out_g(T534)) → pV_out_g(f(T534))
U41_g(T579, pV_out_g(f(T579))) → qN34_out_g(f(f(T579)))
U87_g(T565, qN34_out_g(T565)) → U88_g(T565, rN35_in_g(T565))
rN35_in_g(f(T596)) → U42_g(T596, pN10_in_g(T596))
U42_g(T596, pN10_out_g(T596)) → rN35_out_g(f(T596))
U88_g(T565, rN35_out_g(T565)) → pN1_out_g(T565)
U14_g(T565, pN1_out_g(T565)) → rZ_out_g(f(T565))
rZ_in_g(f(T601)) → U15_g(T601, tJ_in_g(T601))
U15_g(T601, tJ_out_g(T601)) → rZ_out_g(f(T601))
U91_g(T628, rZ_out_g(f(T628))) → U92_g(T628, pN36_in_g(T628))
pN36_in_g(f(T642)) → U43_g(T642, pI_in_g(T642))
U43_g(T642, pI_out_g(T642)) → pN36_out_g(f(T642))
U92_g(T628, pN36_out_g(T628)) → pN2_out_g(T628)
U16_g(T628, pN2_out_g(T628)) → pE_out_g(f(T628))
U3_g(T656, pE_out_g(f(T656))) → qD_out_g(f(T656))
U53_g(T36, qD_out_g(T36)) → U54_g(T36, rX_in_g(T36))
rX_in_g(T51) → U13_g(T51, pY_in_g(T51))
pY_in_g(T51) → U55_g(T51, qH_in_g(T51))
U55_g(T51, qH_out_g(T51)) → U56_g(T51, rZ_in_g(T51))
U56_g(T51, rZ_out_g(T51)) → pY_out_g(T51)
U13_g(T51, pY_out_g(T51)) → rX_out_g(T51)
U54_g(T36, rX_out_g(T36)) → pN6_out_g(T36)
U18_g(T36, pN6_out_g(T36)) → rN5_out_g(T36)
U51_g(T22, rN5_out_g(T22)) → U52_g(T22, pN7_in_g(T22))
pN7_in_g(T614) → U19_g(T614, pN8_in_g(T614))
pN8_in_g(T614) → U89_g(T614, rX_in_g(T614))
U89_g(T614, rX_out_g(T614)) → U90_g(T614, pE_in_g(T614))
U90_g(T614, pE_out_g(T614)) → pN8_out_g(T614)
U19_g(T614, pN8_out_g(T614)) → pN7_out_g(T614)
U52_g(T22, pN7_out_g(T22)) → pN4_out_g(T22)
U17_g(T22, pN4_out_g(T22)) → pN3_out_g(T22)
U49_g(T11, pN3_out_g(T11)) → U50_g(T11, qD_in_g(T11))
U50_g(T11, qD_out_g(T11)) → pB_out_g(T11)
U1_gg(T11, pB_out_g(T11)) → qA_out_gg(T11, f(f(T11)))

The set Q consists of the following terms:

qA_in_gg(x0, x1)
pB_in_g(x0)
pN3_in_g(x0)
pN4_in_g(x0)
rN5_in_g(x0)
pN6_in_g(x0)
qD_in_g(x0)
pE_in_g(x0)
pN2_in_g(x0)
rZ_in_g(x0)
pN1_in_g(x0)
qN34_in_g(x0)
pV_in_g(x0)
pW_in_g(x0)
rT_in_g(x0)
pU_in_g(x0)
qN31_in_g(x0)
pR_in_g(x0)
pS_in_g(x0)
rP_in_g(x0)
pQ_in_g(x0)
qN28_in_g(x0)
pN_in_g(x0)
pO_in_g(x0)
rL_in_g(x0)
pM_in_g(x0)
qN25_in_g(x0)
pF_in_gg(x0, x1)
pG_in_gg(x0, x1)
rN20_in_gg(x0, x1)
pN21_in_gg(x0, x1)
pC_in_gg(x0, x1)
rN37_in_gg(x0, x1)
pN38_in_gg(x0, x1)
U95_gg(x0, x1, x2)
rN40_in_gg(x0, x1)
U47_gg(x0, x1, x2)
tJ_in_g(x0)
pK_in_g(x0)
qH_in_g(x0)
pI_in_g(x0)
rN9_in_g(x0)
pN10_in_g(x0)
qN11_in_g(x0)
pN12_in_g(x0)
rN13_in_g(x0)
pN14_in_g(x0)
qN15_in_g(x0)
pN16_in_g(x0)
rN17_in_g(x0)
pN18_in_g(x0)
qN19_in_g(x0)
U25_g(x0, x1)
U67_g(x0, x1)
U68_g(x0, x1)
U24_g(x0, x1)
U65_g(x0, x1)
U66_g(x0, x1)
U23_g(x0, x1)
U63_g(x0, x1)
U64_g(x0, x1)
U22_g(x0, x1)
U61_g(x0, x1)
U62_g(x0, x1)
U21_g(x0, x1)
U59_g(x0, x1)
U60_g(x0, x1)
U20_g(x0, x1)
U57_g(x0, x1)
U58_g(x0, x1)
U5_g(x0, x1)
U73_g(x0, x1)
tN24_in_g(x0)
U31_g(x0, x1)
U74_g(x0, x1)
U6_g(x0, x1)
U48_gg(x0, x1)
U96_gg(x0, x1, x2)
U44_gg(x0, x1, x2)
U45_gg(x0, x1)
U93_gg(x0, x1, x2)
pN39_in_gg(x0, x1)
U46_gg(x0, x1, x2)
U94_gg(x0, x1, x2)
U2_gg(x0, x1, x2)
U71_gg(x0, x1, x2)
rN23_in_gg(x0, x1)
U29_gg(x0, x1, x2)
U30_gg(x0, x1)
U72_gg(x0, x1, x2)
U26_gg(x0, x1, x2)
U27_gg(x0, x1)
U69_gg(x0, x1, x2)
pN22_in_gg(x0, x1)
U28_gg(x0, x1, x2)
U70_gg(x0, x1, x2)
U4_gg(x0, x1, x2)
U32_g(x0, x1)
U75_g(x0, x1)
rN26_in_g(x0)
U33_g(x0, x1)
U76_g(x0, x1)
U7_g(x0, x1)
U77_g(x0, x1)
pN27_in_g(x0)
U34_g(x0, x1)
U78_g(x0, x1)
U8_g(x0, x1)
U35_g(x0, x1)
U79_g(x0, x1)
rN29_in_g(x0)
U36_g(x0, x1)
U80_g(x0, x1)
U9_g(x0, x1)
U81_g(x0, x1)
pN30_in_g(x0)
U37_g(x0, x1)
U82_g(x0, x1)
U10_g(x0, x1)
U38_g(x0, x1)
U83_g(x0, x1)
rN32_in_g(x0)
U39_g(x0, x1)
U84_g(x0, x1)
U11_g(x0, x1)
U85_g(x0, x1)
pN33_in_g(x0)
U40_g(x0, x1)
U86_g(x0, x1)
U12_g(x0, x1)
U41_g(x0, x1)
U87_g(x0, x1)
rN35_in_g(x0)
U42_g(x0, x1)
U88_g(x0, x1)
U14_g(x0, x1)
U15_g(x0, x1)
U91_g(x0, x1)
pN36_in_g(x0)
U43_g(x0, x1)
U92_g(x0, x1)
U16_g(x0, x1)
U3_g(x0, x1)
U53_g(x0, x1)
rX_in_g(x0)
pY_in_g(x0)
U55_g(x0, x1)
U56_g(x0, x1)
U13_g(x0, x1)
U54_g(x0, x1)
U18_g(x0, x1)
U51_g(x0, x1)
pN7_in_g(x0)
pN8_in_g(x0)
U89_g(x0, x1)
U90_g(x0, x1)
U19_g(x0, x1)
U52_g(x0, x1)
U17_g(x0, x1)
U49_g(x0, x1)
U50_g(x0, x1)
U1_gg(x0, x1)

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

(9) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule PF_IN_GG(T200, T201) → PG_IN_GG(T200, T201) we obtained the following new rules [LPAR04]:

PF_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0) → PG_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0)
PF_IN_GG(f(f(f(f(f(f(f(z0))))))), z0) → PG_IN_GG(f(f(f(f(f(f(f(z0))))))), z0)

(10) Obligation:

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

QA_IN_GG(T11, f(f(T11))) → PB_IN_G(T11)
PB_IN_G(T11) → U49_G(T11, pN3_in_g(T11))
U49_G(T11, pN3_out_g(T11)) → QD_IN_G(T11)
QD_IN_G(f(T656)) → PE_IN_G(f(T656))
PE_IN_G(f(T628)) → PN2_IN_G(T628)
PN2_IN_G(T628) → U91_G(T628, rZ_in_g(f(T628)))
U91_G(T628, rZ_out_g(f(T628))) → PN36_IN_G(T628)
PN36_IN_G(f(T642)) → PI_IN_G(T642)
PI_IN_G(T75) → U57_G(T75, rN9_in_g(T75))
U57_G(T75, rN9_out_g(T75)) → PV_IN_G(T75)
PV_IN_G(f(T534)) → PW_IN_G(T534)
PW_IN_G(T534) → U85_G(T534, rT_in_g(f(T534)))
U85_G(T534, rT_out_g(f(T534))) → PN33_IN_G(T534)
PN33_IN_G(f(T548)) → PN12_IN_G(T548)
PN12_IN_G(T113) → U61_G(T113, rN13_in_g(T113))
U61_G(T113, rN13_out_g(T113)) → PR_IN_G(T113)
PR_IN_G(f(T456)) → PS_IN_G(T456)
PS_IN_G(T456) → U81_G(T456, rP_in_g(f(T456)))
U81_G(T456, rP_out_g(f(T456))) → PN30_IN_G(T456)
PN30_IN_G(f(T470)) → PN16_IN_G(T470)
PN16_IN_G(T151) → U65_G(T151, rN17_in_g(T151))
U65_G(T151, rN17_out_g(T151)) → PN_IN_G(T151)
PN_IN_G(f(T375)) → PO_IN_G(T375)
PO_IN_G(T375) → U77_G(T375, rL_in_g(f(T375)))
U77_G(T375, rL_out_g(f(T375))) → PN27_IN_G(T375)
PN27_IN_G(f(T389)) → PG_IN_GG(f(f(f(f(f(f(f(T389))))))), T389)
PG_IN_GG(T200, T201) → U69_GG(T200, T201, rN20_in_gg(T200, T201))
U69_GG(T200, T201, rN20_out_gg(T200, T201)) → PN22_IN_GG(T200, T201)
PN22_IN_GG(T303, f(T304)) → PG_IN_GG(T303, T304)
PG_IN_GG(T200, T201) → RN20_IN_GG(T200, T201)
RN20_IN_GG(T228, T229) → PN21_IN_GG(T228, T229)
PN21_IN_GG(T228, T229) → U71_GG(T228, T229, qA_in_gg(f(T228), T229))
U71_GG(T228, T229, qA_out_gg(f(T228), T229)) → RN23_IN_GG(T228, T229)
RN23_IN_GG(T254, f(T255)) → PN21_IN_GG(T254, T255)
PN21_IN_GG(T228, T229) → QA_IN_GG(f(T228), T229)
QA_IN_GG(T682, f(f(T683))) → PC_IN_GG(T682, T683)
PC_IN_GG(T682, T683) → U93_GG(T682, T683, rN37_in_gg(T682, T683))
U93_GG(T682, T683, rN37_out_gg(T682, T683)) → PN39_IN_GG(T682, T683)
PN39_IN_GG(T764, f(T765)) → PC_IN_GG(T764, T765)
PC_IN_GG(T682, T683) → RN37_IN_GG(T682, T683)
RN37_IN_GG(T710, T711) → PN38_IN_GG(T710, T711)
PN38_IN_GG(T710, T711) → U95_GG(T710, T711, qA_in_gg(T710, T711))
U95_GG(T710, T711, qA_out_gg(T710, T711)) → RN40_IN_GG(T710, T711)
RN40_IN_GG(T736, f(T737)) → PN38_IN_GG(T736, T737)
PN38_IN_GG(T710, T711) → QA_IN_GG(T710, T711)
RN40_IN_GG(f(T742), f(T742)) → TJ_IN_G(T742)
TJ_IN_G(T270) → PK_IN_G(T270)
PK_IN_G(T270) → U73_G(T270, qH_in_g(f(T270)))
U73_G(T270, qH_out_g(f(T270))) → TN24_IN_G(T270)
TN24_IN_G(f(T281)) → PK_IN_G(T281)
PK_IN_G(T270) → QH_IN_G(f(T270))
QH_IN_G(f(f(T75))) → PI_IN_G(T75)
PI_IN_G(T75) → RN9_IN_G(T75)
RN9_IN_G(T89) → PN10_IN_G(T89)
PN10_IN_G(T89) → U59_G(T89, qN11_in_g(T89))
U59_G(T89, qN11_out_g(T89)) → RT_IN_G(T89)
RT_IN_G(f(T487)) → PU_IN_G(T487)
PU_IN_G(T487) → U83_G(T487, qN31_in_g(T487))
U83_G(T487, qN31_out_g(T487)) → RN32_IN_G(T487)
RN32_IN_G(f(T518)) → PN14_IN_G(T518)
PN14_IN_G(T127) → U63_G(T127, qN15_in_g(T127))
U63_G(T127, qN15_out_g(T127)) → RP_IN_G(T127)
RP_IN_G(f(T409)) → PQ_IN_G(T409)
PQ_IN_G(T409) → U79_G(T409, qN28_in_g(T409))
U79_G(T409, qN28_out_g(T409)) → RN29_IN_G(T409)
RN29_IN_G(f(T440)) → PN18_IN_G(T440)
PN18_IN_G(T165) → U67_G(T165, qN19_in_g(T165))
U67_G(T165, qN19_out_g(T165)) → RL_IN_G(T165)
RL_IN_G(f(T322)) → PM_IN_G(T322)
PM_IN_G(T322) → U75_G(T322, qN25_in_g(T322))
U75_G(T322, qN25_out_g(T322)) → RN26_IN_G(T322)
RN26_IN_G(f(T356)) → PN21_IN_GG(f(f(f(f(f(f(f(T356))))))), T356)
PM_IN_G(T322) → QN25_IN_G(T322)
QN25_IN_G(f(f(T336))) → PF_IN_GG(f(f(f(f(f(f(f(f(T336)))))))), T336)
PN18_IN_G(T165) → QN19_IN_G(T165)
QN19_IN_G(f(f(T179))) → PF_IN_GG(f(f(f(f(f(f(f(T179))))))), T179)
PQ_IN_G(T409) → QN28_IN_G(T409)
QN28_IN_G(f(f(T423))) → PN_IN_G(f(T423))
PN14_IN_G(T127) → QN15_IN_G(T127)
QN15_IN_G(f(f(T151))) → PN16_IN_G(T151)
PN16_IN_G(T151) → RN17_IN_G(T151)
RN17_IN_G(T165) → PN18_IN_G(T165)
PU_IN_G(T487) → QN31_IN_G(T487)
QN31_IN_G(f(f(T501))) → PR_IN_G(f(T501))
PN10_IN_G(T89) → QN11_IN_G(T89)
QN11_IN_G(f(f(T113))) → PN12_IN_G(T113)
PN12_IN_G(T113) → RN13_IN_G(T113)
RN13_IN_G(T127) → PN14_IN_G(T127)
RN37_IN_GG(f(T746), T746) → TJ_IN_G(T746)
RN23_IN_GG(T260, f(T260)) → TJ_IN_G(T260)
RN20_IN_GG(T285, T285) → TJ_IN_G(T285)
PO_IN_G(T375) → RL_IN_G(f(T375))
PS_IN_G(T456) → RP_IN_G(f(T456))
PW_IN_G(T534) → RT_IN_G(f(T534))
PN2_IN_G(T628) → RZ_IN_G(f(T628))
RZ_IN_G(f(T565)) → PN1_IN_G(T565)
PN1_IN_G(T565) → U87_G(T565, qN34_in_g(T565))
U87_G(T565, qN34_out_g(T565)) → RN35_IN_G(T565)
RN35_IN_G(f(T596)) → PN10_IN_G(T596)
PN1_IN_G(T565) → QN34_IN_G(T565)
QN34_IN_G(f(f(T579))) → PV_IN_G(f(T579))
RZ_IN_G(f(T601)) → TJ_IN_G(T601)
PB_IN_G(T11) → PN3_IN_G(T11)
PN3_IN_G(T22) → PN4_IN_G(T22)
PN4_IN_G(T22) → U51_G(T22, rN5_in_g(T22))
U51_G(T22, rN5_out_g(T22)) → PN7_IN_G(T22)
PN7_IN_G(T614) → PN8_IN_G(T614)
PN8_IN_G(T614) → U89_G(T614, rX_in_g(T614))
U89_G(T614, rX_out_g(T614)) → PE_IN_G(T614)
PN8_IN_G(T614) → RX_IN_G(T614)
RX_IN_G(T51) → PY_IN_G(T51)
PY_IN_G(T51) → U55_G(T51, qH_in_g(T51))
U55_G(T51, qH_out_g(T51)) → RZ_IN_G(T51)
PY_IN_G(T51) → QH_IN_G(T51)
PN4_IN_G(T22) → RN5_IN_G(T22)
RN5_IN_G(T36) → PN6_IN_G(T36)
PN6_IN_G(T36) → U53_G(T36, qD_in_g(T36))
U53_G(T36, qD_out_g(T36)) → RX_IN_G(T36)
PN6_IN_G(T36) → QD_IN_G(T36)
PF_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0) → PG_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0)
PF_IN_GG(f(f(f(f(f(f(f(z0))))))), z0) → PG_IN_GG(f(f(f(f(f(f(f(z0))))))), z0)

The TRS R consists of the following rules:

qA_in_gg(a, b) → qA_out_gg(a, b)
qA_in_gg(T11, f(f(T11))) → U1_gg(T11, pB_in_g(T11))
pB_in_g(T11) → U49_g(T11, pN3_in_g(T11))
pN3_in_g(T22) → U17_g(T22, pN4_in_g(T22))
pN4_in_g(T22) → U51_g(T22, rN5_in_g(T22))
rN5_in_g(T36) → U18_g(T36, pN6_in_g(T36))
pN6_in_g(T36) → U53_g(T36, qD_in_g(T36))
qD_in_g(f(T656)) → U3_g(T656, pE_in_g(f(T656)))
pE_in_g(f(T628)) → U16_g(T628, pN2_in_g(T628))
pN2_in_g(T628) → U91_g(T628, rZ_in_g(f(T628)))
rZ_in_g(f(T565)) → U14_g(T565, pN1_in_g(T565))
pN1_in_g(T565) → U87_g(T565, qN34_in_g(T565))
qN34_in_g(f(f(T579))) → U41_g(T579, pV_in_g(f(T579)))
pV_in_g(f(T534)) → U12_g(T534, pW_in_g(T534))
pW_in_g(T534) → U85_g(T534, rT_in_g(f(T534)))
rT_in_g(f(T487)) → U11_g(T487, pU_in_g(T487))
pU_in_g(T487) → U83_g(T487, qN31_in_g(T487))
qN31_in_g(f(f(T501))) → U38_g(T501, pR_in_g(f(T501)))
pR_in_g(f(T456)) → U10_g(T456, pS_in_g(T456))
pS_in_g(T456) → U81_g(T456, rP_in_g(f(T456)))
rP_in_g(f(T409)) → U9_g(T409, pQ_in_g(T409))
pQ_in_g(T409) → U79_g(T409, qN28_in_g(T409))
qN28_in_g(f(f(T423))) → U35_g(T423, pN_in_g(f(T423)))
pN_in_g(f(T375)) → U8_g(T375, pO_in_g(T375))
pO_in_g(T375) → U77_g(T375, rL_in_g(f(T375)))
rL_in_g(f(T322)) → U7_g(T322, pM_in_g(T322))
pM_in_g(T322) → U75_g(T322, qN25_in_g(T322))
qN25_in_g(f(f(T336))) → U32_g(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
pF_in_gg(T200, T201) → U4_gg(T200, T201, pG_in_gg(T200, T201))
pG_in_gg(T200, T201) → U69_gg(T200, T201, rN20_in_gg(T200, T201))
rN20_in_gg(T228, T229) → U26_gg(T228, T229, pN21_in_gg(T228, T229))
pN21_in_gg(T228, T229) → U71_gg(T228, T229, qA_in_gg(f(T228), T229))
qA_in_gg(T682, f(f(T683))) → U2_gg(T682, T683, pC_in_gg(T682, T683))
pC_in_gg(T682, T683) → U93_gg(T682, T683, rN37_in_gg(T682, T683))
rN37_in_gg(T710, T711) → U44_gg(T710, T711, pN38_in_gg(T710, T711))
pN38_in_gg(T710, T711) → U95_gg(T710, T711, qA_in_gg(T710, T711))
U95_gg(T710, T711, qA_out_gg(T710, T711)) → U96_gg(T710, T711, rN40_in_gg(T710, T711))
rN40_in_gg(a, b) → rN40_out_gg(a, b)
rN40_in_gg(T736, f(T737)) → U47_gg(T736, T737, pN38_in_gg(T736, T737))
U47_gg(T736, T737, pN38_out_gg(T736, T737)) → rN40_out_gg(T736, f(T737))
rN40_in_gg(f(T742), f(T742)) → U48_gg(T742, tJ_in_g(T742))
tJ_in_g(T270) → U6_g(T270, pK_in_g(T270))
pK_in_g(T270) → U73_g(T270, qH_in_g(f(T270)))
qH_in_g(f(f(T75))) → U5_g(T75, pI_in_g(T75))
pI_in_g(T75) → U57_g(T75, rN9_in_g(T75))
rN9_in_g(T89) → U20_g(T89, pN10_in_g(T89))
pN10_in_g(T89) → U59_g(T89, qN11_in_g(T89))
qN11_in_g(f(f(T113))) → U21_g(T113, pN12_in_g(T113))
pN12_in_g(T113) → U61_g(T113, rN13_in_g(T113))
rN13_in_g(T127) → U22_g(T127, pN14_in_g(T127))
pN14_in_g(T127) → U63_g(T127, qN15_in_g(T127))
qN15_in_g(f(f(T151))) → U23_g(T151, pN16_in_g(T151))
pN16_in_g(T151) → U65_g(T151, rN17_in_g(T151))
rN17_in_g(T165) → U24_g(T165, pN18_in_g(T165))
pN18_in_g(T165) → U67_g(T165, qN19_in_g(T165))
qN19_in_g(f(f(T179))) → U25_g(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
U25_g(T179, pF_out_gg(f(f(f(f(f(f(f(T179))))))), T179)) → qN19_out_g(f(f(T179)))
U67_g(T165, qN19_out_g(T165)) → U68_g(T165, rL_in_g(T165))
U68_g(T165, rL_out_g(T165)) → pN18_out_g(T165)
U24_g(T165, pN18_out_g(T165)) → rN17_out_g(T165)
U65_g(T151, rN17_out_g(T151)) → U66_g(T151, pN_in_g(T151))
U66_g(T151, pN_out_g(T151)) → pN16_out_g(T151)
U23_g(T151, pN16_out_g(T151)) → qN15_out_g(f(f(T151)))
U63_g(T127, qN15_out_g(T127)) → U64_g(T127, rP_in_g(T127))
U64_g(T127, rP_out_g(T127)) → pN14_out_g(T127)
U22_g(T127, pN14_out_g(T127)) → rN13_out_g(T127)
U61_g(T113, rN13_out_g(T113)) → U62_g(T113, pR_in_g(T113))
U62_g(T113, pR_out_g(T113)) → pN12_out_g(T113)
U21_g(T113, pN12_out_g(T113)) → qN11_out_g(f(f(T113)))
U59_g(T89, qN11_out_g(T89)) → U60_g(T89, rT_in_g(T89))
U60_g(T89, rT_out_g(T89)) → pN10_out_g(T89)
U20_g(T89, pN10_out_g(T89)) → rN9_out_g(T89)
U57_g(T75, rN9_out_g(T75)) → U58_g(T75, pV_in_g(T75))
U58_g(T75, pV_out_g(T75)) → pI_out_g(T75)
U5_g(T75, pI_out_g(T75)) → qH_out_g(f(f(T75)))
U73_g(T270, qH_out_g(f(T270))) → U74_g(T270, tN24_in_g(T270))
tN24_in_g(f(T281)) → U31_g(T281, pK_in_g(T281))
U31_g(T281, pK_out_g(T281)) → tN24_out_g(f(T281))
U74_g(T270, tN24_out_g(T270)) → pK_out_g(T270)
U6_g(T270, pK_out_g(T270)) → tJ_out_g(T270)
U48_gg(T742, tJ_out_g(T742)) → rN40_out_gg(f(T742), f(T742))
U96_gg(T710, T711, rN40_out_gg(T710, T711)) → pN38_out_gg(T710, T711)
U44_gg(T710, T711, pN38_out_gg(T710, T711)) → rN37_out_gg(T710, T711)
rN37_in_gg(f(T746), T746) → U45_gg(T746, tJ_in_g(T746))
U45_gg(T746, tJ_out_g(T746)) → rN37_out_gg(f(T746), T746)
U93_gg(T682, T683, rN37_out_gg(T682, T683)) → U94_gg(T682, T683, pN39_in_gg(T682, T683))
pN39_in_gg(a, b) → pN39_out_gg(a, b)
pN39_in_gg(T764, f(T765)) → U46_gg(T764, T765, pC_in_gg(T764, T765))
U46_gg(T764, T765, pC_out_gg(T764, T765)) → pN39_out_gg(T764, f(T765))
U94_gg(T682, T683, pN39_out_gg(T682, T683)) → pC_out_gg(T682, T683)
U2_gg(T682, T683, pC_out_gg(T682, T683)) → qA_out_gg(T682, f(f(T683)))
U71_gg(T228, T229, qA_out_gg(f(T228), T229)) → U72_gg(T228, T229, rN23_in_gg(T228, T229))
rN23_in_gg(T254, f(T255)) → U29_gg(T254, T255, pN21_in_gg(T254, T255))
U29_gg(T254, T255, pN21_out_gg(T254, T255)) → rN23_out_gg(T254, f(T255))
rN23_in_gg(T260, f(T260)) → U30_gg(T260, tJ_in_g(T260))
U30_gg(T260, tJ_out_g(T260)) → rN23_out_gg(T260, f(T260))
U72_gg(T228, T229, rN23_out_gg(T228, T229)) → pN21_out_gg(T228, T229)
U26_gg(T228, T229, pN21_out_gg(T228, T229)) → rN20_out_gg(T228, T229)
rN20_in_gg(T285, T285) → U27_gg(T285, tJ_in_g(T285))
U27_gg(T285, tJ_out_g(T285)) → rN20_out_gg(T285, T285)
U69_gg(T200, T201, rN20_out_gg(T200, T201)) → U70_gg(T200, T201, pN22_in_gg(T200, T201))
pN22_in_gg(T303, f(T304)) → U28_gg(T303, T304, pG_in_gg(T303, T304))
U28_gg(T303, T304, pG_out_gg(T303, T304)) → pN22_out_gg(T303, f(T304))
U70_gg(T200, T201, pN22_out_gg(T200, T201)) → pG_out_gg(T200, T201)
U4_gg(T200, T201, pG_out_gg(T200, T201)) → pF_out_gg(T200, T201)
U32_g(T336, pF_out_gg(f(f(f(f(f(f(f(f(T336)))))))), T336)) → qN25_out_g(f(f(T336)))
U75_g(T322, qN25_out_g(T322)) → U76_g(T322, rN26_in_g(T322))
rN26_in_g(f(T356)) → U33_g(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
U33_g(T356, pN21_out_gg(f(f(f(f(f(f(f(T356))))))), T356)) → rN26_out_g(f(T356))
U76_g(T322, rN26_out_g(T322)) → pM_out_g(T322)
U7_g(T322, pM_out_g(T322)) → rL_out_g(f(T322))
U77_g(T375, rL_out_g(f(T375))) → U78_g(T375, pN27_in_g(T375))
pN27_in_g(f(T389)) → U34_g(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
U34_g(T389, pG_out_gg(f(f(f(f(f(f(f(T389))))))), T389)) → pN27_out_g(f(T389))
U78_g(T375, pN27_out_g(T375)) → pO_out_g(T375)
U8_g(T375, pO_out_g(T375)) → pN_out_g(f(T375))
U35_g(T423, pN_out_g(f(T423))) → qN28_out_g(f(f(T423)))
U79_g(T409, qN28_out_g(T409)) → U80_g(T409, rN29_in_g(T409))
rN29_in_g(f(T440)) → U36_g(T440, pN18_in_g(T440))
U36_g(T440, pN18_out_g(T440)) → rN29_out_g(f(T440))
U80_g(T409, rN29_out_g(T409)) → pQ_out_g(T409)
U9_g(T409, pQ_out_g(T409)) → rP_out_g(f(T409))
U81_g(T456, rP_out_g(f(T456))) → U82_g(T456, pN30_in_g(T456))
pN30_in_g(f(T470)) → U37_g(T470, pN16_in_g(T470))
U37_g(T470, pN16_out_g(T470)) → pN30_out_g(f(T470))
U82_g(T456, pN30_out_g(T456)) → pS_out_g(T456)
U10_g(T456, pS_out_g(T456)) → pR_out_g(f(T456))
U38_g(T501, pR_out_g(f(T501))) → qN31_out_g(f(f(T501)))
U83_g(T487, qN31_out_g(T487)) → U84_g(T487, rN32_in_g(T487))
rN32_in_g(f(T518)) → U39_g(T518, pN14_in_g(T518))
U39_g(T518, pN14_out_g(T518)) → rN32_out_g(f(T518))
U84_g(T487, rN32_out_g(T487)) → pU_out_g(T487)
U11_g(T487, pU_out_g(T487)) → rT_out_g(f(T487))
U85_g(T534, rT_out_g(f(T534))) → U86_g(T534, pN33_in_g(T534))
pN33_in_g(f(T548)) → U40_g(T548, pN12_in_g(T548))
U40_g(T548, pN12_out_g(T548)) → pN33_out_g(f(T548))
U86_g(T534, pN33_out_g(T534)) → pW_out_g(T534)
U12_g(T534, pW_out_g(T534)) → pV_out_g(f(T534))
U41_g(T579, pV_out_g(f(T579))) → qN34_out_g(f(f(T579)))
U87_g(T565, qN34_out_g(T565)) → U88_g(T565, rN35_in_g(T565))
rN35_in_g(f(T596)) → U42_g(T596, pN10_in_g(T596))
U42_g(T596, pN10_out_g(T596)) → rN35_out_g(f(T596))
U88_g(T565, rN35_out_g(T565)) → pN1_out_g(T565)
U14_g(T565, pN1_out_g(T565)) → rZ_out_g(f(T565))
rZ_in_g(f(T601)) → U15_g(T601, tJ_in_g(T601))
U15_g(T601, tJ_out_g(T601)) → rZ_out_g(f(T601))
U91_g(T628, rZ_out_g(f(T628))) → U92_g(T628, pN36_in_g(T628))
pN36_in_g(f(T642)) → U43_g(T642, pI_in_g(T642))
U43_g(T642, pI_out_g(T642)) → pN36_out_g(f(T642))
U92_g(T628, pN36_out_g(T628)) → pN2_out_g(T628)
U16_g(T628, pN2_out_g(T628)) → pE_out_g(f(T628))
U3_g(T656, pE_out_g(f(T656))) → qD_out_g(f(T656))
U53_g(T36, qD_out_g(T36)) → U54_g(T36, rX_in_g(T36))
rX_in_g(T51) → U13_g(T51, pY_in_g(T51))
pY_in_g(T51) → U55_g(T51, qH_in_g(T51))
U55_g(T51, qH_out_g(T51)) → U56_g(T51, rZ_in_g(T51))
U56_g(T51, rZ_out_g(T51)) → pY_out_g(T51)
U13_g(T51, pY_out_g(T51)) → rX_out_g(T51)
U54_g(T36, rX_out_g(T36)) → pN6_out_g(T36)
U18_g(T36, pN6_out_g(T36)) → rN5_out_g(T36)
U51_g(T22, rN5_out_g(T22)) → U52_g(T22, pN7_in_g(T22))
pN7_in_g(T614) → U19_g(T614, pN8_in_g(T614))
pN8_in_g(T614) → U89_g(T614, rX_in_g(T614))
U89_g(T614, rX_out_g(T614)) → U90_g(T614, pE_in_g(T614))
U90_g(T614, pE_out_g(T614)) → pN8_out_g(T614)
U19_g(T614, pN8_out_g(T614)) → pN7_out_g(T614)
U52_g(T22, pN7_out_g(T22)) → pN4_out_g(T22)
U17_g(T22, pN4_out_g(T22)) → pN3_out_g(T22)
U49_g(T11, pN3_out_g(T11)) → U50_g(T11, qD_in_g(T11))
U50_g(T11, qD_out_g(T11)) → pB_out_g(T11)
U1_gg(T11, pB_out_g(T11)) → qA_out_gg(T11, f(f(T11)))

The set Q consists of the following terms:

qA_in_gg(x0, x1)
pB_in_g(x0)
pN3_in_g(x0)
pN4_in_g(x0)
rN5_in_g(x0)
pN6_in_g(x0)
qD_in_g(x0)
pE_in_g(x0)
pN2_in_g(x0)
rZ_in_g(x0)
pN1_in_g(x0)
qN34_in_g(x0)
pV_in_g(x0)
pW_in_g(x0)
rT_in_g(x0)
pU_in_g(x0)
qN31_in_g(x0)
pR_in_g(x0)
pS_in_g(x0)
rP_in_g(x0)
pQ_in_g(x0)
qN28_in_g(x0)
pN_in_g(x0)
pO_in_g(x0)
rL_in_g(x0)
pM_in_g(x0)
qN25_in_g(x0)
pF_in_gg(x0, x1)
pG_in_gg(x0, x1)
rN20_in_gg(x0, x1)
pN21_in_gg(x0, x1)
pC_in_gg(x0, x1)
rN37_in_gg(x0, x1)
pN38_in_gg(x0, x1)
U95_gg(x0, x1, x2)
rN40_in_gg(x0, x1)
U47_gg(x0, x1, x2)
tJ_in_g(x0)
pK_in_g(x0)
qH_in_g(x0)
pI_in_g(x0)
rN9_in_g(x0)
pN10_in_g(x0)
qN11_in_g(x0)
pN12_in_g(x0)
rN13_in_g(x0)
pN14_in_g(x0)
qN15_in_g(x0)
pN16_in_g(x0)
rN17_in_g(x0)
pN18_in_g(x0)
qN19_in_g(x0)
U25_g(x0, x1)
U67_g(x0, x1)
U68_g(x0, x1)
U24_g(x0, x1)
U65_g(x0, x1)
U66_g(x0, x1)
U23_g(x0, x1)
U63_g(x0, x1)
U64_g(x0, x1)
U22_g(x0, x1)
U61_g(x0, x1)
U62_g(x0, x1)
U21_g(x0, x1)
U59_g(x0, x1)
U60_g(x0, x1)
U20_g(x0, x1)
U57_g(x0, x1)
U58_g(x0, x1)
U5_g(x0, x1)
U73_g(x0, x1)
tN24_in_g(x0)
U31_g(x0, x1)
U74_g(x0, x1)
U6_g(x0, x1)
U48_gg(x0, x1)
U96_gg(x0, x1, x2)
U44_gg(x0, x1, x2)
U45_gg(x0, x1)
U93_gg(x0, x1, x2)
pN39_in_gg(x0, x1)
U46_gg(x0, x1, x2)
U94_gg(x0, x1, x2)
U2_gg(x0, x1, x2)
U71_gg(x0, x1, x2)
rN23_in_gg(x0, x1)
U29_gg(x0, x1, x2)
U30_gg(x0, x1)
U72_gg(x0, x1, x2)
U26_gg(x0, x1, x2)
U27_gg(x0, x1)
U69_gg(x0, x1, x2)
pN22_in_gg(x0, x1)
U28_gg(x0, x1, x2)
U70_gg(x0, x1, x2)
U4_gg(x0, x1, x2)
U32_g(x0, x1)
U75_g(x0, x1)
rN26_in_g(x0)
U33_g(x0, x1)
U76_g(x0, x1)
U7_g(x0, x1)
U77_g(x0, x1)
pN27_in_g(x0)
U34_g(x0, x1)
U78_g(x0, x1)
U8_g(x0, x1)
U35_g(x0, x1)
U79_g(x0, x1)
rN29_in_g(x0)
U36_g(x0, x1)
U80_g(x0, x1)
U9_g(x0, x1)
U81_g(x0, x1)
pN30_in_g(x0)
U37_g(x0, x1)
U82_g(x0, x1)
U10_g(x0, x1)
U38_g(x0, x1)
U83_g(x0, x1)
rN32_in_g(x0)
U39_g(x0, x1)
U84_g(x0, x1)
U11_g(x0, x1)
U85_g(x0, x1)
pN33_in_g(x0)
U40_g(x0, x1)
U86_g(x0, x1)
U12_g(x0, x1)
U41_g(x0, x1)
U87_g(x0, x1)
rN35_in_g(x0)
U42_g(x0, x1)
U88_g(x0, x1)
U14_g(x0, x1)
U15_g(x0, x1)
U91_g(x0, x1)
pN36_in_g(x0)
U43_g(x0, x1)
U92_g(x0, x1)
U16_g(x0, x1)
U3_g(x0, x1)
U53_g(x0, x1)
rX_in_g(x0)
pY_in_g(x0)
U55_g(x0, x1)
U56_g(x0, x1)
U13_g(x0, x1)
U54_g(x0, x1)
U18_g(x0, x1)
U51_g(x0, x1)
pN7_in_g(x0)
pN8_in_g(x0)
U89_g(x0, x1)
U90_g(x0, x1)
U19_g(x0, x1)
U52_g(x0, x1)
U17_g(x0, x1)
U49_g(x0, x1)
U50_g(x0, x1)
U1_gg(x0, x1)

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

(11) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].

The following pairs can be oriented strictly and are deleted.

QA_IN_GG(T11, f(f(T11))) → PB_IN_G(T11)
PE_IN_G(f(T628)) → PN2_IN_G(T628)
PN2_IN_G(T628) → U91_G(T628, rZ_in_g(f(T628)))
U57_G(T75, rN9_out_g(T75)) → PV_IN_G(T75)
PN33_IN_G(f(T548)) → PN12_IN_G(T548)
PN12_IN_G(T113) → U61_G(T113, rN13_in_g(T113))
PN30_IN_G(f(T470)) → PN16_IN_G(T470)
U65_G(T151, rN17_out_g(T151)) → PN_IN_G(T151)
PO_IN_G(T375) → U77_G(T375, rL_in_g(f(T375)))
PG_IN_GG(T200, T201) → U69_GG(T200, T201, rN20_in_gg(T200, T201))
PN21_IN_GG(T228, T229) → U71_GG(T228, T229, qA_in_gg(f(T228), T229))
PN21_IN_GG(T228, T229) → QA_IN_GG(f(T228), T229)
QA_IN_GG(T682, f(f(T683))) → PC_IN_GG(T682, T683)
PC_IN_GG(T682, T683) → U93_GG(T682, T683, rN37_in_gg(T682, T683))
RN40_IN_GG(T736, f(T737)) → PN38_IN_GG(T736, T737)
PN38_IN_GG(T710, T711) → QA_IN_GG(T710, T711)
RN40_IN_GG(f(T742), f(T742)) → TJ_IN_G(T742)
PK_IN_G(T270) → U73_G(T270, qH_in_g(f(T270)))
QH_IN_G(f(f(T75))) → PI_IN_G(T75)
PI_IN_G(T75) → RN9_IN_G(T75)
RN32_IN_G(f(T518)) → PN14_IN_G(T518)
RN29_IN_G(f(T440)) → PN18_IN_G(T440)
RL_IN_G(f(T322)) → PM_IN_G(T322)
QN25_IN_G(f(f(T336))) → PF_IN_GG(f(f(f(f(f(f(f(f(T336)))))))), T336)
QN19_IN_G(f(f(T179))) → PF_IN_GG(f(f(f(f(f(f(f(T179))))))), T179)
PQ_IN_G(T409) → QN28_IN_G(T409)
QN28_IN_G(f(f(T423))) → PN_IN_G(f(T423))
QN15_IN_G(f(f(T151))) → PN16_IN_G(T151)
PN16_IN_G(T151) → RN17_IN_G(T151)
PU_IN_G(T487) → QN31_IN_G(T487)
QN31_IN_G(f(f(T501))) → PR_IN_G(f(T501))
QN11_IN_G(f(f(T113))) → PN12_IN_G(T113)
RN13_IN_G(T127) → PN14_IN_G(T127)
PN1_IN_G(T565) → U87_G(T565, qN34_in_g(T565))
RN35_IN_G(f(T596)) → PN10_IN_G(T596)
PN1_IN_G(T565) → QN34_IN_G(T565)
QN34_IN_G(f(f(T579))) → PV_IN_G(f(T579))
PN8_IN_G(T614) → RX_IN_G(T614)
PN6_IN_G(T36) → U53_G(T36, qD_in_g(T36))

The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(PB_IN_G(x₁)) = 1 + x₁
POL(PC_IN_GG(x₁, x₂)) = 1 + x₂
POL(PE_IN_G(x₁)) = 1 + x₁
POL(PF_IN_GG(x₁, x₂)) = 1 + x₂
POL(PG_IN_GG(x₁, x₂)) = 1 + x₂
POL(PI_IN_G(x₁)) = 1 + x₁
POL(PK_IN_G(x₁)) = 1 + x₁
POL(PM_IN_G(x₁)) = x₁
POL(PN10_IN_G(x₁)) = x₁
POL(PN12_IN_G(x₁)) = 1 + x₁
POL(PN14_IN_G(x₁)) = x₁
POL(PN16_IN_G(x₁)) = 1 + x₁
POL(PN18_IN_G(x₁)) = x₁
POL(PN1_IN_G(x₁)) = 1 + x₁
POL(PN21_IN_GG(x₁, x₂)) = 1 + x₂
POL(PN22_IN_GG(x₁, x₂)) = x₂
POL(PN27_IN_G(x₁)) = x₁
POL(PN2_IN_G(x₁)) = 1 + x₁
POL(PN30_IN_G(x₁)) = 1 + x₁
POL(PN33_IN_G(x₁)) = 1 + x₁
POL(PN36_IN_G(x₁)) = x₁
POL(PN38_IN_GG(x₁, x₂)) = 1 + x₂
POL(PN39_IN_GG(x₁, x₂)) = x₂
POL(PN3_IN_G(x₁)) = 1 + x₁
POL(PN4_IN_G(x₁)) = 1 + x₁
POL(PN6_IN_G(x₁)) = 1 + x₁
POL(PN7_IN_G(x₁)) = 1 + x₁
POL(PN8_IN_G(x₁)) = 1 + x₁
POL(PN_IN_G(x₁)) = x₁
POL(PO_IN_G(x₁)) = 1 + x₁
POL(PQ_IN_G(x₁)) = 1 + x₁
POL(PR_IN_G(x₁)) = x₁
POL(PS_IN_G(x₁)) = 1 + x₁
POL(PU_IN_G(x₁)) = 1 + x₁
POL(PV_IN_G(x₁)) = x₁
POL(PW_IN_G(x₁)) = 1 + x₁
POL(PY_IN_G(x₁)) = x₁
POL(QA_IN_GG(x₁, x₂)) = x₂
POL(QD_IN_G(x₁)) = 1 + x₁
POL(QH_IN_G(x₁)) = x₁
POL(QN11_IN_G(x₁)) = x₁
POL(QN15_IN_G(x₁)) = x₁
POL(QN19_IN_G(x₁)) = x₁
POL(QN25_IN_G(x₁)) = x₁
POL(QN28_IN_G(x₁)) = x₁
POL(QN31_IN_G(x₁)) = x₁
POL(QN34_IN_G(x₁)) = x₁
POL(RL_IN_G(x₁)) = x₁
POL(RN13_IN_G(x₁)) = 1 + x₁
POL(RN17_IN_G(x₁)) = x₁
POL(RN20_IN_GG(x₁, x₂)) = 1 + x₂
POL(RN23_IN_GG(x₁, x₂)) = x₂
POL(RN26_IN_G(x₁)) = x₁
POL(RN29_IN_G(x₁)) = 1 + x₁
POL(RN32_IN_G(x₁)) = 1 + x₁
POL(RN35_IN_G(x₁)) = x₁
POL(RN37_IN_GG(x₁, x₂)) = 1 + x₂
POL(RN40_IN_GG(x₁, x₂)) = 1 + x₂
POL(RN5_IN_G(x₁)) = 1 + x₁
POL(RN9_IN_G(x₁)) = x₁
POL(RP_IN_G(x₁)) = x₁
POL(RT_IN_G(x₁)) = x₁
POL(RX_IN_G(x₁)) = x₁
POL(RZ_IN_G(x₁)) = x₁
POL(TJ_IN_G(x₁)) = 1 + x₁
POL(TN24_IN_G(x₁)) = x₁
POL(U10_g(x₁, x₂)) = 0
POL(U11_g(x₁, x₂)) = 0
POL(U12_g(x₁, x₂)) = 0
POL(U13_g(x₁, x₂)) = 0
POL(U14_g(x₁, x₂)) = 0
POL(U15_g(x₁, x₂)) = 0
POL(U16_g(x₁, x₂)) = 0
POL(U17_g(x₁, x₂)) = 0
POL(U18_g(x₁, x₂)) = 0
POL(U19_g(x₁, x₂)) = 0
POL(U1_gg(x₁, x₂)) = 0
POL(U20_g(x₁, x₂)) = 0
POL(U21_g(x₁, x₂)) = 0
POL(U22_g(x₁, x₂)) = 0
POL(U23_g(x₁, x₂)) = 0
POL(U24_g(x₁, x₂)) = 0
POL(U25_g(x₁, x₂)) = 0
POL(U26_gg(x₁, x₂, x₃)) = 0
POL(U27_gg(x₁, x₂)) = 0
POL(U28_gg(x₁, x₂, x₃)) = 0
POL(U29_gg(x₁, x₂, x₃)) = 0
POL(U2_gg(x₁, x₂, x₃)) = 0
POL(U30_gg(x₁, x₂)) = 0
POL(U31_g(x₁, x₂)) = 0
POL(U32_g(x₁, x₂)) = 0
POL(U33_g(x₁, x₂)) = 0
POL(U34_g(x₁, x₂)) = 0
POL(U35_g(x₁, x₂)) = 0
POL(U36_g(x₁, x₂)) = 0
POL(U37_g(x₁, x₂)) = 0
POL(U38_g(x₁, x₂)) = 0
POL(U39_g(x₁, x₂)) = 0
POL(U3_g(x₁, x₂)) = 0
POL(U40_g(x₁, x₂)) = 0
POL(U41_g(x₁, x₂)) = 0
POL(U42_g(x₁, x₂)) = 0
POL(U43_g(x₁, x₂)) = 0
POL(U44_gg(x₁, x₂, x₃)) = 0
POL(U45_gg(x₁, x₂)) = 0
POL(U46_gg(x₁, x₂, x₃)) = 0
POL(U47_gg(x₁, x₂, x₃)) = 0
POL(U48_gg(x₁, x₂)) = 0
POL(U49_G(x₁, x₂)) = 1 + x₁
POL(U49_g(x₁, x₂)) = 0
POL(U4_gg(x₁, x₂, x₃)) = 0
POL(U50_g(x₁, x₂)) = 0
POL(U51_G(x₁, x₂)) = 1 + x₁
POL(U51_g(x₁, x₂)) = 0
POL(U52_g(x₁, x₂)) = 0
POL(U53_G(x₁, x₂)) = x₁
POL(U53_g(x₁, x₂)) = 0
POL(U54_g(x₁, x₂)) = 0
POL(U55_G(x₁, x₂)) = x₁
POL(U55_g(x₁, x₂)) = 0
POL(U56_g(x₁, x₂)) = 0
POL(U57_G(x₁, x₂)) = 1 + x₁
POL(U57_g(x₁, x₂)) = 0
POL(U58_g(x₁, x₂)) = 0
POL(U59_G(x₁, x₂)) = x₁
POL(U59_g(x₁, x₂)) = 0
POL(U5_g(x₁, x₂)) = 0
POL(U60_g(x₁, x₂)) = 0
POL(U61_G(x₁, x₂)) = x₁
POL(U61_g(x₁, x₂)) = 0
POL(U62_g(x₁, x₂)) = 0
POL(U63_G(x₁, x₂)) = x₁
POL(U63_g(x₁, x₂)) = 0
POL(U64_g(x₁, x₂)) = 0
POL(U65_G(x₁, x₂)) = 1 + x₁
POL(U65_g(x₁, x₂)) = 0
POL(U66_g(x₁, x₂)) = 0
POL(U67_G(x₁, x₂)) = x₁
POL(U67_g(x₁, x₂)) = 0
POL(U68_g(x₁, x₂)) = 0
POL(U69_GG(x₁, x₂, x₃)) = x₂
POL(U69_gg(x₁, x₂, x₃)) = 0
POL(U6_g(x₁, x₂)) = 0
POL(U70_gg(x₁, x₂, x₃)) = 0
POL(U71_GG(x₁, x₂, x₃)) = x₂
POL(U71_gg(x₁, x₂, x₃)) = 0
POL(U72_gg(x₁, x₂, x₃)) = 0
POL(U73_G(x₁, x₂)) = x₁
POL(U73_g(x₁, x₂)) = 0
POL(U74_g(x₁, x₂)) = 0
POL(U75_G(x₁, x₂)) = x₁
POL(U75_g(x₁, x₂)) = 0
POL(U76_g(x₁, x₂)) = 0
POL(U77_G(x₁, x₂)) = x₁
POL(U77_g(x₁, x₂)) = 0
POL(U78_g(x₁, x₂)) = 0
POL(U79_G(x₁, x₂)) = 1 + x₁
POL(U79_g(x₁, x₂)) = 0
POL(U7_g(x₁, x₂)) = 0
POL(U80_g(x₁, x₂)) = 0
POL(U81_G(x₁, x₂)) = 1 + x₁
POL(U81_g(x₁, x₂)) = 0
POL(U82_g(x₁, x₂)) = 0
POL(U83_G(x₁, x₂)) = 1 + x₁
POL(U83_g(x₁, x₂)) = 0
POL(U84_g(x₁, x₂)) = 0
POL(U85_G(x₁, x₂)) = 1 + x₁
POL(U85_g(x₁, x₂)) = 0
POL(U86_g(x₁, x₂)) = 0
POL(U87_G(x₁, x₂)) = x₁
POL(U87_g(x₁, x₂)) = 0
POL(U88_g(x₁, x₂)) = 0
POL(U89_G(x₁, x₂)) = 1 + x₁
POL(U89_g(x₁, x₂)) = 0
POL(U8_g(x₁, x₂)) = 0
POL(U90_g(x₁, x₂)) = 0
POL(U91_G(x₁, x₂)) = x₁
POL(U91_g(x₁, x₂)) = 0
POL(U92_g(x₁, x₂)) = 0
POL(U93_GG(x₁, x₂, x₃)) = x₂
POL(U93_gg(x₁, x₂, x₃)) = 0
POL(U94_gg(x₁, x₂, x₃)) = 0
POL(U95_GG(x₁, x₂, x₃)) = 1 + x₂
POL(U95_gg(x₁, x₂, x₃)) = 0
POL(U96_gg(x₁, x₂, x₃)) = 0
POL(U9_g(x₁, x₂)) = 0
POL(a) = 0
POL(b) = 0
POL(f(x₁)) = 1 + x₁
POL(pB_in_g(x₁)) = 0
POL(pB_out_g(x₁)) = 0
POL(pC_in_gg(x₁, x₂)) = 0
POL(pC_out_gg(x₁, x₂)) = 0
POL(pE_in_g(x₁)) = 0
POL(pE_out_g(x₁)) = 0
POL(pF_in_gg(x₁, x₂)) = 0
POL(pF_out_gg(x₁, x₂)) = 0
POL(pG_in_gg(x₁, x₂)) = 0
POL(pG_out_gg(x₁, x₂)) = 0
POL(pI_in_g(x₁)) = 0
POL(pI_out_g(x₁)) = 0
POL(pK_in_g(x₁)) = 0
POL(pK_out_g(x₁)) = 0
POL(pM_in_g(x₁)) = 0
POL(pM_out_g(x₁)) = 0
POL(pN10_in_g(x₁)) = 0
POL(pN10_out_g(x₁)) = 0
POL(pN12_in_g(x₁)) = 0
POL(pN12_out_g(x₁)) = 0
POL(pN14_in_g(x₁)) = 0
POL(pN14_out_g(x₁)) = 0
POL(pN16_in_g(x₁)) = 0
POL(pN16_out_g(x₁)) = 0
POL(pN18_in_g(x₁)) = 0
POL(pN18_out_g(x₁)) = 0
POL(pN1_in_g(x₁)) = 0
POL(pN1_out_g(x₁)) = 0
POL(pN21_in_gg(x₁, x₂)) = 0
POL(pN21_out_gg(x₁, x₂)) = 0
POL(pN22_in_gg(x₁, x₂)) = 0
POL(pN22_out_gg(x₁, x₂)) = 0
POL(pN27_in_g(x₁)) = 0
POL(pN27_out_g(x₁)) = 0
POL(pN2_in_g(x₁)) = 0
POL(pN2_out_g(x₁)) = 0
POL(pN30_in_g(x₁)) = 0
POL(pN30_out_g(x₁)) = 0
POL(pN33_in_g(x₁)) = 0
POL(pN33_out_g(x₁)) = 0
POL(pN36_in_g(x₁)) = 0
POL(pN36_out_g(x₁)) = 0
POL(pN38_in_gg(x₁, x₂)) = 0
POL(pN38_out_gg(x₁, x₂)) = 0
POL(pN39_in_gg(x₁, x₂)) = 1
POL(pN39_out_gg(x₁, x₂)) = 0
POL(pN3_in_g(x₁)) = 0
POL(pN3_out_g(x₁)) = 0
POL(pN4_in_g(x₁)) = 0
POL(pN4_out_g(x₁)) = 0
POL(pN6_in_g(x₁)) = 0
POL(pN6_out_g(x₁)) = 0
POL(pN7_in_g(x₁)) = 0
POL(pN7_out_g(x₁)) = 0
POL(pN8_in_g(x₁)) = 0
POL(pN8_out_g(x₁)) = 0
POL(pN_in_g(x₁)) = 0
POL(pN_out_g(x₁)) = 0
POL(pO_in_g(x₁)) = 0
POL(pO_out_g(x₁)) = 0
POL(pQ_in_g(x₁)) = 0
POL(pQ_out_g(x₁)) = 0
POL(pR_in_g(x₁)) = 0
POL(pR_out_g(x₁)) = 0
POL(pS_in_g(x₁)) = 0
POL(pS_out_g(x₁)) = 0
POL(pU_in_g(x₁)) = 0
POL(pU_out_g(x₁)) = 0
POL(pV_in_g(x₁)) = 0
POL(pV_out_g(x₁)) = 0
POL(pW_in_g(x₁)) = 0
POL(pW_out_g(x₁)) = 0
POL(pY_in_g(x₁)) = 0
POL(pY_out_g(x₁)) = 0
POL(qA_in_gg(x₁, x₂)) = 0
POL(qA_out_gg(x₁, x₂)) = 0
POL(qD_in_g(x₁)) = 0
POL(qD_out_g(x₁)) = 0
POL(qH_in_g(x₁)) = 0
POL(qH_out_g(x₁)) = 0
POL(qN11_in_g(x₁)) = 0
POL(qN11_out_g(x₁)) = 0
POL(qN15_in_g(x₁)) = 0
POL(qN15_out_g(x₁)) = 0
POL(qN19_in_g(x₁)) = 0
POL(qN19_out_g(x₁)) = 0
POL(qN25_in_g(x₁)) = 0
POL(qN25_out_g(x₁)) = 0
POL(qN28_in_g(x₁)) = 0
POL(qN28_out_g(x₁)) = 0
POL(qN31_in_g(x₁)) = 0
POL(qN31_out_g(x₁)) = 0
POL(qN34_in_g(x₁)) = 0
POL(qN34_out_g(x₁)) = 0
POL(rL_in_g(x₁)) = 0
POL(rL_out_g(x₁)) = 0
POL(rN13_in_g(x₁)) = 0
POL(rN13_out_g(x₁)) = 0
POL(rN17_in_g(x₁)) = 0
POL(rN17_out_g(x₁)) = 0
POL(rN20_in_gg(x₁, x₂)) = 0
POL(rN20_out_gg(x₁, x₂)) = 0
POL(rN23_in_gg(x₁, x₂)) = 0
POL(rN23_out_gg(x₁, x₂)) = 0
POL(rN26_in_g(x₁)) = 0
POL(rN26_out_g(x₁)) = 0
POL(rN29_in_g(x₁)) = 0
POL(rN29_out_g(x₁)) = 0
POL(rN32_in_g(x₁)) = 0
POL(rN32_out_g(x₁)) = 0
POL(rN35_in_g(x₁)) = 0
POL(rN35_out_g(x₁)) = 0
POL(rN37_in_gg(x₁, x₂)) = 0
POL(rN37_out_gg(x₁, x₂)) = 0
POL(rN40_in_gg(x₁, x₂)) = 0
POL(rN40_out_gg(x₁, x₂)) = 0
POL(rN5_in_g(x₁)) = 0
POL(rN5_out_g(x₁)) = 0
POL(rN9_in_g(x₁)) = 0
POL(rN9_out_g(x₁)) = 0
POL(rP_in_g(x₁)) = 0
POL(rP_out_g(x₁)) = 0
POL(rT_in_g(x₁)) = 0
POL(rT_out_g(x₁)) = 0
POL(rX_in_g(x₁)) = 0
POL(rX_out_g(x₁)) = 0
POL(rZ_in_g(x₁)) = 0
POL(rZ_out_g(x₁)) = 0
POL(tJ_in_g(x₁)) = 0
POL(tJ_out_g(x₁)) = 0
POL(tN24_in_g(x₁)) = 0
POL(tN24_out_g(x₁)) = 0

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none

(12) Obligation:

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

PB_IN_G(T11) → U49_G(T11, pN3_in_g(T11))
U49_G(T11, pN3_out_g(T11)) → QD_IN_G(T11)
QD_IN_G(f(T656)) → PE_IN_G(f(T656))
U91_G(T628, rZ_out_g(f(T628))) → PN36_IN_G(T628)
PN36_IN_G(f(T642)) → PI_IN_G(T642)
PI_IN_G(T75) → U57_G(T75, rN9_in_g(T75))
PV_IN_G(f(T534)) → PW_IN_G(T534)
PW_IN_G(T534) → U85_G(T534, rT_in_g(f(T534)))
U85_G(T534, rT_out_g(f(T534))) → PN33_IN_G(T534)
U61_G(T113, rN13_out_g(T113)) → PR_IN_G(T113)
PR_IN_G(f(T456)) → PS_IN_G(T456)
PS_IN_G(T456) → U81_G(T456, rP_in_g(f(T456)))
U81_G(T456, rP_out_g(f(T456))) → PN30_IN_G(T456)
PN16_IN_G(T151) → U65_G(T151, rN17_in_g(T151))
PN_IN_G(f(T375)) → PO_IN_G(T375)
U77_G(T375, rL_out_g(f(T375))) → PN27_IN_G(T375)
PN27_IN_G(f(T389)) → PG_IN_GG(f(f(f(f(f(f(f(T389))))))), T389)
U69_GG(T200, T201, rN20_out_gg(T200, T201)) → PN22_IN_GG(T200, T201)
PN22_IN_GG(T303, f(T304)) → PG_IN_GG(T303, T304)
PG_IN_GG(T200, T201) → RN20_IN_GG(T200, T201)
RN20_IN_GG(T228, T229) → PN21_IN_GG(T228, T229)
U71_GG(T228, T229, qA_out_gg(f(T228), T229)) → RN23_IN_GG(T228, T229)
RN23_IN_GG(T254, f(T255)) → PN21_IN_GG(T254, T255)
U93_GG(T682, T683, rN37_out_gg(T682, T683)) → PN39_IN_GG(T682, T683)
PN39_IN_GG(T764, f(T765)) → PC_IN_GG(T764, T765)
PC_IN_GG(T682, T683) → RN37_IN_GG(T682, T683)
RN37_IN_GG(T710, T711) → PN38_IN_GG(T710, T711)
PN38_IN_GG(T710, T711) → U95_GG(T710, T711, qA_in_gg(T710, T711))
U95_GG(T710, T711, qA_out_gg(T710, T711)) → RN40_IN_GG(T710, T711)
TJ_IN_G(T270) → PK_IN_G(T270)
U73_G(T270, qH_out_g(f(T270))) → TN24_IN_G(T270)
TN24_IN_G(f(T281)) → PK_IN_G(T281)
PK_IN_G(T270) → QH_IN_G(f(T270))
RN9_IN_G(T89) → PN10_IN_G(T89)
PN10_IN_G(T89) → U59_G(T89, qN11_in_g(T89))
U59_G(T89, qN11_out_g(T89)) → RT_IN_G(T89)
RT_IN_G(f(T487)) → PU_IN_G(T487)
PU_IN_G(T487) → U83_G(T487, qN31_in_g(T487))
U83_G(T487, qN31_out_g(T487)) → RN32_IN_G(T487)
PN14_IN_G(T127) → U63_G(T127, qN15_in_g(T127))
U63_G(T127, qN15_out_g(T127)) → RP_IN_G(T127)
RP_IN_G(f(T409)) → PQ_IN_G(T409)
PQ_IN_G(T409) → U79_G(T409, qN28_in_g(T409))
U79_G(T409, qN28_out_g(T409)) → RN29_IN_G(T409)
PN18_IN_G(T165) → U67_G(T165, qN19_in_g(T165))
U67_G(T165, qN19_out_g(T165)) → RL_IN_G(T165)
PM_IN_G(T322) → U75_G(T322, qN25_in_g(T322))
U75_G(T322, qN25_out_g(T322)) → RN26_IN_G(T322)
RN26_IN_G(f(T356)) → PN21_IN_GG(f(f(f(f(f(f(f(T356))))))), T356)
PM_IN_G(T322) → QN25_IN_G(T322)
PN18_IN_G(T165) → QN19_IN_G(T165)
PN14_IN_G(T127) → QN15_IN_G(T127)
RN17_IN_G(T165) → PN18_IN_G(T165)
PN10_IN_G(T89) → QN11_IN_G(T89)
PN12_IN_G(T113) → RN13_IN_G(T113)
RN37_IN_GG(f(T746), T746) → TJ_IN_G(T746)
RN23_IN_GG(T260, f(T260)) → TJ_IN_G(T260)
RN20_IN_GG(T285, T285) → TJ_IN_G(T285)
PO_IN_G(T375) → RL_IN_G(f(T375))
PS_IN_G(T456) → RP_IN_G(f(T456))
PW_IN_G(T534) → RT_IN_G(f(T534))
PN2_IN_G(T628) → RZ_IN_G(f(T628))
RZ_IN_G(f(T565)) → PN1_IN_G(T565)
U87_G(T565, qN34_out_g(T565)) → RN35_IN_G(T565)
RZ_IN_G(f(T601)) → TJ_IN_G(T601)
PB_IN_G(T11) → PN3_IN_G(T11)
PN3_IN_G(T22) → PN4_IN_G(T22)
PN4_IN_G(T22) → U51_G(T22, rN5_in_g(T22))
U51_G(T22, rN5_out_g(T22)) → PN7_IN_G(T22)
PN7_IN_G(T614) → PN8_IN_G(T614)
PN8_IN_G(T614) → U89_G(T614, rX_in_g(T614))
U89_G(T614, rX_out_g(T614)) → PE_IN_G(T614)
RX_IN_G(T51) → PY_IN_G(T51)
PY_IN_G(T51) → U55_G(T51, qH_in_g(T51))
U55_G(T51, qH_out_g(T51)) → RZ_IN_G(T51)
PY_IN_G(T51) → QH_IN_G(T51)
PN4_IN_G(T22) → RN5_IN_G(T22)
RN5_IN_G(T36) → PN6_IN_G(T36)
U53_G(T36, qD_out_g(T36)) → RX_IN_G(T36)
PN6_IN_G(T36) → QD_IN_G(T36)
PF_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0) → PG_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0)
PF_IN_GG(f(f(f(f(f(f(f(z0))))))), z0) → PG_IN_GG(f(f(f(f(f(f(f(z0))))))), z0)

The TRS R consists of the following rules:

qA_in_gg(a, b) → qA_out_gg(a, b)
qA_in_gg(T11, f(f(T11))) → U1_gg(T11, pB_in_g(T11))
pB_in_g(T11) → U49_g(T11, pN3_in_g(T11))
pN3_in_g(T22) → U17_g(T22, pN4_in_g(T22))
pN4_in_g(T22) → U51_g(T22, rN5_in_g(T22))
rN5_in_g(T36) → U18_g(T36, pN6_in_g(T36))
pN6_in_g(T36) → U53_g(T36, qD_in_g(T36))
qD_in_g(f(T656)) → U3_g(T656, pE_in_g(f(T656)))
pE_in_g(f(T628)) → U16_g(T628, pN2_in_g(T628))
pN2_in_g(T628) → U91_g(T628, rZ_in_g(f(T628)))
rZ_in_g(f(T565)) → U14_g(T565, pN1_in_g(T565))
pN1_in_g(T565) → U87_g(T565, qN34_in_g(T565))
qN34_in_g(f(f(T579))) → U41_g(T579, pV_in_g(f(T579)))
pV_in_g(f(T534)) → U12_g(T534, pW_in_g(T534))
pW_in_g(T534) → U85_g(T534, rT_in_g(f(T534)))
rT_in_g(f(T487)) → U11_g(T487, pU_in_g(T487))
pU_in_g(T487) → U83_g(T487, qN31_in_g(T487))
qN31_in_g(f(f(T501))) → U38_g(T501, pR_in_g(f(T501)))
pR_in_g(f(T456)) → U10_g(T456, pS_in_g(T456))
pS_in_g(T456) → U81_g(T456, rP_in_g(f(T456)))
rP_in_g(f(T409)) → U9_g(T409, pQ_in_g(T409))
pQ_in_g(T409) → U79_g(T409, qN28_in_g(T409))
qN28_in_g(f(f(T423))) → U35_g(T423, pN_in_g(f(T423)))
pN_in_g(f(T375)) → U8_g(T375, pO_in_g(T375))
pO_in_g(T375) → U77_g(T375, rL_in_g(f(T375)))
rL_in_g(f(T322)) → U7_g(T322, pM_in_g(T322))
pM_in_g(T322) → U75_g(T322, qN25_in_g(T322))
qN25_in_g(f(f(T336))) → U32_g(T336, pF_in_gg(f(f(f(f(f(f(f(f(T336)))))))), T336))
pF_in_gg(T200, T201) → U4_gg(T200, T201, pG_in_gg(T200, T201))
pG_in_gg(T200, T201) → U69_gg(T200, T201, rN20_in_gg(T200, T201))
rN20_in_gg(T228, T229) → U26_gg(T228, T229, pN21_in_gg(T228, T229))
pN21_in_gg(T228, T229) → U71_gg(T228, T229, qA_in_gg(f(T228), T229))
qA_in_gg(T682, f(f(T683))) → U2_gg(T682, T683, pC_in_gg(T682, T683))
pC_in_gg(T682, T683) → U93_gg(T682, T683, rN37_in_gg(T682, T683))
rN37_in_gg(T710, T711) → U44_gg(T710, T711, pN38_in_gg(T710, T711))
pN38_in_gg(T710, T711) → U95_gg(T710, T711, qA_in_gg(T710, T711))
U95_gg(T710, T711, qA_out_gg(T710, T711)) → U96_gg(T710, T711, rN40_in_gg(T710, T711))
rN40_in_gg(a, b) → rN40_out_gg(a, b)
rN40_in_gg(T736, f(T737)) → U47_gg(T736, T737, pN38_in_gg(T736, T737))
U47_gg(T736, T737, pN38_out_gg(T736, T737)) → rN40_out_gg(T736, f(T737))
rN40_in_gg(f(T742), f(T742)) → U48_gg(T742, tJ_in_g(T742))
tJ_in_g(T270) → U6_g(T270, pK_in_g(T270))
pK_in_g(T270) → U73_g(T270, qH_in_g(f(T270)))
qH_in_g(f(f(T75))) → U5_g(T75, pI_in_g(T75))
pI_in_g(T75) → U57_g(T75, rN9_in_g(T75))
rN9_in_g(T89) → U20_g(T89, pN10_in_g(T89))
pN10_in_g(T89) → U59_g(T89, qN11_in_g(T89))
qN11_in_g(f(f(T113))) → U21_g(T113, pN12_in_g(T113))
pN12_in_g(T113) → U61_g(T113, rN13_in_g(T113))
rN13_in_g(T127) → U22_g(T127, pN14_in_g(T127))
pN14_in_g(T127) → U63_g(T127, qN15_in_g(T127))
qN15_in_g(f(f(T151))) → U23_g(T151, pN16_in_g(T151))
pN16_in_g(T151) → U65_g(T151, rN17_in_g(T151))
rN17_in_g(T165) → U24_g(T165, pN18_in_g(T165))
pN18_in_g(T165) → U67_g(T165, qN19_in_g(T165))
qN19_in_g(f(f(T179))) → U25_g(T179, pF_in_gg(f(f(f(f(f(f(f(T179))))))), T179))
U25_g(T179, pF_out_gg(f(f(f(f(f(f(f(T179))))))), T179)) → qN19_out_g(f(f(T179)))
U67_g(T165, qN19_out_g(T165)) → U68_g(T165, rL_in_g(T165))
U68_g(T165, rL_out_g(T165)) → pN18_out_g(T165)
U24_g(T165, pN18_out_g(T165)) → rN17_out_g(T165)
U65_g(T151, rN17_out_g(T151)) → U66_g(T151, pN_in_g(T151))
U66_g(T151, pN_out_g(T151)) → pN16_out_g(T151)
U23_g(T151, pN16_out_g(T151)) → qN15_out_g(f(f(T151)))
U63_g(T127, qN15_out_g(T127)) → U64_g(T127, rP_in_g(T127))
U64_g(T127, rP_out_g(T127)) → pN14_out_g(T127)
U22_g(T127, pN14_out_g(T127)) → rN13_out_g(T127)
U61_g(T113, rN13_out_g(T113)) → U62_g(T113, pR_in_g(T113))
U62_g(T113, pR_out_g(T113)) → pN12_out_g(T113)
U21_g(T113, pN12_out_g(T113)) → qN11_out_g(f(f(T113)))
U59_g(T89, qN11_out_g(T89)) → U60_g(T89, rT_in_g(T89))
U60_g(T89, rT_out_g(T89)) → pN10_out_g(T89)
U20_g(T89, pN10_out_g(T89)) → rN9_out_g(T89)
U57_g(T75, rN9_out_g(T75)) → U58_g(T75, pV_in_g(T75))
U58_g(T75, pV_out_g(T75)) → pI_out_g(T75)
U5_g(T75, pI_out_g(T75)) → qH_out_g(f(f(T75)))
U73_g(T270, qH_out_g(f(T270))) → U74_g(T270, tN24_in_g(T270))
tN24_in_g(f(T281)) → U31_g(T281, pK_in_g(T281))
U31_g(T281, pK_out_g(T281)) → tN24_out_g(f(T281))
U74_g(T270, tN24_out_g(T270)) → pK_out_g(T270)
U6_g(T270, pK_out_g(T270)) → tJ_out_g(T270)
U48_gg(T742, tJ_out_g(T742)) → rN40_out_gg(f(T742), f(T742))
U96_gg(T710, T711, rN40_out_gg(T710, T711)) → pN38_out_gg(T710, T711)
U44_gg(T710, T711, pN38_out_gg(T710, T711)) → rN37_out_gg(T710, T711)
rN37_in_gg(f(T746), T746) → U45_gg(T746, tJ_in_g(T746))
U45_gg(T746, tJ_out_g(T746)) → rN37_out_gg(f(T746), T746)
U93_gg(T682, T683, rN37_out_gg(T682, T683)) → U94_gg(T682, T683, pN39_in_gg(T682, T683))
pN39_in_gg(a, b) → pN39_out_gg(a, b)
pN39_in_gg(T764, f(T765)) → U46_gg(T764, T765, pC_in_gg(T764, T765))
U46_gg(T764, T765, pC_out_gg(T764, T765)) → pN39_out_gg(T764, f(T765))
U94_gg(T682, T683, pN39_out_gg(T682, T683)) → pC_out_gg(T682, T683)
U2_gg(T682, T683, pC_out_gg(T682, T683)) → qA_out_gg(T682, f(f(T683)))
U71_gg(T228, T229, qA_out_gg(f(T228), T229)) → U72_gg(T228, T229, rN23_in_gg(T228, T229))
rN23_in_gg(T254, f(T255)) → U29_gg(T254, T255, pN21_in_gg(T254, T255))
U29_gg(T254, T255, pN21_out_gg(T254, T255)) → rN23_out_gg(T254, f(T255))
rN23_in_gg(T260, f(T260)) → U30_gg(T260, tJ_in_g(T260))
U30_gg(T260, tJ_out_g(T260)) → rN23_out_gg(T260, f(T260))
U72_gg(T228, T229, rN23_out_gg(T228, T229)) → pN21_out_gg(T228, T229)
U26_gg(T228, T229, pN21_out_gg(T228, T229)) → rN20_out_gg(T228, T229)
rN20_in_gg(T285, T285) → U27_gg(T285, tJ_in_g(T285))
U27_gg(T285, tJ_out_g(T285)) → rN20_out_gg(T285, T285)
U69_gg(T200, T201, rN20_out_gg(T200, T201)) → U70_gg(T200, T201, pN22_in_gg(T200, T201))
pN22_in_gg(T303, f(T304)) → U28_gg(T303, T304, pG_in_gg(T303, T304))
U28_gg(T303, T304, pG_out_gg(T303, T304)) → pN22_out_gg(T303, f(T304))
U70_gg(T200, T201, pN22_out_gg(T200, T201)) → pG_out_gg(T200, T201)
U4_gg(T200, T201, pG_out_gg(T200, T201)) → pF_out_gg(T200, T201)
U32_g(T336, pF_out_gg(f(f(f(f(f(f(f(f(T336)))))))), T336)) → qN25_out_g(f(f(T336)))
U75_g(T322, qN25_out_g(T322)) → U76_g(T322, rN26_in_g(T322))
rN26_in_g(f(T356)) → U33_g(T356, pN21_in_gg(f(f(f(f(f(f(f(T356))))))), T356))
U33_g(T356, pN21_out_gg(f(f(f(f(f(f(f(T356))))))), T356)) → rN26_out_g(f(T356))
U76_g(T322, rN26_out_g(T322)) → pM_out_g(T322)
U7_g(T322, pM_out_g(T322)) → rL_out_g(f(T322))
U77_g(T375, rL_out_g(f(T375))) → U78_g(T375, pN27_in_g(T375))
pN27_in_g(f(T389)) → U34_g(T389, pG_in_gg(f(f(f(f(f(f(f(T389))))))), T389))
U34_g(T389, pG_out_gg(f(f(f(f(f(f(f(T389))))))), T389)) → pN27_out_g(f(T389))
U78_g(T375, pN27_out_g(T375)) → pO_out_g(T375)
U8_g(T375, pO_out_g(T375)) → pN_out_g(f(T375))
U35_g(T423, pN_out_g(f(T423))) → qN28_out_g(f(f(T423)))
U79_g(T409, qN28_out_g(T409)) → U80_g(T409, rN29_in_g(T409))
rN29_in_g(f(T440)) → U36_g(T440, pN18_in_g(T440))
U36_g(T440, pN18_out_g(T440)) → rN29_out_g(f(T440))
U80_g(T409, rN29_out_g(T409)) → pQ_out_g(T409)
U9_g(T409, pQ_out_g(T409)) → rP_out_g(f(T409))
U81_g(T456, rP_out_g(f(T456))) → U82_g(T456, pN30_in_g(T456))
pN30_in_g(f(T470)) → U37_g(T470, pN16_in_g(T470))
U37_g(T470, pN16_out_g(T470)) → pN30_out_g(f(T470))
U82_g(T456, pN30_out_g(T456)) → pS_out_g(T456)
U10_g(T456, pS_out_g(T456)) → pR_out_g(f(T456))
U38_g(T501, pR_out_g(f(T501))) → qN31_out_g(f(f(T501)))
U83_g(T487, qN31_out_g(T487)) → U84_g(T487, rN32_in_g(T487))
rN32_in_g(f(T518)) → U39_g(T518, pN14_in_g(T518))
U39_g(T518, pN14_out_g(T518)) → rN32_out_g(f(T518))
U84_g(T487, rN32_out_g(T487)) → pU_out_g(T487)
U11_g(T487, pU_out_g(T487)) → rT_out_g(f(T487))
U85_g(T534, rT_out_g(f(T534))) → U86_g(T534, pN33_in_g(T534))
pN33_in_g(f(T548)) → U40_g(T548, pN12_in_g(T548))
U40_g(T548, pN12_out_g(T548)) → pN33_out_g(f(T548))
U86_g(T534, pN33_out_g(T534)) → pW_out_g(T534)
U12_g(T534, pW_out_g(T534)) → pV_out_g(f(T534))
U41_g(T579, pV_out_g(f(T579))) → qN34_out_g(f(f(T579)))
U87_g(T565, qN34_out_g(T565)) → U88_g(T565, rN35_in_g(T565))
rN35_in_g(f(T596)) → U42_g(T596, pN10_in_g(T596))
U42_g(T596, pN10_out_g(T596)) → rN35_out_g(f(T596))
U88_g(T565, rN35_out_g(T565)) → pN1_out_g(T565)
U14_g(T565, pN1_out_g(T565)) → rZ_out_g(f(T565))
rZ_in_g(f(T601)) → U15_g(T601, tJ_in_g(T601))
U15_g(T601, tJ_out_g(T601)) → rZ_out_g(f(T601))
U91_g(T628, rZ_out_g(f(T628))) → U92_g(T628, pN36_in_g(T628))
pN36_in_g(f(T642)) → U43_g(T642, pI_in_g(T642))
U43_g(T642, pI_out_g(T642)) → pN36_out_g(f(T642))
U92_g(T628, pN36_out_g(T628)) → pN2_out_g(T628)
U16_g(T628, pN2_out_g(T628)) → pE_out_g(f(T628))
U3_g(T656, pE_out_g(f(T656))) → qD_out_g(f(T656))
U53_g(T36, qD_out_g(T36)) → U54_g(T36, rX_in_g(T36))
rX_in_g(T51) → U13_g(T51, pY_in_g(T51))
pY_in_g(T51) → U55_g(T51, qH_in_g(T51))
U55_g(T51, qH_out_g(T51)) → U56_g(T51, rZ_in_g(T51))
U56_g(T51, rZ_out_g(T51)) → pY_out_g(T51)
U13_g(T51, pY_out_g(T51)) → rX_out_g(T51)
U54_g(T36, rX_out_g(T36)) → pN6_out_g(T36)
U18_g(T36, pN6_out_g(T36)) → rN5_out_g(T36)
U51_g(T22, rN5_out_g(T22)) → U52_g(T22, pN7_in_g(T22))
pN7_in_g(T614) → U19_g(T614, pN8_in_g(T614))
pN8_in_g(T614) → U89_g(T614, rX_in_g(T614))
U89_g(T614, rX_out_g(T614)) → U90_g(T614, pE_in_g(T614))
U90_g(T614, pE_out_g(T614)) → pN8_out_g(T614)
U19_g(T614, pN8_out_g(T614)) → pN7_out_g(T614)
U52_g(T22, pN7_out_g(T22)) → pN4_out_g(T22)
U17_g(T22, pN4_out_g(T22)) → pN3_out_g(T22)
U49_g(T11, pN3_out_g(T11)) → U50_g(T11, qD_in_g(T11))
U50_g(T11, qD_out_g(T11)) → pB_out_g(T11)
U1_gg(T11, pB_out_g(T11)) → qA_out_gg(T11, f(f(T11)))

The set Q consists of the following terms:

qA_in_gg(x0, x1)
pB_in_g(x0)
pN3_in_g(x0)
pN4_in_g(x0)
rN5_in_g(x0)
pN6_in_g(x0)
qD_in_g(x0)
pE_in_g(x0)
pN2_in_g(x0)
rZ_in_g(x0)
pN1_in_g(x0)
qN34_in_g(x0)
pV_in_g(x0)
pW_in_g(x0)
rT_in_g(x0)
pU_in_g(x0)
qN31_in_g(x0)
pR_in_g(x0)
pS_in_g(x0)
rP_in_g(x0)
pQ_in_g(x0)
qN28_in_g(x0)
pN_in_g(x0)
pO_in_g(x0)
rL_in_g(x0)
pM_in_g(x0)
qN25_in_g(x0)
pF_in_gg(x0, x1)
pG_in_gg(x0, x1)
rN20_in_gg(x0, x1)
pN21_in_gg(x0, x1)
pC_in_gg(x0, x1)
rN37_in_gg(x0, x1)
pN38_in_gg(x0, x1)
U95_gg(x0, x1, x2)
rN40_in_gg(x0, x1)
U47_gg(x0, x1, x2)
tJ_in_g(x0)
pK_in_g(x0)
qH_in_g(x0)
pI_in_g(x0)
rN9_in_g(x0)
pN10_in_g(x0)
qN11_in_g(x0)
pN12_in_g(x0)
rN13_in_g(x0)
pN14_in_g(x0)
qN15_in_g(x0)
pN16_in_g(x0)
rN17_in_g(x0)
pN18_in_g(x0)
qN19_in_g(x0)
U25_g(x0, x1)
U67_g(x0, x1)
U68_g(x0, x1)
U24_g(x0, x1)
U65_g(x0, x1)
U66_g(x0, x1)
U23_g(x0, x1)
U63_g(x0, x1)
U64_g(x0, x1)
U22_g(x0, x1)
U61_g(x0, x1)
U62_g(x0, x1)
U21_g(x0, x1)
U59_g(x0, x1)
U60_g(x0, x1)
U20_g(x0, x1)
U57_g(x0, x1)
U58_g(x0, x1)
U5_g(x0, x1)
U73_g(x0, x1)
tN24_in_g(x0)
U31_g(x0, x1)
U74_g(x0, x1)
U6_g(x0, x1)
U48_gg(x0, x1)
U96_gg(x0, x1, x2)
U44_gg(x0, x1, x2)
U45_gg(x0, x1)
U93_gg(x0, x1, x2)
pN39_in_gg(x0, x1)
U46_gg(x0, x1, x2)
U94_gg(x0, x1, x2)
U2_gg(x0, x1, x2)
U71_gg(x0, x1, x2)
rN23_in_gg(x0, x1)
U29_gg(x0, x1, x2)
U30_gg(x0, x1)
U72_gg(x0, x1, x2)
U26_gg(x0, x1, x2)
U27_gg(x0, x1)
U69_gg(x0, x1, x2)
pN22_in_gg(x0, x1)
U28_gg(x0, x1, x2)
U70_gg(x0, x1, x2)
U4_gg(x0, x1, x2)
U32_g(x0, x1)
U75_g(x0, x1)
rN26_in_g(x0)
U33_g(x0, x1)
U76_g(x0, x1)
U7_g(x0, x1)
U77_g(x0, x1)
pN27_in_g(x0)
U34_g(x0, x1)
U78_g(x0, x1)
U8_g(x0, x1)
U35_g(x0, x1)
U79_g(x0, x1)
rN29_in_g(x0)
U36_g(x0, x1)
U80_g(x0, x1)
U9_g(x0, x1)
U81_g(x0, x1)
pN30_in_g(x0)
U37_g(x0, x1)
U82_g(x0, x1)
U10_g(x0, x1)
U38_g(x0, x1)
U83_g(x0, x1)
rN32_in_g(x0)
U39_g(x0, x1)
U84_g(x0, x1)
U11_g(x0, x1)
U85_g(x0, x1)
pN33_in_g(x0)
U40_g(x0, x1)
U86_g(x0, x1)
U12_g(x0, x1)
U41_g(x0, x1)
U87_g(x0, x1)
rN35_in_g(x0)
U42_g(x0, x1)
U88_g(x0, x1)
U14_g(x0, x1)
U15_g(x0, x1)
U91_g(x0, x1)
pN36_in_g(x0)
U43_g(x0, x1)
U92_g(x0, x1)
U16_g(x0, x1)
U3_g(x0, x1)
U53_g(x0, x1)
rX_in_g(x0)
pY_in_g(x0)
U55_g(x0, x1)
U56_g(x0, x1)
U13_g(x0, x1)
U54_g(x0, x1)
U18_g(x0, x1)
U51_g(x0, x1)
pN7_in_g(x0)
pN8_in_g(x0)
U89_g(x0, x1)
U90_g(x0, x1)
U19_g(x0, x1)
U52_g(x0, x1)
U17_g(x0, x1)
U49_g(x0, x1)
U50_g(x0, x1)
U1_gg(x0, x1)

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

(13) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 82 less nodes.

(0) Obligation:

(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)

(2) Obligation:

(3) DependencyPairsProof (EQUIVALENT transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Obligation:

(7) PiDPToQDPProof (EQUIVALENT transformation)

(8) Obligation:

(9) Instantiation (EQUIVALENT transformation)

(10) Obligation:

(11) QDPOrderProof (EQUIVALENT transformation)

(12) Obligation:

(13) DependencyGraphProof (EQUIVALENT transformation)

(14) TRUE