Left Termination proof of /tmp/tmpyZJ1El/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 PrologToDTProblemTransformerProof (⇒, 980 ms)

↳2 TRIPLES

↳3 TriplesToPiDPProof (⇒, 663 ms)

↳4 PiDP

↳5 DependencyGraphProof (⇔, 0 ms)

↳6 PiDP

↳7 PiDPToQDPProof (⇔, 205 ms)

↳8 QDP

↳9 Instantiation (⇔, 0 ms)

↳10 QDP

↳11 QDPOrderProof (⇔, 1351 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) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph DT10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="C: q(T1, T2)\n\nT1 is ground\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: 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];
3 [label="3: 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];
4 [label="4: 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];
5 [label="5: e(T5, T6), SCOPE: 2, CLAUSE: 0\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ?_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];
7 [label="7: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: 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];
11 [label="11: q(T5, T6), SCOPE: 1, CLAUSE: 2\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: q(T5, T6), SCOPE: 1, CLAUSE: 3\n\nT5 is ground\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(p(T11, f(f(T11))), q(T11, f(T11)))\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="D: p(T11, f(f(T11)))\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="A: q(T11, f(T11))\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: 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];
18 [label="18: p(T11, f(f(T11))), SCOPE: 3, CLAUSE: 4\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: p(T11, f(f(T11))), SCOPE: 3, CLAUSE: 5\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: e(T18, f(f(T18)))\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: e(T18, f(f(T18))), SCOPE: 4, CLAUSE: 0\n\nT18 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: ','(r(T22, f(f(T22))), p(T22, f(T22)))\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="N13: r(T22, f(f(T22)))\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: p(T22, f(T22))\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: 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];
27 [label="27: r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 6\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: 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];
29 [label="29: e(T29, f(f(T29)))\n\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: e(T29, f(f(T29))), SCOPE: 6, CLAUSE: 0\n\nT29 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 7\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: r(T22, f(f(T22))), SCOPE: 5, CLAUSE: 8\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(q(T36, f(T36)), r(T36, f(T36)))\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: q(T36, f(T36))\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="N7: r(T36, f(T36))\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: 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];
38 [label="38: r(T36, f(T36)), SCOPE: 7, CLAUSE: 6\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: 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];
40 [label="40: e(T44, f(T44))\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: e(T44, f(T44)), SCOPE: 8, CLAUSE: 0\n\nT44 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: r(T36, f(T36)), SCOPE: 7, CLAUSE: 7\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: r(T36, f(T36)), SCOPE: 7, CLAUSE: 8\n\nT36 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: ','(q(T51, T51), r(T51, T51))\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="H: q(T51, T51)\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="N8: r(T51, T51)\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: 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];
49 [label="49: q(T51, T51), SCOPE: 9, CLAUSE: 1\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: q(T51, T51), SCOPE: 9, CLAUSE: 2 | q(T51, T51), SCOPE: 9, CLAUSE: 3\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: e(T58, T58)\n\nT58 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: e(T58, T58), SCOPE: 10, CLAUSE: 0\n\nT58 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: q(T51, T51), SCOPE: 9, CLAUSE: 3\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: p(f(f(T65)), f(T65))\n\nT65 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: 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];
58 [label="58: p(f(f(T65)), f(T65)), SCOPE: 11, CLAUSE: 4\n\nT65 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: p(f(f(T65)), f(T65)), SCOPE: 11, CLAUSE: 5\n\nT65 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: e(f(f(T71)), f(T71))\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: e(f(f(T71)), f(T71)), SCOPE: 12, CLAUSE: 0\n\nT71 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="I: ','(r(f(f(T75)), f(T75)), p(f(f(T75)), T75))\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="N10: r(f(f(T75)), f(T75))\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="N4: p(f(f(T75)), T75)\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: 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];
67 [label="67: r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 6\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: 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];
69 [label="69: e(f(f(T82)), f(T82))\n\nT82 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: e(f(f(T82)), f(T82)), SCOPE: 14, CLAUSE: 0\n\nT82 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 7\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: r(f(f(T75)), f(T75)), SCOPE: 13, CLAUSE: 8\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="N5: ','(q(f(f(T89)), T89), r(f(f(T89)), T89))\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="N6: q(f(f(T89)), T89)\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="Z: r(f(f(T89)), T89)\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: 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];
78 [label="78: q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 1\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: 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];
80 [label="80: e(f(f(T96)), T96)\n\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: e(f(f(T96)), T96), SCOPE: 16, CLAUSE: 0\n\nT96 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: q(f(f(T89)), T89), SCOPE: 15, CLAUSE: 3\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: p(f(f(f(f(T103)))), f(T103))\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: 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];
87 [label="87: p(f(f(f(f(T103)))), f(T103)), SCOPE: 17, CLAUSE: 4\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: p(f(f(f(f(T103)))), f(T103)), SCOPE: 17, CLAUSE: 5\n\nT103 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: e(f(f(f(f(T109)))), f(T109))\n\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: e(f(f(f(f(T109)))), f(T109)), SCOPE: 18, CLAUSE: 0\n\nT109 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="N2: ','(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];
93 [label="N3: r(f(f(f(f(T113)))), f(T113))\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="W: p(f(f(f(f(T113)))), T113)\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: 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];
96 [label="96: r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 6\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: 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];
98 [label="98: e(f(f(f(f(T120)))), f(T120))\n\nT120 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: e(f(f(f(f(T120)))), f(T120)), SCOPE: 20, CLAUSE: 0\n\nT120 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 7\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: r(f(f(f(f(T113)))), f(T113)), SCOPE: 19, CLAUSE: 8\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="X: ','(q(f(f(f(f(T127)))), T127), r(f(f(f(f(T127)))), T127))\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="Y: q(f(f(f(f(T127)))), T127)\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="S: r(f(f(f(f(T127)))), T127)\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: 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];
107 [label="107: q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 1\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: 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];
109 [label="109: e(f(f(f(f(T134)))), T134)\n\nT134 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: e(f(f(f(f(T134)))), T134), SCOPE: 22, CLAUSE: 0\n\nT134 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: q(f(f(f(f(T127)))), T127), SCOPE: 21, CLAUSE: 3\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: p(f(f(f(f(f(f(T141)))))), f(T141))\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: 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];
116 [label="116: p(f(f(f(f(f(f(T141)))))), f(T141)), SCOPE: 23, CLAUSE: 4\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: p(f(f(f(f(f(f(T141)))))), f(T141)), SCOPE: 23, CLAUSE: 5\n\nT141 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: e(f(f(f(f(f(f(T147)))))), f(T147))\n\nT147 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: e(f(f(f(f(f(f(T147)))))), f(T147)), SCOPE: 24, CLAUSE: 0\n\nT147 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="U: ','(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];
122 [label="V: r(f(f(f(f(f(f(T151)))))), f(T151))\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="P: p(f(f(f(f(f(f(T151)))))), T151)\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: 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];
125 [label="125: r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 6\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: 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];
127 [label="127: e(f(f(f(f(f(f(T158)))))), f(T158))\n\nT158 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: e(f(f(f(f(f(f(T158)))))), f(T158)), SCOPE: 26, CLAUSE: 0\n\nT158 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 7\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: r(f(f(f(f(f(f(T151)))))), f(T151)), SCOPE: 25, CLAUSE: 8\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="Q: ','(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];
133 [label="R: q(f(f(f(f(f(f(T165)))))), T165)\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="N: r(f(f(f(f(f(f(T165)))))), T165)\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: 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];
136 [label="136: q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 1\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: 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];
138 [label="138: e(f(f(f(f(f(f(T172)))))), T172)\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: e(f(f(f(f(f(f(T172)))))), T172), SCOPE: 28, CLAUSE: 0\n\nT172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: q(f(f(f(f(f(f(T165)))))), T165), SCOPE: 27, CLAUSE: 3\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: p(f(f(f(f(f(f(f(f(T179)))))))), f(T179))\n\nT179 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="M: p(f(T181), f(T179))\n\nT179 is ground\nT181 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: 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];
146 [label="146: p(f(T181), f(T179)), SCOPE: 29, CLAUSE: 4\n\nT179 is ground\nT181 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: p(f(T181), f(T179)), SCOPE: 29, CLAUSE: 5\n\nT179 is ground\nT181 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: e(f(T192), f(T193))\n\nT192 is ground\nT193 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: e(f(T192), f(T193)), SCOPE: 30, CLAUSE: 0\n\nT192 is ground\nT193 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="K: ','(r(f(T200), f(T201)), p(f(T200), T201))\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="L: r(f(T200), f(T201))\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: p(f(T200), T201)\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: 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];
155 [label="155: r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 6\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: 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];
157 [label="157: e(f(T214), f(T215))\n\nT214 is ground\nT215 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: e(f(T214), f(T215)), SCOPE: 32, CLAUSE: 0\n\nT214 is ground\nT215 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 7\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: r(f(T200), f(T201)), SCOPE: 31, CLAUSE: 8\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="F: ','(q(f(T228), T229), r(f(T228), T229))\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: q(f(T228), T229)\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: r(f(T228), T229)\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: 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];
166 [label="166: r(f(T228), T229), SCOPE: 33, CLAUSE: 6\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: 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];
168 [label="168: e(f(T244), T245)\n\nT244 is ground\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: e(f(T244), T245), SCOPE: 34, CLAUSE: 0\n\nT244 is ground\nT245 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: r(f(T228), T229), SCOPE: 33, CLAUSE: 7\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: r(f(T228), T229), SCOPE: 33, CLAUSE: 8\n\nT228 is ground\nT229 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: ','(q(f(T254), T255), r(f(T254), T255))\n\nT254 is ground\nT255 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="G: t(f(T260), f(T260))\n\nT260 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: 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];
178 [label="178: t(f(T260), f(T260)), SCOPE: 35, CLAUSE: 9\n\nT260 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: t(f(T260), f(T260)), SCOPE: 35, CLAUSE: 10\n\nT260 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: e(f(T266), f(T266))\n\nT266 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: e(f(T266), f(T266)), SCOPE: 36, CLAUSE: 0\n\nT266 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="J: ','(q(f(T270), f(T270)), t(T270, T270))\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: q(f(T270), f(T270))\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: t(T270, T270)\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: t(T270, T270), SCOPE: 37, CLAUSE: 9 | t(T270, T270), SCOPE: 37, CLAUSE: 10\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: t(T270, T270), SCOPE: 37, CLAUSE: 9\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: t(T270, T270), SCOPE: 37, CLAUSE: 10\n\nT270 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: e(T278, T278)\n\nT278 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: e(T278, T278), SCOPE: 38, CLAUSE: 0\n\nT278 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: ','(q(f(T281), f(T281)), t(T281, T281))\n\nT281 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: t(f(T285), f(T285))\n\nT285 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: 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];
197 [label="197: p(f(T200), T201), SCOPE: 39, CLAUSE: 4\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: p(f(T200), T201), SCOPE: 39, CLAUSE: 5\n\nT200 is ground\nT201 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: e(f(T297), T298)\n\nT297 is ground\nT298 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: e(f(T297), T298), SCOPE: 40, CLAUSE: 0\n\nT297 is ground\nT298 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: ','(r(f(T303), f(T304)), p(f(T303), T304))\n\nT303 is ground\nT304 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: 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];
205 [label="205: r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 6\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: 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];
207 [label="207: e(f(f(f(f(f(f(T312)))))), T312)\n\nT312 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: e(f(f(f(f(f(f(T312)))))), T312), SCOPE: 42, CLAUSE: 0\n\nT312 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 7\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: r(f(f(f(f(f(f(T165)))))), T165), SCOPE: 41, CLAUSE: 8\n\nT165 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: ','(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];
213 [label="213: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="O: q(f(f(f(f(f(f(f(T322))))))), T322)\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: r(f(f(f(f(f(f(f(T322))))))), T322)\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: 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];
217 [label="217: q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 1\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: 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];
219 [label="219: e(f(f(f(f(f(f(f(T329))))))), T329)\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: e(f(f(f(f(f(f(f(T329))))))), T329), SCOPE: 44, CLAUSE: 0\n\nT329 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: q(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 43, CLAUSE: 3\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="223: p(f(f(f(f(f(f(f(f(f(T336))))))))), f(T336))\n\nT336 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
224 [label="224: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
225 [label="225: p(f(T338), f(T336))\n\nT336 is ground\nT338 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
226 [label="226: 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];
227 [label="227: r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 6\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
228 [label="228: 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];
229 [label="229: e(f(f(f(f(f(f(f(T346))))))), T346)\n\nT346 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
230 [label="230: e(f(f(f(f(f(f(f(T346))))))), T346), SCOPE: 46, CLAUSE: 0\n\nT346 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
231 [label="231: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
232 [label="232: r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 7\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
233 [label="233: r(f(f(f(f(f(f(f(T322))))))), T322), SCOPE: 45, CLAUSE: 8\n\nT322 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
234 [label="234: ','(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];
235 [label="235: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
236 [label="236: ','(q(f(T358), T356), r(f(T358), T356))\n\nT356 is ground\nT358 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
237 [label="237: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
238 [label="238: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
239 [label="239: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
240 [label="240: 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];
241 [label="241: p(f(f(f(f(f(f(T151)))))), T151), SCOPE: 47, CLAUSE: 4\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
242 [label="242: p(f(f(f(f(f(f(T151)))))), T151), SCOPE: 47, CLAUSE: 5\n\nT151 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
243 [label="243: e(f(f(f(f(f(f(T369)))))), T369)\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
244 [label="244: e(f(f(f(f(f(f(T369)))))), T369), SCOPE: 48, CLAUSE: 0\n\nT369 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
245 [label="245: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
246 [label="246: ','(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];
247 [label="247: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
248 [label="248: r(f(f(f(f(f(f(f(T375))))))), f(T375))\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
249 [label="249: p(f(f(f(f(f(f(f(T375))))))), T375)\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
250 [label="250: 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];
251 [label="251: p(f(f(f(f(f(f(f(T375))))))), T375), SCOPE: 49, CLAUSE: 4\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
252 [label="252: p(f(f(f(f(f(f(f(T375))))))), T375), SCOPE: 49, CLAUSE: 5\n\nT375 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
253 [label="253: e(f(f(f(f(f(f(f(T383))))))), T383)\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
254 [label="254: e(f(f(f(f(f(f(f(T383))))))), T383), SCOPE: 50, CLAUSE: 0\n\nT383 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
255 [label="255: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
256 [label="256: ','(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];
257 [label="257: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
258 [label="258: ','(r(f(T391), f(T389)), p(f(T391), T389))\n\nT389 is ground\nT391 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
259 [label="259: 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];
260 [label="260: r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 6\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
261 [label="261: 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];
262 [label="262: e(f(f(f(f(T399)))), T399)\n\nT399 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
263 [label="263: e(f(f(f(f(T399)))), T399), SCOPE: 52, CLAUSE: 0\n\nT399 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
264 [label="264: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
265 [label="265: r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 7\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
266 [label="266: r(f(f(f(f(T127)))), T127), SCOPE: 51, CLAUSE: 8\n\nT127 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
267 [label="267: ','(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];
268 [label="268: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
269 [label="T: q(f(f(f(f(f(T409))))), T409)\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
270 [label="270: r(f(f(f(f(f(T409))))), T409)\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
271 [label="271: 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];
272 [label="272: q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 1\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
273 [label="273: 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];
274 [label="274: e(f(f(f(f(f(T416))))), T416)\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
275 [label="275: e(f(f(f(f(f(T416))))), T416), SCOPE: 54, CLAUSE: 0\n\nT416 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
276 [label="276: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
277 [label="277: q(f(f(f(f(f(T409))))), T409), SCOPE: 53, CLAUSE: 3\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
278 [label="278: p(f(f(f(f(f(f(f(T423))))))), f(T423))\n\nT423 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
279 [label="279: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
280 [label="280: 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];
281 [label="281: r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 6\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
282 [label="282: 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];
283 [label="283: e(f(f(f(f(f(T430))))), T430)\n\nT430 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
284 [label="284: e(f(f(f(f(f(T430))))), T430), SCOPE: 56, CLAUSE: 0\n\nT430 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
285 [label="285: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
286 [label="286: r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 7\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
287 [label="287: r(f(f(f(f(f(T409))))), T409), SCOPE: 55, CLAUSE: 8\n\nT409 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
288 [label="288: ','(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];
289 [label="289: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
290 [label="290: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
291 [label="291: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
292 [label="292: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
293 [label="293: 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];
294 [label="294: p(f(f(f(f(T113)))), T113), SCOPE: 57, CLAUSE: 4\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
295 [label="295: p(f(f(f(f(T113)))), T113), SCOPE: 57, CLAUSE: 5\n\nT113 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
296 [label="296: e(f(f(f(f(T450)))), T450)\n\nT450 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
297 [label="297: e(f(f(f(f(T450)))), T450), SCOPE: 58, CLAUSE: 0\n\nT450 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
298 [label="298: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
299 [label="299: ','(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];
300 [label="300: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
301 [label="301: r(f(f(f(f(f(T456))))), f(T456))\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
302 [label="302: p(f(f(f(f(f(T456))))), T456)\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
303 [label="303: 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];
304 [label="304: p(f(f(f(f(f(T456))))), T456), SCOPE: 59, CLAUSE: 4\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
305 [label="305: p(f(f(f(f(f(T456))))), T456), SCOPE: 59, CLAUSE: 5\n\nT456 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
306 [label="306: e(f(f(f(f(f(T464))))), T464)\n\nT464 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
307 [label="307: e(f(f(f(f(f(T464))))), T464), SCOPE: 60, CLAUSE: 0\n\nT464 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
308 [label="308: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
309 [label="309: ','(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];
310 [label="310: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
311 [label="311: 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];
312 [label="312: r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 6\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
313 [label="313: 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];
314 [label="314: e(f(f(T477)), T477)\n\nT477 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
315 [label="315: e(f(f(T477)), T477), SCOPE: 62, CLAUSE: 0\n\nT477 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
316 [label="316: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
317 [label="317: r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 7\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
318 [label="318: r(f(f(T89)), T89), SCOPE: 61, CLAUSE: 8\n\nT89 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
319 [label="319: ','(q(f(f(f(T487))), T487), r(f(f(f(T487))), T487))\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
320 [label="320: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
321 [label="N1: q(f(f(f(T487))), T487)\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
322 [label="322: r(f(f(f(T487))), T487)\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
323 [label="323: 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];
324 [label="324: q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 1\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
325 [label="325: 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];
326 [label="326: e(f(f(f(T494))), T494)\n\nT494 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
327 [label="327: e(f(f(f(T494))), T494), SCOPE: 64, CLAUSE: 0\n\nT494 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
328 [label="328: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
329 [label="329: q(f(f(f(T487))), T487), SCOPE: 63, CLAUSE: 3\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
330 [label="330: p(f(f(f(f(f(T501))))), f(T501))\n\nT501 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
331 [label="331: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
332 [label="332: 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];
333 [label="333: r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 6\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
334 [label="334: 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];
335 [label="335: e(f(f(f(T508))), T508)\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
336 [label="336: e(f(f(f(T508))), T508), SCOPE: 66, CLAUSE: 0\n\nT508 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
337 [label="337: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
338 [label="338: r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 7\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
339 [label="339: r(f(f(f(T487))), T487), SCOPE: 65, CLAUSE: 8\n\nT487 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
340 [label="340: ','(q(f(f(f(f(T518)))), T518), r(f(f(f(f(T518)))), T518))\n\nT518 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
341 [label="341: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
342 [label="342: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
343 [label="343: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
344 [label="344: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
345 [label="345: 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];
346 [label="346: p(f(f(T75)), T75), SCOPE: 67, CLAUSE: 4\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
347 [label="347: p(f(f(T75)), T75), SCOPE: 67, CLAUSE: 5\n\nT75 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
348 [label="348: e(f(f(T528)), T528)\n\nT528 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
349 [label="349: e(f(f(T528)), T528), SCOPE: 68, CLAUSE: 0\n\nT528 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
350 [label="350: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
351 [label="351: ','(r(f(f(f(T534))), f(T534)), p(f(f(f(T534))), T534))\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
352 [label="352: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
353 [label="353: r(f(f(f(T534))), f(T534))\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
354 [label="354: p(f(f(f(T534))), T534)\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
355 [label="355: 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];
356 [label="356: p(f(f(f(T534))), T534), SCOPE: 69, CLAUSE: 4\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
357 [label="357: p(f(f(f(T534))), T534), SCOPE: 69, CLAUSE: 5\n\nT534 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
358 [label="358: e(f(f(f(T542))), T542)\n\nT542 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
359 [label="359: e(f(f(f(T542))), T542), SCOPE: 70, CLAUSE: 0\n\nT542 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
360 [label="360: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
361 [label="361: ','(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];
362 [label="362: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
363 [label="363: 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];
364 [label="364: r(T51, T51), SCOPE: 71, CLAUSE: 6\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
365 [label="365: r(T51, T51), SCOPE: 71, CLAUSE: 7 | r(T51, T51), SCOPE: 71, CLAUSE: 8\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
366 [label="366: e(T555, T555)\n\nT555 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
367 [label="367: e(T555, T555), SCOPE: 72, CLAUSE: 0\n\nT555 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
368 [label="368: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
369 [label="369: r(T51, T51), SCOPE: 71, CLAUSE: 7\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
370 [label="370: r(T51, T51), SCOPE: 71, CLAUSE: 8\n\nT51 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
371 [label="371: ','(q(f(T565), T565), r(f(T565), T565))\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
372 [label="372: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
373 [label="N9: q(f(T565), T565)\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
374 [label="374: r(f(T565), T565)\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
375 [label="375: 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];
376 [label="376: q(f(T565), T565), SCOPE: 73, CLAUSE: 1\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
377 [label="377: 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];
378 [label="378: e(f(T572), T572)\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
379 [label="379: e(f(T572), T572), SCOPE: 74, CLAUSE: 0\n\nT572 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
380 [label="380: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
381 [label="381: q(f(T565), T565), SCOPE: 73, CLAUSE: 3\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
382 [label="382: p(f(f(f(T579))), f(T579))\n\nT579 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
383 [label="383: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
384 [label="384: 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];
385 [label="385: r(f(T565), T565), SCOPE: 75, CLAUSE: 6\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
386 [label="386: 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];
387 [label="387: e(f(T586), T586)\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
388 [label="388: e(f(T586), T586), SCOPE: 76, CLAUSE: 0\n\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
389 [label="389: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
390 [label="390: r(f(T565), T565), SCOPE: 75, CLAUSE: 7\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
391 [label="391: r(f(T565), T565), SCOPE: 75, CLAUSE: 8\n\nT565 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
392 [label="392: ','(q(f(f(T596)), T596), r(f(f(T596)), T596))\n\nT596 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
393 [label="393: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
394 [label="394: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
395 [label="395: t(f(T601), f(T601))\n\nT601 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
396 [label="396: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
397 [label="397: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
398 [label="398: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
399 [label="399: 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];
400 [label="400: p(T22, f(T22)), SCOPE: 77, CLAUSE: 4\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
401 [label="401: p(T22, f(T22)), SCOPE: 77, CLAUSE: 5\n\nT22 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
402 [label="402: e(T610, f(T610))\n\nT610 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
403 [label="403: e(T610, f(T610)), SCOPE: 78, CLAUSE: 0\n\nT610 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
404 [label="404: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
405 [label="405: ','(r(T614, f(T614)), p(T614, T614))\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
406 [label="406: r(T614, f(T614))\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
407 [label="B: p(T614, T614)\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
408 [label="408: p(T614, T614), SCOPE: 79, CLAUSE: 4 | p(T614, T614), SCOPE: 79, CLAUSE: 5\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
409 [label="409: p(T614, T614), SCOPE: 79, CLAUSE: 4\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
410 [label="410: p(T614, T614), SCOPE: 79, CLAUSE: 5\n\nT614 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
411 [label="411: e(T622, T622)\n\nT622 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
412 [label="412: e(T622, T622), SCOPE: 80, CLAUSE: 0\n\nT622 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
413 [label="413: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
414 [label="414: ','(r(f(T628), f(T628)), p(f(T628), T628))\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
415 [label="415: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
416 [label="416: r(f(T628), f(T628))\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
417 [label="417: p(f(T628), T628)\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
418 [label="418: 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];
419 [label="419: p(f(T628), T628), SCOPE: 81, CLAUSE: 4\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
420 [label="420: p(f(T628), T628), SCOPE: 81, CLAUSE: 5\n\nT628 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
421 [label="421: e(f(T636), T636)\n\nT636 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
422 [label="422: e(f(T636), T636), SCOPE: 82, CLAUSE: 0\n\nT636 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
423 [label="423: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
424 [label="424: ','(r(f(f(T642)), f(T642)), p(f(f(T642)), T642))\n\nT642 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
425 [label="425: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
426 [label="426: 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];
427 [label="427: q(T11, f(T11)), SCOPE: 83, CLAUSE: 1\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
428 [label="428: 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];
429 [label="429: e(T649, f(T649))\n\nT649 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
430 [label="430: e(T649, f(T649)), SCOPE: 84, CLAUSE: 0\n\nT649 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
431 [label="431: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
432 [label="432: q(T11, f(T11)), SCOPE: 83, CLAUSE: 3\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
433 [label="433: p(f(T656), f(T656))\n\nT656 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
434 [label="434: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
435 [label="435: p(T662, f(T663))\n\nT662 is ground\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
436 [label="436: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
437 [label="437: 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];
438 [label="438: p(T662, f(T663)), SCOPE: 85, CLAUSE: 4\n\nT662 is ground\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
439 [label="439: p(T662, f(T663)), SCOPE: 85, CLAUSE: 5\n\nT662 is ground\nT663 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
440 [label="440: e(T674, f(T675))\n\nT674 is ground\nT675 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
441 [label="441: e(T674, f(T675)), SCOPE: 86, CLAUSE: 0\n\nT674 is ground\nT675 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
442 [label="442: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
443 [label="E: ','(r(T682, f(T683)), p(T682, T683))\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
444 [label="N12: r(T682, f(T683))\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
445 [label="445: p(T682, T683)\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
446 [label="446: 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];
447 [label="447: r(T682, f(T683)), SCOPE: 87, CLAUSE: 6\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
448 [label="448: 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];
449 [label="449: e(T696, f(T697))\n\nT696 is ground\nT697 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
450 [label="450: e(T696, f(T697)), SCOPE: 88, CLAUSE: 0\n\nT696 is ground\nT697 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
451 [label="451: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
452 [label="452: r(T682, f(T683)), SCOPE: 87, CLAUSE: 7\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
453 [label="453: r(T682, f(T683)), SCOPE: 87, CLAUSE: 8\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
454 [label="N11: ','(q(T710, T711), r(T710, T711))\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
455 [label="455: q(T710, T711)\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
456 [label="456: r(T710, T711)\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
457 [label="457: 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];
458 [label="458: r(T710, T711), SCOPE: 89, CLAUSE: 6\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
459 [label="459: 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];
460 [label="460: e(T726, T727)\n\nT726 is ground\nT727 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
461 [label="461: e(T726, T727), SCOPE: 90, CLAUSE: 0\n\nT726 is ground\nT727 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
462 [label="462: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
463 [label="463: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
464 [label="464: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
465 [label="465: r(T710, T711), SCOPE: 89, CLAUSE: 7\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
466 [label="466: r(T710, T711), SCOPE: 89, CLAUSE: 8\n\nT710 is ground\nT711 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
467 [label="467: ','(q(T736, T737), r(T736, T737))\n\nT736 is ground\nT737 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
468 [label="468: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
469 [label="469: t(f(T742), f(T742))\n\nT742 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
470 [label="470: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
471 [label="471: t(f(T746), f(T746))\n\nT746 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
472 [label="472: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
473 [label="473: 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];
474 [label="474: p(T682, T683), SCOPE: 91, CLAUSE: 4\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
475 [label="475: p(T682, T683), SCOPE: 91, CLAUSE: 5\n\nT682 is ground\nT683 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
476 [label="476: e(T758, T759)\n\nT758 is ground\nT759 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
477 [label="477: e(T758, T759), SCOPE: 92, CLAUSE: 0\n\nT758 is ground\nT759 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
478 [label="478: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
479 [label="479: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
480 [label="480: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
481 [label="481: ','(r(T764, f(T765)), p(T764, T765))\n\nT764 is ground\nT765 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
482 [label="482: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
483 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 483 [arrowhead = none ];
483 -> 2;

484 [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];
2 -> 484 [arrowhead = none ];
484 -> 3;

485 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 485 [arrowhead = none ];
485 -> 4;

486 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 486 [arrowhead = none ];
486 -> 5;

487 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 487 [arrowhead = none ];
487 -> 6;

488 [label="EVAL with clause\ne(a, b).\nand substitutionT5 -> a,\nT6 -> b", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 488 [arrowhead = none ];
488 -> 7;

489 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 489 [arrowhead = none ];
489 -> 8;

490 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 490 [arrowhead = none ];
490 -> 10;

491 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 491 [arrowhead = none ];
491 -> 9;

492 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 492 [arrowhead = none ];
492 -> 11;

493 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
10 -> 493 [arrowhead = none ];
493 -> 12;

494 [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];
11 -> 494 [arrowhead = none ];
494 -> 13;

495 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 495 [arrowhead = none ];
495 -> 14;

496 [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];
12 -> 496 [arrowhead = none ];
496 -> 435;

497 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 497 [arrowhead = none ];
497 -> 436;

498 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
13 -> 498 [arrowhead = none ];
498 -> 15;

499 [label="SPLIT 2\nnew knowledge:\nT11 is ground", fontsize=14, style = filled, fillcolor = violet];
13 -> 499 [arrowhead = none ];
499 -> 16;

500 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 500 [arrowhead = none ];
500 -> 17;

501 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
16 -> 501 [arrowhead = none ];
501 -> 426;

502 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
17 -> 502 [arrowhead = none ];
502 -> 18;

503 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
17 -> 503 [arrowhead = none ];
503 -> 19;

504 [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];
18 -> 504 [arrowhead = none ];
504 -> 20;

505 [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];
19 -> 505 [arrowhead = none ];
505 -> 23;

506 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
20 -> 506 [arrowhead = none ];
506 -> 21;

507 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 507 [arrowhead = none ];
507 -> 22;

508 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
23 -> 508 [arrowhead = none ];
508 -> 24;

509 [label="SPLIT 2\nnew knowledge:\nT22 is ground", fontsize=14, style = filled, fillcolor = violet];
23 -> 509 [arrowhead = none ];
509 -> 25;

510 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
24 -> 510 [arrowhead = none ];
510 -> 26;

511 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
25 -> 511 [arrowhead = none ];
511 -> 399;

512 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 512 [arrowhead = none ];
512 -> 27;

513 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
26 -> 513 [arrowhead = none ];
513 -> 28;

514 [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];
27 -> 514 [arrowhead = none ];
514 -> 29;

515 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
28 -> 515 [arrowhead = none ];
515 -> 32;

516 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
28 -> 516 [arrowhead = none ];
516 -> 33;

517 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
29 -> 517 [arrowhead = none ];
517 -> 30;

518 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 518 [arrowhead = none ];
518 -> 31;

519 [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];
32 -> 519 [arrowhead = none ];
519 -> 34;

520 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
33 -> 520 [arrowhead = none ];
520 -> 398;

521 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
34 -> 521 [arrowhead = none ];
521 -> 35;

522 [label="SPLIT 2\nnew knowledge:\nT36 is ground", fontsize=14, style = filled, fillcolor = violet];
34 -> 522 [arrowhead = none ];
522 -> 36;

523 [label="INSTANCE with matching:\nT11 -> T36", fontsize=14, style = filled, fillcolor = lightgrey];
35 -> 523 [arrowhead = none , style=dashed];
523 -> 16[style=dashed];

524 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
36 -> 524 [arrowhead = none ];
524 -> 37;

525 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
37 -> 525 [arrowhead = none ];
525 -> 38;

526 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
37 -> 526 [arrowhead = none ];
526 -> 39;

527 [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];
38 -> 527 [arrowhead = none ];
527 -> 40;

528 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 528 [arrowhead = none ];
528 -> 43;

529 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
39 -> 529 [arrowhead = none ];
529 -> 44;

530 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
40 -> 530 [arrowhead = none ];
530 -> 41;

531 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 531 [arrowhead = none ];
531 -> 42;

532 [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];
43 -> 532 [arrowhead = none ];
532 -> 45;

533 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
44 -> 533 [arrowhead = none ];
533 -> 397;

534 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
45 -> 534 [arrowhead = none ];
534 -> 46;

535 [label="SPLIT 2\nnew knowledge:\nT51 is ground", fontsize=14, style = filled, fillcolor = violet];
45 -> 535 [arrowhead = none ];
535 -> 47;

536 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
46 -> 536 [arrowhead = none ];
536 -> 48;

537 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
47 -> 537 [arrowhead = none ];
537 -> 363;

538 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
48 -> 538 [arrowhead = none ];
538 -> 49;

539 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
48 -> 539 [arrowhead = none ];
539 -> 50;

540 [label="ONLY EVAL with clause\nq(X102, X103) :- e(X102, X103).\nand substitutionT51 -> T58,\nX102 -> T58,\nX103 -> T58", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 540 [arrowhead = none ];
540 -> 51;

541 [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];
50 -> 541 [arrowhead = none ];
541 -> 54;

542 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
51 -> 542 [arrowhead = none ];
542 -> 52;

543 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
52 -> 543 [arrowhead = none ];
543 -> 53;

544 [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];
54 -> 544 [arrowhead = none ];
544 -> 55;

545 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
54 -> 545 [arrowhead = none ];
545 -> 56;

546 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
55 -> 546 [arrowhead = none ];
546 -> 57;

547 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
57 -> 547 [arrowhead = none ];
547 -> 58;

548 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
57 -> 548 [arrowhead = none ];
548 -> 59;

549 [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];
58 -> 549 [arrowhead = none ];
549 -> 60;

550 [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];
59 -> 550 [arrowhead = none ];
550 -> 63;

551 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
60 -> 551 [arrowhead = none ];
551 -> 61;

552 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
61 -> 552 [arrowhead = none ];
552 -> 62;

553 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
63 -> 553 [arrowhead = none ];
553 -> 64;

554 [label="SPLIT 2\nnew knowledge:\nT75 is ground", fontsize=14, style = filled, fillcolor = violet];
63 -> 554 [arrowhead = none ];
554 -> 65;

555 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
64 -> 555 [arrowhead = none ];
555 -> 66;

556 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
65 -> 556 [arrowhead = none ];
556 -> 345;

557 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 557 [arrowhead = none ];
557 -> 67;

558 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
66 -> 558 [arrowhead = none ];
558 -> 68;

559 [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];
67 -> 559 [arrowhead = none ];
559 -> 69;

560 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 560 [arrowhead = none ];
560 -> 72;

561 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
68 -> 561 [arrowhead = none ];
561 -> 73;

562 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
69 -> 562 [arrowhead = none ];
562 -> 70;

563 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
70 -> 563 [arrowhead = none ];
563 -> 71;

564 [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];
72 -> 564 [arrowhead = none ];
564 -> 74;

565 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
73 -> 565 [arrowhead = none ];
565 -> 344;

566 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
74 -> 566 [arrowhead = none ];
566 -> 75;

567 [label="SPLIT 2\nnew knowledge:\nT89 is ground", fontsize=14, style = filled, fillcolor = violet];
74 -> 567 [arrowhead = none ];
567 -> 76;

568 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
75 -> 568 [arrowhead = none ];
568 -> 77;

569 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
76 -> 569 [arrowhead = none ];
569 -> 311;

570 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 570 [arrowhead = none ];
570 -> 78;

571 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
77 -> 571 [arrowhead = none ];
571 -> 79;

572 [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];
78 -> 572 [arrowhead = none ];
572 -> 80;

573 [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];
79 -> 573 [arrowhead = none ];
573 -> 83;

574 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
80 -> 574 [arrowhead = none ];
574 -> 81;

575 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
81 -> 575 [arrowhead = none ];
575 -> 82;

576 [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];
83 -> 576 [arrowhead = none ];
576 -> 84;

577 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
83 -> 577 [arrowhead = none ];
577 -> 85;

578 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
84 -> 578 [arrowhead = none ];
578 -> 86;

579 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 579 [arrowhead = none ];
579 -> 87;

580 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
86 -> 580 [arrowhead = none ];
580 -> 88;

581 [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];
87 -> 581 [arrowhead = none ];
581 -> 89;

582 [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];
88 -> 582 [arrowhead = none ];
582 -> 92;

583 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
89 -> 583 [arrowhead = none ];
583 -> 90;

584 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
90 -> 584 [arrowhead = none ];
584 -> 91;

585 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
92 -> 585 [arrowhead = none ];
585 -> 93;

586 [label="SPLIT 2\nnew knowledge:\nT113 is ground", fontsize=14, style = filled, fillcolor = violet];
92 -> 586 [arrowhead = none ];
586 -> 94;

587 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
93 -> 587 [arrowhead = none ];
587 -> 95;

588 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
94 -> 588 [arrowhead = none ];
588 -> 293;

589 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
95 -> 589 [arrowhead = none ];
589 -> 96;

590 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
95 -> 590 [arrowhead = none ];
590 -> 97;

591 [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];
96 -> 591 [arrowhead = none ];
591 -> 98;

592 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
97 -> 592 [arrowhead = none ];
592 -> 101;

593 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
97 -> 593 [arrowhead = none ];
593 -> 102;

594 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
98 -> 594 [arrowhead = none ];
594 -> 99;

595 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
99 -> 595 [arrowhead = none ];
595 -> 100;

596 [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];
101 -> 596 [arrowhead = none ];
596 -> 103;

597 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
102 -> 597 [arrowhead = none ];
597 -> 292;

598 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
103 -> 598 [arrowhead = none ];
598 -> 104;

599 [label="SPLIT 2\nnew knowledge:\nT127 is ground", fontsize=14, style = filled, fillcolor = violet];
103 -> 599 [arrowhead = none ];
599 -> 105;

600 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
104 -> 600 [arrowhead = none ];
600 -> 106;

601 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
105 -> 601 [arrowhead = none ];
601 -> 259;

602 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 602 [arrowhead = none ];
602 -> 107;

603 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 603 [arrowhead = none ];
603 -> 108;

604 [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];
107 -> 604 [arrowhead = none ];
604 -> 109;

605 [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];
108 -> 605 [arrowhead = none ];
605 -> 112;

606 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
109 -> 606 [arrowhead = none ];
606 -> 110;

607 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 607 [arrowhead = none ];
607 -> 111;

608 [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];
112 -> 608 [arrowhead = none ];
608 -> 113;

609 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
112 -> 609 [arrowhead = none ];
609 -> 114;

610 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
113 -> 610 [arrowhead = none ];
610 -> 115;

611 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
115 -> 611 [arrowhead = none ];
611 -> 116;

612 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
115 -> 612 [arrowhead = none ];
612 -> 117;

613 [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];
116 -> 613 [arrowhead = none ];
613 -> 118;

614 [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];
117 -> 614 [arrowhead = none ];
614 -> 121;

615 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
118 -> 615 [arrowhead = none ];
615 -> 119;

616 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
119 -> 616 [arrowhead = none ];
616 -> 120;

617 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
121 -> 617 [arrowhead = none ];
617 -> 122;

618 [label="SPLIT 2\nnew knowledge:\nT151 is ground", fontsize=14, style = filled, fillcolor = violet];
121 -> 618 [arrowhead = none ];
618 -> 123;

619 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
122 -> 619 [arrowhead = none ];
619 -> 124;

620 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
123 -> 620 [arrowhead = none ];
620 -> 240;

621 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 621 [arrowhead = none ];
621 -> 125;

622 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
124 -> 622 [arrowhead = none ];
622 -> 126;

623 [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];
125 -> 623 [arrowhead = none ];
623 -> 127;

624 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
126 -> 624 [arrowhead = none ];
624 -> 130;

625 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
126 -> 625 [arrowhead = none ];
625 -> 131;

626 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
127 -> 626 [arrowhead = none ];
626 -> 128;

627 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
128 -> 627 [arrowhead = none ];
627 -> 129;

628 [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];
130 -> 628 [arrowhead = none ];
628 -> 132;

629 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 629 [arrowhead = none ];
629 -> 239;

630 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
132 -> 630 [arrowhead = none ];
630 -> 133;

631 [label="SPLIT 2\nnew knowledge:\nT165 is ground", fontsize=14, style = filled, fillcolor = violet];
132 -> 631 [arrowhead = none ];
631 -> 134;

632 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
133 -> 632 [arrowhead = none ];
632 -> 135;

633 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
134 -> 633 [arrowhead = none ];
633 -> 204;

634 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
135 -> 634 [arrowhead = none ];
634 -> 136;

635 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
135 -> 635 [arrowhead = none ];
635 -> 137;

636 [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];
136 -> 636 [arrowhead = none ];
636 -> 138;

637 [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];
137 -> 637 [arrowhead = none ];
637 -> 141;

638 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
138 -> 638 [arrowhead = none ];
638 -> 139;

639 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
139 -> 639 [arrowhead = none ];
639 -> 140;

640 [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];
141 -> 640 [arrowhead = none ];
640 -> 142;

641 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
141 -> 641 [arrowhead = none ];
641 -> 143;

642 [label="GENERALIZATION\nT181 <-- f(f(f(f(f(f(f(T179)))))))\n\nNew Knowledge:\nT181 is ground", fontsize=14, style = filled, fillcolor = violet];
142 -> 642 [arrowhead = none ];
642 -> 144;

643 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
144 -> 643 [arrowhead = none ];
643 -> 145;

644 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
145 -> 644 [arrowhead = none ];
644 -> 146;

645 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
145 -> 645 [arrowhead = none ];
645 -> 147;

646 [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];
146 -> 646 [arrowhead = none ];
646 -> 148;

647 [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];
147 -> 647 [arrowhead = none ];
647 -> 151;

648 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
148 -> 648 [arrowhead = none ];
648 -> 149;

649 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
149 -> 649 [arrowhead = none ];
649 -> 150;

650 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
151 -> 650 [arrowhead = none ];
650 -> 152;

651 [label="SPLIT 2\nnew knowledge:\nT200 is ground\nT201 is ground", fontsize=14, style = filled, fillcolor = violet];
151 -> 651 [arrowhead = none ];
651 -> 153;

652 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
152 -> 652 [arrowhead = none ];
652 -> 154;

653 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
153 -> 653 [arrowhead = none ];
653 -> 196;

654 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 654 [arrowhead = none ];
654 -> 155;

655 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
154 -> 655 [arrowhead = none ];
655 -> 156;

656 [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];
155 -> 656 [arrowhead = none ];
656 -> 157;

657 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
156 -> 657 [arrowhead = none ];
657 -> 160;

658 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
156 -> 658 [arrowhead = none ];
658 -> 161;

659 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
157 -> 659 [arrowhead = none ];
659 -> 158;

660 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
158 -> 660 [arrowhead = none ];
660 -> 159;

661 [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];
160 -> 661 [arrowhead = none ];
661 -> 162;

662 [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];
161 -> 662 [arrowhead = none ];
662 -> 194;

663 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
161 -> 663 [arrowhead = none ];
663 -> 195;

664 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
162 -> 664 [arrowhead = none ];
664 -> 163;

665 [label="SPLIT 2\nnew knowledge:\nT228 is ground\nT229 is ground", fontsize=14, style = filled, fillcolor = violet];
162 -> 665 [arrowhead = none ];
665 -> 164;

666 [label="INSTANCE with matching:\nT1 -> f(T228)\nT2 -> T229", fontsize=14, style = filled, fillcolor = lightgrey];
163 -> 666 [arrowhead = none , style=dashed];
666 -> 1[style=dashed];

667 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
164 -> 667 [arrowhead = none ];
667 -> 165;

668 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
165 -> 668 [arrowhead = none ];
668 -> 166;

669 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
165 -> 669 [arrowhead = none ];
669 -> 167;

670 [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];
166 -> 670 [arrowhead = none ];
670 -> 168;

671 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
167 -> 671 [arrowhead = none ];
671 -> 171;

672 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
167 -> 672 [arrowhead = none ];
672 -> 172;

673 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
168 -> 673 [arrowhead = none ];
673 -> 169;

674 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
169 -> 674 [arrowhead = none ];
674 -> 170;

675 [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];
171 -> 675 [arrowhead = none ];
675 -> 173;

676 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 676 [arrowhead = none ];
676 -> 174;

677 [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];
172 -> 677 [arrowhead = none ];
677 -> 175;

678 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
172 -> 678 [arrowhead = none ];
678 -> 176;

679 [label="INSTANCE with matching:\nT228 -> T254\nT229 -> T255", fontsize=14, style = filled, fillcolor = lightgrey];
173 -> 679 [arrowhead = none , style=dashed];
679 -> 162[style=dashed];

680 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
175 -> 680 [arrowhead = none ];
680 -> 177;

681 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
177 -> 681 [arrowhead = none ];
681 -> 178;

682 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
177 -> 682 [arrowhead = none ];
682 -> 179;

683 [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];
178 -> 683 [arrowhead = none ];
683 -> 180;

684 [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];
179 -> 684 [arrowhead = none ];
684 -> 183;

685 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
180 -> 685 [arrowhead = none ];
685 -> 181;

686 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
181 -> 686 [arrowhead = none ];
686 -> 182;

687 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
183 -> 687 [arrowhead = none ];
687 -> 184;

688 [label="SPLIT 2\nnew knowledge:\nT270 is ground", fontsize=14, style = filled, fillcolor = violet];
183 -> 688 [arrowhead = none ];
688 -> 185;

689 [label="INSTANCE with matching:\nT51 -> f(T270)", fontsize=14, style = filled, fillcolor = lightgrey];
184 -> 689 [arrowhead = none , style=dashed];
689 -> 46[style=dashed];

690 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
185 -> 690 [arrowhead = none ];
690 -> 186;

691 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 691 [arrowhead = none ];
691 -> 187;

692 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
186 -> 692 [arrowhead = none ];
692 -> 188;

693 [label="ONLY EVAL with clause\nt(X433, X434) :- e(X433, X434).\nand substitutionT270 -> T278,\nX433 -> T278,\nX434 -> T278", fontsize=14, style = filled, fillcolor = lightblue];
187 -> 693 [arrowhead = none ];
693 -> 189;

694 [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];
188 -> 694 [arrowhead = none ];
694 -> 192;

695 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
188 -> 695 [arrowhead = none ];
695 -> 193;

696 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
189 -> 696 [arrowhead = none ];
696 -> 190;

697 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
190 -> 697 [arrowhead = none ];
697 -> 191;

698 [label="INSTANCE with matching:\nT270 -> T281", fontsize=14, style = filled, fillcolor = lightgrey];
192 -> 698 [arrowhead = none , style=dashed];
698 -> 183[style=dashed];

699 [label="INSTANCE with matching:\nT260 -> T285", fontsize=14, style = filled, fillcolor = lightgrey];
194 -> 699 [arrowhead = none , style=dashed];
699 -> 175[style=dashed];

700 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
196 -> 700 [arrowhead = none ];
700 -> 197;

701 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
196 -> 701 [arrowhead = none ];
701 -> 198;

702 [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];
197 -> 702 [arrowhead = none ];
702 -> 199;

703 [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];
198 -> 703 [arrowhead = none ];
703 -> 202;

704 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
198 -> 704 [arrowhead = none ];
704 -> 203;

705 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
199 -> 705 [arrowhead = none ];
705 -> 200;

706 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
200 -> 706 [arrowhead = none ];
706 -> 201;

707 [label="INSTANCE with matching:\nT200 -> T303\nT201 -> T304", fontsize=14, style = filled, fillcolor = lightgrey];
202 -> 707 [arrowhead = none , style=dashed];
707 -> 151[style=dashed];

708 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
204 -> 708 [arrowhead = none ];
708 -> 205;

709 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
204 -> 709 [arrowhead = none ];
709 -> 206;

710 [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];
205 -> 710 [arrowhead = none ];
710 -> 207;

711 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
206 -> 711 [arrowhead = none ];
711 -> 210;

712 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
206 -> 712 [arrowhead = none ];
712 -> 211;

713 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
207 -> 713 [arrowhead = none ];
713 -> 208;

714 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
208 -> 714 [arrowhead = none ];
714 -> 209;

715 [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];
210 -> 715 [arrowhead = none ];
715 -> 212;

716 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
210 -> 716 [arrowhead = none ];
716 -> 213;

717 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
211 -> 717 [arrowhead = none ];
717 -> 238;

718 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
212 -> 718 [arrowhead = none ];
718 -> 214;

719 [label="SPLIT 2\nnew knowledge:\nT322 is ground", fontsize=14, style = filled, fillcolor = violet];
212 -> 719 [arrowhead = none ];
719 -> 215;

720 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
214 -> 720 [arrowhead = none ];
720 -> 216;

721 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
215 -> 721 [arrowhead = none ];
721 -> 226;

722 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
216 -> 722 [arrowhead = none ];
722 -> 217;

723 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
216 -> 723 [arrowhead = none ];
723 -> 218;

724 [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];
217 -> 724 [arrowhead = none ];
724 -> 219;

725 [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];
218 -> 725 [arrowhead = none ];
725 -> 222;

726 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
219 -> 726 [arrowhead = none ];
726 -> 220;

727 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
220 -> 727 [arrowhead = none ];
727 -> 221;

728 [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];
222 -> 728 [arrowhead = none ];
728 -> 223;

729 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
222 -> 729 [arrowhead = none ];
729 -> 224;

730 [label="GENERALIZATION\nT338 <-- f(f(f(f(f(f(f(f(T336))))))))\n\nNew Knowledge:\nT338 is ground", fontsize=14, style = filled, fillcolor = violet];
223 -> 730 [arrowhead = none ];
730 -> 225;

731 [label="INSTANCE with matching:\nT181 -> T338\nT179 -> T336", fontsize=14, style = filled, fillcolor = lightgrey];
225 -> 731 [arrowhead = none , style=dashed];
731 -> 144[style=dashed];

732 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
226 -> 732 [arrowhead = none ];
732 -> 227;

733 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
226 -> 733 [arrowhead = none ];
733 -> 228;

734 [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];
227 -> 734 [arrowhead = none ];
734 -> 229;

735 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
228 -> 735 [arrowhead = none ];
735 -> 232;

736 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
228 -> 736 [arrowhead = none ];
736 -> 233;

737 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
229 -> 737 [arrowhead = none ];
737 -> 230;

738 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
230 -> 738 [arrowhead = none ];
738 -> 231;

739 [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];
232 -> 739 [arrowhead = none ];
739 -> 234;

740 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
232 -> 740 [arrowhead = none ];
740 -> 235;

741 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
233 -> 741 [arrowhead = none ];
741 -> 237;

742 [label="GENERALIZATION\nT358 <-- f(f(f(f(f(f(f(T356)))))))\n\nNew Knowledge:\nT358 is ground", fontsize=14, style = filled, fillcolor = violet];
234 -> 742 [arrowhead = none ];
742 -> 236;

743 [label="INSTANCE with matching:\nT228 -> T358\nT229 -> T356", fontsize=14, style = filled, fillcolor = lightgrey];
236 -> 743 [arrowhead = none , style=dashed];
743 -> 162[style=dashed];

744 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 744 [arrowhead = none ];
744 -> 241;

745 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
240 -> 745 [arrowhead = none ];
745 -> 242;

746 [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];
241 -> 746 [arrowhead = none ];
746 -> 243;

747 [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];
242 -> 747 [arrowhead = none ];
747 -> 246;

748 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
242 -> 748 [arrowhead = none ];
748 -> 247;

749 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
243 -> 749 [arrowhead = none ];
749 -> 244;

750 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
244 -> 750 [arrowhead = none ];
750 -> 245;

751 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
246 -> 751 [arrowhead = none ];
751 -> 248;

752 [label="SPLIT 2\nnew knowledge:\nT375 is ground", fontsize=14, style = filled, fillcolor = violet];
246 -> 752 [arrowhead = none ];
752 -> 249;

753 [label="INSTANCE with matching:\nT165 -> f(T375)", fontsize=14, style = filled, fillcolor = lightgrey];
248 -> 753 [arrowhead = none , style=dashed];
753 -> 134[style=dashed];

754 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
249 -> 754 [arrowhead = none ];
754 -> 250;

755 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
250 -> 755 [arrowhead = none ];
755 -> 251;

756 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
250 -> 756 [arrowhead = none ];
756 -> 252;

757 [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];
251 -> 757 [arrowhead = none ];
757 -> 253;

758 [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];
252 -> 758 [arrowhead = none ];
758 -> 256;

759 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
252 -> 759 [arrowhead = none ];
759 -> 257;

760 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
253 -> 760 [arrowhead = none ];
760 -> 254;

761 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
254 -> 761 [arrowhead = none ];
761 -> 255;

762 [label="GENERALIZATION\nT391 <-- f(f(f(f(f(f(f(T389)))))))\n\nNew Knowledge:\nT391 is ground", fontsize=14, style = filled, fillcolor = violet];
256 -> 762 [arrowhead = none ];
762 -> 258;

763 [label="INSTANCE with matching:\nT200 -> T391\nT201 -> T389", fontsize=14, style = filled, fillcolor = lightgrey];
258 -> 763 [arrowhead = none , style=dashed];
763 -> 151[style=dashed];

764 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
259 -> 764 [arrowhead = none ];
764 -> 260;

765 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
259 -> 765 [arrowhead = none ];
765 -> 261;

766 [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];
260 -> 766 [arrowhead = none ];
766 -> 262;

767 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
261 -> 767 [arrowhead = none ];
767 -> 265;

768 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
261 -> 768 [arrowhead = none ];
768 -> 266;

769 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
262 -> 769 [arrowhead = none ];
769 -> 263;

770 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
263 -> 770 [arrowhead = none ];
770 -> 264;

771 [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];
265 -> 771 [arrowhead = none ];
771 -> 267;

772 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
265 -> 772 [arrowhead = none ];
772 -> 268;

773 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
266 -> 773 [arrowhead = none ];
773 -> 291;

774 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
267 -> 774 [arrowhead = none ];
774 -> 269;

775 [label="SPLIT 2\nnew knowledge:\nT409 is ground", fontsize=14, style = filled, fillcolor = violet];
267 -> 775 [arrowhead = none ];
775 -> 270;

776 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
269 -> 776 [arrowhead = none ];
776 -> 271;

777 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
270 -> 777 [arrowhead = none ];
777 -> 280;

778 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
271 -> 778 [arrowhead = none ];
778 -> 272;

779 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
271 -> 779 [arrowhead = none ];
779 -> 273;

780 [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];
272 -> 780 [arrowhead = none ];
780 -> 274;

781 [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];
273 -> 781 [arrowhead = none ];
781 -> 277;

782 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
274 -> 782 [arrowhead = none ];
782 -> 275;

783 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
275 -> 783 [arrowhead = none ];
783 -> 276;

784 [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];
277 -> 784 [arrowhead = none ];
784 -> 278;

785 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
277 -> 785 [arrowhead = none ];
785 -> 279;

786 [label="INSTANCE with matching:\nT151 -> f(T423)", fontsize=14, style = filled, fillcolor = lightgrey];
278 -> 786 [arrowhead = none , style=dashed];
786 -> 123[style=dashed];

787 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
280 -> 787 [arrowhead = none ];
787 -> 281;

788 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
280 -> 788 [arrowhead = none ];
788 -> 282;

789 [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];
281 -> 789 [arrowhead = none ];
789 -> 283;

790 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
282 -> 790 [arrowhead = none ];
790 -> 286;

791 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
282 -> 791 [arrowhead = none ];
791 -> 287;

792 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
283 -> 792 [arrowhead = none ];
792 -> 284;

793 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
284 -> 793 [arrowhead = none ];
793 -> 285;

794 [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];
286 -> 794 [arrowhead = none ];
794 -> 288;

795 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
286 -> 795 [arrowhead = none ];
795 -> 289;

796 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
287 -> 796 [arrowhead = none ];
796 -> 290;

797 [label="INSTANCE with matching:\nT165 -> T440", fontsize=14, style = filled, fillcolor = lightgrey];
288 -> 797 [arrowhead = none , style=dashed];
797 -> 132[style=dashed];

798 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
293 -> 798 [arrowhead = none ];
798 -> 294;

799 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
293 -> 799 [arrowhead = none ];
799 -> 295;

800 [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];
294 -> 800 [arrowhead = none ];
800 -> 296;

801 [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];
295 -> 801 [arrowhead = none ];
801 -> 299;

802 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
295 -> 802 [arrowhead = none ];
802 -> 300;

803 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
296 -> 803 [arrowhead = none ];
803 -> 297;

804 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
297 -> 804 [arrowhead = none ];
804 -> 298;

805 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
299 -> 805 [arrowhead = none ];
805 -> 301;

806 [label="SPLIT 2\nnew knowledge:\nT456 is ground", fontsize=14, style = filled, fillcolor = violet];
299 -> 806 [arrowhead = none ];
806 -> 302;

807 [label="INSTANCE with matching:\nT127 -> f(T456)", fontsize=14, style = filled, fillcolor = lightgrey];
301 -> 807 [arrowhead = none , style=dashed];
807 -> 105[style=dashed];

808 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
302 -> 808 [arrowhead = none ];
808 -> 303;

809 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
303 -> 809 [arrowhead = none ];
809 -> 304;

810 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
303 -> 810 [arrowhead = none ];
810 -> 305;

811 [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];
304 -> 811 [arrowhead = none ];
811 -> 306;

812 [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];
305 -> 812 [arrowhead = none ];
812 -> 309;

813 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
305 -> 813 [arrowhead = none ];
813 -> 310;

814 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
306 -> 814 [arrowhead = none ];
814 -> 307;

815 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
307 -> 815 [arrowhead = none ];
815 -> 308;

816 [label="INSTANCE with matching:\nT151 -> T470", fontsize=14, style = filled, fillcolor = lightgrey];
309 -> 816 [arrowhead = none , style=dashed];
816 -> 121[style=dashed];

817 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
311 -> 817 [arrowhead = none ];
817 -> 312;

818 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
311 -> 818 [arrowhead = none ];
818 -> 313;

819 [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];
312 -> 819 [arrowhead = none ];
819 -> 314;

820 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
313 -> 820 [arrowhead = none ];
820 -> 317;

821 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
313 -> 821 [arrowhead = none ];
821 -> 318;

822 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
314 -> 822 [arrowhead = none ];
822 -> 315;

823 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
315 -> 823 [arrowhead = none ];
823 -> 316;

824 [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];
317 -> 824 [arrowhead = none ];
824 -> 319;

825 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
317 -> 825 [arrowhead = none ];
825 -> 320;

826 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
318 -> 826 [arrowhead = none ];
826 -> 343;

827 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
319 -> 827 [arrowhead = none ];
827 -> 321;

828 [label="SPLIT 2\nnew knowledge:\nT487 is ground", fontsize=14, style = filled, fillcolor = violet];
319 -> 828 [arrowhead = none ];
828 -> 322;

829 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
321 -> 829 [arrowhead = none ];
829 -> 323;

830 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
322 -> 830 [arrowhead = none ];
830 -> 332;

831 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
323 -> 831 [arrowhead = none ];
831 -> 324;

832 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
323 -> 832 [arrowhead = none ];
832 -> 325;

833 [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];
324 -> 833 [arrowhead = none ];
833 -> 326;

834 [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];
325 -> 834 [arrowhead = none ];
834 -> 329;

835 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
326 -> 835 [arrowhead = none ];
835 -> 327;

836 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
327 -> 836 [arrowhead = none ];
836 -> 328;

837 [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];
329 -> 837 [arrowhead = none ];
837 -> 330;

838 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
329 -> 838 [arrowhead = none ];
838 -> 331;

839 [label="INSTANCE with matching:\nT113 -> f(T501)", fontsize=14, style = filled, fillcolor = lightgrey];
330 -> 839 [arrowhead = none , style=dashed];
839 -> 94[style=dashed];

840 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
332 -> 840 [arrowhead = none ];
840 -> 333;

841 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
332 -> 841 [arrowhead = none ];
841 -> 334;

842 [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];
333 -> 842 [arrowhead = none ];
842 -> 335;

843 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
334 -> 843 [arrowhead = none ];
843 -> 338;

844 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
334 -> 844 [arrowhead = none ];
844 -> 339;

845 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
335 -> 845 [arrowhead = none ];
845 -> 336;

846 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
336 -> 846 [arrowhead = none ];
846 -> 337;

847 [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];
338 -> 847 [arrowhead = none ];
847 -> 340;

848 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
338 -> 848 [arrowhead = none ];
848 -> 341;

849 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
339 -> 849 [arrowhead = none ];
849 -> 342;

850 [label="INSTANCE with matching:\nT127 -> T518", fontsize=14, style = filled, fillcolor = lightgrey];
340 -> 850 [arrowhead = none , style=dashed];
850 -> 103[style=dashed];

851 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
345 -> 851 [arrowhead = none ];
851 -> 346;

852 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
345 -> 852 [arrowhead = none ];
852 -> 347;

853 [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];
346 -> 853 [arrowhead = none ];
853 -> 348;

854 [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];
347 -> 854 [arrowhead = none ];
854 -> 351;

855 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
347 -> 855 [arrowhead = none ];
855 -> 352;

856 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
348 -> 856 [arrowhead = none ];
856 -> 349;

857 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
349 -> 857 [arrowhead = none ];
857 -> 350;

858 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
351 -> 858 [arrowhead = none ];
858 -> 353;

859 [label="SPLIT 2\nnew knowledge:\nT534 is ground", fontsize=14, style = filled, fillcolor = violet];
351 -> 859 [arrowhead = none ];
859 -> 354;

860 [label="INSTANCE with matching:\nT89 -> f(T534)", fontsize=14, style = filled, fillcolor = lightgrey];
353 -> 860 [arrowhead = none , style=dashed];
860 -> 76[style=dashed];

861 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
354 -> 861 [arrowhead = none ];
861 -> 355;

862 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
355 -> 862 [arrowhead = none ];
862 -> 356;

863 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
355 -> 863 [arrowhead = none ];
863 -> 357;

864 [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];
356 -> 864 [arrowhead = none ];
864 -> 358;

865 [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];
357 -> 865 [arrowhead = none ];
865 -> 361;

866 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
357 -> 866 [arrowhead = none ];
866 -> 362;

867 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
358 -> 867 [arrowhead = none ];
867 -> 359;

868 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
359 -> 868 [arrowhead = none ];
868 -> 360;

869 [label="INSTANCE with matching:\nT113 -> T548", fontsize=14, style = filled, fillcolor = lightgrey];
361 -> 869 [arrowhead = none , style=dashed];
869 -> 92[style=dashed];

870 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
363 -> 870 [arrowhead = none ];
870 -> 364;

871 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
363 -> 871 [arrowhead = none ];
871 -> 365;

872 [label="ONLY EVAL with clause\nr(X826, X827) :- e(X826, X827).\nand substitutionT51 -> T555,\nX826 -> T555,\nX827 -> T555", fontsize=14, style = filled, fillcolor = lightblue];
364 -> 872 [arrowhead = none ];
872 -> 366;

873 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
365 -> 873 [arrowhead = none ];
873 -> 369;

874 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
365 -> 874 [arrowhead = none ];
874 -> 370;

875 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
366 -> 875 [arrowhead = none ];
875 -> 367;

876 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
367 -> 876 [arrowhead = none ];
876 -> 368;

877 [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];
369 -> 877 [arrowhead = none ];
877 -> 371;

878 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
369 -> 878 [arrowhead = none ];
878 -> 372;

879 [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];
370 -> 879 [arrowhead = none ];
879 -> 395;

880 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
370 -> 880 [arrowhead = none ];
880 -> 396;

881 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
371 -> 881 [arrowhead = none ];
881 -> 373;

882 [label="SPLIT 2\nnew knowledge:\nT565 is ground", fontsize=14, style = filled, fillcolor = violet];
371 -> 882 [arrowhead = none ];
882 -> 374;

883 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
373 -> 883 [arrowhead = none ];
883 -> 375;

884 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
374 -> 884 [arrowhead = none ];
884 -> 384;

885 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
375 -> 885 [arrowhead = none ];
885 -> 376;

886 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
375 -> 886 [arrowhead = none ];
886 -> 377;

887 [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];
376 -> 887 [arrowhead = none ];
887 -> 378;

888 [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];
377 -> 888 [arrowhead = none ];
888 -> 381;

889 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
378 -> 889 [arrowhead = none ];
889 -> 379;

890 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
379 -> 890 [arrowhead = none ];
890 -> 380;

891 [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];
381 -> 891 [arrowhead = none ];
891 -> 382;

892 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
381 -> 892 [arrowhead = none ];
892 -> 383;

893 [label="INSTANCE with matching:\nT75 -> f(T579)", fontsize=14, style = filled, fillcolor = lightgrey];
382 -> 893 [arrowhead = none , style=dashed];
893 -> 65[style=dashed];

894 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
384 -> 894 [arrowhead = none ];
894 -> 385;

895 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
384 -> 895 [arrowhead = none ];
895 -> 386;

896 [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];
385 -> 896 [arrowhead = none ];
896 -> 387;

897 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
386 -> 897 [arrowhead = none ];
897 -> 390;

898 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
386 -> 898 [arrowhead = none ];
898 -> 391;

899 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
387 -> 899 [arrowhead = none ];
899 -> 388;

900 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
388 -> 900 [arrowhead = none ];
900 -> 389;

901 [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];
390 -> 901 [arrowhead = none ];
901 -> 392;

902 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
390 -> 902 [arrowhead = none ];
902 -> 393;

903 [label="BACKTRACK\nfor clause: r(f(X), f(X)) :- t(f(X), f(X))because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
391 -> 903 [arrowhead = none ];
903 -> 394;

904 [label="INSTANCE with matching:\nT89 -> T596", fontsize=14, style = filled, fillcolor = lightgrey];
392 -> 904 [arrowhead = none , style=dashed];
904 -> 74[style=dashed];

905 [label="INSTANCE with matching:\nT260 -> T601", fontsize=14, style = filled, fillcolor = lightgrey];
395 -> 905 [arrowhead = none , style=dashed];
905 -> 175[style=dashed];

906 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
399 -> 906 [arrowhead = none ];
906 -> 400;

907 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
399 -> 907 [arrowhead = none ];
907 -> 401;

908 [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];
400 -> 908 [arrowhead = none ];
908 -> 402;

909 [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];
401 -> 909 [arrowhead = none ];
909 -> 405;

910 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
402 -> 910 [arrowhead = none ];
910 -> 403;

911 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
403 -> 911 [arrowhead = none ];
911 -> 404;

912 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
405 -> 912 [arrowhead = none ];
912 -> 406;

913 [label="SPLIT 2\nnew knowledge:\nT614 is ground", fontsize=14, style = filled, fillcolor = violet];
405 -> 913 [arrowhead = none ];
913 -> 407;

914 [label="INSTANCE with matching:\nT36 -> T614", fontsize=14, style = filled, fillcolor = lightgrey];
406 -> 914 [arrowhead = none , style=dashed];
914 -> 36[style=dashed];

915 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
407 -> 915 [arrowhead = none ];
915 -> 408;

916 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
408 -> 916 [arrowhead = none ];
916 -> 409;

917 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
408 -> 917 [arrowhead = none ];
917 -> 410;

918 [label="ONLY EVAL with clause\np(X927, X928) :- e(X927, X928).\nand substitutionT614 -> T622,\nX927 -> T622,\nX928 -> T622", fontsize=14, style = filled, fillcolor = lightblue];
409 -> 918 [arrowhead = none ];
918 -> 411;

919 [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];
410 -> 919 [arrowhead = none ];
919 -> 414;

920 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
410 -> 920 [arrowhead = none ];
920 -> 415;

921 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
411 -> 921 [arrowhead = none ];
921 -> 412;

922 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
412 -> 922 [arrowhead = none ];
922 -> 413;

923 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
414 -> 923 [arrowhead = none ];
923 -> 416;

924 [label="SPLIT 2\nnew knowledge:\nT628 is ground", fontsize=14, style = filled, fillcolor = violet];
414 -> 924 [arrowhead = none ];
924 -> 417;

925 [label="INSTANCE with matching:\nT51 -> f(T628)", fontsize=14, style = filled, fillcolor = lightgrey];
416 -> 925 [arrowhead = none , style=dashed];
925 -> 47[style=dashed];

926 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
417 -> 926 [arrowhead = none ];
926 -> 418;

927 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
418 -> 927 [arrowhead = none ];
927 -> 419;

928 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
418 -> 928 [arrowhead = none ];
928 -> 420;

929 [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];
419 -> 929 [arrowhead = none ];
929 -> 421;

930 [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];
420 -> 930 [arrowhead = none ];
930 -> 424;

931 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
420 -> 931 [arrowhead = none ];
931 -> 425;

932 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
421 -> 932 [arrowhead = none ];
932 -> 422;

933 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
422 -> 933 [arrowhead = none ];
933 -> 423;

934 [label="INSTANCE with matching:\nT75 -> T642", fontsize=14, style = filled, fillcolor = lightgrey];
424 -> 934 [arrowhead = none , style=dashed];
934 -> 63[style=dashed];

935 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
426 -> 935 [arrowhead = none ];
935 -> 427;

936 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
426 -> 936 [arrowhead = none ];
936 -> 428;

937 [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];
427 -> 937 [arrowhead = none ];
937 -> 429;

938 [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];
428 -> 938 [arrowhead = none ];
938 -> 432;

939 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
429 -> 939 [arrowhead = none ];
939 -> 430;

940 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
430 -> 940 [arrowhead = none ];
940 -> 431;

941 [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];
432 -> 941 [arrowhead = none ];
941 -> 433;

942 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
432 -> 942 [arrowhead = none ];
942 -> 434;

943 [label="INSTANCE with matching:\nT614 -> f(T656)", fontsize=14, style = filled, fillcolor = lightgrey];
433 -> 943 [arrowhead = none , style=dashed];
943 -> 407[style=dashed];

944 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
435 -> 944 [arrowhead = none ];
944 -> 437;

945 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
437 -> 945 [arrowhead = none ];
945 -> 438;

946 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
437 -> 946 [arrowhead = none ];
946 -> 439;

947 [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];
438 -> 947 [arrowhead = none ];
947 -> 440;

948 [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];
439 -> 948 [arrowhead = none ];
948 -> 443;

949 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
440 -> 949 [arrowhead = none ];
949 -> 441;

950 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
441 -> 950 [arrowhead = none ];
950 -> 442;

951 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
443 -> 951 [arrowhead = none ];
951 -> 444;

952 [label="SPLIT 2\nnew knowledge:\nT682 is ground\nT683 is ground", fontsize=14, style = filled, fillcolor = violet];
443 -> 952 [arrowhead = none ];
952 -> 445;

953 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
444 -> 953 [arrowhead = none ];
953 -> 446;

954 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
445 -> 954 [arrowhead = none ];
954 -> 473;

955 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
446 -> 955 [arrowhead = none ];
955 -> 447;

956 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
446 -> 956 [arrowhead = none ];
956 -> 448;

957 [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];
447 -> 957 [arrowhead = none ];
957 -> 449;

958 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
448 -> 958 [arrowhead = none ];
958 -> 452;

959 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
448 -> 959 [arrowhead = none ];
959 -> 453;

960 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
449 -> 960 [arrowhead = none ];
960 -> 450;

961 [label="BACKTRACK\nfor clause: e(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
450 -> 961 [arrowhead = none ];
961 -> 451;

962 [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];
452 -> 962 [arrowhead = none ];
962 -> 454;

963 [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];
453 -> 963 [arrowhead = none ];
963 -> 471;

964 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
453 -> 964 [arrowhead = none ];
964 -> 472;

965 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
454 -> 965 [arrowhead = none ];
965 -> 455;

966 [label="SPLIT 2\nnew knowledge:\nT710 is ground\nT711 is ground", fontsize=14, style = filled, fillcolor = violet];
454 -> 966 [arrowhead = none ];
966 -> 456;

967 [label="INSTANCE with matching:\nT1 -> T710\nT2 -> T711", fontsize=14, style = filled, fillcolor = lightgrey];
455 -> 967 [arrowhead = none , style=dashed];
967 -> 1[style=dashed];

968 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
456 -> 968 [arrowhead = none ];
968 -> 457;

969 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
457 -> 969 [arrowhead = none ];
969 -> 458;

970 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
457 -> 970 [arrowhead = none ];
970 -> 459;

971 [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];
458 -> 971 [arrowhead = none ];
971 -> 460;

972 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
459 -> 972 [arrowhead = none ];
972 -> 465;

973 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
459 -> 973 [arrowhead = none ];
973 -> 466;

974 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
460 -> 974 [arrowhead = none ];
974 -> 461;

975 [label="EVAL with clause\ne(a, b).\nand substitutionT726 -> a,\nT727 -> b", fontsize=14, style = filled, fillcolor = lightblue];
461 -> 975 [arrowhead = none ];
975 -> 462;

976 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
461 -> 976 [arrowhead = none ];
976 -> 463;

977 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
462 -> 977 [arrowhead = none ];
977 -> 464;

978 [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];
465 -> 978 [arrowhead = none ];
978 -> 467;

979 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
465 -> 979 [arrowhead = none ];
979 -> 468;

980 [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];
466 -> 980 [arrowhead = none ];
980 -> 469;

981 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
466 -> 981 [arrowhead = none ];
981 -> 470;

982 [label="INSTANCE with matching:\nT710 -> T736\nT711 -> T737", fontsize=14, style = filled, fillcolor = lightgrey];
467 -> 982 [arrowhead = none , style=dashed];
982 -> 454[style=dashed];

983 [label="INSTANCE with matching:\nT260 -> T742", fontsize=14, style = filled, fillcolor = lightgrey];
469 -> 983 [arrowhead = none , style=dashed];
983 -> 175[style=dashed];

984 [label="INSTANCE with matching:\nT260 -> T746", fontsize=14, style = filled, fillcolor = lightgrey];
471 -> 984 [arrowhead = none , style=dashed];
984 -> 175[style=dashed];

985 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
473 -> 985 [arrowhead = none ];
985 -> 474;

986 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
473 -> 986 [arrowhead = none ];
986 -> 475;

987 [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];
474 -> 987 [arrowhead = none ];
987 -> 476;

988 [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];
475 -> 988 [arrowhead = none ];
988 -> 481;

989 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
475 -> 989 [arrowhead = none ];
989 -> 482;

990 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
476 -> 990 [arrowhead = none ];
990 -> 477;

991 [label="EVAL with clause\ne(a, b).\nand substitutionT758 -> a,\nT759 -> b", fontsize=14, style = filled, fillcolor = lightblue];
477 -> 991 [arrowhead = none ];
991 -> 478;

992 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
477 -> 992 [arrowhead = none ];
992 -> 479;

993 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
478 -> 993 [arrowhead = none ];
993 -> 480;

994 [label="INSTANCE with matching:\nT682 -> T764\nT683 -> T765", fontsize=14, style = filled, fillcolor = lightgrey];
481 -> 994 [arrowhead = none , style=dashed];
994 -> 443[style=dashed];

}

(2) Obligation:

Triples:

qA(f(X1)) :- pB(f(X1)).
pF(X1, X2) :- qC(f(X1), X2).
pF(X1, f(X2)) :- ','(qcC(f(X1), f(X2)), pF(X1, X2)).
pF(X1, f(X1)) :- ','(qcC(f(X1), f(X1)), tG(X1)).
qH(f(f(X1))) :- pI(X1).
pJ(X1) :- qH(f(X1)).
pJ(f(X1)) :- ','(qcH(f(f(X1))), pJ(X1)).
tG(X1) :- pJ(X1).
pK(X1, X2) :- pF(X1, X2).
pK(X1, X1) :- tG(X1).
pK(X1, f(X2)) :- ','(rcL(X1, f(X2)), pK(X1, X2)).
pM(X1, X2) :- pK(X1, X2).
rN(f(f(f(X1)))) :- pM(f(f(f(f(f(f(f(f(X1)))))))), X1).
rN(f(f(X1))) :- ','(qcO(f(X1)), pF(f(f(f(f(f(f(f(X1))))))), X1)).
pP(f(X1)) :- rN(f(X1)).
pP(f(f(X1))) :- ','(rcN(f(f(X1))), pK(f(f(f(f(f(f(f(X1))))))), X1)).
pQ(f(f(X1))) :- pM(f(f(f(f(f(f(f(X1))))))), X1).
pQ(X1) :- ','(qcR(X1), rN(X1)).
rS(f(f(f(X1)))) :- pP(f(X1)).
rS(f(f(X1))) :- ','(qcT(f(X1)), pQ(X1)).
pU(X1) :- pQ(X1).
pU(X1) :- ','(rcV(X1), pP(X1)).
pW(f(X1)) :- rS(f(X1)).
pW(f(f(X1))) :- ','(rcS(f(f(X1))), pU(X1)).
pX(f(f(X1))) :- pU(X1).
pX(X1) :- ','(qcY(X1), rS(X1)).
rZ(f(f(f(X1)))) :- pW(f(X1)).
rZ(f(f(X1))) :- ','(qcN1(f(X1)), pX(X1)).
pN2(X1) :- pX(X1).
pN2(X1) :- ','(rcN3(X1), pW(X1)).
pN4(f(X1)) :- rZ(f(X1)).
pN4(f(f(X1))) :- ','(rcZ(f(f(X1))), pN2(X1)).
pN5(f(f(X1))) :- pN2(X1).
pN5(X1) :- ','(qcN6(X1), rZ(X1)).
rN7(X1) :- qH(X1).
rN7(X1) :- ','(qcH(X1), rN8(X1)).
rN8(f(f(f(X1)))) :- pN4(f(X1)).
rN8(f(f(X1))) :- ','(qcN9(f(X1)), pN5(X1)).
rN8(f(X1)) :- tG(X1).
pI(X1) :- pN5(X1).
pI(X1) :- ','(rcN10(X1), pN4(X1)).
pB(f(X1)) :- rN8(f(X1)).
pB(f(f(X1))) :- ','(rcN8(f(f(X1))), pI(X1)).
pN11(X1, X2) :- qC(X1, X2).
pN11(X1, f(X2)) :- ','(qcC(X1, f(X2)), pN11(X1, X2)).
pN11(f(X1), f(X1)) :- ','(qcC(f(X1), f(X1)), tG(X1)).
pE(X1, X2) :- pN11(X1, X2).
pE(f(X1), X1) :- tG(X1).
pE(X1, f(X2)) :- ','(rcN12(X1, f(X2)), pE(X1, X2)).
qC(X1, f(f(X1))) :- qA(X1).
qC(X1, f(f(X1))) :- ','(qcA(X1), rN7(X1)).
qC(X1, f(f(X1))) :- ','(rcN13(X1), rN7(X1)).
qC(X1, f(f(X1))) :- ','(rcN13(X1), ','(rcN7(X1), pB(X1))).
qC(X1, f(f(X1))) :- ','(pcD(X1), qA(X1)).
qC(X1, f(f(X2))) :- pE(X1, X2).

Clauses:

qcA(f(X1)) :- pcB(f(X1)).
qcC(a, b).
qcC(X1, f(f(X1))) :- ','(pcD(X1), qcA(X1)).
qcC(X1, f(f(X2))) :- qcE(X1, X2).
qcF(X1, f(X2)) :- ','(qcC(f(X1), f(X2)), qcF(X1, X2)).
qcF(X1, f(X1)) :- ','(qcC(f(X1), f(X1)), tcG(X1)).
qcH(f(f(X1))) :- qcI(X1).
qcJ(f(X1)) :- ','(qcH(f(f(X1))), qcJ(X1)).
tcG(X1) :- qcJ(X1).
qcK(X1, f(X2)) :- ','(rcL(X1, f(X2)), qcK(X1, X2)).
pcM(X1, X2) :- qcK(X1, X2).
rcN(f(f(X1))) :- ','(qcO(f(X1)), qcF(f(f(f(f(f(f(f(X1))))))), X1)).
pcP(f(f(X1))) :- ','(rcN(f(f(X1))), qcK(f(f(f(f(f(f(f(X1))))))), X1)).
qcQ(X1) :- ','(qcR(X1), rcN(X1)).
rcS(f(f(X1))) :- ','(qcT(f(X1)), qcQ(X1)).
qcU(X1) :- ','(rcV(X1), pcP(X1)).
pcW(f(f(X1))) :- ','(rcS(f(f(X1))), qcU(X1)).
qcX(X1) :- ','(qcY(X1), rcS(X1)).
rcZ(f(f(X1))) :- ','(qcN1(f(X1)), qcX(X1)).
qcN2(X1) :- ','(rcN3(X1), pcW(X1)).
pcN4(f(f(X1))) :- ','(rcZ(f(f(X1))), qcN2(X1)).
qcN5(X1) :- ','(qcN6(X1), rcZ(X1)).
rcN7(X1) :- ','(qcH(X1), rcN8(X1)).
rcN8(f(f(X1))) :- ','(qcN9(f(X1)), qcN5(X1)).
rcN8(f(X1)) :- tcG(X1).
qcI(X1) :- ','(rcN10(X1), pcN4(X1)).
pcB(f(f(X1))) :- ','(rcN8(f(f(X1))), qcI(X1)).
qcN11(a, b) :- qcC(a, b).
qcN11(X1, f(X2)) :- ','(qcC(X1, f(X2)), qcN11(X1, X2)).
qcN11(f(X1), f(X1)) :- ','(qcC(f(X1), f(X1)), tcG(X1)).
qcE(a, b) :- rcN12(a, b).
qcE(X1, f(X2)) :- ','(rcN12(X1, f(X2)), qcE(X1, X2)).
pcD(X1) :- ','(rcN13(X1), ','(rcN7(X1), pcB(X1))).
rcN13(X1) :- ','(qcA(X1), rcN7(X1)).
rcN10(X1) :- qcN5(X1).
qcN6(f(f(X1))) :- qcN2(X1).
rcN3(X1) :- qcX(X1).
qcY(f(f(X1))) :- qcU(X1).
rcV(X1) :- qcQ(X1).
qcR(f(f(X1))) :- pcM(f(f(f(f(f(f(f(X1))))))), X1).
rcL(X1, X2) :- qcF(X1, X2).
rcL(X1, X1) :- tcG(X1).
qcO(f(f(X1))) :- pcM(f(f(f(f(f(f(f(f(X1)))))))), X1).
qcT(f(f(X1))) :- pcP(f(X1)).
qcN1(f(f(X1))) :- pcW(f(X1)).
qcN9(f(f(X1))) :- pcN4(f(X1)).
rcN12(X1, X2) :- qcN11(X1, X2).
rcN12(f(X1), X1) :- tcG(X1).

Afs:

qC(x1, x2) = qC(x1, x2)

(3) TriplesToPiDPProof (SOUND transformation)

We use the technique of [DT09]. With regard to the inferred argument filtering the predicates were used in the following modes:
qC_in: (b,b)
qA_in: (b)
pB_in: (b)
rN8_in: (b)
pN4_in: (b)
rZ_in: (b)
pW_in: (b)
rS_in: (b)
pP_in: (b)
rN_in: (b)
pM_in: (b,b)
pK_in: (b,b)
pF_in: (b,b)
qcA_in: (b)
pcB_in: (b)
rcN8_in: (b)
qcN9_in: (b)
pcN4_in: (b)
rcZ_in: (b)
qcN1_in: (b)
pcW_in: (b)
rcS_in: (b)
qcT_in: (b)
pcP_in: (b)
rcN_in: (b)
qcO_in: (b)
pcM_in: (b,b)
qcK_in: (b,b)
rcL_in: (b,b)
qcF_in: (b,b)
qcC_in: (b,b)
pcD_in: (b)
rcN13_in: (b)
rcN7_in: (b)
qcH_in: (b)
qcI_in: (b)
rcN10_in: (b)
qcN5_in: (b)
qcN6_in: (b)
qcN2_in: (b)
rcN3_in: (b)
qcX_in: (b)
qcY_in: (b)
qcU_in: (b)
rcV_in: (b)
qcQ_in: (b)
qcR_in: (b)
tcG_in: (b)
qcJ_in: (b)
qcE_in: (b,b)
rcN12_in: (b,b)
qcN11_in: (b,b)
rN7_in: (b)
qH_in: (b)
pI_in: (b)
pN5_in: (b)
pN2_in: (b)
pX_in: (b)
pU_in: (b)
pQ_in: (b)
tG_in: (b)
pJ_in: (b)
pE_in: (b,b)
pN11_in: (b,b)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

QC_IN_GG(X1, f(f(X1))) → U72_GG(X1, qA_in_g(X1))
QC_IN_GG(X1, f(f(X1))) → QA_IN_G(X1)
QA_IN_G(f(X1)) → U1_G(X1, pB_in_g(f(X1)))
QA_IN_G(f(X1)) → PB_IN_G(f(X1))
PB_IN_G(f(X1)) → U60_G(X1, rN8_in_g(f(X1)))
PB_IN_G(f(X1)) → RN8_IN_G(f(X1))
RN8_IN_G(f(f(f(X1)))) → U53_G(X1, pN4_in_g(f(X1)))
RN8_IN_G(f(f(f(X1)))) → PN4_IN_G(f(X1))
PN4_IN_G(f(X1)) → U44_G(X1, rZ_in_g(f(X1)))
PN4_IN_G(f(X1)) → RZ_IN_G(f(X1))
RZ_IN_G(f(f(f(X1)))) → U38_G(X1, pW_in_g(f(X1)))
RZ_IN_G(f(f(f(X1)))) → PW_IN_G(f(X1))
PW_IN_G(f(X1)) → U32_G(X1, rS_in_g(f(X1)))
PW_IN_G(f(X1)) → RS_IN_G(f(X1))
RS_IN_G(f(f(f(X1)))) → U26_G(X1, pP_in_g(f(X1)))
RS_IN_G(f(f(f(X1)))) → PP_IN_G(f(X1))
PP_IN_G(f(X1)) → U20_G(X1, rN_in_g(f(X1)))
PP_IN_G(f(X1)) → RN_IN_G(f(X1))
RN_IN_G(f(f(f(X1)))) → U17_G(X1, pM_in_gg(f(f(f(f(f(f(f(f(X1)))))))), X1))
RN_IN_G(f(f(f(X1)))) → PM_IN_GG(f(f(f(f(f(f(f(f(X1)))))))), X1)
PM_IN_GG(X1, X2) → U16_GG(X1, X2, pK_in_gg(X1, X2))
PM_IN_GG(X1, X2) → PK_IN_GG(X1, X2)
PK_IN_GG(X1, X2) → U12_GG(X1, X2, pF_in_gg(X1, X2))
PK_IN_GG(X1, X2) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, X2) → U2_GG(X1, X2, qC_in_gg(f(X1), X2))
PF_IN_GG(X1, X2) → QC_IN_GG(f(X1), X2)
QC_IN_GG(X1, f(f(X1))) → U73_GG(X1, qcA_in_g(X1))
U73_GG(X1, qcA_out_g(X1)) → U74_GG(X1, rN7_in_g(X1))
U73_GG(X1, qcA_out_g(X1)) → RN7_IN_G(X1)
RN7_IN_G(X1) → U50_G(X1, qH_in_g(X1))
RN7_IN_G(X1) → QH_IN_G(X1)
QH_IN_G(f(f(X1))) → U7_G(X1, pI_in_g(X1))
QH_IN_G(f(f(X1))) → PI_IN_G(X1)
PI_IN_G(X1) → U57_G(X1, pN5_in_g(X1))
PI_IN_G(X1) → PN5_IN_G(X1)
PN5_IN_G(f(f(X1))) → U47_G(X1, pN2_in_g(X1))
PN5_IN_G(f(f(X1))) → PN2_IN_G(X1)
PN2_IN_G(X1) → U41_G(X1, pX_in_g(X1))
PN2_IN_G(X1) → PX_IN_G(X1)
PX_IN_G(f(f(X1))) → U35_G(X1, pU_in_g(X1))
PX_IN_G(f(f(X1))) → PU_IN_G(X1)
PU_IN_G(X1) → U29_G(X1, pQ_in_g(X1))
PU_IN_G(X1) → PQ_IN_G(X1)
PQ_IN_G(f(f(X1))) → U23_G(X1, pM_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
PQ_IN_G(f(f(X1))) → PM_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PQ_IN_G(X1) → U24_G(X1, qcR_in_g(X1))
U24_G(X1, qcR_out_g(X1)) → U25_G(X1, rN_in_g(X1))
U24_G(X1, qcR_out_g(X1)) → RN_IN_G(X1)
RN_IN_G(f(f(X1))) → U18_G(X1, qcO_in_g(f(X1)))
U18_G(X1, qcO_out_g(f(X1))) → U19_G(X1, pF_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U18_G(X1, qcO_out_g(f(X1))) → PF_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PF_IN_GG(X1, f(X2)) → U3_GG(X1, X2, qcC_in_gg(f(X1), f(X2)))
U3_GG(X1, X2, qcC_out_gg(f(X1), f(X2))) → U4_GG(X1, X2, pF_in_gg(X1, X2))
U3_GG(X1, X2, qcC_out_gg(f(X1), f(X2))) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, f(X1)) → U5_GG(X1, qcC_in_gg(f(X1), f(X1)))
U5_GG(X1, qcC_out_gg(f(X1), f(X1))) → U6_GG(X1, tG_in_g(X1))
U5_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
TG_IN_G(X1) → U11_G(X1, pJ_in_g(X1))
TG_IN_G(X1) → PJ_IN_G(X1)
PJ_IN_G(X1) → U8_G(X1, qH_in_g(f(X1)))
PJ_IN_G(X1) → QH_IN_G(f(X1))
PJ_IN_G(f(X1)) → U9_G(X1, qcH_in_g(f(f(X1))))
U9_G(X1, qcH_out_g(f(f(X1)))) → U10_G(X1, pJ_in_g(X1))
U9_G(X1, qcH_out_g(f(f(X1)))) → PJ_IN_G(X1)
PU_IN_G(X1) → U30_G(X1, rcV_in_g(X1))
U30_G(X1, rcV_out_g(X1)) → U31_G(X1, pP_in_g(X1))
U30_G(X1, rcV_out_g(X1)) → PP_IN_G(X1)
PP_IN_G(f(f(X1))) → U21_G(X1, rcN_in_g(f(f(X1))))
U21_G(X1, rcN_out_g(f(f(X1)))) → U22_G(X1, pK_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U21_G(X1, rcN_out_g(f(f(X1)))) → PK_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PK_IN_GG(X1, X1) → U13_GG(X1, tG_in_g(X1))
PK_IN_GG(X1, X1) → TG_IN_G(X1)
PK_IN_GG(X1, f(X2)) → U14_GG(X1, X2, rcL_in_gg(X1, f(X2)))
U14_GG(X1, X2, rcL_out_gg(X1, f(X2))) → U15_GG(X1, X2, pK_in_gg(X1, X2))
U14_GG(X1, X2, rcL_out_gg(X1, f(X2))) → PK_IN_GG(X1, X2)
PX_IN_G(X1) → U36_G(X1, qcY_in_g(X1))
U36_G(X1, qcY_out_g(X1)) → U37_G(X1, rS_in_g(X1))
U36_G(X1, qcY_out_g(X1)) → RS_IN_G(X1)
RS_IN_G(f(f(X1))) → U27_G(X1, qcT_in_g(f(X1)))
U27_G(X1, qcT_out_g(f(X1))) → U28_G(X1, pQ_in_g(X1))
U27_G(X1, qcT_out_g(f(X1))) → PQ_IN_G(X1)
PN2_IN_G(X1) → U42_G(X1, rcN3_in_g(X1))
U42_G(X1, rcN3_out_g(X1)) → U43_G(X1, pW_in_g(X1))
U42_G(X1, rcN3_out_g(X1)) → PW_IN_G(X1)
PW_IN_G(f(f(X1))) → U33_G(X1, rcS_in_g(f(f(X1))))
U33_G(X1, rcS_out_g(f(f(X1)))) → U34_G(X1, pU_in_g(X1))
U33_G(X1, rcS_out_g(f(f(X1)))) → PU_IN_G(X1)
PN5_IN_G(X1) → U48_G(X1, qcN6_in_g(X1))
U48_G(X1, qcN6_out_g(X1)) → U49_G(X1, rZ_in_g(X1))
U48_G(X1, qcN6_out_g(X1)) → RZ_IN_G(X1)
RZ_IN_G(f(f(X1))) → U39_G(X1, qcN1_in_g(f(X1)))
U39_G(X1, qcN1_out_g(f(X1))) → U40_G(X1, pX_in_g(X1))
U39_G(X1, qcN1_out_g(f(X1))) → PX_IN_G(X1)
PI_IN_G(X1) → U58_G(X1, rcN10_in_g(X1))
U58_G(X1, rcN10_out_g(X1)) → U59_G(X1, pN4_in_g(X1))
U58_G(X1, rcN10_out_g(X1)) → PN4_IN_G(X1)
PN4_IN_G(f(f(X1))) → U45_G(X1, rcZ_in_g(f(f(X1))))
U45_G(X1, rcZ_out_g(f(f(X1)))) → U46_G(X1, pN2_in_g(X1))
U45_G(X1, rcZ_out_g(f(f(X1)))) → PN2_IN_G(X1)
RN7_IN_G(X1) → U51_G(X1, qcH_in_g(X1))
U51_G(X1, qcH_out_g(X1)) → U52_G(X1, rN8_in_g(X1))
U51_G(X1, qcH_out_g(X1)) → RN8_IN_G(X1)
RN8_IN_G(f(f(X1))) → U54_G(X1, qcN9_in_g(f(X1)))
U54_G(X1, qcN9_out_g(f(X1))) → U55_G(X1, pN5_in_g(X1))
U54_G(X1, qcN9_out_g(f(X1))) → PN5_IN_G(X1)
RN8_IN_G(f(X1)) → U56_G(X1, tG_in_g(X1))
RN8_IN_G(f(X1)) → TG_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U75_GG(X1, rcN13_in_g(X1))
U75_GG(X1, rcN13_out_g(X1)) → U76_GG(X1, rN7_in_g(X1))
U75_GG(X1, rcN13_out_g(X1)) → RN7_IN_G(X1)
U75_GG(X1, rcN13_out_g(X1)) → U77_GG(X1, rcN7_in_g(X1))
U77_GG(X1, rcN7_out_g(X1)) → U78_GG(X1, pB_in_g(X1))
U77_GG(X1, rcN7_out_g(X1)) → PB_IN_G(X1)
PB_IN_G(f(f(X1))) → U61_G(X1, rcN8_in_g(f(f(X1))))
U61_G(X1, rcN8_out_g(f(f(X1)))) → U62_G(X1, pI_in_g(X1))
U61_G(X1, rcN8_out_g(f(f(X1)))) → PI_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U79_GG(X1, pcD_in_g(X1))
U79_GG(X1, pcD_out_g(X1)) → U80_GG(X1, qA_in_g(X1))
U79_GG(X1, pcD_out_g(X1)) → QA_IN_G(X1)
QC_IN_GG(X1, f(f(X2))) → U81_GG(X1, X2, pE_in_gg(X1, X2))
QC_IN_GG(X1, f(f(X2))) → PE_IN_GG(X1, X2)
PE_IN_GG(X1, X2) → U68_GG(X1, X2, pN11_in_gg(X1, X2))
PE_IN_GG(X1, X2) → PN11_IN_GG(X1, X2)
PN11_IN_GG(X1, X2) → U63_GG(X1, X2, qC_in_gg(X1, X2))
PN11_IN_GG(X1, X2) → QC_IN_GG(X1, X2)
PN11_IN_GG(X1, f(X2)) → U64_GG(X1, X2, qcC_in_gg(X1, f(X2)))
U64_GG(X1, X2, qcC_out_gg(X1, f(X2))) → U65_GG(X1, X2, pN11_in_gg(X1, X2))
U64_GG(X1, X2, qcC_out_gg(X1, f(X2))) → PN11_IN_GG(X1, X2)
PN11_IN_GG(f(X1), f(X1)) → U66_GG(X1, qcC_in_gg(f(X1), f(X1)))
U66_GG(X1, qcC_out_gg(f(X1), f(X1))) → U67_GG(X1, tG_in_g(X1))
U66_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
PE_IN_GG(f(X1), X1) → U69_GG(X1, tG_in_g(X1))
PE_IN_GG(f(X1), X1) → TG_IN_G(X1)
PE_IN_GG(X1, f(X2)) → U70_GG(X1, X2, rcN12_in_gg(X1, f(X2)))
U70_GG(X1, X2, rcN12_out_gg(X1, f(X2))) → U71_GG(X1, X2, pE_in_gg(X1, X2))
U70_GG(X1, X2, rcN12_out_gg(X1, f(X2))) → PE_IN_GG(X1, X2)

The TRS R consists of the following rules:

qcA_in_g(f(X1)) → U83_g(X1, pcB_in_g(f(X1)))
pcB_in_g(f(f(X1))) → U127_g(X1, rcN8_in_g(f(f(X1))))
rcN8_in_g(f(f(X1))) → U122_g(X1, qcN9_in_g(f(X1)))
qcN9_in_g(f(f(X1))) → U153_g(X1, pcN4_in_g(f(X1)))
pcN4_in_g(f(f(X1))) → U116_g(X1, rcZ_in_g(f(f(X1))))
rcZ_in_g(f(f(X1))) → U112_g(X1, qcN1_in_g(f(X1)))
qcN1_in_g(f(f(X1))) → U152_g(X1, pcW_in_g(f(X1)))
pcW_in_g(f(f(X1))) → U108_g(X1, rcS_in_g(f(f(X1))))
rcS_in_g(f(f(X1))) → U104_g(X1, qcT_in_g(f(X1)))
qcT_in_g(f(f(X1))) → U151_g(X1, pcP_in_g(f(X1)))
pcP_in_g(f(f(X1))) → U100_g(X1, rcN_in_g(f(f(X1))))
rcN_in_g(f(f(X1))) → U98_g(X1, qcO_in_g(f(X1)))
qcO_in_g(f(f(X1))) → U150_g(X1, pcM_in_gg(f(f(f(f(f(f(f(f(X1)))))))), X1))
pcM_in_gg(X1, X2) → U97_gg(X1, X2, qcK_in_gg(X1, X2))
qcK_in_gg(X1, f(X2)) → U95_gg(X1, X2, rcL_in_gg(X1, f(X2)))
rcL_in_gg(X1, X2) → U148_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X2)) → U87_gg(X1, X2, qcC_in_gg(f(X1), f(X2)))
qcC_in_gg(a, b) → qcC_out_gg(a, b)
qcC_in_gg(X1, f(f(X1))) → U84_gg(X1, pcD_in_g(X1))
pcD_in_g(X1) → U137_g(X1, rcN13_in_g(X1))
rcN13_in_g(X1) → U140_g(X1, qcA_in_g(X1))
U140_g(X1, qcA_out_g(X1)) → U141_g(X1, rcN7_in_g(X1))
rcN7_in_g(X1) → U120_g(X1, qcH_in_g(X1))
qcH_in_g(f(f(X1))) → U91_g(X1, qcI_in_g(X1))
qcI_in_g(X1) → U125_g(X1, rcN10_in_g(X1))
rcN10_in_g(X1) → U142_g(X1, qcN5_in_g(X1))
qcN5_in_g(X1) → U118_g(X1, qcN6_in_g(X1))
qcN6_in_g(f(f(X1))) → U143_g(X1, qcN2_in_g(X1))
qcN2_in_g(X1) → U114_g(X1, rcN3_in_g(X1))
rcN3_in_g(X1) → U144_g(X1, qcX_in_g(X1))
qcX_in_g(X1) → U110_g(X1, qcY_in_g(X1))
qcY_in_g(f(f(X1))) → U145_g(X1, qcU_in_g(X1))
qcU_in_g(X1) → U106_g(X1, rcV_in_g(X1))
rcV_in_g(X1) → U146_g(X1, qcQ_in_g(X1))
qcQ_in_g(X1) → U102_g(X1, qcR_in_g(X1))
qcR_in_g(f(f(X1))) → U147_g(X1, pcM_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U147_g(X1, pcM_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → qcR_out_g(f(f(X1)))
U102_g(X1, qcR_out_g(X1)) → U103_g(X1, rcN_in_g(X1))
U103_g(X1, rcN_out_g(X1)) → qcQ_out_g(X1)
U146_g(X1, qcQ_out_g(X1)) → rcV_out_g(X1)
U106_g(X1, rcV_out_g(X1)) → U107_g(X1, pcP_in_g(X1))
U107_g(X1, pcP_out_g(X1)) → qcU_out_g(X1)
U145_g(X1, qcU_out_g(X1)) → qcY_out_g(f(f(X1)))
U110_g(X1, qcY_out_g(X1)) → U111_g(X1, rcS_in_g(X1))
U111_g(X1, rcS_out_g(X1)) → qcX_out_g(X1)
U144_g(X1, qcX_out_g(X1)) → rcN3_out_g(X1)
U114_g(X1, rcN3_out_g(X1)) → U115_g(X1, pcW_in_g(X1))
U115_g(X1, pcW_out_g(X1)) → qcN2_out_g(X1)
U143_g(X1, qcN2_out_g(X1)) → qcN6_out_g(f(f(X1)))
U118_g(X1, qcN6_out_g(X1)) → U119_g(X1, rcZ_in_g(X1))
U119_g(X1, rcZ_out_g(X1)) → qcN5_out_g(X1)
U142_g(X1, qcN5_out_g(X1)) → rcN10_out_g(X1)
U125_g(X1, rcN10_out_g(X1)) → U126_g(X1, pcN4_in_g(X1))
U126_g(X1, pcN4_out_g(X1)) → qcI_out_g(X1)
U91_g(X1, qcI_out_g(X1)) → qcH_out_g(f(f(X1)))
U120_g(X1, qcH_out_g(X1)) → U121_g(X1, rcN8_in_g(X1))
rcN8_in_g(f(X1)) → U124_g(X1, tcG_in_g(X1))
tcG_in_g(X1) → U94_g(X1, qcJ_in_g(X1))
qcJ_in_g(f(X1)) → U92_g(X1, qcH_in_g(f(f(X1))))
U92_g(X1, qcH_out_g(f(f(X1)))) → U93_g(X1, qcJ_in_g(X1))
U93_g(X1, qcJ_out_g(X1)) → qcJ_out_g(f(X1))
U94_g(X1, qcJ_out_g(X1)) → tcG_out_g(X1)
U124_g(X1, tcG_out_g(X1)) → rcN8_out_g(f(X1))
U121_g(X1, rcN8_out_g(X1)) → rcN7_out_g(X1)
U141_g(X1, rcN7_out_g(X1)) → rcN13_out_g(X1)
U137_g(X1, rcN13_out_g(X1)) → U138_g(X1, rcN7_in_g(X1))
U138_g(X1, rcN7_out_g(X1)) → U139_g(X1, pcB_in_g(X1))
U139_g(X1, pcB_out_g(X1)) → pcD_out_g(X1)
U84_gg(X1, pcD_out_g(X1)) → U85_gg(X1, qcA_in_g(X1))
U85_gg(X1, qcA_out_g(X1)) → qcC_out_gg(X1, f(f(X1)))
qcC_in_gg(X1, f(f(X2))) → U86_gg(X1, X2, qcE_in_gg(X1, X2))
qcE_in_gg(a, b) → U134_gg(rcN12_in_gg(a, b))
rcN12_in_gg(X1, X2) → U154_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(a, b) → U129_gg(qcC_in_gg(a, b))
U129_gg(qcC_out_gg(a, b)) → qcN11_out_gg(a, b)
qcN11_in_gg(X1, f(X2)) → U130_gg(X1, X2, qcC_in_gg(X1, f(X2)))
U130_gg(X1, X2, qcC_out_gg(X1, f(X2))) → U131_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(f(X1), f(X1)) → U132_gg(X1, qcC_in_gg(f(X1), f(X1)))
U132_gg(X1, qcC_out_gg(f(X1), f(X1))) → U133_gg(X1, tcG_in_g(X1))
U133_gg(X1, tcG_out_g(X1)) → qcN11_out_gg(f(X1), f(X1))
U131_gg(X1, X2, qcN11_out_gg(X1, X2)) → qcN11_out_gg(X1, f(X2))
U154_gg(X1, X2, qcN11_out_gg(X1, X2)) → rcN12_out_gg(X1, X2)
rcN12_in_gg(f(X1), X1) → U155_gg(X1, tcG_in_g(X1))
U155_gg(X1, tcG_out_g(X1)) → rcN12_out_gg(f(X1), X1)
U134_gg(rcN12_out_gg(a, b)) → qcE_out_gg(a, b)
qcE_in_gg(X1, f(X2)) → U135_gg(X1, X2, rcN12_in_gg(X1, f(X2)))
U135_gg(X1, X2, rcN12_out_gg(X1, f(X2))) → U136_gg(X1, X2, qcE_in_gg(X1, X2))
U136_gg(X1, X2, qcE_out_gg(X1, X2)) → qcE_out_gg(X1, f(X2))
U86_gg(X1, X2, qcE_out_gg(X1, X2)) → qcC_out_gg(X1, f(f(X2)))
U87_gg(X1, X2, qcC_out_gg(f(X1), f(X2))) → U88_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X1)) → U89_gg(X1, qcC_in_gg(f(X1), f(X1)))
U89_gg(X1, qcC_out_gg(f(X1), f(X1))) → U90_gg(X1, tcG_in_g(X1))
U90_gg(X1, tcG_out_g(X1)) → qcF_out_gg(X1, f(X1))
U88_gg(X1, X2, qcF_out_gg(X1, X2)) → qcF_out_gg(X1, f(X2))
U148_gg(X1, X2, qcF_out_gg(X1, X2)) → rcL_out_gg(X1, X2)
rcL_in_gg(X1, X1) → U149_gg(X1, tcG_in_g(X1))
U149_gg(X1, tcG_out_g(X1)) → rcL_out_gg(X1, X1)
U95_gg(X1, X2, rcL_out_gg(X1, f(X2))) → U96_gg(X1, X2, qcK_in_gg(X1, X2))
U96_gg(X1, X2, qcK_out_gg(X1, X2)) → qcK_out_gg(X1, f(X2))
U97_gg(X1, X2, qcK_out_gg(X1, X2)) → pcM_out_gg(X1, X2)
U150_g(X1, pcM_out_gg(f(f(f(f(f(f(f(f(X1)))))))), X1)) → qcO_out_g(f(f(X1)))
U98_g(X1, qcO_out_g(f(X1))) → U99_g(X1, qcF_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U99_g(X1, qcF_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → rcN_out_g(f(f(X1)))
U100_g(X1, rcN_out_g(f(f(X1)))) → U101_g(X1, qcK_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U101_g(X1, qcK_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → pcP_out_g(f(f(X1)))
U151_g(X1, pcP_out_g(f(X1))) → qcT_out_g(f(f(X1)))
U104_g(X1, qcT_out_g(f(X1))) → U105_g(X1, qcQ_in_g(X1))
U105_g(X1, qcQ_out_g(X1)) → rcS_out_g(f(f(X1)))
U108_g(X1, rcS_out_g(f(f(X1)))) → U109_g(X1, qcU_in_g(X1))
U109_g(X1, qcU_out_g(X1)) → pcW_out_g(f(f(X1)))
U152_g(X1, pcW_out_g(f(X1))) → qcN1_out_g(f(f(X1)))
U112_g(X1, qcN1_out_g(f(X1))) → U113_g(X1, qcX_in_g(X1))
U113_g(X1, qcX_out_g(X1)) → rcZ_out_g(f(f(X1)))
U116_g(X1, rcZ_out_g(f(f(X1)))) → U117_g(X1, qcN2_in_g(X1))
U117_g(X1, qcN2_out_g(X1)) → pcN4_out_g(f(f(X1)))
U153_g(X1, pcN4_out_g(f(X1))) → qcN9_out_g(f(f(X1)))
U122_g(X1, qcN9_out_g(f(X1))) → U123_g(X1, qcN5_in_g(X1))
U123_g(X1, qcN5_out_g(X1)) → rcN8_out_g(f(f(X1)))
U127_g(X1, rcN8_out_g(f(f(X1)))) → U128_g(X1, qcI_in_g(X1))
U128_g(X1, qcI_out_g(X1)) → pcB_out_g(f(f(X1)))
U83_g(X1, pcB_out_g(f(X1))) → qcA_out_g(f(X1))

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

Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES

(4) Obligation:

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

QC_IN_GG(X1, f(f(X1))) → U72_GG(X1, qA_in_g(X1))
QC_IN_GG(X1, f(f(X1))) → QA_IN_G(X1)
QA_IN_G(f(X1)) → U1_G(X1, pB_in_g(f(X1)))
QA_IN_G(f(X1)) → PB_IN_G(f(X1))
PB_IN_G(f(X1)) → U60_G(X1, rN8_in_g(f(X1)))
PB_IN_G(f(X1)) → RN8_IN_G(f(X1))
RN8_IN_G(f(f(f(X1)))) → U53_G(X1, pN4_in_g(f(X1)))
RN8_IN_G(f(f(f(X1)))) → PN4_IN_G(f(X1))
PN4_IN_G(f(X1)) → U44_G(X1, rZ_in_g(f(X1)))
PN4_IN_G(f(X1)) → RZ_IN_G(f(X1))
RZ_IN_G(f(f(f(X1)))) → U38_G(X1, pW_in_g(f(X1)))
RZ_IN_G(f(f(f(X1)))) → PW_IN_G(f(X1))
PW_IN_G(f(X1)) → U32_G(X1, rS_in_g(f(X1)))
PW_IN_G(f(X1)) → RS_IN_G(f(X1))
RS_IN_G(f(f(f(X1)))) → U26_G(X1, pP_in_g(f(X1)))
RS_IN_G(f(f(f(X1)))) → PP_IN_G(f(X1))
PP_IN_G(f(X1)) → U20_G(X1, rN_in_g(f(X1)))
PP_IN_G(f(X1)) → RN_IN_G(f(X1))
RN_IN_G(f(f(f(X1)))) → U17_G(X1, pM_in_gg(f(f(f(f(f(f(f(f(X1)))))))), X1))
RN_IN_G(f(f(f(X1)))) → PM_IN_GG(f(f(f(f(f(f(f(f(X1)))))))), X1)
PM_IN_GG(X1, X2) → U16_GG(X1, X2, pK_in_gg(X1, X2))
PM_IN_GG(X1, X2) → PK_IN_GG(X1, X2)
PK_IN_GG(X1, X2) → U12_GG(X1, X2, pF_in_gg(X1, X2))
PK_IN_GG(X1, X2) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, X2) → U2_GG(X1, X2, qC_in_gg(f(X1), X2))
PF_IN_GG(X1, X2) → QC_IN_GG(f(X1), X2)
QC_IN_GG(X1, f(f(X1))) → U73_GG(X1, qcA_in_g(X1))
U73_GG(X1, qcA_out_g(X1)) → U74_GG(X1, rN7_in_g(X1))
U73_GG(X1, qcA_out_g(X1)) → RN7_IN_G(X1)
RN7_IN_G(X1) → U50_G(X1, qH_in_g(X1))
RN7_IN_G(X1) → QH_IN_G(X1)
QH_IN_G(f(f(X1))) → U7_G(X1, pI_in_g(X1))
QH_IN_G(f(f(X1))) → PI_IN_G(X1)
PI_IN_G(X1) → U57_G(X1, pN5_in_g(X1))
PI_IN_G(X1) → PN5_IN_G(X1)
PN5_IN_G(f(f(X1))) → U47_G(X1, pN2_in_g(X1))
PN5_IN_G(f(f(X1))) → PN2_IN_G(X1)
PN2_IN_G(X1) → U41_G(X1, pX_in_g(X1))
PN2_IN_G(X1) → PX_IN_G(X1)
PX_IN_G(f(f(X1))) → U35_G(X1, pU_in_g(X1))
PX_IN_G(f(f(X1))) → PU_IN_G(X1)
PU_IN_G(X1) → U29_G(X1, pQ_in_g(X1))
PU_IN_G(X1) → PQ_IN_G(X1)
PQ_IN_G(f(f(X1))) → U23_G(X1, pM_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
PQ_IN_G(f(f(X1))) → PM_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PQ_IN_G(X1) → U24_G(X1, qcR_in_g(X1))
U24_G(X1, qcR_out_g(X1)) → U25_G(X1, rN_in_g(X1))
U24_G(X1, qcR_out_g(X1)) → RN_IN_G(X1)
RN_IN_G(f(f(X1))) → U18_G(X1, qcO_in_g(f(X1)))
U18_G(X1, qcO_out_g(f(X1))) → U19_G(X1, pF_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U18_G(X1, qcO_out_g(f(X1))) → PF_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PF_IN_GG(X1, f(X2)) → U3_GG(X1, X2, qcC_in_gg(f(X1), f(X2)))
U3_GG(X1, X2, qcC_out_gg(f(X1), f(X2))) → U4_GG(X1, X2, pF_in_gg(X1, X2))
U3_GG(X1, X2, qcC_out_gg(f(X1), f(X2))) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, f(X1)) → U5_GG(X1, qcC_in_gg(f(X1), f(X1)))
U5_GG(X1, qcC_out_gg(f(X1), f(X1))) → U6_GG(X1, tG_in_g(X1))
U5_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
TG_IN_G(X1) → U11_G(X1, pJ_in_g(X1))
TG_IN_G(X1) → PJ_IN_G(X1)
PJ_IN_G(X1) → U8_G(X1, qH_in_g(f(X1)))
PJ_IN_G(X1) → QH_IN_G(f(X1))
PJ_IN_G(f(X1)) → U9_G(X1, qcH_in_g(f(f(X1))))
U9_G(X1, qcH_out_g(f(f(X1)))) → U10_G(X1, pJ_in_g(X1))
U9_G(X1, qcH_out_g(f(f(X1)))) → PJ_IN_G(X1)
PU_IN_G(X1) → U30_G(X1, rcV_in_g(X1))
U30_G(X1, rcV_out_g(X1)) → U31_G(X1, pP_in_g(X1))
U30_G(X1, rcV_out_g(X1)) → PP_IN_G(X1)
PP_IN_G(f(f(X1))) → U21_G(X1, rcN_in_g(f(f(X1))))
U21_G(X1, rcN_out_g(f(f(X1)))) → U22_G(X1, pK_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U21_G(X1, rcN_out_g(f(f(X1)))) → PK_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PK_IN_GG(X1, X1) → U13_GG(X1, tG_in_g(X1))
PK_IN_GG(X1, X1) → TG_IN_G(X1)
PK_IN_GG(X1, f(X2)) → U14_GG(X1, X2, rcL_in_gg(X1, f(X2)))
U14_GG(X1, X2, rcL_out_gg(X1, f(X2))) → U15_GG(X1, X2, pK_in_gg(X1, X2))
U14_GG(X1, X2, rcL_out_gg(X1, f(X2))) → PK_IN_GG(X1, X2)
PX_IN_G(X1) → U36_G(X1, qcY_in_g(X1))
U36_G(X1, qcY_out_g(X1)) → U37_G(X1, rS_in_g(X1))
U36_G(X1, qcY_out_g(X1)) → RS_IN_G(X1)
RS_IN_G(f(f(X1))) → U27_G(X1, qcT_in_g(f(X1)))
U27_G(X1, qcT_out_g(f(X1))) → U28_G(X1, pQ_in_g(X1))
U27_G(X1, qcT_out_g(f(X1))) → PQ_IN_G(X1)
PN2_IN_G(X1) → U42_G(X1, rcN3_in_g(X1))
U42_G(X1, rcN3_out_g(X1)) → U43_G(X1, pW_in_g(X1))
U42_G(X1, rcN3_out_g(X1)) → PW_IN_G(X1)
PW_IN_G(f(f(X1))) → U33_G(X1, rcS_in_g(f(f(X1))))
U33_G(X1, rcS_out_g(f(f(X1)))) → U34_G(X1, pU_in_g(X1))
U33_G(X1, rcS_out_g(f(f(X1)))) → PU_IN_G(X1)
PN5_IN_G(X1) → U48_G(X1, qcN6_in_g(X1))
U48_G(X1, qcN6_out_g(X1)) → U49_G(X1, rZ_in_g(X1))
U48_G(X1, qcN6_out_g(X1)) → RZ_IN_G(X1)
RZ_IN_G(f(f(X1))) → U39_G(X1, qcN1_in_g(f(X1)))
U39_G(X1, qcN1_out_g(f(X1))) → U40_G(X1, pX_in_g(X1))
U39_G(X1, qcN1_out_g(f(X1))) → PX_IN_G(X1)
PI_IN_G(X1) → U58_G(X1, rcN10_in_g(X1))
U58_G(X1, rcN10_out_g(X1)) → U59_G(X1, pN4_in_g(X1))
U58_G(X1, rcN10_out_g(X1)) → PN4_IN_G(X1)
PN4_IN_G(f(f(X1))) → U45_G(X1, rcZ_in_g(f(f(X1))))
U45_G(X1, rcZ_out_g(f(f(X1)))) → U46_G(X1, pN2_in_g(X1))
U45_G(X1, rcZ_out_g(f(f(X1)))) → PN2_IN_G(X1)
RN7_IN_G(X1) → U51_G(X1, qcH_in_g(X1))
U51_G(X1, qcH_out_g(X1)) → U52_G(X1, rN8_in_g(X1))
U51_G(X1, qcH_out_g(X1)) → RN8_IN_G(X1)
RN8_IN_G(f(f(X1))) → U54_G(X1, qcN9_in_g(f(X1)))
U54_G(X1, qcN9_out_g(f(X1))) → U55_G(X1, pN5_in_g(X1))
U54_G(X1, qcN9_out_g(f(X1))) → PN5_IN_G(X1)
RN8_IN_G(f(X1)) → U56_G(X1, tG_in_g(X1))
RN8_IN_G(f(X1)) → TG_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U75_GG(X1, rcN13_in_g(X1))
U75_GG(X1, rcN13_out_g(X1)) → U76_GG(X1, rN7_in_g(X1))
U75_GG(X1, rcN13_out_g(X1)) → RN7_IN_G(X1)
U75_GG(X1, rcN13_out_g(X1)) → U77_GG(X1, rcN7_in_g(X1))
U77_GG(X1, rcN7_out_g(X1)) → U78_GG(X1, pB_in_g(X1))
U77_GG(X1, rcN7_out_g(X1)) → PB_IN_G(X1)
PB_IN_G(f(f(X1))) → U61_G(X1, rcN8_in_g(f(f(X1))))
U61_G(X1, rcN8_out_g(f(f(X1)))) → U62_G(X1, pI_in_g(X1))
U61_G(X1, rcN8_out_g(f(f(X1)))) → PI_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U79_GG(X1, pcD_in_g(X1))
U79_GG(X1, pcD_out_g(X1)) → U80_GG(X1, qA_in_g(X1))
U79_GG(X1, pcD_out_g(X1)) → QA_IN_G(X1)
QC_IN_GG(X1, f(f(X2))) → U81_GG(X1, X2, pE_in_gg(X1, X2))
QC_IN_GG(X1, f(f(X2))) → PE_IN_GG(X1, X2)
PE_IN_GG(X1, X2) → U68_GG(X1, X2, pN11_in_gg(X1, X2))
PE_IN_GG(X1, X2) → PN11_IN_GG(X1, X2)
PN11_IN_GG(X1, X2) → U63_GG(X1, X2, qC_in_gg(X1, X2))
PN11_IN_GG(X1, X2) → QC_IN_GG(X1, X2)
PN11_IN_GG(X1, f(X2)) → U64_GG(X1, X2, qcC_in_gg(X1, f(X2)))
U64_GG(X1, X2, qcC_out_gg(X1, f(X2))) → U65_GG(X1, X2, pN11_in_gg(X1, X2))
U64_GG(X1, X2, qcC_out_gg(X1, f(X2))) → PN11_IN_GG(X1, X2)
PN11_IN_GG(f(X1), f(X1)) → U66_GG(X1, qcC_in_gg(f(X1), f(X1)))
U66_GG(X1, qcC_out_gg(f(X1), f(X1))) → U67_GG(X1, tG_in_g(X1))
U66_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
PE_IN_GG(f(X1), X1) → U69_GG(X1, tG_in_g(X1))
PE_IN_GG(f(X1), X1) → TG_IN_G(X1)
PE_IN_GG(X1, f(X2)) → U70_GG(X1, X2, rcN12_in_gg(X1, f(X2)))
U70_GG(X1, X2, rcN12_out_gg(X1, f(X2))) → U71_GG(X1, X2, pE_in_gg(X1, X2))
U70_GG(X1, X2, rcN12_out_gg(X1, f(X2))) → PE_IN_GG(X1, X2)

The TRS R consists of the following rules:

qcA_in_g(f(X1)) → U83_g(X1, pcB_in_g(f(X1)))
pcB_in_g(f(f(X1))) → U127_g(X1, rcN8_in_g(f(f(X1))))
rcN8_in_g(f(f(X1))) → U122_g(X1, qcN9_in_g(f(X1)))
qcN9_in_g(f(f(X1))) → U153_g(X1, pcN4_in_g(f(X1)))
pcN4_in_g(f(f(X1))) → U116_g(X1, rcZ_in_g(f(f(X1))))
rcZ_in_g(f(f(X1))) → U112_g(X1, qcN1_in_g(f(X1)))
qcN1_in_g(f(f(X1))) → U152_g(X1, pcW_in_g(f(X1)))
pcW_in_g(f(f(X1))) → U108_g(X1, rcS_in_g(f(f(X1))))
rcS_in_g(f(f(X1))) → U104_g(X1, qcT_in_g(f(X1)))
qcT_in_g(f(f(X1))) → U151_g(X1, pcP_in_g(f(X1)))
pcP_in_g(f(f(X1))) → U100_g(X1, rcN_in_g(f(f(X1))))
rcN_in_g(f(f(X1))) → U98_g(X1, qcO_in_g(f(X1)))
qcO_in_g(f(f(X1))) → U150_g(X1, pcM_in_gg(f(f(f(f(f(f(f(f(X1)))))))), X1))
pcM_in_gg(X1, X2) → U97_gg(X1, X2, qcK_in_gg(X1, X2))
qcK_in_gg(X1, f(X2)) → U95_gg(X1, X2, rcL_in_gg(X1, f(X2)))
rcL_in_gg(X1, X2) → U148_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X2)) → U87_gg(X1, X2, qcC_in_gg(f(X1), f(X2)))
qcC_in_gg(a, b) → qcC_out_gg(a, b)
qcC_in_gg(X1, f(f(X1))) → U84_gg(X1, pcD_in_g(X1))
pcD_in_g(X1) → U137_g(X1, rcN13_in_g(X1))
rcN13_in_g(X1) → U140_g(X1, qcA_in_g(X1))
U140_g(X1, qcA_out_g(X1)) → U141_g(X1, rcN7_in_g(X1))
rcN7_in_g(X1) → U120_g(X1, qcH_in_g(X1))
qcH_in_g(f(f(X1))) → U91_g(X1, qcI_in_g(X1))
qcI_in_g(X1) → U125_g(X1, rcN10_in_g(X1))
rcN10_in_g(X1) → U142_g(X1, qcN5_in_g(X1))
qcN5_in_g(X1) → U118_g(X1, qcN6_in_g(X1))
qcN6_in_g(f(f(X1))) → U143_g(X1, qcN2_in_g(X1))
qcN2_in_g(X1) → U114_g(X1, rcN3_in_g(X1))
rcN3_in_g(X1) → U144_g(X1, qcX_in_g(X1))
qcX_in_g(X1) → U110_g(X1, qcY_in_g(X1))
qcY_in_g(f(f(X1))) → U145_g(X1, qcU_in_g(X1))
qcU_in_g(X1) → U106_g(X1, rcV_in_g(X1))
rcV_in_g(X1) → U146_g(X1, qcQ_in_g(X1))
qcQ_in_g(X1) → U102_g(X1, qcR_in_g(X1))
qcR_in_g(f(f(X1))) → U147_g(X1, pcM_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U147_g(X1, pcM_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → qcR_out_g(f(f(X1)))
U102_g(X1, qcR_out_g(X1)) → U103_g(X1, rcN_in_g(X1))
U103_g(X1, rcN_out_g(X1)) → qcQ_out_g(X1)
U146_g(X1, qcQ_out_g(X1)) → rcV_out_g(X1)
U106_g(X1, rcV_out_g(X1)) → U107_g(X1, pcP_in_g(X1))
U107_g(X1, pcP_out_g(X1)) → qcU_out_g(X1)
U145_g(X1, qcU_out_g(X1)) → qcY_out_g(f(f(X1)))
U110_g(X1, qcY_out_g(X1)) → U111_g(X1, rcS_in_g(X1))
U111_g(X1, rcS_out_g(X1)) → qcX_out_g(X1)
U144_g(X1, qcX_out_g(X1)) → rcN3_out_g(X1)
U114_g(X1, rcN3_out_g(X1)) → U115_g(X1, pcW_in_g(X1))
U115_g(X1, pcW_out_g(X1)) → qcN2_out_g(X1)
U143_g(X1, qcN2_out_g(X1)) → qcN6_out_g(f(f(X1)))
U118_g(X1, qcN6_out_g(X1)) → U119_g(X1, rcZ_in_g(X1))
U119_g(X1, rcZ_out_g(X1)) → qcN5_out_g(X1)
U142_g(X1, qcN5_out_g(X1)) → rcN10_out_g(X1)
U125_g(X1, rcN10_out_g(X1)) → U126_g(X1, pcN4_in_g(X1))
U126_g(X1, pcN4_out_g(X1)) → qcI_out_g(X1)
U91_g(X1, qcI_out_g(X1)) → qcH_out_g(f(f(X1)))
U120_g(X1, qcH_out_g(X1)) → U121_g(X1, rcN8_in_g(X1))
rcN8_in_g(f(X1)) → U124_g(X1, tcG_in_g(X1))
tcG_in_g(X1) → U94_g(X1, qcJ_in_g(X1))
qcJ_in_g(f(X1)) → U92_g(X1, qcH_in_g(f(f(X1))))
U92_g(X1, qcH_out_g(f(f(X1)))) → U93_g(X1, qcJ_in_g(X1))
U93_g(X1, qcJ_out_g(X1)) → qcJ_out_g(f(X1))
U94_g(X1, qcJ_out_g(X1)) → tcG_out_g(X1)
U124_g(X1, tcG_out_g(X1)) → rcN8_out_g(f(X1))
U121_g(X1, rcN8_out_g(X1)) → rcN7_out_g(X1)
U141_g(X1, rcN7_out_g(X1)) → rcN13_out_g(X1)
U137_g(X1, rcN13_out_g(X1)) → U138_g(X1, rcN7_in_g(X1))
U138_g(X1, rcN7_out_g(X1)) → U139_g(X1, pcB_in_g(X1))
U139_g(X1, pcB_out_g(X1)) → pcD_out_g(X1)
U84_gg(X1, pcD_out_g(X1)) → U85_gg(X1, qcA_in_g(X1))
U85_gg(X1, qcA_out_g(X1)) → qcC_out_gg(X1, f(f(X1)))
qcC_in_gg(X1, f(f(X2))) → U86_gg(X1, X2, qcE_in_gg(X1, X2))
qcE_in_gg(a, b) → U134_gg(rcN12_in_gg(a, b))
rcN12_in_gg(X1, X2) → U154_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(a, b) → U129_gg(qcC_in_gg(a, b))
U129_gg(qcC_out_gg(a, b)) → qcN11_out_gg(a, b)
qcN11_in_gg(X1, f(X2)) → U130_gg(X1, X2, qcC_in_gg(X1, f(X2)))
U130_gg(X1, X2, qcC_out_gg(X1, f(X2))) → U131_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(f(X1), f(X1)) → U132_gg(X1, qcC_in_gg(f(X1), f(X1)))
U132_gg(X1, qcC_out_gg(f(X1), f(X1))) → U133_gg(X1, tcG_in_g(X1))
U133_gg(X1, tcG_out_g(X1)) → qcN11_out_gg(f(X1), f(X1))
U131_gg(X1, X2, qcN11_out_gg(X1, X2)) → qcN11_out_gg(X1, f(X2))
U154_gg(X1, X2, qcN11_out_gg(X1, X2)) → rcN12_out_gg(X1, X2)
rcN12_in_gg(f(X1), X1) → U155_gg(X1, tcG_in_g(X1))
U155_gg(X1, tcG_out_g(X1)) → rcN12_out_gg(f(X1), X1)
U134_gg(rcN12_out_gg(a, b)) → qcE_out_gg(a, b)
qcE_in_gg(X1, f(X2)) → U135_gg(X1, X2, rcN12_in_gg(X1, f(X2)))
U135_gg(X1, X2, rcN12_out_gg(X1, f(X2))) → U136_gg(X1, X2, qcE_in_gg(X1, X2))
U136_gg(X1, X2, qcE_out_gg(X1, X2)) → qcE_out_gg(X1, f(X2))
U86_gg(X1, X2, qcE_out_gg(X1, X2)) → qcC_out_gg(X1, f(f(X2)))
U87_gg(X1, X2, qcC_out_gg(f(X1), f(X2))) → U88_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X1)) → U89_gg(X1, qcC_in_gg(f(X1), f(X1)))
U89_gg(X1, qcC_out_gg(f(X1), f(X1))) → U90_gg(X1, tcG_in_g(X1))
U90_gg(X1, tcG_out_g(X1)) → qcF_out_gg(X1, f(X1))
U88_gg(X1, X2, qcF_out_gg(X1, X2)) → qcF_out_gg(X1, f(X2))
U148_gg(X1, X2, qcF_out_gg(X1, X2)) → rcL_out_gg(X1, X2)
rcL_in_gg(X1, X1) → U149_gg(X1, tcG_in_g(X1))
U149_gg(X1, tcG_out_g(X1)) → rcL_out_gg(X1, X1)
U95_gg(X1, X2, rcL_out_gg(X1, f(X2))) → U96_gg(X1, X2, qcK_in_gg(X1, X2))
U96_gg(X1, X2, qcK_out_gg(X1, X2)) → qcK_out_gg(X1, f(X2))
U97_gg(X1, X2, qcK_out_gg(X1, X2)) → pcM_out_gg(X1, X2)
U150_g(X1, pcM_out_gg(f(f(f(f(f(f(f(f(X1)))))))), X1)) → qcO_out_g(f(f(X1)))
U98_g(X1, qcO_out_g(f(X1))) → U99_g(X1, qcF_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U99_g(X1, qcF_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → rcN_out_g(f(f(X1)))
U100_g(X1, rcN_out_g(f(f(X1)))) → U101_g(X1, qcK_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U101_g(X1, qcK_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → pcP_out_g(f(f(X1)))
U151_g(X1, pcP_out_g(f(X1))) → qcT_out_g(f(f(X1)))
U104_g(X1, qcT_out_g(f(X1))) → U105_g(X1, qcQ_in_g(X1))
U105_g(X1, qcQ_out_g(X1)) → rcS_out_g(f(f(X1)))
U108_g(X1, rcS_out_g(f(f(X1)))) → U109_g(X1, qcU_in_g(X1))
U109_g(X1, qcU_out_g(X1)) → pcW_out_g(f(f(X1)))
U152_g(X1, pcW_out_g(f(X1))) → qcN1_out_g(f(f(X1)))
U112_g(X1, qcN1_out_g(f(X1))) → U113_g(X1, qcX_in_g(X1))
U113_g(X1, qcX_out_g(X1)) → rcZ_out_g(f(f(X1)))
U116_g(X1, rcZ_out_g(f(f(X1)))) → U117_g(X1, qcN2_in_g(X1))
U117_g(X1, qcN2_out_g(X1)) → pcN4_out_g(f(f(X1)))
U153_g(X1, pcN4_out_g(f(X1))) → qcN9_out_g(f(f(X1)))
U122_g(X1, qcN9_out_g(f(X1))) → U123_g(X1, qcN5_in_g(X1))
U123_g(X1, qcN5_out_g(X1)) → rcN8_out_g(f(f(X1)))
U127_g(X1, rcN8_out_g(f(f(X1)))) → U128_g(X1, qcI_in_g(X1))
U128_g(X1, qcI_out_g(X1)) → pcB_out_g(f(f(X1)))
U83_g(X1, pcB_out_g(f(X1))) → qcA_out_g(f(X1))

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 55 less nodes.

(6) Obligation:

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

QC_IN_GG(X1, f(f(X1))) → QA_IN_G(X1)
QA_IN_G(f(X1)) → PB_IN_G(f(X1))
PB_IN_G(f(X1)) → RN8_IN_G(f(X1))
RN8_IN_G(f(f(f(X1)))) → PN4_IN_G(f(X1))
PN4_IN_G(f(X1)) → RZ_IN_G(f(X1))
RZ_IN_G(f(f(f(X1)))) → PW_IN_G(f(X1))
PW_IN_G(f(X1)) → RS_IN_G(f(X1))
RS_IN_G(f(f(f(X1)))) → PP_IN_G(f(X1))
PP_IN_G(f(X1)) → RN_IN_G(f(X1))
RN_IN_G(f(f(f(X1)))) → PM_IN_GG(f(f(f(f(f(f(f(f(X1)))))))), X1)
PM_IN_GG(X1, X2) → PK_IN_GG(X1, X2)
PK_IN_GG(X1, X2) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, X2) → QC_IN_GG(f(X1), X2)
QC_IN_GG(X1, f(f(X1))) → U73_GG(X1, qcA_in_g(X1))
U73_GG(X1, qcA_out_g(X1)) → RN7_IN_G(X1)
RN7_IN_G(X1) → QH_IN_G(X1)
QH_IN_G(f(f(X1))) → PI_IN_G(X1)
PI_IN_G(X1) → PN5_IN_G(X1)
PN5_IN_G(f(f(X1))) → PN2_IN_G(X1)
PN2_IN_G(X1) → PX_IN_G(X1)
PX_IN_G(f(f(X1))) → PU_IN_G(X1)
PU_IN_G(X1) → PQ_IN_G(X1)
PQ_IN_G(f(f(X1))) → PM_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PQ_IN_G(X1) → U24_G(X1, qcR_in_g(X1))
U24_G(X1, qcR_out_g(X1)) → RN_IN_G(X1)
RN_IN_G(f(f(X1))) → U18_G(X1, qcO_in_g(f(X1)))
U18_G(X1, qcO_out_g(f(X1))) → PF_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PF_IN_GG(X1, f(X2)) → U3_GG(X1, X2, qcC_in_gg(f(X1), f(X2)))
U3_GG(X1, X2, qcC_out_gg(f(X1), f(X2))) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, f(X1)) → U5_GG(X1, qcC_in_gg(f(X1), f(X1)))
U5_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
TG_IN_G(X1) → PJ_IN_G(X1)
PJ_IN_G(X1) → QH_IN_G(f(X1))
PJ_IN_G(f(X1)) → U9_G(X1, qcH_in_g(f(f(X1))))
U9_G(X1, qcH_out_g(f(f(X1)))) → PJ_IN_G(X1)
PU_IN_G(X1) → U30_G(X1, rcV_in_g(X1))
U30_G(X1, rcV_out_g(X1)) → PP_IN_G(X1)
PP_IN_G(f(f(X1))) → U21_G(X1, rcN_in_g(f(f(X1))))
U21_G(X1, rcN_out_g(f(f(X1)))) → PK_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PK_IN_GG(X1, X1) → TG_IN_G(X1)
PK_IN_GG(X1, f(X2)) → U14_GG(X1, X2, rcL_in_gg(X1, f(X2)))
U14_GG(X1, X2, rcL_out_gg(X1, f(X2))) → PK_IN_GG(X1, X2)
PX_IN_G(X1) → U36_G(X1, qcY_in_g(X1))
U36_G(X1, qcY_out_g(X1)) → RS_IN_G(X1)
RS_IN_G(f(f(X1))) → U27_G(X1, qcT_in_g(f(X1)))
U27_G(X1, qcT_out_g(f(X1))) → PQ_IN_G(X1)
PN2_IN_G(X1) → U42_G(X1, rcN3_in_g(X1))
U42_G(X1, rcN3_out_g(X1)) → PW_IN_G(X1)
PW_IN_G(f(f(X1))) → U33_G(X1, rcS_in_g(f(f(X1))))
U33_G(X1, rcS_out_g(f(f(X1)))) → PU_IN_G(X1)
PN5_IN_G(X1) → U48_G(X1, qcN6_in_g(X1))
U48_G(X1, qcN6_out_g(X1)) → RZ_IN_G(X1)
RZ_IN_G(f(f(X1))) → U39_G(X1, qcN1_in_g(f(X1)))
U39_G(X1, qcN1_out_g(f(X1))) → PX_IN_G(X1)
PI_IN_G(X1) → U58_G(X1, rcN10_in_g(X1))
U58_G(X1, rcN10_out_g(X1)) → PN4_IN_G(X1)
PN4_IN_G(f(f(X1))) → U45_G(X1, rcZ_in_g(f(f(X1))))
U45_G(X1, rcZ_out_g(f(f(X1)))) → PN2_IN_G(X1)
RN7_IN_G(X1) → U51_G(X1, qcH_in_g(X1))
U51_G(X1, qcH_out_g(X1)) → RN8_IN_G(X1)
RN8_IN_G(f(f(X1))) → U54_G(X1, qcN9_in_g(f(X1)))
U54_G(X1, qcN9_out_g(f(X1))) → PN5_IN_G(X1)
RN8_IN_G(f(X1)) → TG_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U75_GG(X1, rcN13_in_g(X1))
U75_GG(X1, rcN13_out_g(X1)) → RN7_IN_G(X1)
U75_GG(X1, rcN13_out_g(X1)) → U77_GG(X1, rcN7_in_g(X1))
U77_GG(X1, rcN7_out_g(X1)) → PB_IN_G(X1)
PB_IN_G(f(f(X1))) → U61_G(X1, rcN8_in_g(f(f(X1))))
U61_G(X1, rcN8_out_g(f(f(X1)))) → PI_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U79_GG(X1, pcD_in_g(X1))
U79_GG(X1, pcD_out_g(X1)) → QA_IN_G(X1)
QC_IN_GG(X1, f(f(X2))) → PE_IN_GG(X1, X2)
PE_IN_GG(X1, X2) → PN11_IN_GG(X1, X2)
PN11_IN_GG(X1, X2) → QC_IN_GG(X1, X2)
PN11_IN_GG(X1, f(X2)) → U64_GG(X1, X2, qcC_in_gg(X1, f(X2)))
U64_GG(X1, X2, qcC_out_gg(X1, f(X2))) → PN11_IN_GG(X1, X2)
PN11_IN_GG(f(X1), f(X1)) → U66_GG(X1, qcC_in_gg(f(X1), f(X1)))
U66_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
PE_IN_GG(f(X1), X1) → TG_IN_G(X1)
PE_IN_GG(X1, f(X2)) → U70_GG(X1, X2, rcN12_in_gg(X1, f(X2)))
U70_GG(X1, X2, rcN12_out_gg(X1, f(X2))) → PE_IN_GG(X1, X2)

The TRS R consists of the following rules:

qcA_in_g(f(X1)) → U83_g(X1, pcB_in_g(f(X1)))
pcB_in_g(f(f(X1))) → U127_g(X1, rcN8_in_g(f(f(X1))))
rcN8_in_g(f(f(X1))) → U122_g(X1, qcN9_in_g(f(X1)))
qcN9_in_g(f(f(X1))) → U153_g(X1, pcN4_in_g(f(X1)))
pcN4_in_g(f(f(X1))) → U116_g(X1, rcZ_in_g(f(f(X1))))
rcZ_in_g(f(f(X1))) → U112_g(X1, qcN1_in_g(f(X1)))
qcN1_in_g(f(f(X1))) → U152_g(X1, pcW_in_g(f(X1)))
pcW_in_g(f(f(X1))) → U108_g(X1, rcS_in_g(f(f(X1))))
rcS_in_g(f(f(X1))) → U104_g(X1, qcT_in_g(f(X1)))
qcT_in_g(f(f(X1))) → U151_g(X1, pcP_in_g(f(X1)))
pcP_in_g(f(f(X1))) → U100_g(X1, rcN_in_g(f(f(X1))))
rcN_in_g(f(f(X1))) → U98_g(X1, qcO_in_g(f(X1)))
qcO_in_g(f(f(X1))) → U150_g(X1, pcM_in_gg(f(f(f(f(f(f(f(f(X1)))))))), X1))
pcM_in_gg(X1, X2) → U97_gg(X1, X2, qcK_in_gg(X1, X2))
qcK_in_gg(X1, f(X2)) → U95_gg(X1, X2, rcL_in_gg(X1, f(X2)))
rcL_in_gg(X1, X2) → U148_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X2)) → U87_gg(X1, X2, qcC_in_gg(f(X1), f(X2)))
qcC_in_gg(a, b) → qcC_out_gg(a, b)
qcC_in_gg(X1, f(f(X1))) → U84_gg(X1, pcD_in_g(X1))
pcD_in_g(X1) → U137_g(X1, rcN13_in_g(X1))
rcN13_in_g(X1) → U140_g(X1, qcA_in_g(X1))
U140_g(X1, qcA_out_g(X1)) → U141_g(X1, rcN7_in_g(X1))
rcN7_in_g(X1) → U120_g(X1, qcH_in_g(X1))
qcH_in_g(f(f(X1))) → U91_g(X1, qcI_in_g(X1))
qcI_in_g(X1) → U125_g(X1, rcN10_in_g(X1))
rcN10_in_g(X1) → U142_g(X1, qcN5_in_g(X1))
qcN5_in_g(X1) → U118_g(X1, qcN6_in_g(X1))
qcN6_in_g(f(f(X1))) → U143_g(X1, qcN2_in_g(X1))
qcN2_in_g(X1) → U114_g(X1, rcN3_in_g(X1))
rcN3_in_g(X1) → U144_g(X1, qcX_in_g(X1))
qcX_in_g(X1) → U110_g(X1, qcY_in_g(X1))
qcY_in_g(f(f(X1))) → U145_g(X1, qcU_in_g(X1))
qcU_in_g(X1) → U106_g(X1, rcV_in_g(X1))
rcV_in_g(X1) → U146_g(X1, qcQ_in_g(X1))
qcQ_in_g(X1) → U102_g(X1, qcR_in_g(X1))
qcR_in_g(f(f(X1))) → U147_g(X1, pcM_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U147_g(X1, pcM_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → qcR_out_g(f(f(X1)))
U102_g(X1, qcR_out_g(X1)) → U103_g(X1, rcN_in_g(X1))
U103_g(X1, rcN_out_g(X1)) → qcQ_out_g(X1)
U146_g(X1, qcQ_out_g(X1)) → rcV_out_g(X1)
U106_g(X1, rcV_out_g(X1)) → U107_g(X1, pcP_in_g(X1))
U107_g(X1, pcP_out_g(X1)) → qcU_out_g(X1)
U145_g(X1, qcU_out_g(X1)) → qcY_out_g(f(f(X1)))
U110_g(X1, qcY_out_g(X1)) → U111_g(X1, rcS_in_g(X1))
U111_g(X1, rcS_out_g(X1)) → qcX_out_g(X1)
U144_g(X1, qcX_out_g(X1)) → rcN3_out_g(X1)
U114_g(X1, rcN3_out_g(X1)) → U115_g(X1, pcW_in_g(X1))
U115_g(X1, pcW_out_g(X1)) → qcN2_out_g(X1)
U143_g(X1, qcN2_out_g(X1)) → qcN6_out_g(f(f(X1)))
U118_g(X1, qcN6_out_g(X1)) → U119_g(X1, rcZ_in_g(X1))
U119_g(X1, rcZ_out_g(X1)) → qcN5_out_g(X1)
U142_g(X1, qcN5_out_g(X1)) → rcN10_out_g(X1)
U125_g(X1, rcN10_out_g(X1)) → U126_g(X1, pcN4_in_g(X1))
U126_g(X1, pcN4_out_g(X1)) → qcI_out_g(X1)
U91_g(X1, qcI_out_g(X1)) → qcH_out_g(f(f(X1)))
U120_g(X1, qcH_out_g(X1)) → U121_g(X1, rcN8_in_g(X1))
rcN8_in_g(f(X1)) → U124_g(X1, tcG_in_g(X1))
tcG_in_g(X1) → U94_g(X1, qcJ_in_g(X1))
qcJ_in_g(f(X1)) → U92_g(X1, qcH_in_g(f(f(X1))))
U92_g(X1, qcH_out_g(f(f(X1)))) → U93_g(X1, qcJ_in_g(X1))
U93_g(X1, qcJ_out_g(X1)) → qcJ_out_g(f(X1))
U94_g(X1, qcJ_out_g(X1)) → tcG_out_g(X1)
U124_g(X1, tcG_out_g(X1)) → rcN8_out_g(f(X1))
U121_g(X1, rcN8_out_g(X1)) → rcN7_out_g(X1)
U141_g(X1, rcN7_out_g(X1)) → rcN13_out_g(X1)
U137_g(X1, rcN13_out_g(X1)) → U138_g(X1, rcN7_in_g(X1))
U138_g(X1, rcN7_out_g(X1)) → U139_g(X1, pcB_in_g(X1))
U139_g(X1, pcB_out_g(X1)) → pcD_out_g(X1)
U84_gg(X1, pcD_out_g(X1)) → U85_gg(X1, qcA_in_g(X1))
U85_gg(X1, qcA_out_g(X1)) → qcC_out_gg(X1, f(f(X1)))
qcC_in_gg(X1, f(f(X2))) → U86_gg(X1, X2, qcE_in_gg(X1, X2))
qcE_in_gg(a, b) → U134_gg(rcN12_in_gg(a, b))
rcN12_in_gg(X1, X2) → U154_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(a, b) → U129_gg(qcC_in_gg(a, b))
U129_gg(qcC_out_gg(a, b)) → qcN11_out_gg(a, b)
qcN11_in_gg(X1, f(X2)) → U130_gg(X1, X2, qcC_in_gg(X1, f(X2)))
U130_gg(X1, X2, qcC_out_gg(X1, f(X2))) → U131_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(f(X1), f(X1)) → U132_gg(X1, qcC_in_gg(f(X1), f(X1)))
U132_gg(X1, qcC_out_gg(f(X1), f(X1))) → U133_gg(X1, tcG_in_g(X1))
U133_gg(X1, tcG_out_g(X1)) → qcN11_out_gg(f(X1), f(X1))
U131_gg(X1, X2, qcN11_out_gg(X1, X2)) → qcN11_out_gg(X1, f(X2))
U154_gg(X1, X2, qcN11_out_gg(X1, X2)) → rcN12_out_gg(X1, X2)
rcN12_in_gg(f(X1), X1) → U155_gg(X1, tcG_in_g(X1))
U155_gg(X1, tcG_out_g(X1)) → rcN12_out_gg(f(X1), X1)
U134_gg(rcN12_out_gg(a, b)) → qcE_out_gg(a, b)
qcE_in_gg(X1, f(X2)) → U135_gg(X1, X2, rcN12_in_gg(X1, f(X2)))
U135_gg(X1, X2, rcN12_out_gg(X1, f(X2))) → U136_gg(X1, X2, qcE_in_gg(X1, X2))
U136_gg(X1, X2, qcE_out_gg(X1, X2)) → qcE_out_gg(X1, f(X2))
U86_gg(X1, X2, qcE_out_gg(X1, X2)) → qcC_out_gg(X1, f(f(X2)))
U87_gg(X1, X2, qcC_out_gg(f(X1), f(X2))) → U88_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X1)) → U89_gg(X1, qcC_in_gg(f(X1), f(X1)))
U89_gg(X1, qcC_out_gg(f(X1), f(X1))) → U90_gg(X1, tcG_in_g(X1))
U90_gg(X1, tcG_out_g(X1)) → qcF_out_gg(X1, f(X1))
U88_gg(X1, X2, qcF_out_gg(X1, X2)) → qcF_out_gg(X1, f(X2))
U148_gg(X1, X2, qcF_out_gg(X1, X2)) → rcL_out_gg(X1, X2)
rcL_in_gg(X1, X1) → U149_gg(X1, tcG_in_g(X1))
U149_gg(X1, tcG_out_g(X1)) → rcL_out_gg(X1, X1)
U95_gg(X1, X2, rcL_out_gg(X1, f(X2))) → U96_gg(X1, X2, qcK_in_gg(X1, X2))
U96_gg(X1, X2, qcK_out_gg(X1, X2)) → qcK_out_gg(X1, f(X2))
U97_gg(X1, X2, qcK_out_gg(X1, X2)) → pcM_out_gg(X1, X2)
U150_g(X1, pcM_out_gg(f(f(f(f(f(f(f(f(X1)))))))), X1)) → qcO_out_g(f(f(X1)))
U98_g(X1, qcO_out_g(f(X1))) → U99_g(X1, qcF_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U99_g(X1, qcF_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → rcN_out_g(f(f(X1)))
U100_g(X1, rcN_out_g(f(f(X1)))) → U101_g(X1, qcK_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U101_g(X1, qcK_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → pcP_out_g(f(f(X1)))
U151_g(X1, pcP_out_g(f(X1))) → qcT_out_g(f(f(X1)))
U104_g(X1, qcT_out_g(f(X1))) → U105_g(X1, qcQ_in_g(X1))
U105_g(X1, qcQ_out_g(X1)) → rcS_out_g(f(f(X1)))
U108_g(X1, rcS_out_g(f(f(X1)))) → U109_g(X1, qcU_in_g(X1))
U109_g(X1, qcU_out_g(X1)) → pcW_out_g(f(f(X1)))
U152_g(X1, pcW_out_g(f(X1))) → qcN1_out_g(f(f(X1)))
U112_g(X1, qcN1_out_g(f(X1))) → U113_g(X1, qcX_in_g(X1))
U113_g(X1, qcX_out_g(X1)) → rcZ_out_g(f(f(X1)))
U116_g(X1, rcZ_out_g(f(f(X1)))) → U117_g(X1, qcN2_in_g(X1))
U117_g(X1, qcN2_out_g(X1)) → pcN4_out_g(f(f(X1)))
U153_g(X1, pcN4_out_g(f(X1))) → qcN9_out_g(f(f(X1)))
U122_g(X1, qcN9_out_g(f(X1))) → U123_g(X1, qcN5_in_g(X1))
U123_g(X1, qcN5_out_g(X1)) → rcN8_out_g(f(f(X1)))
U127_g(X1, rcN8_out_g(f(f(X1)))) → U128_g(X1, qcI_in_g(X1))
U128_g(X1, qcI_out_g(X1)) → pcB_out_g(f(f(X1)))
U83_g(X1, pcB_out_g(f(X1))) → qcA_out_g(f(X1))

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:

QC_IN_GG(X1, f(f(X1))) → QA_IN_G(X1)
QA_IN_G(f(X1)) → PB_IN_G(f(X1))
PB_IN_G(f(X1)) → RN8_IN_G(f(X1))
RN8_IN_G(f(f(f(X1)))) → PN4_IN_G(f(X1))
PN4_IN_G(f(X1)) → RZ_IN_G(f(X1))
RZ_IN_G(f(f(f(X1)))) → PW_IN_G(f(X1))
PW_IN_G(f(X1)) → RS_IN_G(f(X1))
RS_IN_G(f(f(f(X1)))) → PP_IN_G(f(X1))
PP_IN_G(f(X1)) → RN_IN_G(f(X1))
RN_IN_G(f(f(f(X1)))) → PM_IN_GG(f(f(f(f(f(f(f(f(X1)))))))), X1)
PM_IN_GG(X1, X2) → PK_IN_GG(X1, X2)
PK_IN_GG(X1, X2) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, X2) → QC_IN_GG(f(X1), X2)
QC_IN_GG(X1, f(f(X1))) → U73_GG(X1, qcA_in_g(X1))
U73_GG(X1, qcA_out_g(X1)) → RN7_IN_G(X1)
RN7_IN_G(X1) → QH_IN_G(X1)
QH_IN_G(f(f(X1))) → PI_IN_G(X1)
PI_IN_G(X1) → PN5_IN_G(X1)
PN5_IN_G(f(f(X1))) → PN2_IN_G(X1)
PN2_IN_G(X1) → PX_IN_G(X1)
PX_IN_G(f(f(X1))) → PU_IN_G(X1)
PU_IN_G(X1) → PQ_IN_G(X1)
PQ_IN_G(f(f(X1))) → PM_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PQ_IN_G(X1) → U24_G(X1, qcR_in_g(X1))
U24_G(X1, qcR_out_g(X1)) → RN_IN_G(X1)
RN_IN_G(f(f(X1))) → U18_G(X1, qcO_in_g(f(X1)))
U18_G(X1, qcO_out_g(f(X1))) → PF_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PF_IN_GG(X1, f(X2)) → U3_GG(X1, X2, qcC_in_gg(f(X1), f(X2)))
U3_GG(X1, X2, qcC_out_gg(f(X1), f(X2))) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, f(X1)) → U5_GG(X1, qcC_in_gg(f(X1), f(X1)))
U5_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
TG_IN_G(X1) → PJ_IN_G(X1)
PJ_IN_G(X1) → QH_IN_G(f(X1))
PJ_IN_G(f(X1)) → U9_G(X1, qcH_in_g(f(f(X1))))
U9_G(X1, qcH_out_g(f(f(X1)))) → PJ_IN_G(X1)
PU_IN_G(X1) → U30_G(X1, rcV_in_g(X1))
U30_G(X1, rcV_out_g(X1)) → PP_IN_G(X1)
PP_IN_G(f(f(X1))) → U21_G(X1, rcN_in_g(f(f(X1))))
U21_G(X1, rcN_out_g(f(f(X1)))) → PK_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PK_IN_GG(X1, X1) → TG_IN_G(X1)
PK_IN_GG(X1, f(X2)) → U14_GG(X1, X2, rcL_in_gg(X1, f(X2)))
U14_GG(X1, X2, rcL_out_gg(X1, f(X2))) → PK_IN_GG(X1, X2)
PX_IN_G(X1) → U36_G(X1, qcY_in_g(X1))
U36_G(X1, qcY_out_g(X1)) → RS_IN_G(X1)
RS_IN_G(f(f(X1))) → U27_G(X1, qcT_in_g(f(X1)))
U27_G(X1, qcT_out_g(f(X1))) → PQ_IN_G(X1)
PN2_IN_G(X1) → U42_G(X1, rcN3_in_g(X1))
U42_G(X1, rcN3_out_g(X1)) → PW_IN_G(X1)
PW_IN_G(f(f(X1))) → U33_G(X1, rcS_in_g(f(f(X1))))
U33_G(X1, rcS_out_g(f(f(X1)))) → PU_IN_G(X1)
PN5_IN_G(X1) → U48_G(X1, qcN6_in_g(X1))
U48_G(X1, qcN6_out_g(X1)) → RZ_IN_G(X1)
RZ_IN_G(f(f(X1))) → U39_G(X1, qcN1_in_g(f(X1)))
U39_G(X1, qcN1_out_g(f(X1))) → PX_IN_G(X1)
PI_IN_G(X1) → U58_G(X1, rcN10_in_g(X1))
U58_G(X1, rcN10_out_g(X1)) → PN4_IN_G(X1)
PN4_IN_G(f(f(X1))) → U45_G(X1, rcZ_in_g(f(f(X1))))
U45_G(X1, rcZ_out_g(f(f(X1)))) → PN2_IN_G(X1)
RN7_IN_G(X1) → U51_G(X1, qcH_in_g(X1))
U51_G(X1, qcH_out_g(X1)) → RN8_IN_G(X1)
RN8_IN_G(f(f(X1))) → U54_G(X1, qcN9_in_g(f(X1)))
U54_G(X1, qcN9_out_g(f(X1))) → PN5_IN_G(X1)
RN8_IN_G(f(X1)) → TG_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U75_GG(X1, rcN13_in_g(X1))
U75_GG(X1, rcN13_out_g(X1)) → RN7_IN_G(X1)
U75_GG(X1, rcN13_out_g(X1)) → U77_GG(X1, rcN7_in_g(X1))
U77_GG(X1, rcN7_out_g(X1)) → PB_IN_G(X1)
PB_IN_G(f(f(X1))) → U61_G(X1, rcN8_in_g(f(f(X1))))
U61_G(X1, rcN8_out_g(f(f(X1)))) → PI_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U79_GG(X1, pcD_in_g(X1))
U79_GG(X1, pcD_out_g(X1)) → QA_IN_G(X1)
QC_IN_GG(X1, f(f(X2))) → PE_IN_GG(X1, X2)
PE_IN_GG(X1, X2) → PN11_IN_GG(X1, X2)
PN11_IN_GG(X1, X2) → QC_IN_GG(X1, X2)
PN11_IN_GG(X1, f(X2)) → U64_GG(X1, X2, qcC_in_gg(X1, f(X2)))
U64_GG(X1, X2, qcC_out_gg(X1, f(X2))) → PN11_IN_GG(X1, X2)
PN11_IN_GG(f(X1), f(X1)) → U66_GG(X1, qcC_in_gg(f(X1), f(X1)))
U66_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
PE_IN_GG(f(X1), X1) → TG_IN_G(X1)
PE_IN_GG(X1, f(X2)) → U70_GG(X1, X2, rcN12_in_gg(X1, f(X2)))
U70_GG(X1, X2, rcN12_out_gg(X1, f(X2))) → PE_IN_GG(X1, X2)

The TRS R consists of the following rules:

qcA_in_g(f(X1)) → U83_g(X1, pcB_in_g(f(X1)))
pcB_in_g(f(f(X1))) → U127_g(X1, rcN8_in_g(f(f(X1))))
rcN8_in_g(f(f(X1))) → U122_g(X1, qcN9_in_g(f(X1)))
qcN9_in_g(f(f(X1))) → U153_g(X1, pcN4_in_g(f(X1)))
pcN4_in_g(f(f(X1))) → U116_g(X1, rcZ_in_g(f(f(X1))))
rcZ_in_g(f(f(X1))) → U112_g(X1, qcN1_in_g(f(X1)))
qcN1_in_g(f(f(X1))) → U152_g(X1, pcW_in_g(f(X1)))
pcW_in_g(f(f(X1))) → U108_g(X1, rcS_in_g(f(f(X1))))
rcS_in_g(f(f(X1))) → U104_g(X1, qcT_in_g(f(X1)))
qcT_in_g(f(f(X1))) → U151_g(X1, pcP_in_g(f(X1)))
pcP_in_g(f(f(X1))) → U100_g(X1, rcN_in_g(f(f(X1))))
rcN_in_g(f(f(X1))) → U98_g(X1, qcO_in_g(f(X1)))
qcO_in_g(f(f(X1))) → U150_g(X1, pcM_in_gg(f(f(f(f(f(f(f(f(X1)))))))), X1))
pcM_in_gg(X1, X2) → U97_gg(X1, X2, qcK_in_gg(X1, X2))
qcK_in_gg(X1, f(X2)) → U95_gg(X1, X2, rcL_in_gg(X1, f(X2)))
rcL_in_gg(X1, X2) → U148_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X2)) → U87_gg(X1, X2, qcC_in_gg(f(X1), f(X2)))
qcC_in_gg(a, b) → qcC_out_gg(a, b)
qcC_in_gg(X1, f(f(X1))) → U84_gg(X1, pcD_in_g(X1))
pcD_in_g(X1) → U137_g(X1, rcN13_in_g(X1))
rcN13_in_g(X1) → U140_g(X1, qcA_in_g(X1))
U140_g(X1, qcA_out_g(X1)) → U141_g(X1, rcN7_in_g(X1))
rcN7_in_g(X1) → U120_g(X1, qcH_in_g(X1))
qcH_in_g(f(f(X1))) → U91_g(X1, qcI_in_g(X1))
qcI_in_g(X1) → U125_g(X1, rcN10_in_g(X1))
rcN10_in_g(X1) → U142_g(X1, qcN5_in_g(X1))
qcN5_in_g(X1) → U118_g(X1, qcN6_in_g(X1))
qcN6_in_g(f(f(X1))) → U143_g(X1, qcN2_in_g(X1))
qcN2_in_g(X1) → U114_g(X1, rcN3_in_g(X1))
rcN3_in_g(X1) → U144_g(X1, qcX_in_g(X1))
qcX_in_g(X1) → U110_g(X1, qcY_in_g(X1))
qcY_in_g(f(f(X1))) → U145_g(X1, qcU_in_g(X1))
qcU_in_g(X1) → U106_g(X1, rcV_in_g(X1))
rcV_in_g(X1) → U146_g(X1, qcQ_in_g(X1))
qcQ_in_g(X1) → U102_g(X1, qcR_in_g(X1))
qcR_in_g(f(f(X1))) → U147_g(X1, pcM_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U147_g(X1, pcM_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → qcR_out_g(f(f(X1)))
U102_g(X1, qcR_out_g(X1)) → U103_g(X1, rcN_in_g(X1))
U103_g(X1, rcN_out_g(X1)) → qcQ_out_g(X1)
U146_g(X1, qcQ_out_g(X1)) → rcV_out_g(X1)
U106_g(X1, rcV_out_g(X1)) → U107_g(X1, pcP_in_g(X1))
U107_g(X1, pcP_out_g(X1)) → qcU_out_g(X1)
U145_g(X1, qcU_out_g(X1)) → qcY_out_g(f(f(X1)))
U110_g(X1, qcY_out_g(X1)) → U111_g(X1, rcS_in_g(X1))
U111_g(X1, rcS_out_g(X1)) → qcX_out_g(X1)
U144_g(X1, qcX_out_g(X1)) → rcN3_out_g(X1)
U114_g(X1, rcN3_out_g(X1)) → U115_g(X1, pcW_in_g(X1))
U115_g(X1, pcW_out_g(X1)) → qcN2_out_g(X1)
U143_g(X1, qcN2_out_g(X1)) → qcN6_out_g(f(f(X1)))
U118_g(X1, qcN6_out_g(X1)) → U119_g(X1, rcZ_in_g(X1))
U119_g(X1, rcZ_out_g(X1)) → qcN5_out_g(X1)
U142_g(X1, qcN5_out_g(X1)) → rcN10_out_g(X1)
U125_g(X1, rcN10_out_g(X1)) → U126_g(X1, pcN4_in_g(X1))
U126_g(X1, pcN4_out_g(X1)) → qcI_out_g(X1)
U91_g(X1, qcI_out_g(X1)) → qcH_out_g(f(f(X1)))
U120_g(X1, qcH_out_g(X1)) → U121_g(X1, rcN8_in_g(X1))
rcN8_in_g(f(X1)) → U124_g(X1, tcG_in_g(X1))
tcG_in_g(X1) → U94_g(X1, qcJ_in_g(X1))
qcJ_in_g(f(X1)) → U92_g(X1, qcH_in_g(f(f(X1))))
U92_g(X1, qcH_out_g(f(f(X1)))) → U93_g(X1, qcJ_in_g(X1))
U93_g(X1, qcJ_out_g(X1)) → qcJ_out_g(f(X1))
U94_g(X1, qcJ_out_g(X1)) → tcG_out_g(X1)
U124_g(X1, tcG_out_g(X1)) → rcN8_out_g(f(X1))
U121_g(X1, rcN8_out_g(X1)) → rcN7_out_g(X1)
U141_g(X1, rcN7_out_g(X1)) → rcN13_out_g(X1)
U137_g(X1, rcN13_out_g(X1)) → U138_g(X1, rcN7_in_g(X1))
U138_g(X1, rcN7_out_g(X1)) → U139_g(X1, pcB_in_g(X1))
U139_g(X1, pcB_out_g(X1)) → pcD_out_g(X1)
U84_gg(X1, pcD_out_g(X1)) → U85_gg(X1, qcA_in_g(X1))
U85_gg(X1, qcA_out_g(X1)) → qcC_out_gg(X1, f(f(X1)))
qcC_in_gg(X1, f(f(X2))) → U86_gg(X1, X2, qcE_in_gg(X1, X2))
qcE_in_gg(a, b) → U134_gg(rcN12_in_gg(a, b))
rcN12_in_gg(X1, X2) → U154_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(a, b) → U129_gg(qcC_in_gg(a, b))
U129_gg(qcC_out_gg(a, b)) → qcN11_out_gg(a, b)
qcN11_in_gg(X1, f(X2)) → U130_gg(X1, X2, qcC_in_gg(X1, f(X2)))
U130_gg(X1, X2, qcC_out_gg(X1, f(X2))) → U131_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(f(X1), f(X1)) → U132_gg(X1, qcC_in_gg(f(X1), f(X1)))
U132_gg(X1, qcC_out_gg(f(X1), f(X1))) → U133_gg(X1, tcG_in_g(X1))
U133_gg(X1, tcG_out_g(X1)) → qcN11_out_gg(f(X1), f(X1))
U131_gg(X1, X2, qcN11_out_gg(X1, X2)) → qcN11_out_gg(X1, f(X2))
U154_gg(X1, X2, qcN11_out_gg(X1, X2)) → rcN12_out_gg(X1, X2)
rcN12_in_gg(f(X1), X1) → U155_gg(X1, tcG_in_g(X1))
U155_gg(X1, tcG_out_g(X1)) → rcN12_out_gg(f(X1), X1)
U134_gg(rcN12_out_gg(a, b)) → qcE_out_gg(a, b)
qcE_in_gg(X1, f(X2)) → U135_gg(X1, X2, rcN12_in_gg(X1, f(X2)))
U135_gg(X1, X2, rcN12_out_gg(X1, f(X2))) → U136_gg(X1, X2, qcE_in_gg(X1, X2))
U136_gg(X1, X2, qcE_out_gg(X1, X2)) → qcE_out_gg(X1, f(X2))
U86_gg(X1, X2, qcE_out_gg(X1, X2)) → qcC_out_gg(X1, f(f(X2)))
U87_gg(X1, X2, qcC_out_gg(f(X1), f(X2))) → U88_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X1)) → U89_gg(X1, qcC_in_gg(f(X1), f(X1)))
U89_gg(X1, qcC_out_gg(f(X1), f(X1))) → U90_gg(X1, tcG_in_g(X1))
U90_gg(X1, tcG_out_g(X1)) → qcF_out_gg(X1, f(X1))
U88_gg(X1, X2, qcF_out_gg(X1, X2)) → qcF_out_gg(X1, f(X2))
U148_gg(X1, X2, qcF_out_gg(X1, X2)) → rcL_out_gg(X1, X2)
rcL_in_gg(X1, X1) → U149_gg(X1, tcG_in_g(X1))
U149_gg(X1, tcG_out_g(X1)) → rcL_out_gg(X1, X1)
U95_gg(X1, X2, rcL_out_gg(X1, f(X2))) → U96_gg(X1, X2, qcK_in_gg(X1, X2))
U96_gg(X1, X2, qcK_out_gg(X1, X2)) → qcK_out_gg(X1, f(X2))
U97_gg(X1, X2, qcK_out_gg(X1, X2)) → pcM_out_gg(X1, X2)
U150_g(X1, pcM_out_gg(f(f(f(f(f(f(f(f(X1)))))))), X1)) → qcO_out_g(f(f(X1)))
U98_g(X1, qcO_out_g(f(X1))) → U99_g(X1, qcF_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U99_g(X1, qcF_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → rcN_out_g(f(f(X1)))
U100_g(X1, rcN_out_g(f(f(X1)))) → U101_g(X1, qcK_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U101_g(X1, qcK_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → pcP_out_g(f(f(X1)))
U151_g(X1, pcP_out_g(f(X1))) → qcT_out_g(f(f(X1)))
U104_g(X1, qcT_out_g(f(X1))) → U105_g(X1, qcQ_in_g(X1))
U105_g(X1, qcQ_out_g(X1)) → rcS_out_g(f(f(X1)))
U108_g(X1, rcS_out_g(f(f(X1)))) → U109_g(X1, qcU_in_g(X1))
U109_g(X1, qcU_out_g(X1)) → pcW_out_g(f(f(X1)))
U152_g(X1, pcW_out_g(f(X1))) → qcN1_out_g(f(f(X1)))
U112_g(X1, qcN1_out_g(f(X1))) → U113_g(X1, qcX_in_g(X1))
U113_g(X1, qcX_out_g(X1)) → rcZ_out_g(f(f(X1)))
U116_g(X1, rcZ_out_g(f(f(X1)))) → U117_g(X1, qcN2_in_g(X1))
U117_g(X1, qcN2_out_g(X1)) → pcN4_out_g(f(f(X1)))
U153_g(X1, pcN4_out_g(f(X1))) → qcN9_out_g(f(f(X1)))
U122_g(X1, qcN9_out_g(f(X1))) → U123_g(X1, qcN5_in_g(X1))
U123_g(X1, qcN5_out_g(X1)) → rcN8_out_g(f(f(X1)))
U127_g(X1, rcN8_out_g(f(f(X1)))) → U128_g(X1, qcI_in_g(X1))
U128_g(X1, qcI_out_g(X1)) → pcB_out_g(f(f(X1)))
U83_g(X1, pcB_out_g(f(X1))) → qcA_out_g(f(X1))

The set Q consists of the following terms:

qcA_in_g(x0)
pcB_in_g(x0)
rcN8_in_g(x0)
qcN9_in_g(x0)
pcN4_in_g(x0)
rcZ_in_g(x0)
qcN1_in_g(x0)
pcW_in_g(x0)
rcS_in_g(x0)
qcT_in_g(x0)
pcP_in_g(x0)
rcN_in_g(x0)
qcO_in_g(x0)
pcM_in_gg(x0, x1)
qcK_in_gg(x0, x1)
rcL_in_gg(x0, x1)
qcF_in_gg(x0, x1)
qcC_in_gg(x0, x1)
pcD_in_g(x0)
rcN13_in_g(x0)
U140_g(x0, x1)
rcN7_in_g(x0)
qcH_in_g(x0)
qcI_in_g(x0)
rcN10_in_g(x0)
qcN5_in_g(x0)
qcN6_in_g(x0)
qcN2_in_g(x0)
rcN3_in_g(x0)
qcX_in_g(x0)
qcY_in_g(x0)
qcU_in_g(x0)
rcV_in_g(x0)
qcQ_in_g(x0)
qcR_in_g(x0)
U147_g(x0, x1)
U102_g(x0, x1)
U103_g(x0, x1)
U146_g(x0, x1)
U106_g(x0, x1)
U107_g(x0, x1)
U145_g(x0, x1)
U110_g(x0, x1)
U111_g(x0, x1)
U144_g(x0, x1)
U114_g(x0, x1)
U115_g(x0, x1)
U143_g(x0, x1)
U118_g(x0, x1)
U119_g(x0, x1)
U142_g(x0, x1)
U125_g(x0, x1)
U126_g(x0, x1)
U91_g(x0, x1)
U120_g(x0, x1)
tcG_in_g(x0)
qcJ_in_g(x0)
U92_g(x0, x1)
U93_g(x0, x1)
U94_g(x0, x1)
U124_g(x0, x1)
U121_g(x0, x1)
U141_g(x0, x1)
U137_g(x0, x1)
U138_g(x0, x1)
U139_g(x0, x1)
U84_gg(x0, x1)
U85_gg(x0, x1)
qcE_in_gg(x0, x1)
rcN12_in_gg(x0, x1)
qcN11_in_gg(x0, x1)
U129_gg(x0)
U130_gg(x0, x1, x2)
U132_gg(x0, x1)
U133_gg(x0, x1)
U131_gg(x0, x1, x2)
U154_gg(x0, x1, x2)
U155_gg(x0, x1)
U134_gg(x0)
U135_gg(x0, x1, x2)
U136_gg(x0, x1, x2)
U86_gg(x0, x1, x2)
U87_gg(x0, x1, x2)
U89_gg(x0, x1)
U90_gg(x0, x1)
U88_gg(x0, x1, x2)
U148_gg(x0, x1, x2)
U149_gg(x0, x1)
U95_gg(x0, x1, x2)
U96_gg(x0, x1, x2)
U97_gg(x0, x1, x2)
U150_g(x0, x1)
U98_g(x0, x1)
U99_g(x0, x1)
U100_g(x0, x1)
U101_g(x0, x1)
U151_g(x0, x1)
U104_g(x0, x1)
U105_g(x0, x1)
U108_g(x0, x1)
U109_g(x0, x1)
U152_g(x0, x1)
U112_g(x0, x1)
U113_g(x0, x1)
U116_g(x0, x1)
U117_g(x0, x1)
U153_g(x0, x1)
U122_g(x0, x1)
U123_g(x0, x1)
U127_g(x0, x1)
U128_g(x0, x1)
U83_g(x0, x1)

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

(9) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule PM_IN_GG(X1, X2) → PK_IN_GG(X1, X2) we obtained the following new rules [LPAR04]:

PM_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0) → PK_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0)
PM_IN_GG(f(f(f(f(f(f(f(z0))))))), z0) → PK_IN_GG(f(f(f(f(f(f(f(z0))))))), z0)

(10) Obligation:

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

QC_IN_GG(X1, f(f(X1))) → QA_IN_G(X1)
QA_IN_G(f(X1)) → PB_IN_G(f(X1))
PB_IN_G(f(X1)) → RN8_IN_G(f(X1))
RN8_IN_G(f(f(f(X1)))) → PN4_IN_G(f(X1))
PN4_IN_G(f(X1)) → RZ_IN_G(f(X1))
RZ_IN_G(f(f(f(X1)))) → PW_IN_G(f(X1))
PW_IN_G(f(X1)) → RS_IN_G(f(X1))
RS_IN_G(f(f(f(X1)))) → PP_IN_G(f(X1))
PP_IN_G(f(X1)) → RN_IN_G(f(X1))
RN_IN_G(f(f(f(X1)))) → PM_IN_GG(f(f(f(f(f(f(f(f(X1)))))))), X1)
PK_IN_GG(X1, X2) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, X2) → QC_IN_GG(f(X1), X2)
QC_IN_GG(X1, f(f(X1))) → U73_GG(X1, qcA_in_g(X1))
U73_GG(X1, qcA_out_g(X1)) → RN7_IN_G(X1)
RN7_IN_G(X1) → QH_IN_G(X1)
QH_IN_G(f(f(X1))) → PI_IN_G(X1)
PI_IN_G(X1) → PN5_IN_G(X1)
PN5_IN_G(f(f(X1))) → PN2_IN_G(X1)
PN2_IN_G(X1) → PX_IN_G(X1)
PX_IN_G(f(f(X1))) → PU_IN_G(X1)
PU_IN_G(X1) → PQ_IN_G(X1)
PQ_IN_G(f(f(X1))) → PM_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PQ_IN_G(X1) → U24_G(X1, qcR_in_g(X1))
U24_G(X1, qcR_out_g(X1)) → RN_IN_G(X1)
RN_IN_G(f(f(X1))) → U18_G(X1, qcO_in_g(f(X1)))
U18_G(X1, qcO_out_g(f(X1))) → PF_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PF_IN_GG(X1, f(X2)) → U3_GG(X1, X2, qcC_in_gg(f(X1), f(X2)))
U3_GG(X1, X2, qcC_out_gg(f(X1), f(X2))) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, f(X1)) → U5_GG(X1, qcC_in_gg(f(X1), f(X1)))
U5_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
TG_IN_G(X1) → PJ_IN_G(X1)
PJ_IN_G(X1) → QH_IN_G(f(X1))
PJ_IN_G(f(X1)) → U9_G(X1, qcH_in_g(f(f(X1))))
U9_G(X1, qcH_out_g(f(f(X1)))) → PJ_IN_G(X1)
PU_IN_G(X1) → U30_G(X1, rcV_in_g(X1))
U30_G(X1, rcV_out_g(X1)) → PP_IN_G(X1)
PP_IN_G(f(f(X1))) → U21_G(X1, rcN_in_g(f(f(X1))))
U21_G(X1, rcN_out_g(f(f(X1)))) → PK_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PK_IN_GG(X1, X1) → TG_IN_G(X1)
PK_IN_GG(X1, f(X2)) → U14_GG(X1, X2, rcL_in_gg(X1, f(X2)))
U14_GG(X1, X2, rcL_out_gg(X1, f(X2))) → PK_IN_GG(X1, X2)
PX_IN_G(X1) → U36_G(X1, qcY_in_g(X1))
U36_G(X1, qcY_out_g(X1)) → RS_IN_G(X1)
RS_IN_G(f(f(X1))) → U27_G(X1, qcT_in_g(f(X1)))
U27_G(X1, qcT_out_g(f(X1))) → PQ_IN_G(X1)
PN2_IN_G(X1) → U42_G(X1, rcN3_in_g(X1))
U42_G(X1, rcN3_out_g(X1)) → PW_IN_G(X1)
PW_IN_G(f(f(X1))) → U33_G(X1, rcS_in_g(f(f(X1))))
U33_G(X1, rcS_out_g(f(f(X1)))) → PU_IN_G(X1)
PN5_IN_G(X1) → U48_G(X1, qcN6_in_g(X1))
U48_G(X1, qcN6_out_g(X1)) → RZ_IN_G(X1)
RZ_IN_G(f(f(X1))) → U39_G(X1, qcN1_in_g(f(X1)))
U39_G(X1, qcN1_out_g(f(X1))) → PX_IN_G(X1)
PI_IN_G(X1) → U58_G(X1, rcN10_in_g(X1))
U58_G(X1, rcN10_out_g(X1)) → PN4_IN_G(X1)
PN4_IN_G(f(f(X1))) → U45_G(X1, rcZ_in_g(f(f(X1))))
U45_G(X1, rcZ_out_g(f(f(X1)))) → PN2_IN_G(X1)
RN7_IN_G(X1) → U51_G(X1, qcH_in_g(X1))
U51_G(X1, qcH_out_g(X1)) → RN8_IN_G(X1)
RN8_IN_G(f(f(X1))) → U54_G(X1, qcN9_in_g(f(X1)))
U54_G(X1, qcN9_out_g(f(X1))) → PN5_IN_G(X1)
RN8_IN_G(f(X1)) → TG_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U75_GG(X1, rcN13_in_g(X1))
U75_GG(X1, rcN13_out_g(X1)) → RN7_IN_G(X1)
U75_GG(X1, rcN13_out_g(X1)) → U77_GG(X1, rcN7_in_g(X1))
U77_GG(X1, rcN7_out_g(X1)) → PB_IN_G(X1)
PB_IN_G(f(f(X1))) → U61_G(X1, rcN8_in_g(f(f(X1))))
U61_G(X1, rcN8_out_g(f(f(X1)))) → PI_IN_G(X1)
QC_IN_GG(X1, f(f(X1))) → U79_GG(X1, pcD_in_g(X1))
U79_GG(X1, pcD_out_g(X1)) → QA_IN_G(X1)
QC_IN_GG(X1, f(f(X2))) → PE_IN_GG(X1, X2)
PE_IN_GG(X1, X2) → PN11_IN_GG(X1, X2)
PN11_IN_GG(X1, X2) → QC_IN_GG(X1, X2)
PN11_IN_GG(X1, f(X2)) → U64_GG(X1, X2, qcC_in_gg(X1, f(X2)))
U64_GG(X1, X2, qcC_out_gg(X1, f(X2))) → PN11_IN_GG(X1, X2)
PN11_IN_GG(f(X1), f(X1)) → U66_GG(X1, qcC_in_gg(f(X1), f(X1)))
U66_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
PE_IN_GG(f(X1), X1) → TG_IN_G(X1)
PE_IN_GG(X1, f(X2)) → U70_GG(X1, X2, rcN12_in_gg(X1, f(X2)))
U70_GG(X1, X2, rcN12_out_gg(X1, f(X2))) → PE_IN_GG(X1, X2)
PM_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0) → PK_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0)
PM_IN_GG(f(f(f(f(f(f(f(z0))))))), z0) → PK_IN_GG(f(f(f(f(f(f(f(z0))))))), z0)

The TRS R consists of the following rules:

qcA_in_g(f(X1)) → U83_g(X1, pcB_in_g(f(X1)))
pcB_in_g(f(f(X1))) → U127_g(X1, rcN8_in_g(f(f(X1))))
rcN8_in_g(f(f(X1))) → U122_g(X1, qcN9_in_g(f(X1)))
qcN9_in_g(f(f(X1))) → U153_g(X1, pcN4_in_g(f(X1)))
pcN4_in_g(f(f(X1))) → U116_g(X1, rcZ_in_g(f(f(X1))))
rcZ_in_g(f(f(X1))) → U112_g(X1, qcN1_in_g(f(X1)))
qcN1_in_g(f(f(X1))) → U152_g(X1, pcW_in_g(f(X1)))
pcW_in_g(f(f(X1))) → U108_g(X1, rcS_in_g(f(f(X1))))
rcS_in_g(f(f(X1))) → U104_g(X1, qcT_in_g(f(X1)))
qcT_in_g(f(f(X1))) → U151_g(X1, pcP_in_g(f(X1)))
pcP_in_g(f(f(X1))) → U100_g(X1, rcN_in_g(f(f(X1))))
rcN_in_g(f(f(X1))) → U98_g(X1, qcO_in_g(f(X1)))
qcO_in_g(f(f(X1))) → U150_g(X1, pcM_in_gg(f(f(f(f(f(f(f(f(X1)))))))), X1))
pcM_in_gg(X1, X2) → U97_gg(X1, X2, qcK_in_gg(X1, X2))
qcK_in_gg(X1, f(X2)) → U95_gg(X1, X2, rcL_in_gg(X1, f(X2)))
rcL_in_gg(X1, X2) → U148_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X2)) → U87_gg(X1, X2, qcC_in_gg(f(X1), f(X2)))
qcC_in_gg(a, b) → qcC_out_gg(a, b)
qcC_in_gg(X1, f(f(X1))) → U84_gg(X1, pcD_in_g(X1))
pcD_in_g(X1) → U137_g(X1, rcN13_in_g(X1))
rcN13_in_g(X1) → U140_g(X1, qcA_in_g(X1))
U140_g(X1, qcA_out_g(X1)) → U141_g(X1, rcN7_in_g(X1))
rcN7_in_g(X1) → U120_g(X1, qcH_in_g(X1))
qcH_in_g(f(f(X1))) → U91_g(X1, qcI_in_g(X1))
qcI_in_g(X1) → U125_g(X1, rcN10_in_g(X1))
rcN10_in_g(X1) → U142_g(X1, qcN5_in_g(X1))
qcN5_in_g(X1) → U118_g(X1, qcN6_in_g(X1))
qcN6_in_g(f(f(X1))) → U143_g(X1, qcN2_in_g(X1))
qcN2_in_g(X1) → U114_g(X1, rcN3_in_g(X1))
rcN3_in_g(X1) → U144_g(X1, qcX_in_g(X1))
qcX_in_g(X1) → U110_g(X1, qcY_in_g(X1))
qcY_in_g(f(f(X1))) → U145_g(X1, qcU_in_g(X1))
qcU_in_g(X1) → U106_g(X1, rcV_in_g(X1))
rcV_in_g(X1) → U146_g(X1, qcQ_in_g(X1))
qcQ_in_g(X1) → U102_g(X1, qcR_in_g(X1))
qcR_in_g(f(f(X1))) → U147_g(X1, pcM_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U147_g(X1, pcM_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → qcR_out_g(f(f(X1)))
U102_g(X1, qcR_out_g(X1)) → U103_g(X1, rcN_in_g(X1))
U103_g(X1, rcN_out_g(X1)) → qcQ_out_g(X1)
U146_g(X1, qcQ_out_g(X1)) → rcV_out_g(X1)
U106_g(X1, rcV_out_g(X1)) → U107_g(X1, pcP_in_g(X1))
U107_g(X1, pcP_out_g(X1)) → qcU_out_g(X1)
U145_g(X1, qcU_out_g(X1)) → qcY_out_g(f(f(X1)))
U110_g(X1, qcY_out_g(X1)) → U111_g(X1, rcS_in_g(X1))
U111_g(X1, rcS_out_g(X1)) → qcX_out_g(X1)
U144_g(X1, qcX_out_g(X1)) → rcN3_out_g(X1)
U114_g(X1, rcN3_out_g(X1)) → U115_g(X1, pcW_in_g(X1))
U115_g(X1, pcW_out_g(X1)) → qcN2_out_g(X1)
U143_g(X1, qcN2_out_g(X1)) → qcN6_out_g(f(f(X1)))
U118_g(X1, qcN6_out_g(X1)) → U119_g(X1, rcZ_in_g(X1))
U119_g(X1, rcZ_out_g(X1)) → qcN5_out_g(X1)
U142_g(X1, qcN5_out_g(X1)) → rcN10_out_g(X1)
U125_g(X1, rcN10_out_g(X1)) → U126_g(X1, pcN4_in_g(X1))
U126_g(X1, pcN4_out_g(X1)) → qcI_out_g(X1)
U91_g(X1, qcI_out_g(X1)) → qcH_out_g(f(f(X1)))
U120_g(X1, qcH_out_g(X1)) → U121_g(X1, rcN8_in_g(X1))
rcN8_in_g(f(X1)) → U124_g(X1, tcG_in_g(X1))
tcG_in_g(X1) → U94_g(X1, qcJ_in_g(X1))
qcJ_in_g(f(X1)) → U92_g(X1, qcH_in_g(f(f(X1))))
U92_g(X1, qcH_out_g(f(f(X1)))) → U93_g(X1, qcJ_in_g(X1))
U93_g(X1, qcJ_out_g(X1)) → qcJ_out_g(f(X1))
U94_g(X1, qcJ_out_g(X1)) → tcG_out_g(X1)
U124_g(X1, tcG_out_g(X1)) → rcN8_out_g(f(X1))
U121_g(X1, rcN8_out_g(X1)) → rcN7_out_g(X1)
U141_g(X1, rcN7_out_g(X1)) → rcN13_out_g(X1)
U137_g(X1, rcN13_out_g(X1)) → U138_g(X1, rcN7_in_g(X1))
U138_g(X1, rcN7_out_g(X1)) → U139_g(X1, pcB_in_g(X1))
U139_g(X1, pcB_out_g(X1)) → pcD_out_g(X1)
U84_gg(X1, pcD_out_g(X1)) → U85_gg(X1, qcA_in_g(X1))
U85_gg(X1, qcA_out_g(X1)) → qcC_out_gg(X1, f(f(X1)))
qcC_in_gg(X1, f(f(X2))) → U86_gg(X1, X2, qcE_in_gg(X1, X2))
qcE_in_gg(a, b) → U134_gg(rcN12_in_gg(a, b))
rcN12_in_gg(X1, X2) → U154_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(a, b) → U129_gg(qcC_in_gg(a, b))
U129_gg(qcC_out_gg(a, b)) → qcN11_out_gg(a, b)
qcN11_in_gg(X1, f(X2)) → U130_gg(X1, X2, qcC_in_gg(X1, f(X2)))
U130_gg(X1, X2, qcC_out_gg(X1, f(X2))) → U131_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(f(X1), f(X1)) → U132_gg(X1, qcC_in_gg(f(X1), f(X1)))
U132_gg(X1, qcC_out_gg(f(X1), f(X1))) → U133_gg(X1, tcG_in_g(X1))
U133_gg(X1, tcG_out_g(X1)) → qcN11_out_gg(f(X1), f(X1))
U131_gg(X1, X2, qcN11_out_gg(X1, X2)) → qcN11_out_gg(X1, f(X2))
U154_gg(X1, X2, qcN11_out_gg(X1, X2)) → rcN12_out_gg(X1, X2)
rcN12_in_gg(f(X1), X1) → U155_gg(X1, tcG_in_g(X1))
U155_gg(X1, tcG_out_g(X1)) → rcN12_out_gg(f(X1), X1)
U134_gg(rcN12_out_gg(a, b)) → qcE_out_gg(a, b)
qcE_in_gg(X1, f(X2)) → U135_gg(X1, X2, rcN12_in_gg(X1, f(X2)))
U135_gg(X1, X2, rcN12_out_gg(X1, f(X2))) → U136_gg(X1, X2, qcE_in_gg(X1, X2))
U136_gg(X1, X2, qcE_out_gg(X1, X2)) → qcE_out_gg(X1, f(X2))
U86_gg(X1, X2, qcE_out_gg(X1, X2)) → qcC_out_gg(X1, f(f(X2)))
U87_gg(X1, X2, qcC_out_gg(f(X1), f(X2))) → U88_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X1)) → U89_gg(X1, qcC_in_gg(f(X1), f(X1)))
U89_gg(X1, qcC_out_gg(f(X1), f(X1))) → U90_gg(X1, tcG_in_g(X1))
U90_gg(X1, tcG_out_g(X1)) → qcF_out_gg(X1, f(X1))
U88_gg(X1, X2, qcF_out_gg(X1, X2)) → qcF_out_gg(X1, f(X2))
U148_gg(X1, X2, qcF_out_gg(X1, X2)) → rcL_out_gg(X1, X2)
rcL_in_gg(X1, X1) → U149_gg(X1, tcG_in_g(X1))
U149_gg(X1, tcG_out_g(X1)) → rcL_out_gg(X1, X1)
U95_gg(X1, X2, rcL_out_gg(X1, f(X2))) → U96_gg(X1, X2, qcK_in_gg(X1, X2))
U96_gg(X1, X2, qcK_out_gg(X1, X2)) → qcK_out_gg(X1, f(X2))
U97_gg(X1, X2, qcK_out_gg(X1, X2)) → pcM_out_gg(X1, X2)
U150_g(X1, pcM_out_gg(f(f(f(f(f(f(f(f(X1)))))))), X1)) → qcO_out_g(f(f(X1)))
U98_g(X1, qcO_out_g(f(X1))) → U99_g(X1, qcF_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U99_g(X1, qcF_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → rcN_out_g(f(f(X1)))
U100_g(X1, rcN_out_g(f(f(X1)))) → U101_g(X1, qcK_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U101_g(X1, qcK_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → pcP_out_g(f(f(X1)))
U151_g(X1, pcP_out_g(f(X1))) → qcT_out_g(f(f(X1)))
U104_g(X1, qcT_out_g(f(X1))) → U105_g(X1, qcQ_in_g(X1))
U105_g(X1, qcQ_out_g(X1)) → rcS_out_g(f(f(X1)))
U108_g(X1, rcS_out_g(f(f(X1)))) → U109_g(X1, qcU_in_g(X1))
U109_g(X1, qcU_out_g(X1)) → pcW_out_g(f(f(X1)))
U152_g(X1, pcW_out_g(f(X1))) → qcN1_out_g(f(f(X1)))
U112_g(X1, qcN1_out_g(f(X1))) → U113_g(X1, qcX_in_g(X1))
U113_g(X1, qcX_out_g(X1)) → rcZ_out_g(f(f(X1)))
U116_g(X1, rcZ_out_g(f(f(X1)))) → U117_g(X1, qcN2_in_g(X1))
U117_g(X1, qcN2_out_g(X1)) → pcN4_out_g(f(f(X1)))
U153_g(X1, pcN4_out_g(f(X1))) → qcN9_out_g(f(f(X1)))
U122_g(X1, qcN9_out_g(f(X1))) → U123_g(X1, qcN5_in_g(X1))
U123_g(X1, qcN5_out_g(X1)) → rcN8_out_g(f(f(X1)))
U127_g(X1, rcN8_out_g(f(f(X1)))) → U128_g(X1, qcI_in_g(X1))
U128_g(X1, qcI_out_g(X1)) → pcB_out_g(f(f(X1)))
U83_g(X1, pcB_out_g(f(X1))) → qcA_out_g(f(X1))

The set Q consists of the following terms:

qcA_in_g(x0)
pcB_in_g(x0)
rcN8_in_g(x0)
qcN9_in_g(x0)
pcN4_in_g(x0)
rcZ_in_g(x0)
qcN1_in_g(x0)
pcW_in_g(x0)
rcS_in_g(x0)
qcT_in_g(x0)
pcP_in_g(x0)
rcN_in_g(x0)
qcO_in_g(x0)
pcM_in_gg(x0, x1)
qcK_in_gg(x0, x1)
rcL_in_gg(x0, x1)
qcF_in_gg(x0, x1)
qcC_in_gg(x0, x1)
pcD_in_g(x0)
rcN13_in_g(x0)
U140_g(x0, x1)
rcN7_in_g(x0)
qcH_in_g(x0)
qcI_in_g(x0)
rcN10_in_g(x0)
qcN5_in_g(x0)
qcN6_in_g(x0)
qcN2_in_g(x0)
rcN3_in_g(x0)
qcX_in_g(x0)
qcY_in_g(x0)
qcU_in_g(x0)
rcV_in_g(x0)
qcQ_in_g(x0)
qcR_in_g(x0)
U147_g(x0, x1)
U102_g(x0, x1)
U103_g(x0, x1)
U146_g(x0, x1)
U106_g(x0, x1)
U107_g(x0, x1)
U145_g(x0, x1)
U110_g(x0, x1)
U111_g(x0, x1)
U144_g(x0, x1)
U114_g(x0, x1)
U115_g(x0, x1)
U143_g(x0, x1)
U118_g(x0, x1)
U119_g(x0, x1)
U142_g(x0, x1)
U125_g(x0, x1)
U126_g(x0, x1)
U91_g(x0, x1)
U120_g(x0, x1)
tcG_in_g(x0)
qcJ_in_g(x0)
U92_g(x0, x1)
U93_g(x0, x1)
U94_g(x0, x1)
U124_g(x0, x1)
U121_g(x0, x1)
U141_g(x0, x1)
U137_g(x0, x1)
U138_g(x0, x1)
U139_g(x0, x1)
U84_gg(x0, x1)
U85_gg(x0, x1)
qcE_in_gg(x0, x1)
rcN12_in_gg(x0, x1)
qcN11_in_gg(x0, x1)
U129_gg(x0)
U130_gg(x0, x1, x2)
U132_gg(x0, x1)
U133_gg(x0, x1)
U131_gg(x0, x1, x2)
U154_gg(x0, x1, x2)
U155_gg(x0, x1)
U134_gg(x0)
U135_gg(x0, x1, x2)
U136_gg(x0, x1, x2)
U86_gg(x0, x1, x2)
U87_gg(x0, x1, x2)
U89_gg(x0, x1)
U90_gg(x0, x1)
U88_gg(x0, x1, x2)
U148_gg(x0, x1, x2)
U149_gg(x0, x1)
U95_gg(x0, x1, x2)
U96_gg(x0, x1, x2)
U97_gg(x0, x1, x2)
U150_g(x0, x1)
U98_g(x0, x1)
U99_g(x0, x1)
U100_g(x0, x1)
U101_g(x0, x1)
U151_g(x0, x1)
U104_g(x0, x1)
U105_g(x0, x1)
U108_g(x0, x1)
U109_g(x0, x1)
U152_g(x0, x1)
U112_g(x0, x1)
U113_g(x0, x1)
U116_g(x0, x1)
U117_g(x0, x1)
U153_g(x0, x1)
U122_g(x0, x1)
U123_g(x0, x1)
U127_g(x0, x1)
U128_g(x0, x1)
U83_g(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.

QC_IN_GG(X1, f(f(X1))) → QA_IN_G(X1)
RN8_IN_G(f(f(f(X1)))) → PN4_IN_G(f(X1))
PN4_IN_G(f(X1)) → RZ_IN_G(f(X1))
RZ_IN_G(f(f(f(X1)))) → PW_IN_G(f(X1))
RS_IN_G(f(f(f(X1)))) → PP_IN_G(f(X1))
RN_IN_G(f(f(f(X1)))) → PM_IN_GG(f(f(f(f(f(f(f(f(X1)))))))), X1)
PK_IN_GG(X1, X2) → PF_IN_GG(X1, X2)
QC_IN_GG(X1, f(f(X1))) → U73_GG(X1, qcA_in_g(X1))
QH_IN_G(f(f(X1))) → PI_IN_G(X1)
PI_IN_G(X1) → PN5_IN_G(X1)
PN5_IN_G(f(f(X1))) → PN2_IN_G(X1)
PX_IN_G(f(f(X1))) → PU_IN_G(X1)
PQ_IN_G(f(f(X1))) → PM_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
RN_IN_G(f(f(X1))) → U18_G(X1, qcO_in_g(f(X1)))
PF_IN_GG(X1, f(X2)) → U3_GG(X1, X2, qcC_in_gg(f(X1), f(X2)))
PJ_IN_G(f(X1)) → U9_G(X1, qcH_in_g(f(f(X1))))
PP_IN_G(f(f(X1))) → U21_G(X1, rcN_in_g(f(f(X1))))
PK_IN_GG(X1, f(X2)) → U14_GG(X1, X2, rcL_in_gg(X1, f(X2)))
RS_IN_G(f(f(X1))) → U27_G(X1, qcT_in_g(f(X1)))
PW_IN_G(f(f(X1))) → U33_G(X1, rcS_in_g(f(f(X1))))
RZ_IN_G(f(f(X1))) → U39_G(X1, qcN1_in_g(f(X1)))
U39_G(X1, qcN1_out_g(f(X1))) → PX_IN_G(X1)
PN4_IN_G(f(f(X1))) → U45_G(X1, rcZ_in_g(f(f(X1))))
RN8_IN_G(f(f(X1))) → U54_G(X1, qcN9_in_g(f(X1)))
QC_IN_GG(X1, f(f(X1))) → U75_GG(X1, rcN13_in_g(X1))
PB_IN_G(f(f(X1))) → U61_G(X1, rcN8_in_g(f(f(X1))))
QC_IN_GG(X1, f(f(X1))) → U79_GG(X1, pcD_in_g(X1))
QC_IN_GG(X1, f(f(X2))) → PE_IN_GG(X1, X2)
PE_IN_GG(X1, X2) → PN11_IN_GG(X1, X2)
PN11_IN_GG(X1, f(X2)) → U64_GG(X1, X2, qcC_in_gg(X1, f(X2)))
PE_IN_GG(X1, f(X2)) → U70_GG(X1, X2, rcN12_in_gg(X1, f(X2)))

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

POL(PB_IN_G(x₁)) = x₁
POL(PE_IN_GG(x₁, x₂)) = 1 + x₂
POL(PF_IN_GG(x₁, x₂)) = x₂
POL(PI_IN_G(x₁)) = 1 + x₁
POL(PJ_IN_G(x₁)) = 1 + x₁
POL(PK_IN_GG(x₁, x₂)) = 1 + x₂
POL(PM_IN_GG(x₁, x₂)) = 1 + x₂
POL(PN11_IN_GG(x₁, x₂)) = x₂
POL(PN2_IN_G(x₁)) = x₁
POL(PN4_IN_G(x₁)) = 1 + x₁
POL(PN5_IN_G(x₁)) = x₁
POL(PP_IN_G(x₁)) = 1 + x₁
POL(PQ_IN_G(x₁)) = 1 + x₁
POL(PU_IN_G(x₁)) = 1 + x₁
POL(PW_IN_G(x₁)) = x₁
POL(PX_IN_G(x₁)) = x₁
POL(QA_IN_G(x₁)) = x₁
POL(QC_IN_GG(x₁, x₂)) = x₂
POL(QH_IN_G(x₁)) = x₁
POL(RN7_IN_G(x₁)) = x₁
POL(RN8_IN_G(x₁)) = x₁
POL(RN_IN_G(x₁)) = 1 + x₁
POL(RS_IN_G(x₁)) = x₁
POL(RZ_IN_G(x₁)) = x₁
POL(TG_IN_G(x₁)) = 1 + x₁
POL(U100_g(x₁, x₂)) = 0
POL(U101_g(x₁, x₂)) = 0
POL(U102_g(x₁, x₂)) = 0
POL(U103_g(x₁, x₂)) = 0
POL(U104_g(x₁, x₂)) = 0
POL(U105_g(x₁, x₂)) = 0
POL(U106_g(x₁, x₂)) = 0
POL(U107_g(x₁, x₂)) = 0
POL(U108_g(x₁, x₂)) = 0
POL(U109_g(x₁, x₂)) = 0
POL(U110_g(x₁, x₂)) = 0
POL(U111_g(x₁, x₂)) = 0
POL(U112_g(x₁, x₂)) = 0
POL(U113_g(x₁, x₂)) = 0
POL(U114_g(x₁, x₂)) = 0
POL(U115_g(x₁, x₂)) = 0
POL(U116_g(x₁, x₂)) = 0
POL(U117_g(x₁, x₂)) = 0
POL(U118_g(x₁, x₂)) = 0
POL(U119_g(x₁, x₂)) = 0
POL(U120_g(x₁, x₂)) = 0
POL(U121_g(x₁, x₂)) = 0
POL(U122_g(x₁, x₂)) = 0
POL(U123_g(x₁, x₂)) = 0
POL(U124_g(x₁, x₂)) = 0
POL(U125_g(x₁, x₂)) = 0
POL(U126_g(x₁, x₂)) = 0
POL(U127_g(x₁, x₂)) = 0
POL(U128_g(x₁, x₂)) = 0
POL(U129_gg(x₁)) = 0
POL(U130_gg(x₁, x₂, x₃)) = 0
POL(U131_gg(x₁, x₂, x₃)) = 0
POL(U132_gg(x₁, x₂)) = 0
POL(U133_gg(x₁, x₂)) = 0
POL(U134_gg(x₁)) = 0
POL(U135_gg(x₁, x₂, x₃)) = 0
POL(U136_gg(x₁, x₂, x₃)) = 0
POL(U137_g(x₁, x₂)) = 0
POL(U138_g(x₁, x₂)) = 0
POL(U139_g(x₁, x₂)) = 0
POL(U140_g(x₁, x₂)) = 0
POL(U141_g(x₁, x₂)) = 0
POL(U142_g(x₁, x₂)) = 0
POL(U143_g(x₁, x₂)) = 0
POL(U144_g(x₁, x₂)) = 0
POL(U145_g(x₁, x₂)) = 0
POL(U146_g(x₁, x₂)) = 0
POL(U147_g(x₁, x₂)) = 0
POL(U148_gg(x₁, x₂, x₃)) = 0
POL(U149_gg(x₁, x₂)) = 0
POL(U14_GG(x₁, x₂, x₃)) = 1 + x₂
POL(U150_g(x₁, x₂)) = 0
POL(U151_g(x₁, x₂)) = 0
POL(U152_g(x₁, x₂)) = 0
POL(U153_g(x₁, x₂)) = 0
POL(U154_gg(x₁, x₂, x₃)) = 0
POL(U155_gg(x₁, x₂)) = 0
POL(U18_G(x₁, x₂)) = x₁
POL(U21_G(x₁, x₂)) = 1 + x₁
POL(U24_G(x₁, x₂)) = 1 + x₁
POL(U27_G(x₁, x₂)) = 1 + x₁
POL(U30_G(x₁, x₂)) = 1 + x₁
POL(U33_G(x₁, x₂)) = 1 + x₁
POL(U36_G(x₁, x₂)) = x₁
POL(U39_G(x₁, x₂)) = 1 + x₁
POL(U3_GG(x₁, x₂, x₃)) = x₂
POL(U42_G(x₁, x₂)) = x₁
POL(U45_G(x₁, x₂)) = x₁
POL(U48_G(x₁, x₂)) = x₁
POL(U51_G(x₁, x₂)) = x₁
POL(U54_G(x₁, x₂)) = x₁
POL(U58_G(x₁, x₂)) = 1 + x₁
POL(U5_GG(x₁, x₂)) = 1 + x₁
POL(U61_G(x₁, x₂)) = 1 + x₁
POL(U64_GG(x₁, x₂, x₃)) = x₂
POL(U66_GG(x₁, x₂)) = 1 + x₁
POL(U70_GG(x₁, x₂, x₃)) = 1 + x₂
POL(U73_GG(x₁, x₂)) = x₁
POL(U75_GG(x₁, x₂)) = x₁
POL(U77_GG(x₁, x₂)) = x₁
POL(U79_GG(x₁, x₂)) = x₁
POL(U83_g(x₁, x₂)) = 0
POL(U84_gg(x₁, x₂)) = 0
POL(U85_gg(x₁, x₂)) = 0
POL(U86_gg(x₁, x₂, x₃)) = 0
POL(U87_gg(x₁, x₂, x₃)) = 0
POL(U88_gg(x₁, x₂, x₃)) = 0
POL(U89_gg(x₁, x₂)) = 0
POL(U90_gg(x₁, x₂)) = 0
POL(U91_g(x₁, x₂)) = 0
POL(U92_g(x₁, x₂)) = 0
POL(U93_g(x₁, x₂)) = 0
POL(U94_g(x₁, x₂)) = 0
POL(U95_gg(x₁, x₂, x₃)) = 0
POL(U96_gg(x₁, x₂, x₃)) = 0
POL(U97_gg(x₁, x₂, x₃)) = 0
POL(U98_g(x₁, x₂)) = 0
POL(U99_g(x₁, x₂)) = 0
POL(U9_G(x₁, x₂)) = 1 + x₁
POL(a) = 0
POL(b) = 0
POL(f(x₁)) = 1 + x₁
POL(pcB_in_g(x₁)) = 0
POL(pcB_out_g(x₁)) = 0
POL(pcD_in_g(x₁)) = 0
POL(pcD_out_g(x₁)) = 0
POL(pcM_in_gg(x₁, x₂)) = 0
POL(pcM_out_gg(x₁, x₂)) = 0
POL(pcN4_in_g(x₁)) = 0
POL(pcN4_out_g(x₁)) = 0
POL(pcP_in_g(x₁)) = 0
POL(pcP_out_g(x₁)) = 0
POL(pcW_in_g(x₁)) = 0
POL(pcW_out_g(x₁)) = 0
POL(qcA_in_g(x₁)) = 0
POL(qcA_out_g(x₁)) = 0
POL(qcC_in_gg(x₁, x₂)) = 0
POL(qcC_out_gg(x₁, x₂)) = 0
POL(qcE_in_gg(x₁, x₂)) = 0
POL(qcE_out_gg(x₁, x₂)) = 0
POL(qcF_in_gg(x₁, x₂)) = 0
POL(qcF_out_gg(x₁, x₂)) = 0
POL(qcH_in_g(x₁)) = 0
POL(qcH_out_g(x₁)) = 0
POL(qcI_in_g(x₁)) = 0
POL(qcI_out_g(x₁)) = 0
POL(qcJ_in_g(x₁)) = 0
POL(qcJ_out_g(x₁)) = 0
POL(qcK_in_gg(x₁, x₂)) = 0
POL(qcK_out_gg(x₁, x₂)) = 0
POL(qcN11_in_gg(x₁, x₂)) = 0
POL(qcN11_out_gg(x₁, x₂)) = 0
POL(qcN1_in_g(x₁)) = 0
POL(qcN1_out_g(x₁)) = 0
POL(qcN2_in_g(x₁)) = 0
POL(qcN2_out_g(x₁)) = 0
POL(qcN5_in_g(x₁)) = 0
POL(qcN5_out_g(x₁)) = 0
POL(qcN6_in_g(x₁)) = 0
POL(qcN6_out_g(x₁)) = 0
POL(qcN9_in_g(x₁)) = 0
POL(qcN9_out_g(x₁)) = 0
POL(qcO_in_g(x₁)) = 0
POL(qcO_out_g(x₁)) = 0
POL(qcQ_in_g(x₁)) = 0
POL(qcQ_out_g(x₁)) = 0
POL(qcR_in_g(x₁)) = 0
POL(qcR_out_g(x₁)) = 0
POL(qcT_in_g(x₁)) = 0
POL(qcT_out_g(x₁)) = 0
POL(qcU_in_g(x₁)) = 0
POL(qcU_out_g(x₁)) = 0
POL(qcX_in_g(x₁)) = 0
POL(qcX_out_g(x₁)) = 0
POL(qcY_in_g(x₁)) = 0
POL(qcY_out_g(x₁)) = 0
POL(rcL_in_gg(x₁, x₂)) = 0
POL(rcL_out_gg(x₁, x₂)) = 0
POL(rcN10_in_g(x₁)) = 0
POL(rcN10_out_g(x₁)) = 0
POL(rcN12_in_gg(x₁, x₂)) = 0
POL(rcN12_out_gg(x₁, x₂)) = 0
POL(rcN13_in_g(x₁)) = 0
POL(rcN13_out_g(x₁)) = 0
POL(rcN3_in_g(x₁)) = 0
POL(rcN3_out_g(x₁)) = 0
POL(rcN7_in_g(x₁)) = 0
POL(rcN7_out_g(x₁)) = 0
POL(rcN8_in_g(x₁)) = 0
POL(rcN8_out_g(x₁)) = 0
POL(rcN_in_g(x₁)) = 0
POL(rcN_out_g(x₁)) = 0
POL(rcS_in_g(x₁)) = 0
POL(rcS_out_g(x₁)) = 0
POL(rcV_in_g(x₁)) = 0
POL(rcV_out_g(x₁)) = 0
POL(rcZ_in_g(x₁)) = 0
POL(rcZ_out_g(x₁)) = 0
POL(tcG_in_g(x₁)) = 0
POL(tcG_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:

QA_IN_G(f(X1)) → PB_IN_G(f(X1))
PB_IN_G(f(X1)) → RN8_IN_G(f(X1))
PW_IN_G(f(X1)) → RS_IN_G(f(X1))
PP_IN_G(f(X1)) → RN_IN_G(f(X1))
PF_IN_GG(X1, X2) → QC_IN_GG(f(X1), X2)
U73_GG(X1, qcA_out_g(X1)) → RN7_IN_G(X1)
RN7_IN_G(X1) → QH_IN_G(X1)
PN2_IN_G(X1) → PX_IN_G(X1)
PU_IN_G(X1) → PQ_IN_G(X1)
PQ_IN_G(X1) → U24_G(X1, qcR_in_g(X1))
U24_G(X1, qcR_out_g(X1)) → RN_IN_G(X1)
U18_G(X1, qcO_out_g(f(X1))) → PF_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
U3_GG(X1, X2, qcC_out_gg(f(X1), f(X2))) → PF_IN_GG(X1, X2)
PF_IN_GG(X1, f(X1)) → U5_GG(X1, qcC_in_gg(f(X1), f(X1)))
U5_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
TG_IN_G(X1) → PJ_IN_G(X1)
PJ_IN_G(X1) → QH_IN_G(f(X1))
U9_G(X1, qcH_out_g(f(f(X1)))) → PJ_IN_G(X1)
PU_IN_G(X1) → U30_G(X1, rcV_in_g(X1))
U30_G(X1, rcV_out_g(X1)) → PP_IN_G(X1)
U21_G(X1, rcN_out_g(f(f(X1)))) → PK_IN_GG(f(f(f(f(f(f(f(X1))))))), X1)
PK_IN_GG(X1, X1) → TG_IN_G(X1)
U14_GG(X1, X2, rcL_out_gg(X1, f(X2))) → PK_IN_GG(X1, X2)
PX_IN_G(X1) → U36_G(X1, qcY_in_g(X1))
U36_G(X1, qcY_out_g(X1)) → RS_IN_G(X1)
U27_G(X1, qcT_out_g(f(X1))) → PQ_IN_G(X1)
PN2_IN_G(X1) → U42_G(X1, rcN3_in_g(X1))
U42_G(X1, rcN3_out_g(X1)) → PW_IN_G(X1)
U33_G(X1, rcS_out_g(f(f(X1)))) → PU_IN_G(X1)
PN5_IN_G(X1) → U48_G(X1, qcN6_in_g(X1))
U48_G(X1, qcN6_out_g(X1)) → RZ_IN_G(X1)
PI_IN_G(X1) → U58_G(X1, rcN10_in_g(X1))
U58_G(X1, rcN10_out_g(X1)) → PN4_IN_G(X1)
U45_G(X1, rcZ_out_g(f(f(X1)))) → PN2_IN_G(X1)
RN7_IN_G(X1) → U51_G(X1, qcH_in_g(X1))
U51_G(X1, qcH_out_g(X1)) → RN8_IN_G(X1)
U54_G(X1, qcN9_out_g(f(X1))) → PN5_IN_G(X1)
RN8_IN_G(f(X1)) → TG_IN_G(X1)
U75_GG(X1, rcN13_out_g(X1)) → RN7_IN_G(X1)
U75_GG(X1, rcN13_out_g(X1)) → U77_GG(X1, rcN7_in_g(X1))
U77_GG(X1, rcN7_out_g(X1)) → PB_IN_G(X1)
U61_G(X1, rcN8_out_g(f(f(X1)))) → PI_IN_G(X1)
U79_GG(X1, pcD_out_g(X1)) → QA_IN_G(X1)
PN11_IN_GG(X1, X2) → QC_IN_GG(X1, X2)
U64_GG(X1, X2, qcC_out_gg(X1, f(X2))) → PN11_IN_GG(X1, X2)
PN11_IN_GG(f(X1), f(X1)) → U66_GG(X1, qcC_in_gg(f(X1), f(X1)))
U66_GG(X1, qcC_out_gg(f(X1), f(X1))) → TG_IN_G(X1)
PE_IN_GG(f(X1), X1) → TG_IN_G(X1)
U70_GG(X1, X2, rcN12_out_gg(X1, f(X2))) → PE_IN_GG(X1, X2)
PM_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0) → PK_IN_GG(f(f(f(f(f(f(f(f(z0)))))))), z0)
PM_IN_GG(f(f(f(f(f(f(f(z0))))))), z0) → PK_IN_GG(f(f(f(f(f(f(f(z0))))))), z0)

The TRS R consists of the following rules:

qcA_in_g(f(X1)) → U83_g(X1, pcB_in_g(f(X1)))
pcB_in_g(f(f(X1))) → U127_g(X1, rcN8_in_g(f(f(X1))))
rcN8_in_g(f(f(X1))) → U122_g(X1, qcN9_in_g(f(X1)))
qcN9_in_g(f(f(X1))) → U153_g(X1, pcN4_in_g(f(X1)))
pcN4_in_g(f(f(X1))) → U116_g(X1, rcZ_in_g(f(f(X1))))
rcZ_in_g(f(f(X1))) → U112_g(X1, qcN1_in_g(f(X1)))
qcN1_in_g(f(f(X1))) → U152_g(X1, pcW_in_g(f(X1)))
pcW_in_g(f(f(X1))) → U108_g(X1, rcS_in_g(f(f(X1))))
rcS_in_g(f(f(X1))) → U104_g(X1, qcT_in_g(f(X1)))
qcT_in_g(f(f(X1))) → U151_g(X1, pcP_in_g(f(X1)))
pcP_in_g(f(f(X1))) → U100_g(X1, rcN_in_g(f(f(X1))))
rcN_in_g(f(f(X1))) → U98_g(X1, qcO_in_g(f(X1)))
qcO_in_g(f(f(X1))) → U150_g(X1, pcM_in_gg(f(f(f(f(f(f(f(f(X1)))))))), X1))
pcM_in_gg(X1, X2) → U97_gg(X1, X2, qcK_in_gg(X1, X2))
qcK_in_gg(X1, f(X2)) → U95_gg(X1, X2, rcL_in_gg(X1, f(X2)))
rcL_in_gg(X1, X2) → U148_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X2)) → U87_gg(X1, X2, qcC_in_gg(f(X1), f(X2)))
qcC_in_gg(a, b) → qcC_out_gg(a, b)
qcC_in_gg(X1, f(f(X1))) → U84_gg(X1, pcD_in_g(X1))
pcD_in_g(X1) → U137_g(X1, rcN13_in_g(X1))
rcN13_in_g(X1) → U140_g(X1, qcA_in_g(X1))
U140_g(X1, qcA_out_g(X1)) → U141_g(X1, rcN7_in_g(X1))
rcN7_in_g(X1) → U120_g(X1, qcH_in_g(X1))
qcH_in_g(f(f(X1))) → U91_g(X1, qcI_in_g(X1))
qcI_in_g(X1) → U125_g(X1, rcN10_in_g(X1))
rcN10_in_g(X1) → U142_g(X1, qcN5_in_g(X1))
qcN5_in_g(X1) → U118_g(X1, qcN6_in_g(X1))
qcN6_in_g(f(f(X1))) → U143_g(X1, qcN2_in_g(X1))
qcN2_in_g(X1) → U114_g(X1, rcN3_in_g(X1))
rcN3_in_g(X1) → U144_g(X1, qcX_in_g(X1))
qcX_in_g(X1) → U110_g(X1, qcY_in_g(X1))
qcY_in_g(f(f(X1))) → U145_g(X1, qcU_in_g(X1))
qcU_in_g(X1) → U106_g(X1, rcV_in_g(X1))
rcV_in_g(X1) → U146_g(X1, qcQ_in_g(X1))
qcQ_in_g(X1) → U102_g(X1, qcR_in_g(X1))
qcR_in_g(f(f(X1))) → U147_g(X1, pcM_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U147_g(X1, pcM_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → qcR_out_g(f(f(X1)))
U102_g(X1, qcR_out_g(X1)) → U103_g(X1, rcN_in_g(X1))
U103_g(X1, rcN_out_g(X1)) → qcQ_out_g(X1)
U146_g(X1, qcQ_out_g(X1)) → rcV_out_g(X1)
U106_g(X1, rcV_out_g(X1)) → U107_g(X1, pcP_in_g(X1))
U107_g(X1, pcP_out_g(X1)) → qcU_out_g(X1)
U145_g(X1, qcU_out_g(X1)) → qcY_out_g(f(f(X1)))
U110_g(X1, qcY_out_g(X1)) → U111_g(X1, rcS_in_g(X1))
U111_g(X1, rcS_out_g(X1)) → qcX_out_g(X1)
U144_g(X1, qcX_out_g(X1)) → rcN3_out_g(X1)
U114_g(X1, rcN3_out_g(X1)) → U115_g(X1, pcW_in_g(X1))
U115_g(X1, pcW_out_g(X1)) → qcN2_out_g(X1)
U143_g(X1, qcN2_out_g(X1)) → qcN6_out_g(f(f(X1)))
U118_g(X1, qcN6_out_g(X1)) → U119_g(X1, rcZ_in_g(X1))
U119_g(X1, rcZ_out_g(X1)) → qcN5_out_g(X1)
U142_g(X1, qcN5_out_g(X1)) → rcN10_out_g(X1)
U125_g(X1, rcN10_out_g(X1)) → U126_g(X1, pcN4_in_g(X1))
U126_g(X1, pcN4_out_g(X1)) → qcI_out_g(X1)
U91_g(X1, qcI_out_g(X1)) → qcH_out_g(f(f(X1)))
U120_g(X1, qcH_out_g(X1)) → U121_g(X1, rcN8_in_g(X1))
rcN8_in_g(f(X1)) → U124_g(X1, tcG_in_g(X1))
tcG_in_g(X1) → U94_g(X1, qcJ_in_g(X1))
qcJ_in_g(f(X1)) → U92_g(X1, qcH_in_g(f(f(X1))))
U92_g(X1, qcH_out_g(f(f(X1)))) → U93_g(X1, qcJ_in_g(X1))
U93_g(X1, qcJ_out_g(X1)) → qcJ_out_g(f(X1))
U94_g(X1, qcJ_out_g(X1)) → tcG_out_g(X1)
U124_g(X1, tcG_out_g(X1)) → rcN8_out_g(f(X1))
U121_g(X1, rcN8_out_g(X1)) → rcN7_out_g(X1)
U141_g(X1, rcN7_out_g(X1)) → rcN13_out_g(X1)
U137_g(X1, rcN13_out_g(X1)) → U138_g(X1, rcN7_in_g(X1))
U138_g(X1, rcN7_out_g(X1)) → U139_g(X1, pcB_in_g(X1))
U139_g(X1, pcB_out_g(X1)) → pcD_out_g(X1)
U84_gg(X1, pcD_out_g(X1)) → U85_gg(X1, qcA_in_g(X1))
U85_gg(X1, qcA_out_g(X1)) → qcC_out_gg(X1, f(f(X1)))
qcC_in_gg(X1, f(f(X2))) → U86_gg(X1, X2, qcE_in_gg(X1, X2))
qcE_in_gg(a, b) → U134_gg(rcN12_in_gg(a, b))
rcN12_in_gg(X1, X2) → U154_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(a, b) → U129_gg(qcC_in_gg(a, b))
U129_gg(qcC_out_gg(a, b)) → qcN11_out_gg(a, b)
qcN11_in_gg(X1, f(X2)) → U130_gg(X1, X2, qcC_in_gg(X1, f(X2)))
U130_gg(X1, X2, qcC_out_gg(X1, f(X2))) → U131_gg(X1, X2, qcN11_in_gg(X1, X2))
qcN11_in_gg(f(X1), f(X1)) → U132_gg(X1, qcC_in_gg(f(X1), f(X1)))
U132_gg(X1, qcC_out_gg(f(X1), f(X1))) → U133_gg(X1, tcG_in_g(X1))
U133_gg(X1, tcG_out_g(X1)) → qcN11_out_gg(f(X1), f(X1))
U131_gg(X1, X2, qcN11_out_gg(X1, X2)) → qcN11_out_gg(X1, f(X2))
U154_gg(X1, X2, qcN11_out_gg(X1, X2)) → rcN12_out_gg(X1, X2)
rcN12_in_gg(f(X1), X1) → U155_gg(X1, tcG_in_g(X1))
U155_gg(X1, tcG_out_g(X1)) → rcN12_out_gg(f(X1), X1)
U134_gg(rcN12_out_gg(a, b)) → qcE_out_gg(a, b)
qcE_in_gg(X1, f(X2)) → U135_gg(X1, X2, rcN12_in_gg(X1, f(X2)))
U135_gg(X1, X2, rcN12_out_gg(X1, f(X2))) → U136_gg(X1, X2, qcE_in_gg(X1, X2))
U136_gg(X1, X2, qcE_out_gg(X1, X2)) → qcE_out_gg(X1, f(X2))
U86_gg(X1, X2, qcE_out_gg(X1, X2)) → qcC_out_gg(X1, f(f(X2)))
U87_gg(X1, X2, qcC_out_gg(f(X1), f(X2))) → U88_gg(X1, X2, qcF_in_gg(X1, X2))
qcF_in_gg(X1, f(X1)) → U89_gg(X1, qcC_in_gg(f(X1), f(X1)))
U89_gg(X1, qcC_out_gg(f(X1), f(X1))) → U90_gg(X1, tcG_in_g(X1))
U90_gg(X1, tcG_out_g(X1)) → qcF_out_gg(X1, f(X1))
U88_gg(X1, X2, qcF_out_gg(X1, X2)) → qcF_out_gg(X1, f(X2))
U148_gg(X1, X2, qcF_out_gg(X1, X2)) → rcL_out_gg(X1, X2)
rcL_in_gg(X1, X1) → U149_gg(X1, tcG_in_g(X1))
U149_gg(X1, tcG_out_g(X1)) → rcL_out_gg(X1, X1)
U95_gg(X1, X2, rcL_out_gg(X1, f(X2))) → U96_gg(X1, X2, qcK_in_gg(X1, X2))
U96_gg(X1, X2, qcK_out_gg(X1, X2)) → qcK_out_gg(X1, f(X2))
U97_gg(X1, X2, qcK_out_gg(X1, X2)) → pcM_out_gg(X1, X2)
U150_g(X1, pcM_out_gg(f(f(f(f(f(f(f(f(X1)))))))), X1)) → qcO_out_g(f(f(X1)))
U98_g(X1, qcO_out_g(f(X1))) → U99_g(X1, qcF_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U99_g(X1, qcF_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → rcN_out_g(f(f(X1)))
U100_g(X1, rcN_out_g(f(f(X1)))) → U101_g(X1, qcK_in_gg(f(f(f(f(f(f(f(X1))))))), X1))
U101_g(X1, qcK_out_gg(f(f(f(f(f(f(f(X1))))))), X1)) → pcP_out_g(f(f(X1)))
U151_g(X1, pcP_out_g(f(X1))) → qcT_out_g(f(f(X1)))
U104_g(X1, qcT_out_g(f(X1))) → U105_g(X1, qcQ_in_g(X1))
U105_g(X1, qcQ_out_g(X1)) → rcS_out_g(f(f(X1)))
U108_g(X1, rcS_out_g(f(f(X1)))) → U109_g(X1, qcU_in_g(X1))
U109_g(X1, qcU_out_g(X1)) → pcW_out_g(f(f(X1)))
U152_g(X1, pcW_out_g(f(X1))) → qcN1_out_g(f(f(X1)))
U112_g(X1, qcN1_out_g(f(X1))) → U113_g(X1, qcX_in_g(X1))
U113_g(X1, qcX_out_g(X1)) → rcZ_out_g(f(f(X1)))
U116_g(X1, rcZ_out_g(f(f(X1)))) → U117_g(X1, qcN2_in_g(X1))
U117_g(X1, qcN2_out_g(X1)) → pcN4_out_g(f(f(X1)))
U153_g(X1, pcN4_out_g(f(X1))) → qcN9_out_g(f(f(X1)))
U122_g(X1, qcN9_out_g(f(X1))) → U123_g(X1, qcN5_in_g(X1))
U123_g(X1, qcN5_out_g(X1)) → rcN8_out_g(f(f(X1)))
U127_g(X1, rcN8_out_g(f(f(X1)))) → U128_g(X1, qcI_in_g(X1))
U128_g(X1, qcI_out_g(X1)) → pcB_out_g(f(f(X1)))
U83_g(X1, pcB_out_g(f(X1))) → qcA_out_g(f(X1))

The set Q consists of the following terms:

qcA_in_g(x0)
pcB_in_g(x0)
rcN8_in_g(x0)
qcN9_in_g(x0)
pcN4_in_g(x0)
rcZ_in_g(x0)
qcN1_in_g(x0)
pcW_in_g(x0)
rcS_in_g(x0)
qcT_in_g(x0)
pcP_in_g(x0)
rcN_in_g(x0)
qcO_in_g(x0)
pcM_in_gg(x0, x1)
qcK_in_gg(x0, x1)
rcL_in_gg(x0, x1)
qcF_in_gg(x0, x1)
qcC_in_gg(x0, x1)
pcD_in_g(x0)
rcN13_in_g(x0)
U140_g(x0, x1)
rcN7_in_g(x0)
qcH_in_g(x0)
qcI_in_g(x0)
rcN10_in_g(x0)
qcN5_in_g(x0)
qcN6_in_g(x0)
qcN2_in_g(x0)
rcN3_in_g(x0)
qcX_in_g(x0)
qcY_in_g(x0)
qcU_in_g(x0)
rcV_in_g(x0)
qcQ_in_g(x0)
qcR_in_g(x0)
U147_g(x0, x1)
U102_g(x0, x1)
U103_g(x0, x1)
U146_g(x0, x1)
U106_g(x0, x1)
U107_g(x0, x1)
U145_g(x0, x1)
U110_g(x0, x1)
U111_g(x0, x1)
U144_g(x0, x1)
U114_g(x0, x1)
U115_g(x0, x1)
U143_g(x0, x1)
U118_g(x0, x1)
U119_g(x0, x1)
U142_g(x0, x1)
U125_g(x0, x1)
U126_g(x0, x1)
U91_g(x0, x1)
U120_g(x0, x1)
tcG_in_g(x0)
qcJ_in_g(x0)
U92_g(x0, x1)
U93_g(x0, x1)
U94_g(x0, x1)
U124_g(x0, x1)
U121_g(x0, x1)
U141_g(x0, x1)
U137_g(x0, x1)
U138_g(x0, x1)
U139_g(x0, x1)
U84_gg(x0, x1)
U85_gg(x0, x1)
qcE_in_gg(x0, x1)
rcN12_in_gg(x0, x1)
qcN11_in_gg(x0, x1)
U129_gg(x0)
U130_gg(x0, x1, x2)
U132_gg(x0, x1)
U133_gg(x0, x1)
U131_gg(x0, x1, x2)
U154_gg(x0, x1, x2)
U155_gg(x0, x1)
U134_gg(x0)
U135_gg(x0, x1, x2)
U136_gg(x0, x1, x2)
U86_gg(x0, x1, x2)
U87_gg(x0, x1, x2)
U89_gg(x0, x1)
U90_gg(x0, x1)
U88_gg(x0, x1, x2)
U148_gg(x0, x1, x2)
U149_gg(x0, x1)
U95_gg(x0, x1, x2)
U96_gg(x0, x1, x2)
U97_gg(x0, x1, x2)
U150_g(x0, x1)
U98_g(x0, x1)
U99_g(x0, x1)
U100_g(x0, x1)
U101_g(x0, x1)
U151_g(x0, x1)
U104_g(x0, x1)
U105_g(x0, x1)
U108_g(x0, x1)
U109_g(x0, x1)
U152_g(x0, x1)
U112_g(x0, x1)
U113_g(x0, x1)
U116_g(x0, x1)
U117_g(x0, x1)
U153_g(x0, x1)
U122_g(x0, x1)
U123_g(x0, x1)
U127_g(x0, x1)
U128_g(x0, x1)
U83_g(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 51 less nodes.

(0) Obligation:

(1) PrologToDTProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) TriplesToPiDPProof (SOUND 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