Left Termination proof of /tmp/tmpMzpDds/subset-oi.pl

Left Termination of the query pattern subset_in_2(a, g) w.r.t. the given Prolog program could not be shown:

0 Prolog

↳1 PrologToDTProblemTransformerProof (⇐)

↳2 TRIPLES

↳3 TriplesToPiDPProof (⇐)

↳4 PiDP

↳5 DependencyGraphProof (⇔)

↳6 AND

    ↳7 PiDP

        ↳8 UsableRulesProof (⇔)

        ↳9 PiDP

        ↳10 PiDPToQDPProof (⇔)

        ↳11 QDP

        ↳12 QDPSizeChangeProof (⇔)

        ↳13 YES

    ↳14 PiDP

        ↳15 UsableRulesProof (⇔)

        ↳16 PiDP

        ↳17 PiDPToQDPProof (⇐)

        ↳18 QDP

        ↳19 QDPSizeChangeProof (⇔)

        ↳20 YES

    ↳21 PiDP

        ↳22 UsableRulesProof (⇔)

        ↳23 PiDP

        ↳24 PiDPToQDPProof (⇐)

        ↳25 QDP

        ↳26 Rewriting (⇔)

        ↳27 QDP

        ↳28 UsableRulesProof (⇔)

        ↳29 QDP

        ↳30 QReductionProof (⇔)

        ↳31 QDP

        ↳32 Narrowing (⇐)

        ↳33 QDP

        ↳34 Instantiation (⇔)

        ↳35 QDP

        ↳36 Instantiation (⇔)

        ↳37 QDP

        ↳38 Instantiation (⇔)

        ↳39 QDP

        ↳40 Instantiation (⇔)

        ↳41 QDP

        ↳42 Instantiation (⇔)

        ↳43 QDP

        ↳44 Instantiation (⇔)

        ↳45 QDP

        ↳46 Instantiation (⇔)

        ↳47 QDP

        ↳48 Instantiation (⇔)

        ↳49 QDP

        ↳50 Instantiation (⇔)

        ↳51 QDP

        ↳52 Instantiation (⇔)

        ↳53 QDP

        ↳54 Instantiation (⇔)

        ↳55 QDP

        ↳56 Instantiation (⇔)

        ↳57 QDP

        ↳58 NonTerminationProof (⇔)

        ↳59 NO

(0) Obligation:

Clauses:

subset(X, Y) :- subsetchecked(X, [], Y).
subsetchecked([], X1, X2).
subsetchecked(.(X, Xs), Ys, Zs) :- ','(member(X, Zs), ','(not_member(X, Ys), subsetchecked(Xs, .(X, Ys), Zs))).
member(X, .(X, X3)).
member(X, .(X4, Xs)) :- member(X, Xs).
not_member(X, Y) :- ','(member(X, Y), ','(!, failure(a))).
not_member(X5, X6).
failure(b).

Queries:

subset(a,g).

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: subset(T1, T2)\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: subset(T1, T2), SCOPE: 1, CLAUSE: 0\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: subsetchecked(T7, [], T6)\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: subsetchecked(T7, [], T6), SCOPE: 2, CLAUSE: 1 | subsetchecked(T7, [], T6), SCOPE: 2, CLAUSE: 2\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: subsetchecked(T7, [], T6), SCOPE: 2, CLAUSE: 1\n\nT6 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: subsetchecked(T7, [], T6), SCOPE: 2, CLAUSE: 2\n\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: ','(member(T22, T21), ','(not_member(T22, []), subsetchecked(T23, .(T22, []), T21)))\n\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: member(T22, T21)\n\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: ','(not_member(T28, []), subsetchecked(T29, .(T28, []), T21))\n\nT21 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: member(T22, T21), SCOPE: 3, CLAUSE: 3 | member(T22, T21), SCOPE: 3, CLAUSE: 4\n\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: member(T22, T21), SCOPE: 3, CLAUSE: 3\n\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: member(T22, T21), SCOPE: 3, CLAUSE: 4\n\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: member(T53, T52)\n\nT52 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: not_member(T28, [])\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: subsetchecked(T29, .(T28, []), T21)\n\nT21 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: not_member(T28, []), SCOPE: 4, CLAUSE: 5 | not_member(T28, []), SCOPE: 4, CLAUSE: 6\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: not_member(T28, []), SCOPE: 4, CLAUSE: 5\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: not_member(T28, []), SCOPE: 4, CLAUSE: 6\n\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: ','(member(T70, []), ','(!_4, failure(a)))\n\nT70 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: member(T70, [])\n\nT70 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: ','(!_4, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: member(T70, []), SCOPE: 5, CLAUSE: 3 | member(T70, []), SCOPE: 5, CLAUSE: 4\n\nT70 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: member(T70, []), SCOPE: 5, CLAUSE: 4\n\nT70 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: failure(a), SCOPE: 6, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: subsetchecked(T29, .(T28, []), T21), SCOPE: 7, CLAUSE: 1 | subsetchecked(T29, .(T28, []), T21), SCOPE: 7, CLAUSE: 2\n\nT21 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: subsetchecked(T29, .(T28, []), T21), SCOPE: 7, CLAUSE: 1\n\nT21 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: subsetchecked(T29, .(T28, []), T21), SCOPE: 7, CLAUSE: 2\n\nT21 is ground\nT28 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(member(T108, T107), ','(not_member(T108, .(T106, [])), subsetchecked(T109, .(T108, .(T106, [])), T107)))\n\nT106 is ground\nT107 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: member(T108, T107)\n\nT107 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: ','(not_member(T114, .(T106, [])), subsetchecked(T115, .(T114, .(T106, [])), T107))\n\nT106 is ground\nT107 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: not_member(T114, .(T106, []))\n\nT106 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: subsetchecked(T115, .(T114, .(T106, [])), T107)\n\nT106 is ground\nT107 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: not_member(T114, .(T106, [])), SCOPE: 8, CLAUSE: 5 | not_member(T114, .(T106, [])), SCOPE: 8, CLAUSE: 6\n\nT106 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: not_member(T114, .(T106, [])), SCOPE: 8, CLAUSE: 5\n\nT106 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: not_member(T114, .(T106, [])), SCOPE: 8, CLAUSE: 6\n\nT106 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: ','(member(T136, .(T137, [])), ','(!_8, failure(a)))\n\nT136 is ground\nT137 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: member(T136, .(T137, []))\n\nT136 is ground\nT137 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: ','(!_8, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: failure(a), SCOPE: 9, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: subsetchecked(T115, .(T114, .(T106, [])), T107), SCOPE: 10, CLAUSE: 1 | subsetchecked(T115, .(T114, .(T106, [])), T107), SCOPE: 10, CLAUSE: 2\n\nT106 is ground\nT107 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: subsetchecked(T115, .(T114, .(T106, [])), T107), SCOPE: 10, CLAUSE: 1\n\nT106 is ground\nT107 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: subsetchecked(T115, .(T114, .(T106, [])), T107), SCOPE: 10, CLAUSE: 2\n\nT106 is ground\nT107 is ground\nT114 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: ','(member(T184, T183), ','(not_member(T184, .(T181, .(T182, []))), subsetchecked(T185, .(T184, .(T181, .(T182, []))), T183)))\n\nT181 is ground\nT182 is ground\nT183 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: member(T184, T183)\n\nT183 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: ','(not_member(T190, .(T181, .(T182, []))), subsetchecked(T191, .(T190, .(T181, .(T182, []))), T183))\n\nT181 is ground\nT182 is ground\nT183 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: not_member(T190, .(T181, .(T182, [])))\n\nT181 is ground\nT182 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: subsetchecked(T191, .(T190, .(T181, .(T182, []))), T183)\n\nT181 is ground\nT182 is ground\nT183 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: not_member(T190, .(T181, .(T182, []))), SCOPE: 11, CLAUSE: 5 | not_member(T190, .(T181, .(T182, []))), SCOPE: 11, CLAUSE: 6\n\nT181 is ground\nT182 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: not_member(T190, .(T181, .(T182, []))), SCOPE: 11, CLAUSE: 5\n\nT181 is ground\nT182 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: not_member(T190, .(T181, .(T182, []))), SCOPE: 11, CLAUSE: 6\n\nT181 is ground\nT182 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: ','(member(T222, .(T223, .(T224, []))), ','(!_11, failure(a)))\n\nT222 is ground\nT223 is ground\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: member(T222, .(T223, .(T224, [])))\n\nT222 is ground\nT223 is ground\nT224 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: ','(!_11, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: failure(a), SCOPE: 12, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: subsetchecked(T191, .(T190, .(T181, .(T182, []))), T183), SCOPE: 13, CLAUSE: 1 | subsetchecked(T191, .(T190, .(T181, .(T182, []))), T183), SCOPE: 13, CLAUSE: 2\n\nT181 is ground\nT182 is ground\nT183 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: subsetchecked(T191, .(T190, .(T181, .(T182, []))), T183), SCOPE: 13, CLAUSE: 1\n\nT181 is ground\nT182 is ground\nT183 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: subsetchecked(T191, .(T190, .(T181, .(T182, []))), T183), SCOPE: 13, CLAUSE: 2\n\nT181 is ground\nT182 is ground\nT183 is ground\nT190 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: ','(member(T288, T287), ','(not_member(T288, .(T284, .(T285, .(T286, [])))), subsetchecked(T289, .(T288, .(T284, .(T285, .(T286, [])))), T287)))\n\nT284 is ground\nT285 is ground\nT286 is ground\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: member(T288, T287)\n\nT287 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: ','(not_member(T294, .(T284, .(T285, .(T286, [])))), subsetchecked(T295, .(T294, .(T284, .(T285, .(T286, [])))), T287))\n\nT284 is ground\nT285 is ground\nT286 is ground\nT287 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: not_member(T294, .(T284, .(T285, .(T286, []))))\n\nT284 is ground\nT285 is ground\nT286 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: subsetchecked(T295, .(T294, .(T284, .(T285, .(T286, [])))), T287)\n\nT284 is ground\nT285 is ground\nT286 is ground\nT287 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: not_member(T294, .(T284, .(T285, .(T286, [])))), SCOPE: 14, CLAUSE: 5 | not_member(T294, .(T284, .(T285, .(T286, [])))), SCOPE: 14, CLAUSE: 6\n\nT284 is ground\nT285 is ground\nT286 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: not_member(T294, .(T284, .(T285, .(T286, [])))), SCOPE: 14, CLAUSE: 5\n\nT284 is ground\nT285 is ground\nT286 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: not_member(T294, .(T284, .(T285, .(T286, [])))), SCOPE: 14, CLAUSE: 6\n\nT284 is ground\nT285 is ground\nT286 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: ','(member(T336, .(T337, .(T338, .(T339, [])))), ','(!_14, failure(a)))\n\nT336 is ground\nT337 is ground\nT338 is ground\nT339 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: member(T336, .(T337, .(T338, .(T339, []))))\n\nT336 is ground\nT337 is ground\nT338 is ground\nT339 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: ','(!_14, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: failure(a), SCOPE: 15, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: subsetchecked(T295, .(T294, .(T284, .(T285, .(T286, [])))), T287), SCOPE: 16, CLAUSE: 1 | subsetchecked(T295, .(T294, .(T284, .(T285, .(T286, [])))), T287), SCOPE: 16, CLAUSE: 2\n\nT284 is ground\nT285 is ground\nT286 is ground\nT287 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: subsetchecked(T295, .(T294, .(T284, .(T285, .(T286, [])))), T287), SCOPE: 16, CLAUSE: 1\n\nT284 is ground\nT285 is ground\nT286 is ground\nT287 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: subsetchecked(T295, .(T294, .(T284, .(T285, .(T286, [])))), T287), SCOPE: 16, CLAUSE: 2\n\nT284 is ground\nT285 is ground\nT286 is ground\nT287 is ground\nT294 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: ','(member(T420, T419), ','(not_member(T420, .(T415, .(T416, .(T417, .(T418, []))))), subsetchecked(T421, .(T420, .(T415, .(T416, .(T417, .(T418, []))))), T419)))\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT419 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: member(T420, T419)\n\nT419 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(not_member(T426, .(T415, .(T416, .(T417, .(T418, []))))), subsetchecked(T427, .(T426, .(T415, .(T416, .(T417, .(T418, []))))), T419))\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT419 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: not_member(T426, .(T415, .(T416, .(T417, .(T418, [])))))\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: subsetchecked(T427, .(T426, .(T415, .(T416, .(T417, .(T418, []))))), T419)\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT419 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: not_member(T426, .(T415, .(T416, .(T417, .(T418, []))))), SCOPE: 17, CLAUSE: 5 | not_member(T426, .(T415, .(T416, .(T417, .(T418, []))))), SCOPE: 17, CLAUSE: 6\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: not_member(T426, .(T415, .(T416, .(T417, .(T418, []))))), SCOPE: 17, CLAUSE: 5\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: not_member(T426, .(T415, .(T416, .(T417, .(T418, []))))), SCOPE: 17, CLAUSE: 6\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: ','(member(T478, .(T479, .(T480, .(T481, .(T482, []))))), ','(!_17, failure(a)))\n\nT478 is ground\nT479 is ground\nT480 is ground\nT481 is ground\nT482 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: member(T478, .(T479, .(T480, .(T481, .(T482, [])))))\n\nT478 is ground\nT479 is ground\nT480 is ground\nT481 is ground\nT482 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: ','(!_17, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: failure(a), SCOPE: 18, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: subsetchecked(T427, .(T426, .(T415, .(T416, .(T417, .(T418, []))))), T419), SCOPE: 19, CLAUSE: 1 | subsetchecked(T427, .(T426, .(T415, .(T416, .(T417, .(T418, []))))), T419), SCOPE: 19, CLAUSE: 2\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT419 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: subsetchecked(T427, .(T426, .(T415, .(T416, .(T417, .(T418, []))))), T419), SCOPE: 19, CLAUSE: 1\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT419 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: subsetchecked(T427, .(T426, .(T415, .(T416, .(T417, .(T418, []))))), T419), SCOPE: 19, CLAUSE: 2\n\nT415 is ground\nT416 is ground\nT417 is ground\nT418 is ground\nT419 is ground\nT426 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
133 [label="133: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
134 [label="134: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
135 [label="135: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
136 [label="136: ','(member(T580, T579), ','(not_member(T580, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), subsetchecked(T581, .(T580, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), T579)))\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT579 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: member(T580, T579)\n\nT579 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: ','(not_member(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), subsetchecked(T587, .(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), T579))\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT579 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: not_member(T586, .(T574, .(T575, .(T576, .(T577, .(T578, []))))))\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: subsetchecked(T587, .(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), T579)\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT579 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: not_member(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), SCOPE: 20, CLAUSE: 5 | not_member(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), SCOPE: 20, CLAUSE: 6\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: not_member(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), SCOPE: 20, CLAUSE: 5\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: not_member(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), SCOPE: 20, CLAUSE: 6\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: ','(member(T648, .(T649, .(T650, .(T651, .(T652, .(T653, [])))))), ','(!_20, failure(a)))\n\nT648 is ground\nT649 is ground\nT650 is ground\nT651 is ground\nT652 is ground\nT653 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: member(T648, .(T649, .(T650, .(T651, .(T652, .(T653, []))))))\n\nT648 is ground\nT649 is ground\nT650 is ground\nT651 is ground\nT652 is ground\nT653 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ','(!_20, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: failure(a), SCOPE: 21, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: subsetchecked(T587, .(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), T579), SCOPE: 22, CLAUSE: 1 | subsetchecked(T587, .(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), T579), SCOPE: 22, CLAUSE: 2\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT579 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: subsetchecked(T587, .(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), T579), SCOPE: 22, CLAUSE: 1\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT579 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: subsetchecked(T587, .(T586, .(T574, .(T575, .(T576, .(T577, .(T578, [])))))), T579), SCOPE: 22, CLAUSE: 2\n\nT574 is ground\nT575 is ground\nT576 is ground\nT577 is ground\nT578 is ground\nT579 is ground\nT586 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(member(T768, T767), ','(not_member(T768, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), subsetchecked(T769, .(T768, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), T767)))\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT767 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: member(T768, T767)\n\nT767 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: ','(not_member(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), subsetchecked(T775, .(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), T767))\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT767 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: not_member(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, [])))))))\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: subsetchecked(T775, .(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), T767)\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT767 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: not_member(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), SCOPE: 23, CLAUSE: 5 | not_member(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), SCOPE: 23, CLAUSE: 6\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: not_member(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), SCOPE: 23, CLAUSE: 5\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: not_member(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), SCOPE: 23, CLAUSE: 6\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: ','(member(T846, .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, []))))))), ','(!_23, failure(a)))\n\nT846 is ground\nT847 is ground\nT848 is ground\nT849 is ground\nT850 is ground\nT851 is ground\nT852 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: member(T846, .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, [])))))))\n\nT846 is ground\nT847 is ground\nT848 is ground\nT849 is ground\nT850 is ground\nT851 is ground\nT852 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: ','(!_23, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: failure(a), SCOPE: 24, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: subsetchecked(T775, .(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), T767), SCOPE: 25, CLAUSE: 1 | subsetchecked(T775, .(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), T767), SCOPE: 25, CLAUSE: 2\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT767 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: subsetchecked(T775, .(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), T767), SCOPE: 25, CLAUSE: 1\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT767 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: subsetchecked(T775, .(T774, .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))), T767), SCOPE: 25, CLAUSE: 2\n\nT761 is ground\nT762 is ground\nT763 is ground\nT764 is ground\nT765 is ground\nT766 is ground\nT767 is ground\nT774 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: ','(member(T984, T983), ','(not_member(T984, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))), subsetchecked(T985, .(T984, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))), T983)))\n\nT976 is ground\nT977 is ground\nT978 is ground\nT979 is ground\nT980 is ground\nT981 is ground\nT982 is ground\nT983 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: ','(member(T984, T983), ','(not_member(T984, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))), subsetchecked(T985, .(T984, T990), T983)))\n\nT976 is ground\nT977 is ground\nT978 is ground\nT979 is ground\nT980 is ground\nT981 is ground\nT982 is ground\nT983 is ground\nT990 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: member(T984, T983)\n\nT983 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: ','(not_member(T995, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))), subsetchecked(T996, .(T995, T990), T983))\n\nT976 is ground\nT977 is ground\nT978 is ground\nT979 is ground\nT980 is ground\nT981 is ground\nT982 is ground\nT983 is ground\nT990 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: not_member(T995, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, []))))))))\n\nT976 is ground\nT977 is ground\nT978 is ground\nT979 is ground\nT980 is ground\nT981 is ground\nT982 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: subsetchecked(T996, .(T995, T990), T983)\n\nT983 is ground\nT990 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: not_member(T995, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))), SCOPE: 26, CLAUSE: 5 | not_member(T995, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))), SCOPE: 26, CLAUSE: 6\n\nT976 is ground\nT977 is ground\nT978 is ground\nT979 is ground\nT980 is ground\nT981 is ground\nT982 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: not_member(T995, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))), SCOPE: 26, CLAUSE: 5\n\nT976 is ground\nT977 is ground\nT978 is ground\nT979 is ground\nT980 is ground\nT981 is ground\nT982 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: not_member(T995, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))), SCOPE: 26, CLAUSE: 6\n\nT976 is ground\nT977 is ground\nT978 is ground\nT979 is ground\nT980 is ground\nT981 is ground\nT982 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: ','(member(T1077, .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, [])))))))), ','(!_26, failure(a)))\n\nT1077 is ground\nT1078 is ground\nT1079 is ground\nT1080 is ground\nT1081 is ground\nT1082 is ground\nT1083 is ground\nT1084 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: member(T1077, .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, []))))))))\n\nT1077 is ground\nT1078 is ground\nT1079 is ground\nT1080 is ground\nT1081 is ground\nT1082 is ground\nT1083 is ground\nT1084 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: ','(!_26, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: failure(a), SCOPE: 27, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: subsetchecked(T996, .(T995, T990), T983), SCOPE: 28, CLAUSE: 1 | subsetchecked(T996, .(T995, T990), T983), SCOPE: 28, CLAUSE: 2\n\nT983 is ground\nT990 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: subsetchecked(T996, .(T995, T990), T983), SCOPE: 28, CLAUSE: 1\n\nT983 is ground\nT990 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: subsetchecked(T996, .(T995, T990), T983), SCOPE: 28, CLAUSE: 2\n\nT983 is ground\nT990 is ground\nT995 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: ','(member(T1173, T1172), ','(not_member(T1173, .(T1170, T1171)), subsetchecked(T1174, .(T1173, .(T1170, T1171)), T1172)))\n\nT1170 is ground\nT1171 is ground\nT1172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: member(T1173, T1172)\n\nT1172 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: ','(not_member(T1179, .(T1170, T1171)), subsetchecked(T1180, .(T1179, .(T1170, T1171)), T1172))\n\nT1170 is ground\nT1171 is ground\nT1172 is ground\nT1179 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: not_member(T1179, .(T1170, T1171))\n\nT1170 is ground\nT1171 is ground\nT1179 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: subsetchecked(T1180, .(T1179, .(T1170, T1171)), T1172)\n\nT1170 is ground\nT1171 is ground\nT1172 is ground\nT1179 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="212: not_member(T1179, .(T1170, T1171)), SCOPE: 29, CLAUSE: 5 | not_member(T1179, .(T1170, T1171)), SCOPE: 29, CLAUSE: 6\n\nT1170 is ground\nT1171 is ground\nT1179 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
213 [label="213: not_member(T1179, .(T1170, T1171)), SCOPE: 29, CLAUSE: 5\n\nT1170 is ground\nT1171 is ground\nT1179 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
214 [label="214: not_member(T1179, .(T1170, T1171)), SCOPE: 29, CLAUSE: 6\n\nT1170 is ground\nT1171 is ground\nT1179 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
215 [label="215: ','(member(T1211, .(T1212, T1213)), ','(!_29, failure(a)))\n\nT1211 is ground\nT1212 is ground\nT1213 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
216 [label="216: member(T1211, .(T1212, T1213))\n\nT1211 is ground\nT1212 is ground\nT1213 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
217 [label="217: ','(!_29, failure(a))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
218 [label="218: failure(a)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
219 [label="219: failure(a), SCOPE: 30, CLAUSE: 7\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
220 [label="220: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
221 [label="221: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
222 [label="222: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
223 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 223 [arrowhead = none ];
223 -> 2;

224 [label="ONLY EVAL with clause\nsubset(X9, X10) :- subsetchecked(X9, [], X10).\nand substitution\nT1 -> T7\nX9 -> T7\nT2 -> T6\nX10 -> T6\nT5 -> T7", fontsize=14, style = filled, fillcolor = white];
2 -> 224 [arrowhead = none ];
224 -> 3;

225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 225 [arrowhead = none ];
225 -> 4;

226 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 226 [arrowhead = none ];
226 -> 5;

227 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
4 -> 227 [arrowhead = none ];
227 -> 6;

228 [label="EVAL with clause\nsubsetchecked([], X19, X20).\nand substitution\nT7 -> []\nX19 -> []\nT6 -> T12\nX20 -> T12", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 228 [arrowhead = none ];
228 -> 7;

229 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 229 [arrowhead = none ];
229 -> 8;

230 [label="EVAL with clause\nsubsetchecked(.(X31, X32), X33, X34) :- ','(member(X31, X34), ','(not_member(X31, X33), subsetchecked(X32, .(X31, X33), X34))).\nand substitution\nX31 -> T22\nX32 -> T23\nT7 -> .(T22, T23)\nX33 -> []\nT6 -> T21\nX34 -> T21\nT19 -> T22\nT20 -> T23", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 230 [arrowhead = none ];
230 -> 10;

231 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 231 [arrowhead = none ];
231 -> 11;

232 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 232 [arrowhead = none ];
232 -> 9;

233 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
10 -> 233 [arrowhead = none ];
233 -> 12;

234 [label="SPLIT 2\nnew knowledge:\nT28 is ground\nreplacements:\nT22 -> T28\nT23 -> T29", fontsize=14, style = filled, fillcolor = violet];
10 -> 234 [arrowhead = none ];
234 -> 13;

235 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
12 -> 235 [arrowhead = none ];
235 -> 14;

236 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
13 -> 236 [arrowhead = none ];
236 -> 22;

237 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
13 -> 237 [arrowhead = none ];
237 -> 23;

238 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 238 [arrowhead = none ];
238 -> 15;

239 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 239 [arrowhead = none ];
239 -> 16;

240 [label="EVAL with clause\nmember(X55, .(X55, X56)).\nand substitution\nT22 -> T42\nX55 -> T42\nX56 -> T43\nT21 -> .(T42, T43)", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 240 [arrowhead = none ];
240 -> 17;

241 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 241 [arrowhead = none ];
241 -> 18;

242 [label="EVAL with clause\nmember(X65, .(X66, X67)) :- member(X65, X67).\nand substitution\nT22 -> T53\nX65 -> T53\nX66 -> T51\nX67 -> T52\nT21 -> .(T51, T52)\nT50 -> T53", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 242 [arrowhead = none ];
242 -> 20;

243 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 243 [arrowhead = none ];
243 -> 21;

244 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 244 [arrowhead = none ];
244 -> 19;

245 [label="INSTANCE with matching:\nT22 -> T53\nT21 -> T52", fontsize=14, style = filled, fillcolor = lightgrey];
20 -> 245 [arrowhead = none , style=dashed];
245 -> 12[style=dashed];

246 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
22 -> 246 [arrowhead = none ];
246 -> 24;

247 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
23 -> 247 [arrowhead = none ];
247 -> 38;

248 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 248 [arrowhead = none ];
248 -> 25;

249 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
24 -> 249 [arrowhead = none ];
249 -> 26;

250 [label="ONLY EVAL with clause\nnot_member(X101, X102) :- ','(member(X101, X102), ','(!_4, failure(a))).\nand substitution\nT28 -> T70\nX101 -> T70\nX102 -> []", fontsize=14, style = filled, fillcolor = white];
25 -> 250 [arrowhead = none ];
250 -> 27;

251 [label="ONLY EVAL with clause\nnot_member(X126, X127).\nand substitution\nT28 -> T81\nX126 -> T81\nX127 -> []", fontsize=14, style = filled, fillcolor = white];
26 -> 251 [arrowhead = none ];
251 -> 36;

252 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
27 -> 252 [arrowhead = none ];
252 -> 28;

253 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
27 -> 253 [arrowhead = none ];
253 -> 29;

254 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
28 -> 254 [arrowhead = none ];
254 -> 30;

255 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
29 -> 255 [arrowhead = none ];
255 -> 33;

256 [label="BACKTRACK\nfor clause: member(X, .(X, X3))because of non-unification", fontsize=14, style = filled, fillcolor = white];
30 -> 256 [arrowhead = none ];
256 -> 31;

257 [label="BACKTRACK\nfor clause: member(X, .(X4, Xs)) :- member(X, Xs)because of non-unification", fontsize=14, style = filled, fillcolor = white];
31 -> 257 [arrowhead = none ];
257 -> 32;

258 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
33 -> 258 [arrowhead = none ];
258 -> 34;

259 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
34 -> 259 [arrowhead = none ];
259 -> 35;

260 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 260 [arrowhead = none ];
260 -> 37;

261 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 261 [arrowhead = none ];
261 -> 39;

262 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
38 -> 262 [arrowhead = none ];
262 -> 40;

263 [label="EVAL with clause\nsubsetchecked([], X140, X141).\nand substitution\nT29 -> []\nT28 -> T94\nX140 -> .(T94, [])\nT21 -> T95\nX141 -> T95", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 263 [arrowhead = none ];
263 -> 41;

264 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
39 -> 264 [arrowhead = none ];
264 -> 42;

265 [label="EVAL with clause\nsubsetchecked(.(X152, X153), X154, X155) :- ','(member(X152, X155), ','(not_member(X152, X154), subsetchecked(X153, .(X152, X154), X155))).\nand substitution\nX152 -> T108\nX153 -> T109\nT29 -> .(T108, T109)\nT28 -> T106\nX154 -> .(T106, [])\nT21 -> T107\nX155 -> T107\nT104 -> T108\nT105 -> T109", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 265 [arrowhead = none ];
265 -> 44;

266 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
40 -> 266 [arrowhead = none ];
266 -> 45;

267 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 267 [arrowhead = none ];
267 -> 43;

268 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
44 -> 268 [arrowhead = none ];
268 -> 46;

269 [label="SPLIT 2\nnew knowledge:\nT114 is ground\nreplacements:\nT108 -> T114\nT109 -> T115", fontsize=14, style = filled, fillcolor = violet];
44 -> 269 [arrowhead = none ];
269 -> 47;

270 [label="INSTANCE with matching:\nT22 -> T108\nT21 -> T107", fontsize=14, style = filled, fillcolor = lightgrey];
46 -> 270 [arrowhead = none , style=dashed];
270 -> 12[style=dashed];

271 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
47 -> 271 [arrowhead = none ];
271 -> 48;

272 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
47 -> 272 [arrowhead = none ];
272 -> 49;

273 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
48 -> 273 [arrowhead = none ];
273 -> 50;

274 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
49 -> 274 [arrowhead = none ];
274 -> 61;

275 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 275 [arrowhead = none ];
275 -> 51;

276 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
50 -> 276 [arrowhead = none ];
276 -> 52;

277 [label="ONLY EVAL with clause\nnot_member(X188, X189) :- ','(member(X188, X189), ','(!_8, failure(a))).\nand substitution\nT114 -> T136\nX188 -> T136\nT106 -> T137\nX189 -> .(T137, [])", fontsize=14, style = filled, fillcolor = white];
51 -> 277 [arrowhead = none ];
277 -> 53;

278 [label="ONLY EVAL with clause\nnot_member(X202, X203).\nand substitution\nT114 -> T146\nX202 -> T146\nT106 -> T147\nX203 -> .(T147, [])", fontsize=14, style = filled, fillcolor = white];
52 -> 278 [arrowhead = none ];
278 -> 59;

279 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
53 -> 279 [arrowhead = none ];
279 -> 54;

280 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
53 -> 280 [arrowhead = none ];
280 -> 55;

281 [label="INSTANCE with matching:\nT22 -> T136\nT21 -> .(T137, [])", fontsize=14, style = filled, fillcolor = lightgrey];
54 -> 281 [arrowhead = none , style=dashed];
281 -> 12[style=dashed];

282 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
55 -> 282 [arrowhead = none ];
282 -> 56;

283 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
56 -> 283 [arrowhead = none ];
283 -> 57;

284 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
57 -> 284 [arrowhead = none ];
284 -> 58;

285 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 285 [arrowhead = none ];
285 -> 60;

286 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
61 -> 286 [arrowhead = none ];
286 -> 62;

287 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
61 -> 287 [arrowhead = none ];
287 -> 63;

288 [label="EVAL with clause\nsubsetchecked([], X216, X217).\nand substitution\nT115 -> []\nT114 -> T166\nT106 -> T167\nX216 -> .(T166, .(T167, []))\nT107 -> T168\nX217 -> T168", fontsize=14, style = filled, fillcolor = lightblue];
62 -> 288 [arrowhead = none ];
288 -> 64;

289 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
62 -> 289 [arrowhead = none ];
289 -> 65;

290 [label="EVAL with clause\nsubsetchecked(.(X228, X229), X230, X231) :- ','(member(X228, X231), ','(not_member(X228, X230), subsetchecked(X229, .(X228, X230), X231))).\nand substitution\nX228 -> T184\nX229 -> T185\nT115 -> .(T184, T185)\nT114 -> T181\nT106 -> T182\nX230 -> .(T181, .(T182, []))\nT107 -> T183\nX231 -> T183\nT179 -> T184\nT180 -> T185", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 290 [arrowhead = none ];
290 -> 67;

291 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 291 [arrowhead = none ];
291 -> 68;

292 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
64 -> 292 [arrowhead = none ];
292 -> 66;

293 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
67 -> 293 [arrowhead = none ];
293 -> 69;

294 [label="SPLIT 2\nnew knowledge:\nT190 is ground\nreplacements:\nT184 -> T190\nT185 -> T191", fontsize=14, style = filled, fillcolor = violet];
67 -> 294 [arrowhead = none ];
294 -> 70;

295 [label="INSTANCE with matching:\nT22 -> T184\nT21 -> T183", fontsize=14, style = filled, fillcolor = lightgrey];
69 -> 295 [arrowhead = none , style=dashed];
295 -> 12[style=dashed];

296 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
70 -> 296 [arrowhead = none ];
296 -> 71;

297 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
70 -> 297 [arrowhead = none ];
297 -> 72;

298 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
71 -> 298 [arrowhead = none ];
298 -> 73;

299 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
72 -> 299 [arrowhead = none ];
299 -> 84;

300 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
73 -> 300 [arrowhead = none ];
300 -> 74;

301 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
73 -> 301 [arrowhead = none ];
301 -> 75;

302 [label="ONLY EVAL with clause\nnot_member(X264, X265) :- ','(member(X264, X265), ','(!_11, failure(a))).\nand substitution\nT190 -> T222\nX264 -> T222\nT181 -> T223\nT182 -> T224\nX265 -> .(T223, .(T224, []))", fontsize=14, style = filled, fillcolor = white];
74 -> 302 [arrowhead = none ];
302 -> 76;

303 [label="ONLY EVAL with clause\nnot_member(X278, X279).\nand substitution\nT190 -> T239\nX278 -> T239\nT181 -> T240\nT182 -> T241\nX279 -> .(T240, .(T241, []))", fontsize=14, style = filled, fillcolor = white];
75 -> 303 [arrowhead = none ];
303 -> 82;

304 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
76 -> 304 [arrowhead = none ];
304 -> 77;

305 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
76 -> 305 [arrowhead = none ];
305 -> 78;

306 [label="INSTANCE with matching:\nT22 -> T222\nT21 -> .(T223, .(T224, []))", fontsize=14, style = filled, fillcolor = lightgrey];
77 -> 306 [arrowhead = none , style=dashed];
306 -> 12[style=dashed];

307 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
78 -> 307 [arrowhead = none ];
307 -> 79;

308 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
79 -> 308 [arrowhead = none ];
308 -> 80;

309 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
80 -> 309 [arrowhead = none ];
309 -> 81;

310 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
82 -> 310 [arrowhead = none ];
310 -> 83;

311 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 311 [arrowhead = none ];
311 -> 85;

312 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
84 -> 312 [arrowhead = none ];
312 -> 86;

313 [label="EVAL with clause\nsubsetchecked([], X292, X293).\nand substitution\nT191 -> []\nT190 -> T266\nT181 -> T267\nT182 -> T268\nX292 -> .(T266, .(T267, .(T268, [])))\nT183 -> T269\nX293 -> T269", fontsize=14, style = filled, fillcolor = lightblue];
85 -> 313 [arrowhead = none ];
313 -> 87;

314 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
85 -> 314 [arrowhead = none ];
314 -> 88;

315 [label="EVAL with clause\nsubsetchecked(.(X304, X305), X306, X307) :- ','(member(X304, X307), ','(not_member(X304, X306), subsetchecked(X305, .(X304, X306), X307))).\nand substitution\nX304 -> T288\nX305 -> T289\nT191 -> .(T288, T289)\nT190 -> T284\nT181 -> T285\nT182 -> T286\nX306 -> .(T284, .(T285, .(T286, [])))\nT183 -> T287\nX307 -> T287\nT282 -> T288\nT283 -> T289", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 315 [arrowhead = none ];
315 -> 90;

316 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 316 [arrowhead = none ];
316 -> 91;

317 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
87 -> 317 [arrowhead = none ];
317 -> 89;

318 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
90 -> 318 [arrowhead = none ];
318 -> 92;

319 [label="SPLIT 2\nnew knowledge:\nT294 is ground\nreplacements:\nT288 -> T294\nT289 -> T295", fontsize=14, style = filled, fillcolor = violet];
90 -> 319 [arrowhead = none ];
319 -> 93;

320 [label="INSTANCE with matching:\nT22 -> T288\nT21 -> T287", fontsize=14, style = filled, fillcolor = lightgrey];
92 -> 320 [arrowhead = none , style=dashed];
320 -> 12[style=dashed];

321 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
93 -> 321 [arrowhead = none ];
321 -> 94;

322 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
93 -> 322 [arrowhead = none ];
322 -> 95;

323 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
94 -> 323 [arrowhead = none ];
323 -> 96;

324 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
95 -> 324 [arrowhead = none ];
324 -> 107;

325 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 325 [arrowhead = none ];
325 -> 97;

326 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
96 -> 326 [arrowhead = none ];
326 -> 98;

327 [label="ONLY EVAL with clause\nnot_member(X340, X341) :- ','(member(X340, X341), ','(!_14, failure(a))).\nand substitution\nT294 -> T336\nX340 -> T336\nT284 -> T337\nT285 -> T338\nT286 -> T339\nX341 -> .(T337, .(T338, .(T339, [])))", fontsize=14, style = filled, fillcolor = white];
97 -> 327 [arrowhead = none ];
327 -> 99;

328 [label="ONLY EVAL with clause\nnot_member(X354, X355).\nand substitution\nT294 -> T360\nX354 -> T360\nT284 -> T361\nT285 -> T362\nT286 -> T363\nX355 -> .(T361, .(T362, .(T363, [])))", fontsize=14, style = filled, fillcolor = white];
98 -> 328 [arrowhead = none ];
328 -> 105;

329 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
99 -> 329 [arrowhead = none ];
329 -> 100;

330 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
99 -> 330 [arrowhead = none ];
330 -> 101;

331 [label="INSTANCE with matching:\nT22 -> T336\nT21 -> .(T337, .(T338, .(T339, [])))", fontsize=14, style = filled, fillcolor = lightgrey];
100 -> 331 [arrowhead = none , style=dashed];
331 -> 12[style=dashed];

332 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
101 -> 332 [arrowhead = none ];
332 -> 102;

333 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
102 -> 333 [arrowhead = none ];
333 -> 103;

334 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
103 -> 334 [arrowhead = none ];
334 -> 104;

335 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 335 [arrowhead = none ];
335 -> 106;

336 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
107 -> 336 [arrowhead = none ];
336 -> 108;

337 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
107 -> 337 [arrowhead = none ];
337 -> 109;

338 [label="EVAL with clause\nsubsetchecked([], X368, X369).\nand substitution\nT295 -> []\nT294 -> T394\nT284 -> T395\nT285 -> T396\nT286 -> T397\nX368 -> .(T394, .(T395, .(T396, .(T397, []))))\nT287 -> T398\nX369 -> T398", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 338 [arrowhead = none ];
338 -> 110;

339 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
108 -> 339 [arrowhead = none ];
339 -> 111;

340 [label="EVAL with clause\nsubsetchecked(.(X380, X381), X382, X383) :- ','(member(X380, X383), ','(not_member(X380, X382), subsetchecked(X381, .(X380, X382), X383))).\nand substitution\nX380 -> T420\nX381 -> T421\nT295 -> .(T420, T421)\nT294 -> T415\nT284 -> T416\nT285 -> T417\nT286 -> T418\nX382 -> .(T415, .(T416, .(T417, .(T418, []))))\nT287 -> T419\nX383 -> T419\nT413 -> T420\nT414 -> T421", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 340 [arrowhead = none ];
340 -> 113;

341 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 341 [arrowhead = none ];
341 -> 114;

342 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 342 [arrowhead = none ];
342 -> 112;

343 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
113 -> 343 [arrowhead = none ];
343 -> 115;

344 [label="SPLIT 2\nnew knowledge:\nT426 is ground\nreplacements:\nT420 -> T426\nT421 -> T427", fontsize=14, style = filled, fillcolor = violet];
113 -> 344 [arrowhead = none ];
344 -> 116;

345 [label="INSTANCE with matching:\nT22 -> T420\nT21 -> T419", fontsize=14, style = filled, fillcolor = lightgrey];
115 -> 345 [arrowhead = none , style=dashed];
345 -> 12[style=dashed];

346 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
116 -> 346 [arrowhead = none ];
346 -> 117;

347 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
116 -> 347 [arrowhead = none ];
347 -> 118;

348 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
117 -> 348 [arrowhead = none ];
348 -> 119;

349 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
118 -> 349 [arrowhead = none ];
349 -> 130;

350 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
119 -> 350 [arrowhead = none ];
350 -> 120;

351 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
119 -> 351 [arrowhead = none ];
351 -> 121;

352 [label="ONLY EVAL with clause\nnot_member(X416, X417) :- ','(member(X416, X417), ','(!_17, failure(a))).\nand substitution\nT426 -> T478\nX416 -> T478\nT415 -> T479\nT416 -> T480\nT417 -> T481\nT418 -> T482\nX417 -> .(T479, .(T480, .(T481, .(T482, []))))", fontsize=14, style = filled, fillcolor = white];
120 -> 352 [arrowhead = none ];
352 -> 122;

353 [label="ONLY EVAL with clause\nnot_member(X430, X431).\nand substitution\nT426 -> T509\nX430 -> T509\nT415 -> T510\nT416 -> T511\nT417 -> T512\nT418 -> T513\nX431 -> .(T510, .(T511, .(T512, .(T513, []))))", fontsize=14, style = filled, fillcolor = white];
121 -> 353 [arrowhead = none ];
353 -> 128;

354 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
122 -> 354 [arrowhead = none ];
354 -> 123;

355 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
122 -> 355 [arrowhead = none ];
355 -> 124;

356 [label="INSTANCE with matching:\nT22 -> T478\nT21 -> .(T479, .(T480, .(T481, .(T482, []))))", fontsize=14, style = filled, fillcolor = lightgrey];
123 -> 356 [arrowhead = none , style=dashed];
356 -> 12[style=dashed];

357 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
124 -> 357 [arrowhead = none ];
357 -> 125;

358 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
125 -> 358 [arrowhead = none ];
358 -> 126;

359 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
126 -> 359 [arrowhead = none ];
359 -> 127;

360 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
128 -> 360 [arrowhead = none ];
360 -> 129;

361 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
130 -> 361 [arrowhead = none ];
361 -> 131;

362 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
130 -> 362 [arrowhead = none ];
362 -> 132;

363 [label="EVAL with clause\nsubsetchecked([], X444, X445).\nand substitution\nT427 -> []\nT426 -> T550\nT415 -> T551\nT416 -> T552\nT417 -> T553\nT418 -> T554\nX444 -> .(T550, .(T551, .(T552, .(T553, .(T554, [])))))\nT419 -> T555\nX445 -> T555", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 363 [arrowhead = none ];
363 -> 133;

364 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 364 [arrowhead = none ];
364 -> 134;

365 [label="EVAL with clause\nsubsetchecked(.(X456, X457), X458, X459) :- ','(member(X456, X459), ','(not_member(X456, X458), subsetchecked(X457, .(X456, X458), X459))).\nand substitution\nX456 -> T580\nX457 -> T581\nT427 -> .(T580, T581)\nT426 -> T574\nT415 -> T575\nT416 -> T576\nT417 -> T577\nT418 -> T578\nX458 -> .(T574, .(T575, .(T576, .(T577, .(T578, [])))))\nT419 -> T579\nX459 -> T579\nT572 -> T580\nT573 -> T581", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 365 [arrowhead = none ];
365 -> 136;

366 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
132 -> 366 [arrowhead = none ];
366 -> 137;

367 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
133 -> 367 [arrowhead = none ];
367 -> 135;

368 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
136 -> 368 [arrowhead = none ];
368 -> 138;

369 [label="SPLIT 2\nnew knowledge:\nT586 is ground\nreplacements:\nT580 -> T586\nT581 -> T587", fontsize=14, style = filled, fillcolor = violet];
136 -> 369 [arrowhead = none ];
369 -> 139;

370 [label="INSTANCE with matching:\nT22 -> T580\nT21 -> T579", fontsize=14, style = filled, fillcolor = lightgrey];
138 -> 370 [arrowhead = none , style=dashed];
370 -> 12[style=dashed];

371 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
139 -> 371 [arrowhead = none ];
371 -> 140;

372 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
139 -> 372 [arrowhead = none ];
372 -> 141;

373 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
140 -> 373 [arrowhead = none ];
373 -> 142;

374 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
141 -> 374 [arrowhead = none ];
374 -> 153;

375 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 375 [arrowhead = none ];
375 -> 143;

376 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
142 -> 376 [arrowhead = none ];
376 -> 144;

377 [label="ONLY EVAL with clause\nnot_member(X492, X493) :- ','(member(X492, X493), ','(!_20, failure(a))).\nand substitution\nT586 -> T648\nX492 -> T648\nT574 -> T649\nT575 -> T650\nT576 -> T651\nT577 -> T652\nT578 -> T653\nX493 -> .(T649, .(T650, .(T651, .(T652, .(T653, [])))))", fontsize=14, style = filled, fillcolor = white];
143 -> 377 [arrowhead = none ];
377 -> 145;

378 [label="ONLY EVAL with clause\nnot_member(X506, X507).\nand substitution\nT586 -> T686\nX506 -> T686\nT574 -> T687\nT575 -> T688\nT576 -> T689\nT577 -> T690\nT578 -> T691\nX507 -> .(T687, .(T688, .(T689, .(T690, .(T691, [])))))", fontsize=14, style = filled, fillcolor = white];
144 -> 378 [arrowhead = none ];
378 -> 151;

379 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
145 -> 379 [arrowhead = none ];
379 -> 146;

380 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
145 -> 380 [arrowhead = none ];
380 -> 147;

381 [label="INSTANCE with matching:\nT22 -> T648\nT21 -> .(T649, .(T650, .(T651, .(T652, .(T653, [])))))", fontsize=14, style = filled, fillcolor = lightgrey];
146 -> 381 [arrowhead = none , style=dashed];
381 -> 12[style=dashed];

382 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
147 -> 382 [arrowhead = none ];
382 -> 148;

383 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
148 -> 383 [arrowhead = none ];
383 -> 149;

384 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
149 -> 384 [arrowhead = none ];
384 -> 150;

385 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
151 -> 385 [arrowhead = none ];
385 -> 152;

386 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
153 -> 386 [arrowhead = none ];
386 -> 154;

387 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
153 -> 387 [arrowhead = none ];
387 -> 155;

388 [label="EVAL with clause\nsubsetchecked([], X520, X521).\nand substitution\nT587 -> []\nT586 -> T734\nT574 -> T735\nT575 -> T736\nT576 -> T737\nT577 -> T738\nT578 -> T739\nX520 -> .(T734, .(T735, .(T736, .(T737, .(T738, .(T739, []))))))\nT579 -> T740\nX521 -> T740", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 388 [arrowhead = none ];
388 -> 156;

389 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 389 [arrowhead = none ];
389 -> 157;

390 [label="EVAL with clause\nsubsetchecked(.(X532, X533), X534, X535) :- ','(member(X532, X535), ','(not_member(X532, X534), subsetchecked(X533, .(X532, X534), X535))).\nand substitution\nX532 -> T768\nX533 -> T769\nT587 -> .(T768, T769)\nT586 -> T761\nT574 -> T762\nT575 -> T763\nT576 -> T764\nT577 -> T765\nT578 -> T766\nX534 -> .(T761, .(T762, .(T763, .(T764, .(T765, .(T766, []))))))\nT579 -> T767\nX535 -> T767\nT759 -> T768\nT760 -> T769", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 390 [arrowhead = none ];
390 -> 159;

391 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
155 -> 391 [arrowhead = none ];
391 -> 160;

392 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
156 -> 392 [arrowhead = none ];
392 -> 158;

393 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
159 -> 393 [arrowhead = none ];
393 -> 161;

394 [label="SPLIT 2\nnew knowledge:\nT774 is ground\nreplacements:\nT768 -> T774\nT769 -> T775", fontsize=14, style = filled, fillcolor = violet];
159 -> 394 [arrowhead = none ];
394 -> 162;

395 [label="INSTANCE with matching:\nT22 -> T768\nT21 -> T767", fontsize=14, style = filled, fillcolor = lightgrey];
161 -> 395 [arrowhead = none , style=dashed];
395 -> 12[style=dashed];

396 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
162 -> 396 [arrowhead = none ];
396 -> 163;

397 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
162 -> 397 [arrowhead = none ];
397 -> 164;

398 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
163 -> 398 [arrowhead = none ];
398 -> 165;

399 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
164 -> 399 [arrowhead = none ];
399 -> 176;

400 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
165 -> 400 [arrowhead = none ];
400 -> 166;

401 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
165 -> 401 [arrowhead = none ];
401 -> 167;

402 [label="ONLY EVAL with clause\nnot_member(X568, X569) :- ','(member(X568, X569), ','(!_23, failure(a))).\nand substitution\nT774 -> T846\nX568 -> T846\nT761 -> T847\nT762 -> T848\nT763 -> T849\nT764 -> T850\nT765 -> T851\nT766 -> T852\nX569 -> .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, []))))))", fontsize=14, style = filled, fillcolor = white];
166 -> 402 [arrowhead = none ];
402 -> 168;

403 [label="ONLY EVAL with clause\nnot_member(X582, X583).\nand substitution\nT774 -> T891\nX582 -> T891\nT761 -> T892\nT762 -> T893\nT763 -> T894\nT764 -> T895\nT765 -> T896\nT766 -> T897\nX583 -> .(T892, .(T893, .(T894, .(T895, .(T896, .(T897, []))))))", fontsize=14, style = filled, fillcolor = white];
167 -> 403 [arrowhead = none ];
403 -> 174;

404 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
168 -> 404 [arrowhead = none ];
404 -> 169;

405 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
168 -> 405 [arrowhead = none ];
405 -> 170;

406 [label="INSTANCE with matching:\nT22 -> T846\nT21 -> .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, []))))))", fontsize=14, style = filled, fillcolor = lightgrey];
169 -> 406 [arrowhead = none , style=dashed];
406 -> 12[style=dashed];

407 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
170 -> 407 [arrowhead = none ];
407 -> 171;

408 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
171 -> 408 [arrowhead = none ];
408 -> 172;

409 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
172 -> 409 [arrowhead = none ];
409 -> 173;

410 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
174 -> 410 [arrowhead = none ];
410 -> 175;

411 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 411 [arrowhead = none ];
411 -> 177;

412 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
176 -> 412 [arrowhead = none ];
412 -> 178;

413 [label="EVAL with clause\nsubsetchecked([], X596, X597).\nand substitution\nT775 -> []\nT774 -> T946\nT761 -> T947\nT762 -> T948\nT763 -> T949\nT764 -> T950\nT765 -> T951\nT766 -> T952\nX596 -> .(T946, .(T947, .(T948, .(T949, .(T950, .(T951, .(T952, [])))))))\nT767 -> T953\nX597 -> T953", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 413 [arrowhead = none ];
413 -> 179;

414 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
177 -> 414 [arrowhead = none ];
414 -> 180;

415 [label="EVAL with clause\nsubsetchecked(.(X608, X609), X610, X611) :- ','(member(X608, X611), ','(not_member(X608, X610), subsetchecked(X609, .(X608, X610), X611))).\nand substitution\nX608 -> T984\nX609 -> T985\nT775 -> .(T984, T985)\nT774 -> T976\nT761 -> T977\nT762 -> T978\nT763 -> T979\nT764 -> T980\nT765 -> T981\nT766 -> T982\nX610 -> .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))\nT767 -> T983\nX611 -> T983\nT974 -> T984\nT975 -> T985", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 415 [arrowhead = none ];
415 -> 182;

416 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 416 [arrowhead = none ];
416 -> 183;

417 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
179 -> 417 [arrowhead = none ];
417 -> 181;

418 [label="GENERALIZATION\nT990 <-- .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))\n\nNew Knowledge:\nT990 is ground", fontsize=14, style = filled, fillcolor = violet];
182 -> 418 [arrowhead = none ];
418 -> 184;

419 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
184 -> 419 [arrowhead = none ];
419 -> 185;

420 [label="SPLIT 2\nnew knowledge:\nT995 is ground\nreplacements:\nT984 -> T995\nT985 -> T996", fontsize=14, style = filled, fillcolor = violet];
184 -> 420 [arrowhead = none ];
420 -> 186;

421 [label="INSTANCE with matching:\nT22 -> T984\nT21 -> T983", fontsize=14, style = filled, fillcolor = lightgrey];
185 -> 421 [arrowhead = none , style=dashed];
421 -> 12[style=dashed];

422 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
186 -> 422 [arrowhead = none ];
422 -> 187;

423 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
186 -> 423 [arrowhead = none ];
423 -> 188;

424 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
187 -> 424 [arrowhead = none ];
424 -> 189;

425 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
188 -> 425 [arrowhead = none ];
425 -> 200;

426 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
189 -> 426 [arrowhead = none ];
426 -> 190;

427 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
189 -> 427 [arrowhead = none ];
427 -> 191;

428 [label="ONLY EVAL with clause\nnot_member(X648, X649) :- ','(member(X648, X649), ','(!_26, failure(a))).\nand substitution\nT995 -> T1077\nX648 -> T1077\nT976 -> T1078\nT977 -> T1079\nT978 -> T1080\nT979 -> T1081\nT980 -> T1082\nT981 -> T1083\nT982 -> T1084\nX649 -> .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, [])))))))", fontsize=14, style = filled, fillcolor = white];
190 -> 428 [arrowhead = none ];
428 -> 192;

429 [label="ONLY EVAL with clause\nnot_member(X662, X663).\nand substitution\nT995 -> T1129\nX662 -> T1129\nT976 -> T1130\nT977 -> T1131\nT978 -> T1132\nT979 -> T1133\nT980 -> T1134\nT981 -> T1135\nT982 -> T1136\nX663 -> .(T1130, .(T1131, .(T1132, .(T1133, .(T1134, .(T1135, .(T1136, [])))))))", fontsize=14, style = filled, fillcolor = white];
191 -> 429 [arrowhead = none ];
429 -> 198;

430 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
192 -> 430 [arrowhead = none ];
430 -> 193;

431 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
192 -> 431 [arrowhead = none ];
431 -> 194;

432 [label="INSTANCE with matching:\nT22 -> T1077\nT21 -> .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, [])))))))", fontsize=14, style = filled, fillcolor = lightgrey];
193 -> 432 [arrowhead = none , style=dashed];
432 -> 12[style=dashed];

433 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
194 -> 433 [arrowhead = none ];
433 -> 195;

434 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
195 -> 434 [arrowhead = none ];
434 -> 196;

435 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
196 -> 435 [arrowhead = none ];
435 -> 197;

436 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
198 -> 436 [arrowhead = none ];
436 -> 199;

437 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
200 -> 437 [arrowhead = none ];
437 -> 201;

438 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
200 -> 438 [arrowhead = none ];
438 -> 202;

439 [label="EVAL with clause\nsubsetchecked([], X676, X677).\nand substitution\nT996 -> []\nT995 -> T1155\nT990 -> T1156\nX676 -> .(T1155, T1156)\nT983 -> T1157\nX677 -> T1157", fontsize=14, style = filled, fillcolor = lightblue];
201 -> 439 [arrowhead = none ];
439 -> 203;

440 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
201 -> 440 [arrowhead = none ];
440 -> 204;

441 [label="EVAL with clause\nsubsetchecked(.(X688, X689), X690, X691) :- ','(member(X688, X691), ','(not_member(X688, X690), subsetchecked(X689, .(X688, X690), X691))).\nand substitution\nX688 -> T1173\nX689 -> T1174\nT996 -> .(T1173, T1174)\nT995 -> T1170\nT990 -> T1171\nX690 -> .(T1170, T1171)\nT983 -> T1172\nX691 -> T1172\nT1168 -> T1173\nT1169 -> T1174", fontsize=14, style = filled, fillcolor = lightblue];
202 -> 441 [arrowhead = none ];
441 -> 206;

442 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightblue];
202 -> 442 [arrowhead = none ];
442 -> 207;

443 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
203 -> 443 [arrowhead = none ];
443 -> 205;

444 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
206 -> 444 [arrowhead = none ];
444 -> 208;

445 [label="SPLIT 2\nnew knowledge:\nT1179 is ground\nreplacements:\nT1173 -> T1179\nT1174 -> T1180", fontsize=14, style = filled, fillcolor = violet];
206 -> 445 [arrowhead = none ];
445 -> 209;

446 [label="INSTANCE with matching:\nT22 -> T1173\nT21 -> T1172", fontsize=14, style = filled, fillcolor = lightgrey];
208 -> 446 [arrowhead = none , style=dashed];
446 -> 12[style=dashed];

447 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
209 -> 447 [arrowhead = none ];
447 -> 210;

448 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
209 -> 448 [arrowhead = none ];
448 -> 211;

449 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
210 -> 449 [arrowhead = none ];
449 -> 212;

450 [label="INSTANCE with matching:\nT996 -> T1180\nT995 -> T1179\nT990 -> .(T1170, T1171)\nT983 -> T1172", fontsize=14, style = filled, fillcolor = lightgrey];
211 -> 450 [arrowhead = none , style=dashed];
450 -> 188[style=dashed];

451 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
212 -> 451 [arrowhead = none ];
451 -> 213;

452 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
212 -> 452 [arrowhead = none ];
452 -> 214;

453 [label="ONLY EVAL with clause\nnot_member(X724, X725) :- ','(member(X724, X725), ','(!_29, failure(a))).\nand substitution\nT1179 -> T1211\nX724 -> T1211\nT1170 -> T1212\nT1171 -> T1213\nX725 -> .(T1212, T1213)", fontsize=14, style = filled, fillcolor = white];
213 -> 453 [arrowhead = none ];
453 -> 215;

454 [label="ONLY EVAL with clause\nnot_member(X738, X739).\nand substitution\nT1179 -> T1228\nX738 -> T1228\nT1170 -> T1229\nT1171 -> T1230\nX739 -> .(T1229, T1230)", fontsize=14, style = filled, fillcolor = white];
214 -> 454 [arrowhead = none ];
454 -> 221;

455 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
215 -> 455 [arrowhead = none ];
455 -> 216;

456 [label="SPLIT 2", fontsize=14, style = filled, fillcolor = violet];
215 -> 456 [arrowhead = none ];
456 -> 217;

457 [label="INSTANCE with matching:\nT22 -> T1211\nT21 -> .(T1212, T1213)", fontsize=14, style = filled, fillcolor = lightgrey];
216 -> 457 [arrowhead = none , style=dashed];
457 -> 12[style=dashed];

458 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
217 -> 458 [arrowhead = none ];
458 -> 218;

459 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
218 -> 459 [arrowhead = none ];
459 -> 219;

460 [label="BACKTRACK\nfor clause: failure(b)because of non-unification", fontsize=14, style = filled, fillcolor = white];
219 -> 460 [arrowhead = none ];
460 -> 220;

461 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
221 -> 461 [arrowhead = none ];
461 -> 222;

}

(2) Obligation:

Triples:

member12(T53, .(T51, T52)) :- member12(T53, T52).
subsetchecked188(.(T1173, T1174), T1170, T1171, T1172) :- member12(T1173, T1172).
subsetchecked188(.(T1211, T1180), T1212, T1213, T1172) :- ','(memberc12(T1211, T1172), member12(T1211, .(T1212, T1213))).
subsetchecked188(.(T1179, T1180), T1170, T1171, T1172) :- ','(memberc12(T1179, T1172), ','(not_memberc210(T1179, T1170, T1171), subsetchecked188(T1180, T1179, .(T1170, T1171), T1172))).
p184(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, T990) :- member12(T984, T983).
p184(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990) :- ','(memberc12(T1077, T983), member12(T1077, .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, []))))))))).
p184(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990) :- ','(memberc12(T995, T983), ','(not_memberc187(T995, T976, T977, T978, T979, T980, T981, T982), subsetchecked188(T996, T995, T990, T983))).
subset1(.(T22, T23), T21) :- member12(T22, T21).
subset1(.(T106, .(T108, T109)), T107) :- ','(memberc12(T106, T107), ','(not_memberc22(T106), member12(T108, T107))).
subset1(.(T137, .(T136, T115)), T107) :- ','(memberc12(T137, T107), ','(not_memberc22(T137), ','(memberc12(T136, T107), member12(T136, .(T137, []))))).
subset1(.(T182, .(T181, .(T184, T185))), T183) :- ','(memberc12(T182, T183), ','(not_memberc22(T182), ','(memberc12(T181, T183), ','(not_memberc48(T181, T182), member12(T184, T183))))).
subset1(.(T224, .(T223, .(T222, T191))), T183) :- ','(memberc12(T224, T183), ','(not_memberc22(T224), ','(memberc12(T223, T183), ','(not_memberc48(T223, T224), ','(memberc12(T222, T183), member12(T222, .(T223, .(T224, [])))))))).
subset1(.(T286, .(T285, .(T284, .(T288, T289)))), T287) :- ','(memberc12(T286, T287), ','(not_memberc22(T286), ','(memberc12(T285, T287), ','(not_memberc48(T285, T286), ','(memberc12(T284, T287), ','(not_memberc71(T284, T285, T286), member12(T288, T287))))))).
subset1(.(T339, .(T338, .(T337, .(T336, T295)))), T287) :- ','(memberc12(T339, T287), ','(not_memberc22(T339), ','(memberc12(T338, T287), ','(not_memberc48(T338, T339), ','(memberc12(T337, T287), ','(not_memberc71(T337, T338, T339), ','(memberc12(T336, T287), member12(T336, .(T337, .(T338, .(T339, []))))))))))).
subset1(.(T418, .(T417, .(T416, .(T415, .(T420, T421))))), T419) :- ','(memberc12(T418, T419), ','(not_memberc22(T418), ','(memberc12(T417, T419), ','(not_memberc48(T417, T418), ','(memberc12(T416, T419), ','(not_memberc71(T416, T417, T418), ','(memberc12(T415, T419), ','(not_memberc94(T415, T416, T417, T418), member12(T420, T419))))))))).
subset1(.(T482, .(T481, .(T480, .(T479, .(T478, T427))))), T419) :- ','(memberc12(T482, T419), ','(not_memberc22(T482), ','(memberc12(T481, T419), ','(not_memberc48(T481, T482), ','(memberc12(T480, T419), ','(not_memberc71(T480, T481, T482), ','(memberc12(T479, T419), ','(not_memberc94(T479, T480, T481, T482), ','(memberc12(T478, T419), member12(T478, .(T479, .(T480, .(T481, .(T482, [])))))))))))))).
subset1(.(T578, .(T577, .(T576, .(T575, .(T574, .(T580, T581)))))), T579) :- ','(memberc12(T578, T579), ','(not_memberc22(T578), ','(memberc12(T577, T579), ','(not_memberc48(T577, T578), ','(memberc12(T576, T579), ','(not_memberc71(T576, T577, T578), ','(memberc12(T575, T579), ','(not_memberc94(T575, T576, T577, T578), ','(memberc12(T574, T579), ','(not_memberc117(T574, T575, T576, T577, T578), member12(T580, T579))))))))))).
subset1(.(T653, .(T652, .(T651, .(T650, .(T649, .(T648, T587)))))), T579) :- ','(memberc12(T653, T579), ','(not_memberc22(T653), ','(memberc12(T652, T579), ','(not_memberc48(T652, T653), ','(memberc12(T651, T579), ','(not_memberc71(T651, T652, T653), ','(memberc12(T650, T579), ','(not_memberc94(T650, T651, T652, T653), ','(memberc12(T649, T579), ','(not_memberc117(T649, T650, T651, T652, T653), ','(memberc12(T648, T579), member12(T648, .(T649, .(T650, .(T651, .(T652, .(T653, []))))))))))))))))).
subset1(.(T766, .(T765, .(T764, .(T763, .(T762, .(T761, .(T768, T769))))))), T767) :- ','(memberc12(T766, T767), ','(not_memberc22(T766), ','(memberc12(T765, T767), ','(not_memberc48(T765, T766), ','(memberc12(T764, T767), ','(not_memberc71(T764, T765, T766), ','(memberc12(T763, T767), ','(not_memberc94(T763, T764, T765, T766), ','(memberc12(T762, T767), ','(not_memberc117(T762, T763, T764, T765, T766), ','(memberc12(T761, T767), ','(not_memberc140(T761, T762, T763, T764, T765, T766), member12(T768, T767))))))))))))).
subset1(.(T852, .(T851, .(T850, .(T849, .(T848, .(T847, .(T846, T775))))))), T767) :- ','(memberc12(T852, T767), ','(not_memberc22(T852), ','(memberc12(T851, T767), ','(not_memberc48(T851, T852), ','(memberc12(T850, T767), ','(not_memberc71(T850, T851, T852), ','(memberc12(T849, T767), ','(not_memberc94(T849, T850, T851, T852), ','(memberc12(T848, T767), ','(not_memberc117(T848, T849, T850, T851, T852), ','(memberc12(T847, T767), ','(not_memberc140(T847, T848, T849, T850, T851, T852), ','(memberc12(T846, T767), member12(T846, .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, [])))))))))))))))))))).
subset1(.(T982, .(T981, .(T980, .(T979, .(T978, .(T977, .(T976, .(T984, T985)))))))), T983) :- ','(memberc12(T982, T983), ','(not_memberc22(T982), ','(memberc12(T981, T983), ','(not_memberc48(T981, T982), ','(memberc12(T980, T983), ','(not_memberc71(T980, T981, T982), ','(memberc12(T979, T983), ','(not_memberc94(T979, T980, T981, T982), ','(memberc12(T978, T983), ','(not_memberc117(T978, T979, T980, T981, T982), ','(memberc12(T977, T983), ','(not_memberc140(T977, T978, T979, T980, T981, T982), ','(memberc12(T976, T983), ','(not_memberc163(T976, T977, T978, T979, T980, T981, T982), p184(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))))))))))))))))).

Clauses:

memberc12(T42, .(T42, T43)).
memberc12(T53, .(T51, T52)) :- memberc12(T53, T52).
subsetcheckedc188([], T1155, T1156, T1157).
subsetcheckedc188(.(T1179, T1180), T1170, T1171, T1172) :- ','(memberc12(T1179, T1172), ','(not_memberc210(T1179, T1170, T1171), subsetcheckedc188(T1180, T1179, .(T1170, T1171), T1172))).
qc184(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990) :- ','(memberc12(T995, T983), ','(not_memberc187(T995, T976, T977, T978, T979, T980, T981, T982), subsetcheckedc188(T996, T995, T990, T983))).
not_memberc22(T81).
not_memberc48(T146, T147).
not_memberc71(T239, T240, T241).
not_memberc94(T360, T361, T362, T363).
not_memberc117(T509, T510, T511, T512, T513).
not_memberc140(T686, T687, T688, T689, T690, T691).
not_memberc163(T891, T892, T893, T894, T895, T896, T897).
not_memberc187(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136).
not_memberc210(T1228, T1229, T1230).

Afs:

subset1(x1, x2) = subset1(x2)

(3) TriplesToPiDPProof (SOUND transformation)

We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:
subset1_in: (f,b)
member12_in: (f,b) (b,b)
memberc12_in: (f,b)
p184_in: (f,b,b,b,b,b,b,b,b,f,b)
subsetchecked188_in: (f,b,b,b)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:

SUBSET1_IN_AG(.(T22, T23), T21) → U14_AG(T22, T23, T21, member12_in_ag(T22, T21))
SUBSET1_IN_AG(.(T22, T23), T21) → MEMBER12_IN_AG(T22, T21)
MEMBER12_IN_AG(T53, .(T51, T52)) → U1_AG(T53, T51, T52, member12_in_ag(T53, T52))
MEMBER12_IN_AG(T53, .(T51, T52)) → MEMBER12_IN_AG(T53, T52)
SUBSET1_IN_AG(.(T106, .(T108, T109)), T107) → U15_AG(T106, T108, T109, T107, memberc12_in_ag(T106, T107))
U15_AG(T106, T108, T109, T107, memberc12_out_ag(T106, T107)) → U16_AG(T106, T108, T109, T107, not_memberc22_in_g(T106))
U16_AG(T106, T108, T109, T107, not_memberc22_out_g(T106)) → U17_AG(T106, T108, T109, T107, member12_in_ag(T108, T107))
U16_AG(T106, T108, T109, T107, not_memberc22_out_g(T106)) → MEMBER12_IN_AG(T108, T107)
SUBSET1_IN_AG(.(T137, .(T136, T115)), T107) → U18_AG(T137, T136, T115, T107, memberc12_in_ag(T137, T107))
U18_AG(T137, T136, T115, T107, memberc12_out_ag(T137, T107)) → U19_AG(T137, T136, T115, T107, not_memberc22_in_g(T137))
U19_AG(T137, T136, T115, T107, not_memberc22_out_g(T137)) → U20_AG(T137, T136, T115, T107, memberc12_in_ag(T136, T107))
U20_AG(T137, T136, T115, T107, memberc12_out_ag(T136, T107)) → U21_AG(T137, T136, T115, T107, member12_in_gg(T136, .(T137, [])))
U20_AG(T137, T136, T115, T107, memberc12_out_ag(T136, T107)) → MEMBER12_IN_GG(T136, .(T137, []))
MEMBER12_IN_GG(T53, .(T51, T52)) → U1_GG(T53, T51, T52, member12_in_gg(T53, T52))
MEMBER12_IN_GG(T53, .(T51, T52)) → MEMBER12_IN_GG(T53, T52)
SUBSET1_IN_AG(.(T182, .(T181, .(T184, T185))), T183) → U22_AG(T182, T181, T184, T185, T183, memberc12_in_ag(T182, T183))
U22_AG(T182, T181, T184, T185, T183, memberc12_out_ag(T182, T183)) → U23_AG(T182, T181, T184, T185, T183, not_memberc22_in_g(T182))
U23_AG(T182, T181, T184, T185, T183, not_memberc22_out_g(T182)) → U24_AG(T182, T181, T184, T185, T183, memberc12_in_ag(T181, T183))
U24_AG(T182, T181, T184, T185, T183, memberc12_out_ag(T181, T183)) → U25_AG(T182, T181, T184, T185, T183, not_memberc48_in_gg(T181, T182))
U25_AG(T182, T181, T184, T185, T183, not_memberc48_out_gg(T181, T182)) → U26_AG(T182, T181, T184, T185, T183, member12_in_ag(T184, T183))
U25_AG(T182, T181, T184, T185, T183, not_memberc48_out_gg(T181, T182)) → MEMBER12_IN_AG(T184, T183)
SUBSET1_IN_AG(.(T224, .(T223, .(T222, T191))), T183) → U27_AG(T224, T223, T222, T191, T183, memberc12_in_ag(T224, T183))
U27_AG(T224, T223, T222, T191, T183, memberc12_out_ag(T224, T183)) → U28_AG(T224, T223, T222, T191, T183, not_memberc22_in_g(T224))
U28_AG(T224, T223, T222, T191, T183, not_memberc22_out_g(T224)) → U29_AG(T224, T223, T222, T191, T183, memberc12_in_ag(T223, T183))
U29_AG(T224, T223, T222, T191, T183, memberc12_out_ag(T223, T183)) → U30_AG(T224, T223, T222, T191, T183, not_memberc48_in_gg(T223, T224))
U30_AG(T224, T223, T222, T191, T183, not_memberc48_out_gg(T223, T224)) → U31_AG(T224, T223, T222, T191, T183, memberc12_in_ag(T222, T183))
U31_AG(T224, T223, T222, T191, T183, memberc12_out_ag(T222, T183)) → U32_AG(T224, T223, T222, T191, T183, member12_in_gg(T222, .(T223, .(T224, []))))
U31_AG(T224, T223, T222, T191, T183, memberc12_out_ag(T222, T183)) → MEMBER12_IN_GG(T222, .(T223, .(T224, [])))
SUBSET1_IN_AG(.(T286, .(T285, .(T284, .(T288, T289)))), T287) → U33_AG(T286, T285, T284, T288, T289, T287, memberc12_in_ag(T286, T287))
U33_AG(T286, T285, T284, T288, T289, T287, memberc12_out_ag(T286, T287)) → U34_AG(T286, T285, T284, T288, T289, T287, not_memberc22_in_g(T286))
U34_AG(T286, T285, T284, T288, T289, T287, not_memberc22_out_g(T286)) → U35_AG(T286, T285, T284, T288, T289, T287, memberc12_in_ag(T285, T287))
U35_AG(T286, T285, T284, T288, T289, T287, memberc12_out_ag(T285, T287)) → U36_AG(T286, T285, T284, T288, T289, T287, not_memberc48_in_gg(T285, T286))
U36_AG(T286, T285, T284, T288, T289, T287, not_memberc48_out_gg(T285, T286)) → U37_AG(T286, T285, T284, T288, T289, T287, memberc12_in_ag(T284, T287))
U37_AG(T286, T285, T284, T288, T289, T287, memberc12_out_ag(T284, T287)) → U38_AG(T286, T285, T284, T288, T289, T287, not_memberc71_in_ggg(T284, T285, T286))
U38_AG(T286, T285, T284, T288, T289, T287, not_memberc71_out_ggg(T284, T285, T286)) → U39_AG(T286, T285, T284, T288, T289, T287, member12_in_ag(T288, T287))
U38_AG(T286, T285, T284, T288, T289, T287, not_memberc71_out_ggg(T284, T285, T286)) → MEMBER12_IN_AG(T288, T287)
SUBSET1_IN_AG(.(T339, .(T338, .(T337, .(T336, T295)))), T287) → U40_AG(T339, T338, T337, T336, T295, T287, memberc12_in_ag(T339, T287))
U40_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T339, T287)) → U41_AG(T339, T338, T337, T336, T295, T287, not_memberc22_in_g(T339))
U41_AG(T339, T338, T337, T336, T295, T287, not_memberc22_out_g(T339)) → U42_AG(T339, T338, T337, T336, T295, T287, memberc12_in_ag(T338, T287))
U42_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T338, T287)) → U43_AG(T339, T338, T337, T336, T295, T287, not_memberc48_in_gg(T338, T339))
U43_AG(T339, T338, T337, T336, T295, T287, not_memberc48_out_gg(T338, T339)) → U44_AG(T339, T338, T337, T336, T295, T287, memberc12_in_ag(T337, T287))
U44_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T337, T287)) → U45_AG(T339, T338, T337, T336, T295, T287, not_memberc71_in_ggg(T337, T338, T339))
U45_AG(T339, T338, T337, T336, T295, T287, not_memberc71_out_ggg(T337, T338, T339)) → U46_AG(T339, T338, T337, T336, T295, T287, memberc12_in_ag(T336, T287))
U46_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T336, T287)) → U47_AG(T339, T338, T337, T336, T295, T287, member12_in_gg(T336, .(T337, .(T338, .(T339, [])))))
U46_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T336, T287)) → MEMBER12_IN_GG(T336, .(T337, .(T338, .(T339, []))))
SUBSET1_IN_AG(.(T418, .(T417, .(T416, .(T415, .(T420, T421))))), T419) → U48_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_in_ag(T418, T419))
U48_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_out_ag(T418, T419)) → U49_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc22_in_g(T418))
U49_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc22_out_g(T418)) → U50_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_in_ag(T417, T419))
U50_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_out_ag(T417, T419)) → U51_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc48_in_gg(T417, T418))
U51_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc48_out_gg(T417, T418)) → U52_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_in_ag(T416, T419))
U52_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_out_ag(T416, T419)) → U53_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc71_in_ggg(T416, T417, T418))
U53_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc71_out_ggg(T416, T417, T418)) → U54_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_in_ag(T415, T419))
U54_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_out_ag(T415, T419)) → U55_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc94_in_gggg(T415, T416, T417, T418))
U55_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc94_out_gggg(T415, T416, T417, T418)) → U56_AG(T418, T417, T416, T415, T420, T421, T419, member12_in_ag(T420, T419))
U55_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc94_out_gggg(T415, T416, T417, T418)) → MEMBER12_IN_AG(T420, T419)
SUBSET1_IN_AG(.(T482, .(T481, .(T480, .(T479, .(T478, T427))))), T419) → U57_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T482, T419))
U57_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T482, T419)) → U58_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc22_in_g(T482))
U58_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc22_out_g(T482)) → U59_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T481, T419))
U59_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T481, T419)) → U60_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc48_in_gg(T481, T482))
U60_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc48_out_gg(T481, T482)) → U61_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T480, T419))
U61_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T480, T419)) → U62_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc71_in_ggg(T480, T481, T482))
U62_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc71_out_ggg(T480, T481, T482)) → U63_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T479, T419))
U63_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T479, T419)) → U64_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc94_in_gggg(T479, T480, T481, T482))
U64_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc94_out_gggg(T479, T480, T481, T482)) → U65_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T478, T419))
U65_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T478, T419)) → U66_AG(T482, T481, T480, T479, T478, T427, T419, member12_in_gg(T478, .(T479, .(T480, .(T481, .(T482, []))))))
U65_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T478, T419)) → MEMBER12_IN_GG(T478, .(T479, .(T480, .(T481, .(T482, [])))))
SUBSET1_IN_AG(.(T578, .(T577, .(T576, .(T575, .(T574, .(T580, T581)))))), T579) → U67_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T578, T579))
U67_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T578, T579)) → U68_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc22_in_g(T578))
U68_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc22_out_g(T578)) → U69_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T577, T579))
U69_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T577, T579)) → U70_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc48_in_gg(T577, T578))
U70_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc48_out_gg(T577, T578)) → U71_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T576, T579))
U71_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T576, T579)) → U72_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc71_in_ggg(T576, T577, T578))
U72_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc71_out_ggg(T576, T577, T578)) → U73_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T575, T579))
U73_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T575, T579)) → U74_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc94_in_gggg(T575, T576, T577, T578))
U74_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc94_out_gggg(T575, T576, T577, T578)) → U75_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T574, T579))
U75_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T574, T579)) → U76_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc117_in_ggggg(T574, T575, T576, T577, T578))
U76_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc117_out_ggggg(T574, T575, T576, T577, T578)) → U77_AG(T578, T577, T576, T575, T574, T580, T581, T579, member12_in_ag(T580, T579))
U76_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc117_out_ggggg(T574, T575, T576, T577, T578)) → MEMBER12_IN_AG(T580, T579)
SUBSET1_IN_AG(.(T653, .(T652, .(T651, .(T650, .(T649, .(T648, T587)))))), T579) → U78_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T653, T579))
U78_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T653, T579)) → U79_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc22_in_g(T653))
U79_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc22_out_g(T653)) → U80_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T652, T579))
U80_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T652, T579)) → U81_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc48_in_gg(T652, T653))
U81_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc48_out_gg(T652, T653)) → U82_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T651, T579))
U82_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T651, T579)) → U83_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc71_in_ggg(T651, T652, T653))
U83_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc71_out_ggg(T651, T652, T653)) → U84_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T650, T579))
U84_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T650, T579)) → U85_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc94_in_gggg(T650, T651, T652, T653))
U85_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc94_out_gggg(T650, T651, T652, T653)) → U86_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T649, T579))
U86_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T649, T579)) → U87_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc117_in_ggggg(T649, T650, T651, T652, T653))
U87_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc117_out_ggggg(T649, T650, T651, T652, T653)) → U88_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T648, T579))
U88_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T648, T579)) → U89_AG(T653, T652, T651, T650, T649, T648, T587, T579, member12_in_gg(T648, .(T649, .(T650, .(T651, .(T652, .(T653, [])))))))
U88_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T648, T579)) → MEMBER12_IN_GG(T648, .(T649, .(T650, .(T651, .(T652, .(T653, []))))))
SUBSET1_IN_AG(.(T766, .(T765, .(T764, .(T763, .(T762, .(T761, .(T768, T769))))))), T767) → U90_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T766, T767))
U90_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T766, T767)) → U91_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc22_in_g(T766))
U91_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc22_out_g(T766)) → U92_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T765, T767))
U92_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T765, T767)) → U93_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc48_in_gg(T765, T766))
U93_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc48_out_gg(T765, T766)) → U94_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T764, T767))
U94_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T764, T767)) → U95_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc71_in_ggg(T764, T765, T766))
U95_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc71_out_ggg(T764, T765, T766)) → U96_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T763, T767))
U96_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T763, T767)) → U97_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc94_in_gggg(T763, T764, T765, T766))
U97_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc94_out_gggg(T763, T764, T765, T766)) → U98_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T762, T767))
U98_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T762, T767)) → U99_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc117_in_ggggg(T762, T763, T764, T765, T766))
U99_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc117_out_ggggg(T762, T763, T764, T765, T766)) → U100_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T761, T767))
U100_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T761, T767)) → U101_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc140_in_gggggg(T761, T762, T763, T764, T765, T766))
U101_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc140_out_gggggg(T761, T762, T763, T764, T765, T766)) → U102_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, member12_in_ag(T768, T767))
U101_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc140_out_gggggg(T761, T762, T763, T764, T765, T766)) → MEMBER12_IN_AG(T768, T767)
SUBSET1_IN_AG(.(T852, .(T851, .(T850, .(T849, .(T848, .(T847, .(T846, T775))))))), T767) → U103_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T852, T767))
U103_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T852, T767)) → U104_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc22_in_g(T852))
U104_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc22_out_g(T852)) → U105_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T851, T767))
U105_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T851, T767)) → U106_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc48_in_gg(T851, T852))
U106_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc48_out_gg(T851, T852)) → U107_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T850, T767))
U107_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T850, T767)) → U108_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc71_in_ggg(T850, T851, T852))
U108_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc71_out_ggg(T850, T851, T852)) → U109_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T849, T767))
U109_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T849, T767)) → U110_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc94_in_gggg(T849, T850, T851, T852))
U110_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc94_out_gggg(T849, T850, T851, T852)) → U111_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T848, T767))
U111_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T848, T767)) → U112_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc117_in_ggggg(T848, T849, T850, T851, T852))
U112_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc117_out_ggggg(T848, T849, T850, T851, T852)) → U113_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T847, T767))
U113_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T847, T767)) → U114_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc140_in_gggggg(T847, T848, T849, T850, T851, T852))
U114_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc140_out_gggggg(T847, T848, T849, T850, T851, T852)) → U115_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T846, T767))
U115_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T846, T767)) → U116_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, member12_in_gg(T846, .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, []))))))))
U115_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T846, T767)) → MEMBER12_IN_GG(T846, .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, [])))))))
SUBSET1_IN_AG(.(T982, .(T981, .(T980, .(T979, .(T978, .(T977, .(T976, .(T984, T985)))))))), T983) → U117_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T982, T983))
U117_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T982, T983)) → U118_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc22_in_g(T982))
U118_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc22_out_g(T982)) → U119_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T981, T983))
U119_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T981, T983)) → U120_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc48_in_gg(T981, T982))
U120_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc48_out_gg(T981, T982)) → U121_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T980, T983))
U121_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T980, T983)) → U122_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc71_in_ggg(T980, T981, T982))
U122_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc71_out_ggg(T980, T981, T982)) → U123_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T979, T983))
U123_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T979, T983)) → U124_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc94_in_gggg(T979, T980, T981, T982))
U124_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc94_out_gggg(T979, T980, T981, T982)) → U125_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T978, T983))
U125_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T978, T983)) → U126_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc117_in_ggggg(T978, T979, T980, T981, T982))
U126_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc117_out_ggggg(T978, T979, T980, T981, T982)) → U127_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T977, T983))
U127_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T977, T983)) → U128_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc140_in_gggggg(T977, T978, T979, T980, T981, T982))
U128_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc140_out_gggggg(T977, T978, T979, T980, T981, T982)) → U129_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T976, T983))
U129_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T976, T983)) → U130_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc163_in_ggggggg(T976, T977, T978, T979, T980, T981, T982))
U130_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc163_out_ggggggg(T976, T977, T978, T979, T980, T981, T982)) → U131_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, p184_in_aggggggggag(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))))
U130_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc163_out_ggggggg(T976, T977, T978, T979, T980, T981, T982)) → P184_IN_AGGGGGGGGAG(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, []))))))))
P184_IN_AGGGGGGGGAG(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, T990) → U8_AGGGGGGGGAG(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, T990, member12_in_ag(T984, T983))
P184_IN_AGGGGGGGGAG(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, T990) → MEMBER12_IN_AG(T984, T983)
P184_IN_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990) → U9_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990, memberc12_in_ag(T1077, T983))
U9_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990, memberc12_out_ag(T1077, T983)) → U10_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990, member12_in_gg(T1077, .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, [])))))))))
U9_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990, memberc12_out_ag(T1077, T983)) → MEMBER12_IN_GG(T1077, .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, []))))))))
P184_IN_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990) → U11_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, memberc12_in_ag(T995, T983))
U11_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, memberc12_out_ag(T995, T983)) → U12_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, not_memberc187_in_gggggggg(T995, T976, T977, T978, T979, T980, T981, T982))
U12_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, not_memberc187_out_gggggggg(T995, T976, T977, T978, T979, T980, T981, T982)) → U13_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, subsetchecked188_in_aggg(T996, T995, T990, T983))
U12_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, not_memberc187_out_gggggggg(T995, T976, T977, T978, T979, T980, T981, T982)) → SUBSETCHECKED188_IN_AGGG(T996, T995, T990, T983)
SUBSETCHECKED188_IN_AGGG(.(T1173, T1174), T1170, T1171, T1172) → U2_AGGG(T1173, T1174, T1170, T1171, T1172, member12_in_ag(T1173, T1172))
SUBSETCHECKED188_IN_AGGG(.(T1173, T1174), T1170, T1171, T1172) → MEMBER12_IN_AG(T1173, T1172)
SUBSETCHECKED188_IN_AGGG(.(T1211, T1180), T1212, T1213, T1172) → U3_AGGG(T1211, T1180, T1212, T1213, T1172, memberc12_in_ag(T1211, T1172))
U3_AGGG(T1211, T1180, T1212, T1213, T1172, memberc12_out_ag(T1211, T1172)) → U4_AGGG(T1211, T1180, T1212, T1213, T1172, member12_in_gg(T1211, .(T1212, T1213)))
U3_AGGG(T1211, T1180, T1212, T1213, T1172, memberc12_out_ag(T1211, T1172)) → MEMBER12_IN_GG(T1211, .(T1212, T1213))
SUBSETCHECKED188_IN_AGGG(.(T1179, T1180), T1170, T1171, T1172) → U5_AGGG(T1179, T1180, T1170, T1171, T1172, memberc12_in_ag(T1179, T1172))
U5_AGGG(T1179, T1180, T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_in_ggg(T1179, T1170, T1171))
U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → U7_AGGG(T1179, T1180, T1170, T1171, T1172, subsetchecked188_in_aggg(T1180, T1179, .(T1170, T1171), T1172))
U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1180, T1179, .(T1170, T1171), T1172)

The TRS R consists of the following rules:

memberc12_in_ag(T42, .(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(T53, .(T51, T52)) → U133_ag(T53, T51, T52, memberc12_in_ag(T53, T52))
U133_ag(T53, T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))
not_memberc22_in_g(T81) → not_memberc22_out_g(T81)
not_memberc48_in_gg(T146, T147) → not_memberc48_out_gg(T146, T147)
not_memberc71_in_ggg(T239, T240, T241) → not_memberc71_out_ggg(T239, T240, T241)
not_memberc94_in_gggg(T360, T361, T362, T363) → not_memberc94_out_gggg(T360, T361, T362, T363)
not_memberc117_in_ggggg(T509, T510, T511, T512, T513) → not_memberc117_out_ggggg(T509, T510, T511, T512, T513)
not_memberc140_in_gggggg(T686, T687, T688, T689, T690, T691) → not_memberc140_out_gggggg(T686, T687, T688, T689, T690, T691)
not_memberc163_in_ggggggg(T891, T892, T893, T894, T895, T896, T897) → not_memberc163_out_ggggggg(T891, T892, T893, T894, T895, T896, T897)
not_memberc187_in_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136) → not_memberc187_out_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136)
not_memberc210_in_ggg(T1228, T1229, T1230) → not_memberc210_out_ggg(T1228, T1229, T1230)

The argument filtering Pi contains the following mapping:
member12_in_ag(x1, x2) = member12_in_ag(x2)
.(x1, x2) = .(x1, x2)
memberc12_in_ag(x1, x2) = memberc12_in_ag(x2)
memberc12_out_ag(x1, x2) = memberc12_out_ag(x1, x2)
U133_ag(x1, x2, x3, x4) = U133_ag(x2, x3, x4)
not_memberc22_in_g(x1) = not_memberc22_in_g(x1)
not_memberc22_out_g(x1) = not_memberc22_out_g(x1)
member12_in_gg(x1, x2) = member12_in_gg(x1, x2)
[] = []
not_memberc48_in_gg(x1, x2) = not_memberc48_in_gg(x1, x2)
not_memberc48_out_gg(x1, x2) = not_memberc48_out_gg(x1, x2)
not_memberc71_in_ggg(x1, x2, x3) = not_memberc71_in_ggg(x1, x2, x3)
not_memberc71_out_ggg(x1, x2, x3) = not_memberc71_out_ggg(x1, x2, x3)
not_memberc94_in_gggg(x1, x2, x3, x4) = not_memberc94_in_gggg(x1, x2, x3, x4)
not_memberc94_out_gggg(x1, x2, x3, x4) = not_memberc94_out_gggg(x1, x2, x3, x4)
not_memberc117_in_ggggg(x1, x2, x3, x4, x5) = not_memberc117_in_ggggg(x1, x2, x3, x4, x5)
not_memberc117_out_ggggg(x1, x2, x3, x4, x5) = not_memberc117_out_ggggg(x1, x2, x3, x4, x5)
not_memberc140_in_gggggg(x1, x2, x3, x4, x5, x6) = not_memberc140_in_gggggg(x1, x2, x3, x4, x5, x6)
not_memberc140_out_gggggg(x1, x2, x3, x4, x5, x6) = not_memberc140_out_gggggg(x1, x2, x3, x4, x5, x6)
not_memberc163_in_ggggggg(x1, x2, x3, x4, x5, x6, x7) = not_memberc163_in_ggggggg(x1, x2, x3, x4, x5, x6, x7)
not_memberc163_out_ggggggg(x1, x2, x3, x4, x5, x6, x7) = not_memberc163_out_ggggggg(x1, x2, x3, x4, x5, x6, x7)
p184_in_aggggggggag(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = p184_in_aggggggggag(x2, x3, x4, x5, x6, x7, x8, x9, x11)
not_memberc187_in_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8) = not_memberc187_in_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8)
not_memberc187_out_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8) = not_memberc187_out_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8)
subsetchecked188_in_aggg(x1, x2, x3, x4) = subsetchecked188_in_aggg(x2, x3, x4)
not_memberc210_in_ggg(x1, x2, x3) = not_memberc210_in_ggg(x1, x2, x3)
not_memberc210_out_ggg(x1, x2, x3) = not_memberc210_out_ggg(x1, x2, x3)
SUBSET1_IN_AG(x1, x2) = SUBSET1_IN_AG(x2)
U14_AG(x1, x2, x3, x4) = U14_AG(x3, x4)
MEMBER12_IN_AG(x1, x2) = MEMBER12_IN_AG(x2)
U1_AG(x1, x2, x3, x4) = U1_AG(x2, x3, x4)
U15_AG(x1, x2, x3, x4, x5) = U15_AG(x4, x5)
U16_AG(x1, x2, x3, x4, x5) = U16_AG(x4, x5)
U17_AG(x1, x2, x3, x4, x5) = U17_AG(x4, x5)
U18_AG(x1, x2, x3, x4, x5) = U18_AG(x4, x5)
U19_AG(x1, x2, x3, x4, x5) = U19_AG(x1, x4, x5)
U20_AG(x1, x2, x3, x4, x5) = U20_AG(x1, x4, x5)
U21_AG(x1, x2, x3, x4, x5) = U21_AG(x4, x5)
MEMBER12_IN_GG(x1, x2) = MEMBER12_IN_GG(x1, x2)
U1_GG(x1, x2, x3, x4) = U1_GG(x1, x2, x3, x4)
U22_AG(x1, x2, x3, x4, x5, x6) = U22_AG(x5, x6)
U23_AG(x1, x2, x3, x4, x5, x6) = U23_AG(x1, x5, x6)
U24_AG(x1, x2, x3, x4, x5, x6) = U24_AG(x1, x5, x6)
U25_AG(x1, x2, x3, x4, x5, x6) = U25_AG(x5, x6)
U26_AG(x1, x2, x3, x4, x5, x6) = U26_AG(x5, x6)
U27_AG(x1, x2, x3, x4, x5, x6) = U27_AG(x5, x6)
U28_AG(x1, x2, x3, x4, x5, x6) = U28_AG(x1, x5, x6)
U29_AG(x1, x2, x3, x4, x5, x6) = U29_AG(x1, x5, x6)
U30_AG(x1, x2, x3, x4, x5, x6) = U30_AG(x1, x2, x5, x6)
U31_AG(x1, x2, x3, x4, x5, x6) = U31_AG(x1, x2, x5, x6)
U32_AG(x1, x2, x3, x4, x5, x6) = U32_AG(x5, x6)
U33_AG(x1, x2, x3, x4, x5, x6, x7) = U33_AG(x6, x7)
U34_AG(x1, x2, x3, x4, x5, x6, x7) = U34_AG(x1, x6, x7)
U35_AG(x1, x2, x3, x4, x5, x6, x7) = U35_AG(x1, x6, x7)
U36_AG(x1, x2, x3, x4, x5, x6, x7) = U36_AG(x1, x2, x6, x7)
U37_AG(x1, x2, x3, x4, x5, x6, x7) = U37_AG(x1, x2, x6, x7)
U38_AG(x1, x2, x3, x4, x5, x6, x7) = U38_AG(x6, x7)
U39_AG(x1, x2, x3, x4, x5, x6, x7) = U39_AG(x6, x7)
U40_AG(x1, x2, x3, x4, x5, x6, x7) = U40_AG(x6, x7)
U41_AG(x1, x2, x3, x4, x5, x6, x7) = U41_AG(x1, x6, x7)
U42_AG(x1, x2, x3, x4, x5, x6, x7) = U42_AG(x1, x6, x7)
U43_AG(x1, x2, x3, x4, x5, x6, x7) = U43_AG(x1, x2, x6, x7)
U44_AG(x1, x2, x3, x4, x5, x6, x7) = U44_AG(x1, x2, x6, x7)
U45_AG(x1, x2, x3, x4, x5, x6, x7) = U45_AG(x1, x2, x3, x6, x7)
U46_AG(x1, x2, x3, x4, x5, x6, x7) = U46_AG(x1, x2, x3, x6, x7)
U47_AG(x1, x2, x3, x4, x5, x6, x7) = U47_AG(x6, x7)
U48_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U48_AG(x7, x8)
U49_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U49_AG(x1, x7, x8)
U50_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U50_AG(x1, x7, x8)
U51_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U51_AG(x1, x2, x7, x8)
U52_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U52_AG(x1, x2, x7, x8)
U53_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U53_AG(x1, x2, x3, x7, x8)
U54_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U54_AG(x1, x2, x3, x7, x8)
U55_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U55_AG(x7, x8)
U56_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U56_AG(x7, x8)
U57_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U57_AG(x7, x8)
U58_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U58_AG(x1, x7, x8)
U59_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U59_AG(x1, x7, x8)
U60_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U60_AG(x1, x2, x7, x8)
U61_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U61_AG(x1, x2, x7, x8)
U62_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U62_AG(x1, x2, x3, x7, x8)
U63_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U63_AG(x1, x2, x3, x7, x8)
U64_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U64_AG(x1, x2, x3, x4, x7, x8)
U65_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U65_AG(x1, x2, x3, x4, x7, x8)
U66_AG(x1, x2, x3, x4, x5, x6, x7, x8) = U66_AG(x7, x8)
U67_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U67_AG(x8, x9)
U68_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U68_AG(x1, x8, x9)
U69_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U69_AG(x1, x8, x9)
U70_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U70_AG(x1, x2, x8, x9)
U71_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U71_AG(x1, x2, x8, x9)
U72_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U72_AG(x1, x2, x3, x8, x9)
U73_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U73_AG(x1, x2, x3, x8, x9)
U74_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U74_AG(x1, x2, x3, x4, x8, x9)
U75_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U75_AG(x1, x2, x3, x4, x8, x9)
U76_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U76_AG(x8, x9)
U77_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U77_AG(x8, x9)
U78_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U78_AG(x8, x9)
U79_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U79_AG(x1, x8, x9)
U80_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U80_AG(x1, x8, x9)
U81_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U81_AG(x1, x2, x8, x9)
U82_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U82_AG(x1, x2, x8, x9)
U83_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U83_AG(x1, x2, x3, x8, x9)
U84_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U84_AG(x1, x2, x3, x8, x9)
U85_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U85_AG(x1, x2, x3, x4, x8, x9)
U86_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U86_AG(x1, x2, x3, x4, x8, x9)
U87_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U87_AG(x1, x2, x3, x4, x5, x8, x9)
U88_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U88_AG(x1, x2, x3, x4, x5, x8, x9)
U89_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U89_AG(x8, x9)
U90_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U90_AG(x9, x10)
U91_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U91_AG(x1, x9, x10)
U92_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U92_AG(x1, x9, x10)
U93_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U93_AG(x1, x2, x9, x10)
U94_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U94_AG(x1, x2, x9, x10)
U95_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U95_AG(x1, x2, x3, x9, x10)
U96_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U96_AG(x1, x2, x3, x9, x10)
U97_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U97_AG(x1, x2, x3, x4, x9, x10)
U98_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U98_AG(x1, x2, x3, x4, x9, x10)
U99_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U99_AG(x1, x2, x3, x4, x5, x9, x10)
U100_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U100_AG(x1, x2, x3, x4, x5, x9, x10)
U101_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U101_AG(x9, x10)
U102_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U102_AG(x9, x10)
U103_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U103_AG(x9, x10)
U104_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U104_AG(x1, x9, x10)
U105_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U105_AG(x1, x9, x10)
U106_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U106_AG(x1, x2, x9, x10)
U107_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U107_AG(x1, x2, x9, x10)
U108_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U108_AG(x1, x2, x3, x9, x10)
U109_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U109_AG(x1, x2, x3, x9, x10)
U110_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U110_AG(x1, x2, x3, x4, x9, x10)
U111_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U111_AG(x1, x2, x3, x4, x9, x10)
U112_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U112_AG(x1, x2, x3, x4, x5, x9, x10)
U113_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U113_AG(x1, x2, x3, x4, x5, x9, x10)
U114_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U114_AG(x1, x2, x3, x4, x5, x6, x9, x10)
U115_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U115_AG(x1, x2, x3, x4, x5, x6, x9, x10)
U116_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) = U116_AG(x9, x10)
U117_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U117_AG(x10, x11)
U118_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U118_AG(x1, x10, x11)
U119_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U119_AG(x1, x10, x11)
U120_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U120_AG(x1, x2, x10, x11)
U121_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U121_AG(x1, x2, x10, x11)
U122_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U122_AG(x1, x2, x3, x10, x11)
U123_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U123_AG(x1, x2, x3, x10, x11)
U124_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U124_AG(x1, x2, x3, x4, x10, x11)
U125_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U125_AG(x1, x2, x3, x4, x10, x11)
U126_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U126_AG(x1, x2, x3, x4, x5, x10, x11)
U127_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U127_AG(x1, x2, x3, x4, x5, x10, x11)
U128_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U128_AG(x1, x2, x3, x4, x5, x6, x10, x11)
U129_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U129_AG(x1, x2, x3, x4, x5, x6, x10, x11)
U130_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U130_AG(x1, x2, x3, x4, x5, x6, x7, x10, x11)
U131_AG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = U131_AG(x10, x11)
P184_IN_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) = P184_IN_AGGGGGGGGAG(x2, x3, x4, x5, x6, x7, x8, x9, x11)
U8_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) = U8_AGGGGGGGGAG(x2, x3, x4, x5, x6, x7, x8, x9, x11, x12)
U9_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) = U9_AGGGGGGGGAG(x2, x3, x4, x5, x6, x7, x8, x9, x11, x12)
U10_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) = U10_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x11, x12)
U11_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) = U11_AGGGGGGGGAG(x2, x3, x4, x5, x6, x7, x8, x9, x11, x12)
U12_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) = U12_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x11, x12)
U13_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) = U13_AGGGGGGGGAG(x1, x2, x3, x4, x5, x6, x7, x8, x9, x11, x12)
SUBSETCHECKED188_IN_AGGG(x1, x2, x3, x4) = SUBSETCHECKED188_IN_AGGG(x2, x3, x4)
U2_AGGG(x1, x2, x3, x4, x5, x6) = U2_AGGG(x3, x4, x5, x6)
U3_AGGG(x1, x2, x3, x4, x5, x6) = U3_AGGG(x3, x4, x5, x6)
U4_AGGG(x1, x2, x3, x4, x5, x6) = U4_AGGG(x3, x4, x5, x6)
U5_AGGG(x1, x2, x3, x4, x5, x6) = U5_AGGG(x3, x4, x5, x6)
U6_AGGG(x1, x2, x3, x4, x5, x6) = U6_AGGG(x1, x3, x4, x5, x6)
U7_AGGG(x1, x2, x3, x4, x5, x6) = U7_AGGG(x3, x4, x5, x6)

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:

SUBSET1_IN_AG(.(T22, T23), T21) → U14_AG(T22, T23, T21, member12_in_ag(T22, T21))
SUBSET1_IN_AG(.(T22, T23), T21) → MEMBER12_IN_AG(T22, T21)
MEMBER12_IN_AG(T53, .(T51, T52)) → U1_AG(T53, T51, T52, member12_in_ag(T53, T52))
MEMBER12_IN_AG(T53, .(T51, T52)) → MEMBER12_IN_AG(T53, T52)
SUBSET1_IN_AG(.(T106, .(T108, T109)), T107) → U15_AG(T106, T108, T109, T107, memberc12_in_ag(T106, T107))
U15_AG(T106, T108, T109, T107, memberc12_out_ag(T106, T107)) → U16_AG(T106, T108, T109, T107, not_memberc22_in_g(T106))
U16_AG(T106, T108, T109, T107, not_memberc22_out_g(T106)) → U17_AG(T106, T108, T109, T107, member12_in_ag(T108, T107))
U16_AG(T106, T108, T109, T107, not_memberc22_out_g(T106)) → MEMBER12_IN_AG(T108, T107)
SUBSET1_IN_AG(.(T137, .(T136, T115)), T107) → U18_AG(T137, T136, T115, T107, memberc12_in_ag(T137, T107))
U18_AG(T137, T136, T115, T107, memberc12_out_ag(T137, T107)) → U19_AG(T137, T136, T115, T107, not_memberc22_in_g(T137))
U19_AG(T137, T136, T115, T107, not_memberc22_out_g(T137)) → U20_AG(T137, T136, T115, T107, memberc12_in_ag(T136, T107))
U20_AG(T137, T136, T115, T107, memberc12_out_ag(T136, T107)) → U21_AG(T137, T136, T115, T107, member12_in_gg(T136, .(T137, [])))
U20_AG(T137, T136, T115, T107, memberc12_out_ag(T136, T107)) → MEMBER12_IN_GG(T136, .(T137, []))
MEMBER12_IN_GG(T53, .(T51, T52)) → U1_GG(T53, T51, T52, member12_in_gg(T53, T52))
MEMBER12_IN_GG(T53, .(T51, T52)) → MEMBER12_IN_GG(T53, T52)
SUBSET1_IN_AG(.(T182, .(T181, .(T184, T185))), T183) → U22_AG(T182, T181, T184, T185, T183, memberc12_in_ag(T182, T183))
U22_AG(T182, T181, T184, T185, T183, memberc12_out_ag(T182, T183)) → U23_AG(T182, T181, T184, T185, T183, not_memberc22_in_g(T182))
U23_AG(T182, T181, T184, T185, T183, not_memberc22_out_g(T182)) → U24_AG(T182, T181, T184, T185, T183, memberc12_in_ag(T181, T183))
U24_AG(T182, T181, T184, T185, T183, memberc12_out_ag(T181, T183)) → U25_AG(T182, T181, T184, T185, T183, not_memberc48_in_gg(T181, T182))
U25_AG(T182, T181, T184, T185, T183, not_memberc48_out_gg(T181, T182)) → U26_AG(T182, T181, T184, T185, T183, member12_in_ag(T184, T183))
U25_AG(T182, T181, T184, T185, T183, not_memberc48_out_gg(T181, T182)) → MEMBER12_IN_AG(T184, T183)
SUBSET1_IN_AG(.(T224, .(T223, .(T222, T191))), T183) → U27_AG(T224, T223, T222, T191, T183, memberc12_in_ag(T224, T183))
U27_AG(T224, T223, T222, T191, T183, memberc12_out_ag(T224, T183)) → U28_AG(T224, T223, T222, T191, T183, not_memberc22_in_g(T224))
U28_AG(T224, T223, T222, T191, T183, not_memberc22_out_g(T224)) → U29_AG(T224, T223, T222, T191, T183, memberc12_in_ag(T223, T183))
U29_AG(T224, T223, T222, T191, T183, memberc12_out_ag(T223, T183)) → U30_AG(T224, T223, T222, T191, T183, not_memberc48_in_gg(T223, T224))
U30_AG(T224, T223, T222, T191, T183, not_memberc48_out_gg(T223, T224)) → U31_AG(T224, T223, T222, T191, T183, memberc12_in_ag(T222, T183))
U31_AG(T224, T223, T222, T191, T183, memberc12_out_ag(T222, T183)) → U32_AG(T224, T223, T222, T191, T183, member12_in_gg(T222, .(T223, .(T224, []))))
U31_AG(T224, T223, T222, T191, T183, memberc12_out_ag(T222, T183)) → MEMBER12_IN_GG(T222, .(T223, .(T224, [])))
SUBSET1_IN_AG(.(T286, .(T285, .(T284, .(T288, T289)))), T287) → U33_AG(T286, T285, T284, T288, T289, T287, memberc12_in_ag(T286, T287))
U33_AG(T286, T285, T284, T288, T289, T287, memberc12_out_ag(T286, T287)) → U34_AG(T286, T285, T284, T288, T289, T287, not_memberc22_in_g(T286))
U34_AG(T286, T285, T284, T288, T289, T287, not_memberc22_out_g(T286)) → U35_AG(T286, T285, T284, T288, T289, T287, memberc12_in_ag(T285, T287))
U35_AG(T286, T285, T284, T288, T289, T287, memberc12_out_ag(T285, T287)) → U36_AG(T286, T285, T284, T288, T289, T287, not_memberc48_in_gg(T285, T286))
U36_AG(T286, T285, T284, T288, T289, T287, not_memberc48_out_gg(T285, T286)) → U37_AG(T286, T285, T284, T288, T289, T287, memberc12_in_ag(T284, T287))
U37_AG(T286, T285, T284, T288, T289, T287, memberc12_out_ag(T284, T287)) → U38_AG(T286, T285, T284, T288, T289, T287, not_memberc71_in_ggg(T284, T285, T286))
U38_AG(T286, T285, T284, T288, T289, T287, not_memberc71_out_ggg(T284, T285, T286)) → U39_AG(T286, T285, T284, T288, T289, T287, member12_in_ag(T288, T287))
U38_AG(T286, T285, T284, T288, T289, T287, not_memberc71_out_ggg(T284, T285, T286)) → MEMBER12_IN_AG(T288, T287)
SUBSET1_IN_AG(.(T339, .(T338, .(T337, .(T336, T295)))), T287) → U40_AG(T339, T338, T337, T336, T295, T287, memberc12_in_ag(T339, T287))
U40_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T339, T287)) → U41_AG(T339, T338, T337, T336, T295, T287, not_memberc22_in_g(T339))
U41_AG(T339, T338, T337, T336, T295, T287, not_memberc22_out_g(T339)) → U42_AG(T339, T338, T337, T336, T295, T287, memberc12_in_ag(T338, T287))
U42_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T338, T287)) → U43_AG(T339, T338, T337, T336, T295, T287, not_memberc48_in_gg(T338, T339))
U43_AG(T339, T338, T337, T336, T295, T287, not_memberc48_out_gg(T338, T339)) → U44_AG(T339, T338, T337, T336, T295, T287, memberc12_in_ag(T337, T287))
U44_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T337, T287)) → U45_AG(T339, T338, T337, T336, T295, T287, not_memberc71_in_ggg(T337, T338, T339))
U45_AG(T339, T338, T337, T336, T295, T287, not_memberc71_out_ggg(T337, T338, T339)) → U46_AG(T339, T338, T337, T336, T295, T287, memberc12_in_ag(T336, T287))
U46_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T336, T287)) → U47_AG(T339, T338, T337, T336, T295, T287, member12_in_gg(T336, .(T337, .(T338, .(T339, [])))))
U46_AG(T339, T338, T337, T336, T295, T287, memberc12_out_ag(T336, T287)) → MEMBER12_IN_GG(T336, .(T337, .(T338, .(T339, []))))
SUBSET1_IN_AG(.(T418, .(T417, .(T416, .(T415, .(T420, T421))))), T419) → U48_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_in_ag(T418, T419))
U48_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_out_ag(T418, T419)) → U49_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc22_in_g(T418))
U49_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc22_out_g(T418)) → U50_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_in_ag(T417, T419))
U50_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_out_ag(T417, T419)) → U51_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc48_in_gg(T417, T418))
U51_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc48_out_gg(T417, T418)) → U52_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_in_ag(T416, T419))
U52_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_out_ag(T416, T419)) → U53_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc71_in_ggg(T416, T417, T418))
U53_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc71_out_ggg(T416, T417, T418)) → U54_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_in_ag(T415, T419))
U54_AG(T418, T417, T416, T415, T420, T421, T419, memberc12_out_ag(T415, T419)) → U55_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc94_in_gggg(T415, T416, T417, T418))
U55_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc94_out_gggg(T415, T416, T417, T418)) → U56_AG(T418, T417, T416, T415, T420, T421, T419, member12_in_ag(T420, T419))
U55_AG(T418, T417, T416, T415, T420, T421, T419, not_memberc94_out_gggg(T415, T416, T417, T418)) → MEMBER12_IN_AG(T420, T419)
SUBSET1_IN_AG(.(T482, .(T481, .(T480, .(T479, .(T478, T427))))), T419) → U57_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T482, T419))
U57_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T482, T419)) → U58_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc22_in_g(T482))
U58_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc22_out_g(T482)) → U59_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T481, T419))
U59_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T481, T419)) → U60_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc48_in_gg(T481, T482))
U60_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc48_out_gg(T481, T482)) → U61_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T480, T419))
U61_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T480, T419)) → U62_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc71_in_ggg(T480, T481, T482))
U62_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc71_out_ggg(T480, T481, T482)) → U63_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T479, T419))
U63_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T479, T419)) → U64_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc94_in_gggg(T479, T480, T481, T482))
U64_AG(T482, T481, T480, T479, T478, T427, T419, not_memberc94_out_gggg(T479, T480, T481, T482)) → U65_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_in_ag(T478, T419))
U65_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T478, T419)) → U66_AG(T482, T481, T480, T479, T478, T427, T419, member12_in_gg(T478, .(T479, .(T480, .(T481, .(T482, []))))))
U65_AG(T482, T481, T480, T479, T478, T427, T419, memberc12_out_ag(T478, T419)) → MEMBER12_IN_GG(T478, .(T479, .(T480, .(T481, .(T482, [])))))
SUBSET1_IN_AG(.(T578, .(T577, .(T576, .(T575, .(T574, .(T580, T581)))))), T579) → U67_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T578, T579))
U67_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T578, T579)) → U68_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc22_in_g(T578))
U68_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc22_out_g(T578)) → U69_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T577, T579))
U69_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T577, T579)) → U70_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc48_in_gg(T577, T578))
U70_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc48_out_gg(T577, T578)) → U71_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T576, T579))
U71_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T576, T579)) → U72_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc71_in_ggg(T576, T577, T578))
U72_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc71_out_ggg(T576, T577, T578)) → U73_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T575, T579))
U73_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T575, T579)) → U74_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc94_in_gggg(T575, T576, T577, T578))
U74_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc94_out_gggg(T575, T576, T577, T578)) → U75_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_in_ag(T574, T579))
U75_AG(T578, T577, T576, T575, T574, T580, T581, T579, memberc12_out_ag(T574, T579)) → U76_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc117_in_ggggg(T574, T575, T576, T577, T578))
U76_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc117_out_ggggg(T574, T575, T576, T577, T578)) → U77_AG(T578, T577, T576, T575, T574, T580, T581, T579, member12_in_ag(T580, T579))
U76_AG(T578, T577, T576, T575, T574, T580, T581, T579, not_memberc117_out_ggggg(T574, T575, T576, T577, T578)) → MEMBER12_IN_AG(T580, T579)
SUBSET1_IN_AG(.(T653, .(T652, .(T651, .(T650, .(T649, .(T648, T587)))))), T579) → U78_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T653, T579))
U78_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T653, T579)) → U79_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc22_in_g(T653))
U79_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc22_out_g(T653)) → U80_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T652, T579))
U80_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T652, T579)) → U81_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc48_in_gg(T652, T653))
U81_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc48_out_gg(T652, T653)) → U82_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T651, T579))
U82_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T651, T579)) → U83_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc71_in_ggg(T651, T652, T653))
U83_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc71_out_ggg(T651, T652, T653)) → U84_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T650, T579))
U84_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T650, T579)) → U85_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc94_in_gggg(T650, T651, T652, T653))
U85_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc94_out_gggg(T650, T651, T652, T653)) → U86_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T649, T579))
U86_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T649, T579)) → U87_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc117_in_ggggg(T649, T650, T651, T652, T653))
U87_AG(T653, T652, T651, T650, T649, T648, T587, T579, not_memberc117_out_ggggg(T649, T650, T651, T652, T653)) → U88_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_in_ag(T648, T579))
U88_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T648, T579)) → U89_AG(T653, T652, T651, T650, T649, T648, T587, T579, member12_in_gg(T648, .(T649, .(T650, .(T651, .(T652, .(T653, [])))))))
U88_AG(T653, T652, T651, T650, T649, T648, T587, T579, memberc12_out_ag(T648, T579)) → MEMBER12_IN_GG(T648, .(T649, .(T650, .(T651, .(T652, .(T653, []))))))
SUBSET1_IN_AG(.(T766, .(T765, .(T764, .(T763, .(T762, .(T761, .(T768, T769))))))), T767) → U90_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T766, T767))
U90_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T766, T767)) → U91_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc22_in_g(T766))
U91_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc22_out_g(T766)) → U92_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T765, T767))
U92_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T765, T767)) → U93_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc48_in_gg(T765, T766))
U93_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc48_out_gg(T765, T766)) → U94_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T764, T767))
U94_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T764, T767)) → U95_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc71_in_ggg(T764, T765, T766))
U95_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc71_out_ggg(T764, T765, T766)) → U96_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T763, T767))
U96_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T763, T767)) → U97_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc94_in_gggg(T763, T764, T765, T766))
U97_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc94_out_gggg(T763, T764, T765, T766)) → U98_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T762, T767))
U98_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T762, T767)) → U99_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc117_in_ggggg(T762, T763, T764, T765, T766))
U99_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc117_out_ggggg(T762, T763, T764, T765, T766)) → U100_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_in_ag(T761, T767))
U100_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, memberc12_out_ag(T761, T767)) → U101_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc140_in_gggggg(T761, T762, T763, T764, T765, T766))
U101_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc140_out_gggggg(T761, T762, T763, T764, T765, T766)) → U102_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, member12_in_ag(T768, T767))
U101_AG(T766, T765, T764, T763, T762, T761, T768, T769, T767, not_memberc140_out_gggggg(T761, T762, T763, T764, T765, T766)) → MEMBER12_IN_AG(T768, T767)
SUBSET1_IN_AG(.(T852, .(T851, .(T850, .(T849, .(T848, .(T847, .(T846, T775))))))), T767) → U103_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T852, T767))
U103_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T852, T767)) → U104_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc22_in_g(T852))
U104_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc22_out_g(T852)) → U105_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T851, T767))
U105_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T851, T767)) → U106_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc48_in_gg(T851, T852))
U106_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc48_out_gg(T851, T852)) → U107_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T850, T767))
U107_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T850, T767)) → U108_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc71_in_ggg(T850, T851, T852))
U108_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc71_out_ggg(T850, T851, T852)) → U109_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T849, T767))
U109_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T849, T767)) → U110_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc94_in_gggg(T849, T850, T851, T852))
U110_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc94_out_gggg(T849, T850, T851, T852)) → U111_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T848, T767))
U111_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T848, T767)) → U112_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc117_in_ggggg(T848, T849, T850, T851, T852))
U112_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc117_out_ggggg(T848, T849, T850, T851, T852)) → U113_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T847, T767))
U113_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T847, T767)) → U114_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc140_in_gggggg(T847, T848, T849, T850, T851, T852))
U114_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, not_memberc140_out_gggggg(T847, T848, T849, T850, T851, T852)) → U115_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_in_ag(T846, T767))
U115_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T846, T767)) → U116_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, member12_in_gg(T846, .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, []))))))))
U115_AG(T852, T851, T850, T849, T848, T847, T846, T775, T767, memberc12_out_ag(T846, T767)) → MEMBER12_IN_GG(T846, .(T847, .(T848, .(T849, .(T850, .(T851, .(T852, [])))))))
SUBSET1_IN_AG(.(T982, .(T981, .(T980, .(T979, .(T978, .(T977, .(T976, .(T984, T985)))))))), T983) → U117_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T982, T983))
U117_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T982, T983)) → U118_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc22_in_g(T982))
U118_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc22_out_g(T982)) → U119_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T981, T983))
U119_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T981, T983)) → U120_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc48_in_gg(T981, T982))
U120_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc48_out_gg(T981, T982)) → U121_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T980, T983))
U121_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T980, T983)) → U122_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc71_in_ggg(T980, T981, T982))
U122_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc71_out_ggg(T980, T981, T982)) → U123_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T979, T983))
U123_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T979, T983)) → U124_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc94_in_gggg(T979, T980, T981, T982))
U124_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc94_out_gggg(T979, T980, T981, T982)) → U125_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T978, T983))
U125_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T978, T983)) → U126_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc117_in_ggggg(T978, T979, T980, T981, T982))
U126_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc117_out_ggggg(T978, T979, T980, T981, T982)) → U127_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T977, T983))
U127_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T977, T983)) → U128_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc140_in_gggggg(T977, T978, T979, T980, T981, T982))
U128_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc140_out_gggggg(T977, T978, T979, T980, T981, T982)) → U129_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_in_ag(T976, T983))
U129_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, memberc12_out_ag(T976, T983)) → U130_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc163_in_ggggggg(T976, T977, T978, T979, T980, T981, T982))
U130_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc163_out_ggggggg(T976, T977, T978, T979, T980, T981, T982)) → U131_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, p184_in_aggggggggag(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, [])))))))))
U130_AG(T982, T981, T980, T979, T978, T977, T976, T984, T985, T983, not_memberc163_out_ggggggg(T976, T977, T978, T979, T980, T981, T982)) → P184_IN_AGGGGGGGGAG(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, .(T976, .(T977, .(T978, .(T979, .(T980, .(T981, .(T982, []))))))))
P184_IN_AGGGGGGGGAG(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, T990) → U8_AGGGGGGGGAG(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, T990, member12_in_ag(T984, T983))
P184_IN_AGGGGGGGGAG(T984, T983, T976, T977, T978, T979, T980, T981, T982, T985, T990) → MEMBER12_IN_AG(T984, T983)
P184_IN_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990) → U9_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990, memberc12_in_ag(T1077, T983))
U9_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990, memberc12_out_ag(T1077, T983)) → U10_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990, member12_in_gg(T1077, .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, [])))))))))
U9_AGGGGGGGGAG(T1077, T983, T1078, T1079, T1080, T1081, T1082, T1083, T1084, T996, T990, memberc12_out_ag(T1077, T983)) → MEMBER12_IN_GG(T1077, .(T1078, .(T1079, .(T1080, .(T1081, .(T1082, .(T1083, .(T1084, []))))))))
P184_IN_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990) → U11_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, memberc12_in_ag(T995, T983))
U11_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, memberc12_out_ag(T995, T983)) → U12_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, not_memberc187_in_gggggggg(T995, T976, T977, T978, T979, T980, T981, T982))
U12_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, not_memberc187_out_gggggggg(T995, T976, T977, T978, T979, T980, T981, T982)) → U13_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, subsetchecked188_in_aggg(T996, T995, T990, T983))
U12_AGGGGGGGGAG(T995, T983, T976, T977, T978, T979, T980, T981, T982, T996, T990, not_memberc187_out_gggggggg(T995, T976, T977, T978, T979, T980, T981, T982)) → SUBSETCHECKED188_IN_AGGG(T996, T995, T990, T983)
SUBSETCHECKED188_IN_AGGG(.(T1173, T1174), T1170, T1171, T1172) → U2_AGGG(T1173, T1174, T1170, T1171, T1172, member12_in_ag(T1173, T1172))
SUBSETCHECKED188_IN_AGGG(.(T1173, T1174), T1170, T1171, T1172) → MEMBER12_IN_AG(T1173, T1172)
SUBSETCHECKED188_IN_AGGG(.(T1211, T1180), T1212, T1213, T1172) → U3_AGGG(T1211, T1180, T1212, T1213, T1172, memberc12_in_ag(T1211, T1172))
U3_AGGG(T1211, T1180, T1212, T1213, T1172, memberc12_out_ag(T1211, T1172)) → U4_AGGG(T1211, T1180, T1212, T1213, T1172, member12_in_gg(T1211, .(T1212, T1213)))
U3_AGGG(T1211, T1180, T1212, T1213, T1172, memberc12_out_ag(T1211, T1172)) → MEMBER12_IN_GG(T1211, .(T1212, T1213))
SUBSETCHECKED188_IN_AGGG(.(T1179, T1180), T1170, T1171, T1172) → U5_AGGG(T1179, T1180, T1170, T1171, T1172, memberc12_in_ag(T1179, T1172))
U5_AGGG(T1179, T1180, T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_in_ggg(T1179, T1170, T1171))
U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → U7_AGGG(T1179, T1180, T1170, T1171, T1172, subsetchecked188_in_aggg(T1180, T1179, .(T1170, T1171), T1172))
U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1180, T1179, .(T1170, T1171), T1172)

The TRS R consists of the following rules:

memberc12_in_ag(T42, .(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(T53, .(T51, T52)) → U133_ag(T53, T51, T52, memberc12_in_ag(T53, T52))
U133_ag(T53, T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))
not_memberc22_in_g(T81) → not_memberc22_out_g(T81)
not_memberc48_in_gg(T146, T147) → not_memberc48_out_gg(T146, T147)
not_memberc71_in_ggg(T239, T240, T241) → not_memberc71_out_ggg(T239, T240, T241)
not_memberc94_in_gggg(T360, T361, T362, T363) → not_memberc94_out_gggg(T360, T361, T362, T363)
not_memberc117_in_ggggg(T509, T510, T511, T512, T513) → not_memberc117_out_ggggg(T509, T510, T511, T512, T513)
not_memberc140_in_gggggg(T686, T687, T688, T689, T690, T691) → not_memberc140_out_gggggg(T686, T687, T688, T689, T690, T691)
not_memberc163_in_ggggggg(T891, T892, T893, T894, T895, T896, T897) → not_memberc163_out_ggggggg(T891, T892, T893, T894, T895, T896, T897)
not_memberc187_in_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136) → not_memberc187_out_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136)
not_memberc210_in_ggg(T1228, T1229, T1230) → not_memberc210_out_ggg(T1228, T1229, T1230)

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 3 SCCs with 149 less nodes.

(6) Complex Obligation (AND)

(7) Obligation:

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

MEMBER12_IN_GG(T53, .(T51, T52)) → MEMBER12_IN_GG(T53, T52)

The TRS R consists of the following rules:

memberc12_in_ag(T42, .(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(T53, .(T51, T52)) → U133_ag(T53, T51, T52, memberc12_in_ag(T53, T52))
U133_ag(T53, T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))
not_memberc22_in_g(T81) → not_memberc22_out_g(T81)
not_memberc48_in_gg(T146, T147) → not_memberc48_out_gg(T146, T147)
not_memberc71_in_ggg(T239, T240, T241) → not_memberc71_out_ggg(T239, T240, T241)
not_memberc94_in_gggg(T360, T361, T362, T363) → not_memberc94_out_gggg(T360, T361, T362, T363)
not_memberc117_in_ggggg(T509, T510, T511, T512, T513) → not_memberc117_out_ggggg(T509, T510, T511, T512, T513)
not_memberc140_in_gggggg(T686, T687, T688, T689, T690, T691) → not_memberc140_out_gggggg(T686, T687, T688, T689, T690, T691)
not_memberc163_in_ggggggg(T891, T892, T893, T894, T895, T896, T897) → not_memberc163_out_ggggggg(T891, T892, T893, T894, T895, T896, T897)
not_memberc187_in_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136) → not_memberc187_out_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136)
not_memberc210_in_ggg(T1228, T1229, T1230) → not_memberc210_out_ggg(T1228, T1229, T1230)

The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
memberc12_in_ag(x1, x2) = memberc12_in_ag(x2)
memberc12_out_ag(x1, x2) = memberc12_out_ag(x1, x2)
U133_ag(x1, x2, x3, x4) = U133_ag(x2, x3, x4)
not_memberc22_in_g(x1) = not_memberc22_in_g(x1)
not_memberc22_out_g(x1) = not_memberc22_out_g(x1)
not_memberc48_in_gg(x1, x2) = not_memberc48_in_gg(x1, x2)
not_memberc48_out_gg(x1, x2) = not_memberc48_out_gg(x1, x2)
not_memberc71_in_ggg(x1, x2, x3) = not_memberc71_in_ggg(x1, x2, x3)
not_memberc71_out_ggg(x1, x2, x3) = not_memberc71_out_ggg(x1, x2, x3)
not_memberc94_in_gggg(x1, x2, x3, x4) = not_memberc94_in_gggg(x1, x2, x3, x4)
not_memberc94_out_gggg(x1, x2, x3, x4) = not_memberc94_out_gggg(x1, x2, x3, x4)
not_memberc117_in_ggggg(x1, x2, x3, x4, x5) = not_memberc117_in_ggggg(x1, x2, x3, x4, x5)
not_memberc117_out_ggggg(x1, x2, x3, x4, x5) = not_memberc117_out_ggggg(x1, x2, x3, x4, x5)
not_memberc140_in_gggggg(x1, x2, x3, x4, x5, x6) = not_memberc140_in_gggggg(x1, x2, x3, x4, x5, x6)
not_memberc140_out_gggggg(x1, x2, x3, x4, x5, x6) = not_memberc140_out_gggggg(x1, x2, x3, x4, x5, x6)
not_memberc163_in_ggggggg(x1, x2, x3, x4, x5, x6, x7) = not_memberc163_in_ggggggg(x1, x2, x3, x4, x5, x6, x7)
not_memberc163_out_ggggggg(x1, x2, x3, x4, x5, x6, x7) = not_memberc163_out_ggggggg(x1, x2, x3, x4, x5, x6, x7)
not_memberc187_in_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8) = not_memberc187_in_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8)
not_memberc187_out_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8) = not_memberc187_out_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8)
not_memberc210_in_ggg(x1, x2, x3) = not_memberc210_in_ggg(x1, x2, x3)
not_memberc210_out_ggg(x1, x2, x3) = not_memberc210_out_ggg(x1, x2, x3)
MEMBER12_IN_GG(x1, x2) = MEMBER12_IN_GG(x1, x2)

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

(8) UsableRulesProof (EQUIVALENT transformation)

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

(9) Obligation:

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

MEMBER12_IN_GG(T53, .(T51, T52)) → MEMBER12_IN_GG(T53, T52)

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

(10) PiDPToQDPProof (EQUIVALENT transformation)

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

(11) Obligation:

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

MEMBER12_IN_GG(T53, .(T51, T52)) → MEMBER12_IN_GG(T53, T52)

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

(12) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

MEMBER12_IN_GG(T53, .(T51, T52)) → MEMBER12_IN_GG(T53, T52)
The graph contains the following edges 1 >= 1, 2 > 2

(13) YES

(14) Obligation:

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

MEMBER12_IN_AG(T53, .(T51, T52)) → MEMBER12_IN_AG(T53, T52)

The TRS R consists of the following rules:

memberc12_in_ag(T42, .(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(T53, .(T51, T52)) → U133_ag(T53, T51, T52, memberc12_in_ag(T53, T52))
U133_ag(T53, T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))
not_memberc22_in_g(T81) → not_memberc22_out_g(T81)
not_memberc48_in_gg(T146, T147) → not_memberc48_out_gg(T146, T147)
not_memberc71_in_ggg(T239, T240, T241) → not_memberc71_out_ggg(T239, T240, T241)
not_memberc94_in_gggg(T360, T361, T362, T363) → not_memberc94_out_gggg(T360, T361, T362, T363)
not_memberc117_in_ggggg(T509, T510, T511, T512, T513) → not_memberc117_out_ggggg(T509, T510, T511, T512, T513)
not_memberc140_in_gggggg(T686, T687, T688, T689, T690, T691) → not_memberc140_out_gggggg(T686, T687, T688, T689, T690, T691)
not_memberc163_in_ggggggg(T891, T892, T893, T894, T895, T896, T897) → not_memberc163_out_ggggggg(T891, T892, T893, T894, T895, T896, T897)
not_memberc187_in_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136) → not_memberc187_out_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136)
not_memberc210_in_ggg(T1228, T1229, T1230) → not_memberc210_out_ggg(T1228, T1229, T1230)

The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
memberc12_in_ag(x1, x2) = memberc12_in_ag(x2)
memberc12_out_ag(x1, x2) = memberc12_out_ag(x1, x2)
U133_ag(x1, x2, x3, x4) = U133_ag(x2, x3, x4)
not_memberc22_in_g(x1) = not_memberc22_in_g(x1)
not_memberc22_out_g(x1) = not_memberc22_out_g(x1)
not_memberc48_in_gg(x1, x2) = not_memberc48_in_gg(x1, x2)
not_memberc48_out_gg(x1, x2) = not_memberc48_out_gg(x1, x2)
not_memberc71_in_ggg(x1, x2, x3) = not_memberc71_in_ggg(x1, x2, x3)
not_memberc71_out_ggg(x1, x2, x3) = not_memberc71_out_ggg(x1, x2, x3)
not_memberc94_in_gggg(x1, x2, x3, x4) = not_memberc94_in_gggg(x1, x2, x3, x4)
not_memberc94_out_gggg(x1, x2, x3, x4) = not_memberc94_out_gggg(x1, x2, x3, x4)
not_memberc117_in_ggggg(x1, x2, x3, x4, x5) = not_memberc117_in_ggggg(x1, x2, x3, x4, x5)
not_memberc117_out_ggggg(x1, x2, x3, x4, x5) = not_memberc117_out_ggggg(x1, x2, x3, x4, x5)
not_memberc140_in_gggggg(x1, x2, x3, x4, x5, x6) = not_memberc140_in_gggggg(x1, x2, x3, x4, x5, x6)
not_memberc140_out_gggggg(x1, x2, x3, x4, x5, x6) = not_memberc140_out_gggggg(x1, x2, x3, x4, x5, x6)
not_memberc163_in_ggggggg(x1, x2, x3, x4, x5, x6, x7) = not_memberc163_in_ggggggg(x1, x2, x3, x4, x5, x6, x7)
not_memberc163_out_ggggggg(x1, x2, x3, x4, x5, x6, x7) = not_memberc163_out_ggggggg(x1, x2, x3, x4, x5, x6, x7)
not_memberc187_in_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8) = not_memberc187_in_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8)
not_memberc187_out_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8) = not_memberc187_out_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8)
not_memberc210_in_ggg(x1, x2, x3) = not_memberc210_in_ggg(x1, x2, x3)
not_memberc210_out_ggg(x1, x2, x3) = not_memberc210_out_ggg(x1, x2, x3)
MEMBER12_IN_AG(x1, x2) = MEMBER12_IN_AG(x2)

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

(15) UsableRulesProof (EQUIVALENT transformation)

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

(16) Obligation:

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

MEMBER12_IN_AG(T53, .(T51, T52)) → MEMBER12_IN_AG(T53, T52)

R is empty.
The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
MEMBER12_IN_AG(x1, x2) = MEMBER12_IN_AG(x2)

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

(17) PiDPToQDPProof (SOUND transformation)

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

(18) Obligation:

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

MEMBER12_IN_AG(.(T51, T52)) → MEMBER12_IN_AG(T52)

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

(19) QDPSizeChangeProof (EQUIVALENT transformation)

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

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

MEMBER12_IN_AG(.(T51, T52)) → MEMBER12_IN_AG(T52)
The graph contains the following edges 1 > 1

(20) YES

(21) Obligation:

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

SUBSETCHECKED188_IN_AGGG(.(T1179, T1180), T1170, T1171, T1172) → U5_AGGG(T1179, T1180, T1170, T1171, T1172, memberc12_in_ag(T1179, T1172))
U5_AGGG(T1179, T1180, T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_in_ggg(T1179, T1170, T1171))
U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1180, T1179, .(T1170, T1171), T1172)

The TRS R consists of the following rules:

memberc12_in_ag(T42, .(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(T53, .(T51, T52)) → U133_ag(T53, T51, T52, memberc12_in_ag(T53, T52))
U133_ag(T53, T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))
not_memberc22_in_g(T81) → not_memberc22_out_g(T81)
not_memberc48_in_gg(T146, T147) → not_memberc48_out_gg(T146, T147)
not_memberc71_in_ggg(T239, T240, T241) → not_memberc71_out_ggg(T239, T240, T241)
not_memberc94_in_gggg(T360, T361, T362, T363) → not_memberc94_out_gggg(T360, T361, T362, T363)
not_memberc117_in_ggggg(T509, T510, T511, T512, T513) → not_memberc117_out_ggggg(T509, T510, T511, T512, T513)
not_memberc140_in_gggggg(T686, T687, T688, T689, T690, T691) → not_memberc140_out_gggggg(T686, T687, T688, T689, T690, T691)
not_memberc163_in_ggggggg(T891, T892, T893, T894, T895, T896, T897) → not_memberc163_out_ggggggg(T891, T892, T893, T894, T895, T896, T897)
not_memberc187_in_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136) → not_memberc187_out_gggggggg(T1129, T1130, T1131, T1132, T1133, T1134, T1135, T1136)
not_memberc210_in_ggg(T1228, T1229, T1230) → not_memberc210_out_ggg(T1228, T1229, T1230)

The argument filtering Pi contains the following mapping:
.(x1, x2) = .(x1, x2)
memberc12_in_ag(x1, x2) = memberc12_in_ag(x2)
memberc12_out_ag(x1, x2) = memberc12_out_ag(x1, x2)
U133_ag(x1, x2, x3, x4) = U133_ag(x2, x3, x4)
not_memberc22_in_g(x1) = not_memberc22_in_g(x1)
not_memberc22_out_g(x1) = not_memberc22_out_g(x1)
not_memberc48_in_gg(x1, x2) = not_memberc48_in_gg(x1, x2)
not_memberc48_out_gg(x1, x2) = not_memberc48_out_gg(x1, x2)
not_memberc71_in_ggg(x1, x2, x3) = not_memberc71_in_ggg(x1, x2, x3)
not_memberc71_out_ggg(x1, x2, x3) = not_memberc71_out_ggg(x1, x2, x3)
not_memberc94_in_gggg(x1, x2, x3, x4) = not_memberc94_in_gggg(x1, x2, x3, x4)
not_memberc94_out_gggg(x1, x2, x3, x4) = not_memberc94_out_gggg(x1, x2, x3, x4)
not_memberc117_in_ggggg(x1, x2, x3, x4, x5) = not_memberc117_in_ggggg(x1, x2, x3, x4, x5)
not_memberc117_out_ggggg(x1, x2, x3, x4, x5) = not_memberc117_out_ggggg(x1, x2, x3, x4, x5)
not_memberc140_in_gggggg(x1, x2, x3, x4, x5, x6) = not_memberc140_in_gggggg(x1, x2, x3, x4, x5, x6)
not_memberc140_out_gggggg(x1, x2, x3, x4, x5, x6) = not_memberc140_out_gggggg(x1, x2, x3, x4, x5, x6)
not_memberc163_in_ggggggg(x1, x2, x3, x4, x5, x6, x7) = not_memberc163_in_ggggggg(x1, x2, x3, x4, x5, x6, x7)
not_memberc163_out_ggggggg(x1, x2, x3, x4, x5, x6, x7) = not_memberc163_out_ggggggg(x1, x2, x3, x4, x5, x6, x7)
not_memberc187_in_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8) = not_memberc187_in_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8)
not_memberc187_out_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8) = not_memberc187_out_gggggggg(x1, x2, x3, x4, x5, x6, x7, x8)
not_memberc210_in_ggg(x1, x2, x3) = not_memberc210_in_ggg(x1, x2, x3)
not_memberc210_out_ggg(x1, x2, x3) = not_memberc210_out_ggg(x1, x2, x3)
SUBSETCHECKED188_IN_AGGG(x1, x2, x3, x4) = SUBSETCHECKED188_IN_AGGG(x2, x3, x4)
U5_AGGG(x1, x2, x3, x4, x5, x6) = U5_AGGG(x3, x4, x5, x6)
U6_AGGG(x1, x2, x3, x4, x5, x6) = U6_AGGG(x1, x3, x4, x5, x6)

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

(22) UsableRulesProof (EQUIVALENT transformation)

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

(23) Obligation:

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

SUBSETCHECKED188_IN_AGGG(.(T1179, T1180), T1170, T1171, T1172) → U5_AGGG(T1179, T1180, T1170, T1171, T1172, memberc12_in_ag(T1179, T1172))
U5_AGGG(T1179, T1180, T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_in_ggg(T1179, T1170, T1171))
U6_AGGG(T1179, T1180, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1180, T1179, .(T1170, T1171), T1172)

The TRS R consists of the following rules:

memberc12_in_ag(T42, .(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(T53, .(T51, T52)) → U133_ag(T53, T51, T52, memberc12_in_ag(T53, T52))
not_memberc210_in_ggg(T1228, T1229, T1230) → not_memberc210_out_ggg(T1228, T1229, T1230)
U133_ag(T53, T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

(24) PiDPToQDPProof (SOUND transformation)

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

(25) Obligation:

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

SUBSETCHECKED188_IN_AGGG(T1170, T1171, T1172) → U5_AGGG(T1170, T1171, T1172, memberc12_in_ag(T1172))
U5_AGGG(T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_in_ggg(T1179, T1170, T1171))
U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1179, .(T1170, T1171), T1172)

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
not_memberc210_in_ggg(T1228, T1229, T1230) → not_memberc210_out_ggg(T1228, T1229, T1230)
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
not_memberc210_in_ggg(x0, x1, x2)
U133_ag(x0, x1, x2)

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

(26) Rewriting (EQUIVALENT transformation)

By rewriting [LPAR04] the rule U5_AGGG(T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_in_ggg(T1179, T1170, T1171)) at position [4] we obtained the following new rules [LPAR04]:

U5_AGGG(T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171))

(27) Obligation:

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

SUBSETCHECKED188_IN_AGGG(T1170, T1171, T1172) → U5_AGGG(T1170, T1171, T1172, memberc12_in_ag(T1172))
U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1179, .(T1170, T1171), T1172)
U5_AGGG(T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
not_memberc210_in_ggg(T1228, T1229, T1230) → not_memberc210_out_ggg(T1228, T1229, T1230)
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
not_memberc210_in_ggg(x0, x1, x2)
U133_ag(x0, x1, x2)

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

(28) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(29) Obligation:

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

SUBSETCHECKED188_IN_AGGG(T1170, T1171, T1172) → U5_AGGG(T1170, T1171, T1172, memberc12_in_ag(T1172))
U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1179, .(T1170, T1171), T1172)
U5_AGGG(T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
not_memberc210_in_ggg(x0, x1, x2)
U133_ag(x0, x1, x2)

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

(30) QReductionProof (EQUIVALENT transformation)

We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].

not_memberc210_in_ggg(x0, x1, x2)

(31) Obligation:

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

SUBSETCHECKED188_IN_AGGG(T1170, T1171, T1172) → U5_AGGG(T1170, T1171, T1172, memberc12_in_ag(T1172))
U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1179, .(T1170, T1171), T1172)
U5_AGGG(T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(32) Narrowing (SOUND transformation)

By narrowing [LPAR04] the rule SUBSETCHECKED188_IN_AGGG(T1170, T1171, T1172) → U5_AGGG(T1170, T1171, T1172, memberc12_in_ag(T1172)) at position [3] we obtained the following new rules [LPAR04]:

SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), memberc12_out_ag(x0, .(x0, x1)))
SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), U133_ag(x0, x1, memberc12_in_ag(x1)))

(33) Obligation:

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

U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1179, .(T1170, T1171), T1172)
U5_AGGG(T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171))
SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), memberc12_out_ag(x0, .(x0, x1)))
SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), U133_ag(x0, x1, memberc12_in_ag(x1)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(34) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U5_AGGG(T1170, T1171, T1172, memberc12_out_ag(T1179, T1172)) → U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) we obtained the following new rules [LPAR04]:

U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(z2, .(z2, z3))) → U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1))
U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(x3, .(z2, z3))) → U6_AGGG(x3, z0, z1, .(z2, z3), not_memberc210_out_ggg(x3, z0, z1))

(35) Obligation:

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

U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1179, .(T1170, T1171), T1172)
SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), memberc12_out_ag(x0, .(x0, x1)))
SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), U133_ag(x0, x1, memberc12_in_ag(x1)))
U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(z2, .(z2, z3))) → U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1))
U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(x3, .(z2, z3))) → U6_AGGG(x3, z0, z1, .(z2, z3), not_memberc210_out_ggg(x3, z0, z1))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(36) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U6_AGGG(T1179, T1170, T1171, T1172, not_memberc210_out_ggg(T1179, T1170, T1171)) → SUBSETCHECKED188_IN_AGGG(T1179, .(T1170, T1171), T1172) we obtained the following new rules [LPAR04]:

U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z2, .(z0, z1), .(z2, z3))
U6_AGGG(z4, z0, z1, .(z2, z3), not_memberc210_out_ggg(z4, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, z1), .(z2, z3))

(37) Obligation:

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

SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), memberc12_out_ag(x0, .(x0, x1)))
SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), U133_ag(x0, x1, memberc12_in_ag(x1)))
U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(z2, .(z2, z3))) → U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1))
U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(x3, .(z2, z3))) → U6_AGGG(x3, z0, z1, .(z2, z3), not_memberc210_out_ggg(x3, z0, z1))
U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z2, .(z0, z1), .(z2, z3))
U6_AGGG(z4, z0, z1, .(z2, z3), not_memberc210_out_ggg(z4, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, z1), .(z2, z3))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(38) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), memberc12_out_ag(x0, .(x0, x1))) we obtained the following new rules [LPAR04]:

SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4)))

(39) Obligation:

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

SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), U133_ag(x0, x1, memberc12_in_ag(x1)))
U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(z2, .(z2, z3))) → U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1))
U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(x3, .(z2, z3))) → U6_AGGG(x3, z0, z1, .(z2, z3), not_memberc210_out_ggg(x3, z0, z1))
U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z2, .(z0, z1), .(z2, z3))
U6_AGGG(z4, z0, z1, .(z2, z3), not_memberc210_out_ggg(z4, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, z1), .(z2, z3))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(40) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule SUBSETCHECKED188_IN_AGGG(y0, y1, .(x0, x1)) → U5_AGGG(y0, y1, .(x0, x1), U133_ag(x0, x1, memberc12_in_ag(x1))) we obtained the following new rules [LPAR04]:

SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))

(41) Obligation:

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

U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(z2, .(z2, z3))) → U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1))
U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(x3, .(z2, z3))) → U6_AGGG(x3, z0, z1, .(z2, z3), not_memberc210_out_ggg(x3, z0, z1))
U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z2, .(z0, z1), .(z2, z3))
U6_AGGG(z4, z0, z1, .(z2, z3), not_memberc210_out_ggg(z4, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, z1), .(z2, z3))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(42) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(z2, .(z2, z3))) → U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1)) we obtained the following new rules [LPAR04]:

U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))

(43) Obligation:

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

U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(x3, .(z2, z3))) → U6_AGGG(x3, z0, z1, .(z2, z3), not_memberc210_out_ggg(x3, z0, z1))
U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z2, .(z0, z1), .(z2, z3))
U6_AGGG(z4, z0, z1, .(z2, z3), not_memberc210_out_ggg(z4, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, z1), .(z2, z3))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(44) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U5_AGGG(z0, z1, .(z2, z3), memberc12_out_ag(x3, .(z2, z3))) → U6_AGGG(x3, z0, z1, .(z2, z3), not_memberc210_out_ggg(x3, z0, z1)) we obtained the following new rules [LPAR04]:

U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(x4, .(z0, z3))) → U6_AGGG(x4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(x4, .(z3, z4))) → U6_AGGG(x4, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(x4, z0, .(z1, z2)))

(45) Obligation:

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

U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z2, .(z0, z1), .(z2, z3))
U6_AGGG(z4, z0, z1, .(z2, z3), not_memberc210_out_ggg(z4, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, z1), .(z2, z3))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(x4, .(z0, z3))) → U6_AGGG(x4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(x4, .(z3, z4))) → U6_AGGG(x4, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(x4, z0, .(z1, z2)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(46) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U6_AGGG(z2, z0, z1, .(z2, z3), not_memberc210_out_ggg(z2, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z2, .(z0, z1), .(z2, z3)) we obtained the following new rules [LPAR04]:

U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z3, .(z0, .(z1, z2)), .(z3, z4))

(47) Obligation:

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

U6_AGGG(z4, z0, z1, .(z2, z3), not_memberc210_out_ggg(z4, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, z1), .(z2, z3))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(x4, .(z0, z3))) → U6_AGGG(x4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(x4, .(z3, z4))) → U6_AGGG(x4, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z3, .(z0, .(z1, z2)), .(z3, z4))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(48) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule U6_AGGG(z4, z0, z1, .(z2, z3), not_memberc210_out_ggg(z4, z0, z1)) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, z1), .(z2, z3)) we obtained the following new rules [LPAR04]:

U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z3, .(z0, .(z1, z2)), .(z3, z4))
U6_AGGG(z4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z4, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z5, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z5, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z5, .(z0, .(z1, z2)), .(z3, z4))

(49) Obligation:

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

SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(x4, .(z0, z3))) → U6_AGGG(x4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(x4, .(z3, z4))) → U6_AGGG(x4, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z3, .(z0, .(z1, z2)), .(z3, z4))
U6_AGGG(z4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z4, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z5, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z5, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z5, .(z0, .(z1, z2)), .(z3, z4))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(50) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) we obtained the following new rules [LPAR04]:

SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), memberc12_out_ag(z0, .(z0, z4)))

(51) Obligation:

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

SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(x4, .(z0, z3))) → U6_AGGG(x4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(x4, .(z3, z4))) → U6_AGGG(x4, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z3, .(z0, .(z1, z2)), .(z3, z4))
U6_AGGG(z4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z4, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z5, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z5, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z5, .(z0, .(z1, z2)), .(z3, z4))
SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), memberc12_out_ag(z0, .(z0, z4)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(52) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) we obtained the following new rules [LPAR04]:

SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), memberc12_out_ag(z0, .(z0, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4), memberc12_out_ag(z1, .(z1, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5), memberc12_out_ag(z4, .(z4, z5)))

(53) Obligation:

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

SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(x4, .(z0, z3))) → U6_AGGG(x4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(x4, .(z3, z4))) → U6_AGGG(x4, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z3, .(z0, .(z1, z2)), .(z3, z4))
U6_AGGG(z4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z4, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z5, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z5, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z5, .(z0, .(z1, z2)), .(z3, z4))
SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), memberc12_out_ag(z0, .(z0, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4), memberc12_out_ag(z1, .(z1, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5), memberc12_out_ag(z4, .(z4, z5)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(54) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z0, z3)) → U5_AGGG(z0, .(z1, z2), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3))) we obtained the following new rules [LPAR04]:

SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), U133_ag(z0, z4, memberc12_in_ag(z4)))

(55) Obligation:

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

SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(x4, .(z0, z3))) → U6_AGGG(x4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(x4, .(z3, z4))) → U6_AGGG(x4, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z3, .(z0, .(z1, z2)), .(z3, z4))
U6_AGGG(z4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z4, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z5, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z5, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z5, .(z0, .(z1, z2)), .(z3, z4))
SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), memberc12_out_ag(z0, .(z0, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4), memberc12_out_ag(z1, .(z1, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5), memberc12_out_ag(z4, .(z4, z5)))
SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), U133_ag(z0, z4, memberc12_in_ag(z4)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(56) Instantiation (EQUIVALENT transformation)

By instantiating [LPAR04] the rule SUBSETCHECKED188_IN_AGGG(z0, .(z1, z2), .(z3, z4)) → U5_AGGG(z0, .(z1, z2), .(z3, z4), U133_ag(z3, z4, memberc12_in_ag(z4))) we obtained the following new rules [LPAR04]:

SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), U133_ag(z0, z4, memberc12_in_ag(z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4), U133_ag(z1, z4, memberc12_in_ag(z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5), U133_ag(z4, z5, memberc12_in_ag(z5)))

(57) Obligation:

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

U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(z3, .(z3, z4))) → U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(x4, .(z0, z3))) → U6_AGGG(x4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U5_AGGG(z0, .(z1, z2), .(z3, z4), memberc12_out_ag(x4, .(z3, z4))) → U6_AGGG(x4, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(x4, z0, .(z1, z2)))
U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z3, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z3, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z3, .(z0, .(z1, z2)), .(z3, z4))
U6_AGGG(z4, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z4, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z4, .(z0, .(z1, z2)), .(z0, z3))
U6_AGGG(z5, z0, .(z1, z2), .(z3, z4), not_memberc210_out_ggg(z5, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z5, .(z0, .(z1, z2)), .(z3, z4))
SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), memberc12_out_ag(z0, .(z0, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4), memberc12_out_ag(z1, .(z1, z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5), memberc12_out_ag(z4, .(z4, z5)))
SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), U133_ag(z0, z3, memberc12_in_ag(z3)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z0, z4), U133_ag(z0, z4, memberc12_in_ag(z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z1, z4), U133_ag(z1, z4, memberc12_in_ag(z4)))
SUBSETCHECKED188_IN_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5)) → U5_AGGG(z0, .(z1, .(z2, z3)), .(z4, z5), U133_ag(z4, z5, memberc12_in_ag(z5)))

The TRS R consists of the following rules:

memberc12_in_ag(.(T42, T43)) → memberc12_out_ag(T42, .(T42, T43))
memberc12_in_ag(.(T51, T52)) → U133_ag(T51, T52, memberc12_in_ag(T52))
U133_ag(T51, T52, memberc12_out_ag(T53, T52)) → memberc12_out_ag(T53, .(T51, T52))

The set Q consists of the following terms:

memberc12_in_ag(x0)
U133_ag(x0, x1, x2)

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

(58) NonTerminationProof (EQUIVALENT transformation)

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

s = U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) evaluates to t =U6_AGGG(z0, z0, .(z0, .(z1, z2)), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z0, .(z1, z2))))

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

Matcher: [z1 / z0, z2 / .(z1, z2)]
Semiunifier: [ ]

Rewriting sequence

U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2))) → SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3))
with rule U6_AGGG(z0', z0', .(z1', z2'), .(z0', z3'), not_memberc210_out_ggg(z0', z0', .(z1', z2'))) → SUBSETCHECKED188_IN_AGGG(z0', .(z0', .(z1', z2')), .(z0', z3')) at position [] and matcher [z0' / z0, z1' / z1, z2' / z2, z3' / z3]

SUBSETCHECKED188_IN_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3)) → U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), memberc12_out_ag(z0, .(z0, z3)))
with rule SUBSETCHECKED188_IN_AGGG(z0', .(z0', .(z1', z2')), .(z0', z3')) → U5_AGGG(z0', .(z0', .(z1', z2')), .(z0', z3'), memberc12_out_ag(z0', .(z0', z3'))) at position [] and matcher [z0' / z0, z1' / z1, z2' / z2, z3' / z3]

U5_AGGG(z0, .(z0, .(z1, z2)), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z0, .(z1, z2)), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z0, .(z1, z2))))
with rule U5_AGGG(z0, .(z1, z2), .(z0, z3), memberc12_out_ag(z0, .(z0, z3))) → U6_AGGG(z0, z0, .(z1, z2), .(z0, z3), not_memberc210_out_ggg(z0, z0, .(z1, z2)))

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

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

(0) Obligation:

(1) PrologToDTProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) TriplesToPiDPProof (SOUND transformation)

(4) Obligation:

(5) DependencyGraphProof (EQUIVALENT transformation)

(6) Complex Obligation (AND)

(7) Obligation:

(8) UsableRulesProof (EQUIVALENT transformation)

(9) Obligation:

(10) PiDPToQDPProof (EQUIVALENT transformation)

(11) Obligation:

(12) QDPSizeChangeProof (EQUIVALENT transformation)

(13) YES

(14) Obligation:

(15) UsableRulesProof (EQUIVALENT transformation)

(16) Obligation:

(17) PiDPToQDPProof (SOUND transformation)

(18) Obligation:

(19) QDPSizeChangeProof (EQUIVALENT transformation)

(20) YES

(21) Obligation:

(22) UsableRulesProof (EQUIVALENT transformation)

(23) Obligation:

(24) PiDPToQDPProof (SOUND transformation)

(25) Obligation:

(26) Rewriting (EQUIVALENT transformation)

(27) Obligation:

(28) UsableRulesProof (EQUIVALENT transformation)

(29) Obligation:

(30) QReductionProof (EQUIVALENT transformation)

(31) Obligation:

(32) Narrowing (SOUND transformation)

(33) Obligation:

(34) Instantiation (EQUIVALENT transformation)

(35) Obligation:

(36) Instantiation (EQUIVALENT transformation)

(37) Obligation:

(38) Instantiation (EQUIVALENT transformation)

(39) Obligation:

(40) Instantiation (EQUIVALENT transformation)

(41) Obligation:

(42) Instantiation (EQUIVALENT transformation)

(43) Obligation:

(44) Instantiation (EQUIVALENT transformation)

(45) Obligation:

(46) Instantiation (EQUIVALENT transformation)

(47) Obligation:

(48) Instantiation (EQUIVALENT transformation)

(49) Obligation:

(50) Instantiation (EQUIVALENT transformation)

(51) Obligation:

(52) Instantiation (EQUIVALENT transformation)

(53) Obligation:

(54) Instantiation (EQUIVALENT transformation)

(55) Obligation:

(56) Instantiation (EQUIVALENT transformation)

(57) Obligation:

(58) NonTerminationProof (EQUIVALENT transformation)

(59) NO