Left Termination proof of /tmp/tmpvxnzcA/delete-ffb.pl

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

0 Prolog

↳1 PrologToPrologProblemTransformerProof (⇒, 684 ms)

↳2 Prolog

↳3 PrologToPiTRSProof (⇒, 265 ms)

↳4 PiTRS

↳5 DependencyPairsProof (⇔, 1274 ms)

↳6 PiDP

↳7 DependencyGraphProof (⇔, 0 ms)

↳8 AND

    ↳9 PiDP

        ↳10 UsableRulesProof (⇔, 0 ms)

        ↳11 PiDP

        ↳12 PiDPToQDPProof (⇒, 0 ms)

        ↳13 QDP

        ↳14 QDPSizeChangeProof (⇔, 0 ms)

        ↳15 YES

    ↳16 PiDP

        ↳17 UsableRulesProof (⇔, 0 ms)

        ↳18 PiDP

        ↳19 PiDPToQDPProof (⇔, 0 ms)

        ↳20 QDP

        ↳21 QDPSizeChangeProof (⇔, 0 ms)

        ↳22 YES

    ↳23 PiDP

        ↳24 UsableRulesProof (⇔, 0 ms)

        ↳25 PiDP

        ↳26 PiDPToQDPProof (⇔, 0 ms)

        ↳27 QDP

        ↳28 QDPSizeChangeProof (⇔, 0 ms)

        ↳29 YES

    ↳30 PiDP

        ↳31 UsableRulesProof (⇔, 0 ms)

        ↳32 PiDP

        ↳33 PiDPToQDPProof (⇒, 0 ms)

        ↳34 QDP

        ↳35 QDPSizeChangeProof (⇔, 0 ms)

        ↳36 YES

    ↳37 PiDP

        ↳38 UsableRulesProof (⇔, 0 ms)

        ↳39 PiDP

        ↳40 PiDPToQDPProof (⇒, 0 ms)

        ↳41 QDP

        ↳42 QDPSizeChangeProof (⇔, 0 ms)

        ↳43 YES

    ↳44 PiDP

        ↳45 UsableRulesProof (⇔, 0 ms)

        ↳46 PiDP

        ↳47 PiDPToQDPProof (⇒, 6 ms)

        ↳48 QDP

        ↳49 QDPSizeChangeProof (⇔, 0 ms)

        ↳50 YES

    ↳51 PiDP

        ↳52 UsableRulesProof (⇔, 0 ms)

        ↳53 PiDP

        ↳54 PiDPToQDPProof (⇒, 0 ms)

        ↳55 QDP

        ↳56 QDPSizeChangeProof (⇔, 0 ms)

        ↳57 YES

(0) Obligation:

Clauses:

delete(X, tree(X, void, Right), Right).
delete(X, tree(X, Left, void), Left).
delete(X, tree(X, Left, Right), tree(Y, Left, Right1)) :- delmin(Right, Y, Right1).
delete(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), delete(X, Left, Left1)).
delete(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), delete(X, Right, Right1)).
delmin(tree(Y, void, Right), Y, Right).
delmin(tree(X, Left, X1), Y, tree(X, Left1, X2)) :- delmin(Left, Y, Left1).
less(0, s(X3)).
less(s(X), s(Y)) :- less(X, Y).

Query: delete(a,a,g)

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph ICLP10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: delete(T1, T2, T3)\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 0 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT3 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: true | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT3 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: delete(T1, T2, T7), SCOPE: 1, CLAUSE: 1 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT7 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | delete(T1, T2, T11), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T11), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T11), SCOPE: 1, CLAUSE: 4\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: delete(T1, T2, T7), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT7 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: delete(T1, T2, T11), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T11), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T11), SCOPE: 1, CLAUSE: 4\n\nT11 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: delmin(T22, T20, T21) | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: delete(T1, T2, T11), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T11), SCOPE: 1, CLAUSE: 4\n\nT11 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, T11) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 5 | delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 6 | ?_2 | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 5\n\nT20 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 6 | ?_2 | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: delmin(T22, T20, T21), SCOPE: 2, CLAUSE: 6\n\nT20 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: ?_2 | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: delmin(T63, T60, T61)\n\nT60 is ground\nT61 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: delmin(T63, T60, T61), SCOPE: 3, CLAUSE: 5 | delmin(T63, T60, T61), SCOPE: 3, CLAUSE: 6\n\nT60 is ground\nT61 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: delmin(T63, T60, T61), SCOPE: 3, CLAUSE: 5\n\nT60 is ground\nT61 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: delmin(T63, T60, T61), SCOPE: 3, CLAUSE: 6\n\nT60 is ground\nT61 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: delmin(T96, T93, T94)\n\nT93 is ground\nT94 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 3\n\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: delete(T1, T2, tree(T20, T18, T21)), SCOPE: 1, CLAUSE: 4\n\nT20 is ground\nT18 is ground\nT21 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: ','(less(T126, T122), delete(T126, T127, T125))\n\nT122 is ground\nT125 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: less(T126, T122)\n\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: delete(T130, T131, T125)\n\nT125 is ground\nT130 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: less(T126, T122), SCOPE: 4, CLAUSE: 7 | less(T126, T122), SCOPE: 4, CLAUSE: 8\n\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: less(T126, T122), SCOPE: 4, CLAUSE: 7\n\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: less(T126, T122), SCOPE: 4, CLAUSE: 8\n\nT122 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: less(T145, T144)\n\nT144 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(less(T163, T167), delete(T167, T168, T166))\n\nT163 is ground\nT166 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: less(T163, T167)\n\nT163 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="47: delete(T171, T172, T166)\n\nT166 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
48 [label="48: less(T163, T167), SCOPE: 5, CLAUSE: 7 | less(T163, T167), SCOPE: 5, CLAUSE: 8\n\nT163 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
49 [label="49: less(T163, T167), SCOPE: 5, CLAUSE: 7\n\nT163 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
50 [label="50: less(T163, T167), SCOPE: 5, CLAUSE: 8\n\nT163 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
51 [label="51: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
52 [label="52: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
53 [label="53: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
54 [label="54: less(T184, T186)\n\nT184 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
55 [label="55: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
56 [label="56: ','(less(T203, T199), delete(T203, T204, T202)) | delete(T1, T2, tree(T199, T202, T201)), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT202 is ground\nT201 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(T199, T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
57 [label="57: delete(T1, T2, T11), SCOPE: 1, CLAUSE: 4\n\nT11 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T1, T2, T11) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, T2, T11) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
58 [label="58: ','(less(T203, T199), delete(T203, T204, T202)), SCOPE: 6, CLAUSE: 7 | ','(less(T203, T199), delete(T203, T204, T202)), SCOPE: 6, CLAUSE: 8 | ?_6 | delete(T1, T2, tree(T199, T202, T201)), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT202 is ground\nT201 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(T199, T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
59 [label="59: ','(less(T203, T199), delete(T203, T204, T202)), SCOPE: 6, CLAUSE: 7\n\nT199 is ground\nT202 is ground\nT201 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(T199, T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
60 [label="60: ','(less(T203, T199), delete(T203, T204, T202)), SCOPE: 6, CLAUSE: 8 | ?_6 | delete(T1, T2, tree(T199, T202, T201)), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT202 is ground\nT201 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(T199, T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
61 [label="61: delete(0, T210, T202)\n\nT202 is ground\nT201 is ground\nT209 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(s(T209), T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
62 [label="62: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
63 [label="63: ','(less(T203, T199), delete(T203, T204, T202)), SCOPE: 6, CLAUSE: 8\n\nT199 is ground\nT202 is ground\nT201 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(T199, T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
64 [label="64: ?_6 | delete(T1, T2, tree(T199, T202, T201)), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT202 is ground\nT201 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(T199, T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
65 [label="65: ','(less(T223, T222), delete(s(T223), T224, T202))\n\nT202 is ground\nT201 is ground\nT222 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(s(T222), T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
66 [label="66: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
67 [label="67: less(T223, T222)\n\nT202 is ground\nT201 is ground\nT222 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(s(T222), T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
68 [label="68: delete(s(T227), T228, T202)\n\nT202 is ground\nT201 is ground\nT222 is ground\nT227 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T229, T230, tree(s(T222), T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
69 [label="69: delete(T1, T2, tree(T199, T202, T201)), SCOPE: 1, CLAUSE: 4\n\nT199 is ground\nT202 is ground\nT201 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(T199, T202, T201)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
70 [label="70: ','(less(T248, T252), delete(T252, T253, T251))\n\nT248 is ground\nT249 is ground\nT251 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\ndelete(T1, T2, tree(T248, T249, T251)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))", fontsize=16, style=filled, fillcolor=lightyellow];
71 [label="71: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
72 [label="72: ','(less(T262, T266), delete(T266, T267, T265))\n\nT262 is ground\nT263 is ground\nT265 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T1, T2, tree(T262, T263, T265)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, T2, tree(T262, T263, T265)) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
73 [label="73: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
74 [label="74: ','(less(T262, T266), delete(T266, T267, T265)), SCOPE: 7, CLAUSE: 7 | ','(less(T262, T266), delete(T266, T267, T265)), SCOPE: 7, CLAUSE: 8\n\nT262 is ground\nT263 is ground\nT265 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T1, T2, tree(T262, T263, T265)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, T2, tree(T262, T263, T265)) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
75 [label="75: ','(less(T262, T266), delete(T266, T267, T265)), SCOPE: 7, CLAUSE: 7\n\nT262 is ground\nT263 is ground\nT265 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T1, T2, tree(T262, T263, T265)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, T2, tree(T262, T263, T265)) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
76 [label="76: ','(less(T262, T266), delete(T266, T267, T265)), SCOPE: 7, CLAUSE: 8\n\nT262 is ground\nT263 is ground\nT265 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T1, T2, tree(T262, T263, T265)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, T2, tree(T262, T263, T265)) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
77 [label="77: delete(s(T274), T273, T265)\n\nT263 is ground\nT265 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T1, T2, tree(0, T263, T265)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, T2, tree(0, T263, T265)) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
78 [label="78: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
79 [label="79: ','(less(T283, T285), delete(s(T285), T286, T265))\n\nT263 is ground\nT265 is ground\nT283 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T1, T2, tree(s(T283), T263, T265)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, T2, tree(s(T283), T263, T265)) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
80 [label="80: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
81 [label="81: less(T283, T285)\n\nT263 is ground\nT265 is ground\nT283 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T1, T2, tree(s(T283), T263, T265)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T1, T2, tree(s(T283), T263, T265)) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
82 [label="82: delete(s(T289), T290, T265)\n\nT263 is ground\nT265 is ground\nT283 is ground\nX17 is free\nX18 is free\nX19 is free\nX20 is free\nX21 is free\nX185 is free\nX186 is free\nX187 is free\nX188 is free\nX189 is free\ndelete(T291, T292, tree(s(T283), T263, T265)) !=? delete(X17, tree(X17, X18, X19), tree(X20, X18, X21))\ndelete(T291, T292, tree(s(T283), T263, T265)) !=? delete(X185, tree(X186, X187, X188), tree(X186, X189, X188))", fontsize=16, style=filled, fillcolor=lightyellow];
83 [label="83: delmin(T309, T307, T308) | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 4\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
84 [label="84: delete(T1, T2, T7), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT7 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, T7) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
85 [label="85: delmin(T309, T307, T308), SCOPE: 8, CLAUSE: 5 | delmin(T309, T307, T308), SCOPE: 8, CLAUSE: 6 | ?_8 | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 4\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
86 [label="86: delmin(T309, T307, T308), SCOPE: 8, CLAUSE: 5\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
87 [label="87: delmin(T309, T307, T308), SCOPE: 8, CLAUSE: 6 | ?_8 | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 4\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
88 [label="88: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
89 [label="89: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
90 [label="90: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
91 [label="91: delmin(T309, T307, T308), SCOPE: 8, CLAUSE: 6\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
92 [label="92: ?_8 | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 4\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
93 [label="93: delmin(T350, T347, T348)\n\nT305 is ground\nT347 is ground\nT344 is ground\nT348 is ground\nT349 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T347, T305, tree(T344, T348, T349))) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
94 [label="94: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
95 [label="95: delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 4\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
96 [label="96: delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 3\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
97 [label="97: delete(T1, T2, tree(T307, T305, T308)), SCOPE: 1, CLAUSE: 4\n\nT307 is ground\nT305 is ground\nT308 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T307, T305, T308)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
98 [label="98: ','(less(T380, T376), delete(T380, T381, T379))\n\nT376 is ground\nT379 is ground\nT378 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T376, T379, T378)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
99 [label="99: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
100 [label="100: ','(less(T395, T399), delete(T399, T400, T398))\n\nT395 is ground\nT396 is ground\nT398 is ground\nX10 is free\nX11 is free\ndelete(T1, T2, tree(T395, T396, T398)) !=? delete(X10, tree(X10, X11, void), X11)", fontsize=16, style=filled, fillcolor=lightyellow];
101 [label="101: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
102 [label="102: ','(less(T413, T409), delete(T413, T414, T412)) | delete(T1, T2, tree(T409, T412, T411)), SCOPE: 1, CLAUSE: 4\n\nT409 is ground\nT412 is ground\nT411 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
103 [label="103: delete(T1, T2, T7), SCOPE: 1, CLAUSE: 4\n\nT7 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\nX370 is free\nX371 is free\nX372 is free\nX373 is free\nX374 is free\ndelete(T1, T2, T7) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, T7) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))\ndelete(T1, T2, T7) !=? delete(X370, tree(X371, X372, X373), tree(X371, X374, X373))", fontsize=16, style=filled, fillcolor=lightyellow];
104 [label="104: ','(less(T413, T409), delete(T413, T414, T412)), SCOPE: 9, CLAUSE: 7 | ','(less(T413, T409), delete(T413, T414, T412)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(T1, T2, tree(T409, T412, T411)), SCOPE: 1, CLAUSE: 4\n\nT409 is ground\nT412 is ground\nT411 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
105 [label="105: ','(less(T413, T409), delete(T413, T414, T412)), SCOPE: 9, CLAUSE: 7\n\nT409 is ground\nT412 is ground\nT411 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
106 [label="106: ','(less(T413, T409), delete(T413, T414, T412)), SCOPE: 9, CLAUSE: 8 | ?_9 | delete(T1, T2, tree(T409, T412, T411)), SCOPE: 1, CLAUSE: 4\n\nT409 is ground\nT412 is ground\nT411 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
107 [label="107: delete(0, T420, T412)\n\nT412 is ground\nT411 is ground\nT419 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(s(T419), T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(s(T419), T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
108 [label="108: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
109 [label="109: ','(less(T413, T409), delete(T413, T414, T412)), SCOPE: 9, CLAUSE: 8\n\nT409 is ground\nT412 is ground\nT411 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
110 [label="110: ?_9 | delete(T1, T2, tree(T409, T412, T411)), SCOPE: 1, CLAUSE: 4\n\nT409 is ground\nT412 is ground\nT411 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
111 [label="111: ','(less(T433, T432), delete(s(T433), T434, T412))\n\nT412 is ground\nT411 is ground\nT432 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(s(T432), T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(s(T432), T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
112 [label="112: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
113 [label="113: delete(T1, T2, tree(T409, T412, T411)), SCOPE: 1, CLAUSE: 4\n\nT409 is ground\nT412 is ground\nT411 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T409, T412, T411)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
114 [label="114: ','(less(T448, T452), delete(T452, T453, T451))\n\nT448 is ground\nT449 is ground\nT451 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\ndelete(T1, T2, tree(T448, T449, T451)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T448, T449, T451)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))", fontsize=16, style=filled, fillcolor=lightyellow];
115 [label="115: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
116 [label="116: ','(less(T462, T466), delete(T466, T467, T465))\n\nT462 is ground\nT463 is ground\nT465 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\nX370 is free\nX371 is free\nX372 is free\nX373 is free\nX374 is free\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X370, tree(X371, X372, X373), tree(X371, X374, X373))", fontsize=16, style=filled, fillcolor=lightyellow];
117 [label="117: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
118 [label="118: ','(less(T462, T466), delete(T466, T467, T465)), SCOPE: 10, CLAUSE: 7 | ','(less(T462, T466), delete(T466, T467, T465)), SCOPE: 10, CLAUSE: 8\n\nT462 is ground\nT463 is ground\nT465 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\nX370 is free\nX371 is free\nX372 is free\nX373 is free\nX374 is free\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X370, tree(X371, X372, X373), tree(X371, X374, X373))", fontsize=16, style=filled, fillcolor=lightyellow];
119 [label="119: ','(less(T462, T466), delete(T466, T467, T465)), SCOPE: 10, CLAUSE: 7\n\nT462 is ground\nT463 is ground\nT465 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\nX370 is free\nX371 is free\nX372 is free\nX373 is free\nX374 is free\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X370, tree(X371, X372, X373), tree(X371, X374, X373))", fontsize=16, style=filled, fillcolor=lightyellow];
120 [label="120: ','(less(T462, T466), delete(T466, T467, T465)), SCOPE: 10, CLAUSE: 8\n\nT462 is ground\nT463 is ground\nT465 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\nX370 is free\nX371 is free\nX372 is free\nX373 is free\nX374 is free\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))\ndelete(T1, T2, tree(T462, T463, T465)) !=? delete(X370, tree(X371, X372, X373), tree(X371, X374, X373))", fontsize=16, style=filled, fillcolor=lightyellow];
121 [label="121: delete(s(T474), T473, T465)\n\nT463 is ground\nT465 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\nX370 is free\nX371 is free\nX372 is free\nX373 is free\nX374 is free\ndelete(T1, T2, tree(0, T463, T465)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(0, T463, T465)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))\ndelete(T1, T2, tree(0, T463, T465)) !=? delete(X370, tree(X371, X372, X373), tree(X371, X374, X373))", fontsize=16, style=filled, fillcolor=lightyellow];
122 [label="122: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
123 [label="123: ','(less(T483, T485), delete(s(T485), T486, T465))\n\nT463 is ground\nT465 is ground\nT483 is ground\nX10 is free\nX11 is free\nX272 is free\nX273 is free\nX274 is free\nX275 is free\nX276 is free\nX370 is free\nX371 is free\nX372 is free\nX373 is free\nX374 is free\ndelete(T1, T2, tree(s(T483), T463, T465)) !=? delete(X10, tree(X10, X11, void), X11)\ndelete(T1, T2, tree(s(T483), T463, T465)) !=? delete(X272, tree(X272, X273, X274), tree(X275, X273, X276))\ndelete(T1, T2, tree(s(T483), T463, T465)) !=? delete(X370, tree(X371, X372, X373), tree(X371, X374, X373))", fontsize=16, style=filled, fillcolor=lightyellow];
124 [label="124: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
125 [label="125: true | delete(T1, T2, T492), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T492), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T492), SCOPE: 1, CLAUSE: 4\n\nT492 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, T492) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
126 [label="126: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT3 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
127 [label="127: delete(T1, T2, T492), SCOPE: 1, CLAUSE: 2 | delete(T1, T2, T492), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T492), SCOPE: 1, CLAUSE: 4\n\nT492 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, T492) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
128 [label="128: delmin(T503, T501, T502) | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 4\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
129 [label="129: delete(T1, T2, T492), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T492), SCOPE: 1, CLAUSE: 4\n\nT492 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, T492) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T492) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
130 [label="130: delmin(T503, T501, T502), SCOPE: 11, CLAUSE: 5 | delmin(T503, T501, T502), SCOPE: 11, CLAUSE: 6 | ?_11 | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 4\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
131 [label="131: delmin(T503, T501, T502), SCOPE: 11, CLAUSE: 5\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
132 [label="132: delmin(T503, T501, T502), SCOPE: 11, CLAUSE: 6 | ?_11 | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 4\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", 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: delmin(T503, T501, T502), SCOPE: 11, CLAUSE: 6\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
137 [label="137: ?_11 | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 4\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
138 [label="138: delmin(T544, T541, T542)\n\nT499 is ground\nT541 is ground\nT538 is ground\nT542 is ground\nT543 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T541, T499, tree(T538, T542, T543))) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
139 [label="139: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
140 [label="140: delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 4\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
141 [label="141: delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 3\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
142 [label="142: delete(T1, T2, tree(T501, T499, T502)), SCOPE: 1, CLAUSE: 4\n\nT501 is ground\nT499 is ground\nT502 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T501, T499, T502)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
143 [label="143: ','(less(T574, T570), delete(T574, T575, T573))\n\nT570 is ground\nT573 is ground\nT572 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T570, T573, T572)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
144 [label="144: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
145 [label="145: ','(less(T589, T593), delete(T593, T594, T592))\n\nT589 is ground\nT590 is ground\nT592 is ground\nX6 is free\nX7 is free\ndelete(T1, T2, tree(T589, T590, T592)) !=? delete(X6, tree(X6, void, X7), X7)", fontsize=16, style=filled, fillcolor=lightyellow];
146 [label="146: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
147 [label="147: ','(less(T607, T603), delete(T607, T608, T606)) | delete(T1, T2, tree(T603, T606, T605)), SCOPE: 1, CLAUSE: 4\n\nT603 is ground\nT606 is ground\nT605 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
148 [label="148: delete(T1, T2, T492), SCOPE: 1, CLAUSE: 4\n\nT492 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX547 is free\nX548 is free\nX549 is free\nX550 is free\nX551 is free\ndelete(T1, T2, T492) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T492) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))\ndelete(T1, T2, T492) !=? delete(X547, tree(X548, X549, X550), tree(X548, X551, X550))", fontsize=16, style=filled, fillcolor=lightyellow];
149 [label="149: ','(less(T607, T603), delete(T607, T608, T606)), SCOPE: 12, CLAUSE: 7 | ','(less(T607, T603), delete(T607, T608, T606)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(T1, T2, tree(T603, T606, T605)), SCOPE: 1, CLAUSE: 4\n\nT603 is ground\nT606 is ground\nT605 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
150 [label="150: ','(less(T607, T603), delete(T607, T608, T606)), SCOPE: 12, CLAUSE: 7\n\nT603 is ground\nT606 is ground\nT605 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
151 [label="151: ','(less(T607, T603), delete(T607, T608, T606)), SCOPE: 12, CLAUSE: 8 | ?_12 | delete(T1, T2, tree(T603, T606, T605)), SCOPE: 1, CLAUSE: 4\n\nT603 is ground\nT606 is ground\nT605 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
152 [label="152: delete(0, T614, T606)\n\nT606 is ground\nT605 is ground\nT613 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(s(T613), T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(s(T613), T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
153 [label="153: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
154 [label="154: ','(less(T607, T603), delete(T607, T608, T606)), SCOPE: 12, CLAUSE: 8\n\nT603 is ground\nT606 is ground\nT605 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
155 [label="155: ?_12 | delete(T1, T2, tree(T603, T606, T605)), SCOPE: 1, CLAUSE: 4\n\nT603 is ground\nT606 is ground\nT605 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
156 [label="156: ','(less(T627, T626), delete(s(T627), T628, T606))\n\nT606 is ground\nT605 is ground\nT626 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(s(T626), T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(s(T626), T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
157 [label="157: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
158 [label="158: delete(T1, T2, tree(T603, T606, T605)), SCOPE: 1, CLAUSE: 4\n\nT603 is ground\nT606 is ground\nT605 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T603, T606, T605)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
159 [label="159: ','(less(T642, T646), delete(T646, T647, T645))\n\nT642 is ground\nT643 is ground\nT645 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\ndelete(T1, T2, tree(T642, T643, T645)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T642, T643, T645)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))", fontsize=16, style=filled, fillcolor=lightyellow];
160 [label="160: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
161 [label="161: ','(less(T656, T660), delete(T660, T661, T659))\n\nT656 is ground\nT657 is ground\nT659 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX547 is free\nX548 is free\nX549 is free\nX550 is free\nX551 is free\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X547, tree(X548, X549, X550), tree(X548, X551, X550))", fontsize=16, style=filled, fillcolor=lightyellow];
162 [label="162: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
163 [label="163: ','(less(T656, T660), delete(T660, T661, T659)), SCOPE: 13, CLAUSE: 7 | ','(less(T656, T660), delete(T660, T661, T659)), SCOPE: 13, CLAUSE: 8\n\nT656 is ground\nT657 is ground\nT659 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX547 is free\nX548 is free\nX549 is free\nX550 is free\nX551 is free\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X547, tree(X548, X549, X550), tree(X548, X551, X550))", fontsize=16, style=filled, fillcolor=lightyellow];
164 [label="164: ','(less(T656, T660), delete(T660, T661, T659)), SCOPE: 13, CLAUSE: 7\n\nT656 is ground\nT657 is ground\nT659 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX547 is free\nX548 is free\nX549 is free\nX550 is free\nX551 is free\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X547, tree(X548, X549, X550), tree(X548, X551, X550))", fontsize=16, style=filled, fillcolor=lightyellow];
165 [label="165: ','(less(T656, T660), delete(T660, T661, T659)), SCOPE: 13, CLAUSE: 8\n\nT656 is ground\nT657 is ground\nT659 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX547 is free\nX548 is free\nX549 is free\nX550 is free\nX551 is free\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))\ndelete(T1, T2, tree(T656, T657, T659)) !=? delete(X547, tree(X548, X549, X550), tree(X548, X551, X550))", fontsize=16, style=filled, fillcolor=lightyellow];
166 [label="166: delete(s(T668), T667, T659)\n\nT657 is ground\nT659 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX547 is free\nX548 is free\nX549 is free\nX550 is free\nX551 is free\ndelete(T1, T2, tree(0, T657, T659)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(0, T657, T659)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))\ndelete(T1, T2, tree(0, T657, T659)) !=? delete(X547, tree(X548, X549, X550), tree(X548, X551, X550))", fontsize=16, style=filled, fillcolor=lightyellow];
167 [label="167: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
168 [label="168: ','(less(T677, T679), delete(s(T679), T680, T659))\n\nT657 is ground\nT659 is ground\nT677 is ground\nX6 is free\nX7 is free\nX449 is free\nX450 is free\nX451 is free\nX452 is free\nX453 is free\nX547 is free\nX548 is free\nX549 is free\nX550 is free\nX551 is free\ndelete(T1, T2, tree(s(T677), T657, T659)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(s(T677), T657, T659)) !=? delete(X449, tree(X449, X450, X451), tree(X452, X450, X453))\ndelete(T1, T2, tree(s(T677), T657, T659)) !=? delete(X547, tree(X548, X549, X550), tree(X548, X551, X550))", fontsize=16, style=filled, fillcolor=lightyellow];
169 [label="169: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
170 [label="170: delmin(T693, T691, T692) | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 4\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
171 [label="171: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT3 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, T3) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
172 [label="172: delmin(T693, T691, T692), SCOPE: 14, CLAUSE: 5 | delmin(T693, T691, T692), SCOPE: 14, CLAUSE: 6 | ?_14 | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 4\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
173 [label="173: delmin(T693, T691, T692), SCOPE: 14, CLAUSE: 5\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
174 [label="174: delmin(T693, T691, T692), SCOPE: 14, CLAUSE: 6 | ?_14 | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 4\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
175 [label="175: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
176 [label="176: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
177 [label="177: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
178 [label="178: delmin(T693, T691, T692), SCOPE: 14, CLAUSE: 6\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
179 [label="179: ?_14 | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 4\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
180 [label="180: delmin(T734, T731, T732)\n\nT689 is ground\nT731 is ground\nT728 is ground\nT732 is ground\nT733 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T731, T689, tree(T728, T732, T733))) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T731, T689, tree(T728, T732, T733))) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
181 [label="181: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
182 [label="182: delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 3 | delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 4\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
183 [label="183: delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 3\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
184 [label="184: delete(T1, T2, tree(T691, T689, T692)), SCOPE: 1, CLAUSE: 4\n\nT691 is ground\nT689 is ground\nT692 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T691, T689, T692)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
185 [label="185: ','(less(T764, T760), delete(T764, T765, T763))\n\nT760 is ground\nT763 is ground\nT762 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T760, T763, T762)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T760, T763, T762)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
186 [label="186: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
187 [label="187: ','(less(T779, T783), delete(T783, T784, T782))\n\nT779 is ground\nT780 is ground\nT782 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\ndelete(T1, T2, tree(T779, T780, T782)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T779, T780, T782)) !=? delete(X442, tree(X442, X443, void), X443)", fontsize=16, style=filled, fillcolor=lightyellow];
188 [label="188: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
189 [label="189: ','(less(T797, T793), delete(T797, T798, T796)) | delete(T1, T2, tree(T793, T796, T795)), SCOPE: 1, CLAUSE: 4\n\nT793 is ground\nT796 is ground\nT795 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
190 [label="190: delete(T1, T2, T3), SCOPE: 1, CLAUSE: 4\n\nT3 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\nX720 is free\nX721 is free\nX722 is free\nX723 is free\nX724 is free\ndelete(T1, T2, T3) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, T3) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, T3) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))\ndelete(T1, T2, T3) !=? delete(X720, tree(X721, X722, X723), tree(X721, X724, X723))", fontsize=16, style=filled, fillcolor=lightyellow];
191 [label="191: ','(less(T797, T793), delete(T797, T798, T796)), SCOPE: 15, CLAUSE: 7 | ','(less(T797, T793), delete(T797, T798, T796)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(T1, T2, tree(T793, T796, T795)), SCOPE: 1, CLAUSE: 4\n\nT793 is ground\nT796 is ground\nT795 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
192 [label="192: ','(less(T797, T793), delete(T797, T798, T796)), SCOPE: 15, CLAUSE: 7\n\nT793 is ground\nT796 is ground\nT795 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
193 [label="193: ','(less(T797, T793), delete(T797, T798, T796)), SCOPE: 15, CLAUSE: 8 | ?_15 | delete(T1, T2, tree(T793, T796, T795)), SCOPE: 1, CLAUSE: 4\n\nT793 is ground\nT796 is ground\nT795 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
194 [label="194: delete(0, T804, T796)\n\nT796 is ground\nT795 is ground\nT803 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(s(T803), T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(s(T803), T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(s(T803), T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
195 [label="195: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
196 [label="196: ','(less(T797, T793), delete(T797, T798, T796)), SCOPE: 15, CLAUSE: 8\n\nT793 is ground\nT796 is ground\nT795 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
197 [label="197: ?_15 | delete(T1, T2, tree(T793, T796, T795)), SCOPE: 1, CLAUSE: 4\n\nT793 is ground\nT796 is ground\nT795 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
198 [label="198: ','(less(T817, T816), delete(s(T817), T818, T796))\n\nT796 is ground\nT795 is ground\nT816 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(s(T816), T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(s(T816), T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(s(T816), T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
199 [label="199: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
200 [label="200: delete(T1, T2, tree(T793, T796, T795)), SCOPE: 1, CLAUSE: 4\n\nT793 is ground\nT796 is ground\nT795 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T793, T796, T795)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
201 [label="201: ','(less(T832, T836), delete(T836, T837, T835))\n\nT832 is ground\nT833 is ground\nT835 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\ndelete(T1, T2, tree(T832, T833, T835)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T832, T833, T835)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T832, T833, T835)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))", fontsize=16, style=filled, fillcolor=lightyellow];
202 [label="202: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
203 [label="203: ','(less(T846, T850), delete(T850, T851, T849))\n\nT846 is ground\nT847 is ground\nT849 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\nX720 is free\nX721 is free\nX722 is free\nX723 is free\nX724 is free\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X720, tree(X721, X722, X723), tree(X721, X724, X723))", fontsize=16, style=filled, fillcolor=lightyellow];
204 [label="204: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
205 [label="205: ','(less(T846, T850), delete(T850, T851, T849)), SCOPE: 16, CLAUSE: 7 | ','(less(T846, T850), delete(T850, T851, T849)), SCOPE: 16, CLAUSE: 8\n\nT846 is ground\nT847 is ground\nT849 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\nX720 is free\nX721 is free\nX722 is free\nX723 is free\nX724 is free\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X720, tree(X721, X722, X723), tree(X721, X724, X723))", fontsize=16, style=filled, fillcolor=lightyellow];
206 [label="206: ','(less(T846, T850), delete(T850, T851, T849)), SCOPE: 16, CLAUSE: 7\n\nT846 is ground\nT847 is ground\nT849 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\nX720 is free\nX721 is free\nX722 is free\nX723 is free\nX724 is free\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X720, tree(X721, X722, X723), tree(X721, X724, X723))", fontsize=16, style=filled, fillcolor=lightyellow];
207 [label="207: ','(less(T846, T850), delete(T850, T851, T849)), SCOPE: 16, CLAUSE: 8\n\nT846 is ground\nT847 is ground\nT849 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\nX720 is free\nX721 is free\nX722 is free\nX723 is free\nX724 is free\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))\ndelete(T1, T2, tree(T846, T847, T849)) !=? delete(X720, tree(X721, X722, X723), tree(X721, X724, X723))", fontsize=16, style=filled, fillcolor=lightyellow];
208 [label="208: delete(s(T858), T857, T849)\n\nT847 is ground\nT849 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\nX720 is free\nX721 is free\nX722 is free\nX723 is free\nX724 is free\ndelete(T1, T2, tree(0, T847, T849)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(0, T847, T849)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(0, T847, T849)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))\ndelete(T1, T2, tree(0, T847, T849)) !=? delete(X720, tree(X721, X722, X723), tree(X721, X724, X723))", fontsize=16, style=filled, fillcolor=lightyellow];
209 [label="209: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
210 [label="210: ','(less(T867, T869), delete(s(T869), T870, T849))\n\nT847 is ground\nT849 is ground\nT867 is ground\nX6 is free\nX7 is free\nX442 is free\nX443 is free\nX622 is free\nX623 is free\nX624 is free\nX625 is free\nX626 is free\nX720 is free\nX721 is free\nX722 is free\nX723 is free\nX724 is free\ndelete(T1, T2, tree(s(T867), T847, T849)) !=? delete(X6, tree(X6, void, X7), X7)\ndelete(T1, T2, tree(s(T867), T847, T849)) !=? delete(X442, tree(X442, X443, void), X443)\ndelete(T1, T2, tree(s(T867), T847, T849)) !=? delete(X622, tree(X622, X623, X624), tree(X625, X623, X626))\ndelete(T1, T2, tree(s(T867), T847, T849)) !=? delete(X720, tree(X721, X722, X723), tree(X721, X724, X723))", fontsize=16, style=filled, fillcolor=lightyellow];
211 [label="211: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
212 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 212 [arrowhead = none ];
212 -> 2;

213 [label="EVAL with clause\ndelete(X6, tree(X6, void, X7), X7).\nand substitutionT1 -> T6,\nX6 -> T6,\nX7 -> T7,\nT2 -> tree(T6, void, T7),\nT3 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 213 [arrowhead = none ];
213 -> 3;

214 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 214 [arrowhead = none ];
214 -> 4;

215 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 215 [arrowhead = none ];
215 -> 5;

216 [label="EVAL with clause\ndelete(X442, tree(X442, X443, void), X443).\nand substitutionT1 -> T491,\nX442 -> T491,\nX443 -> T492,\nT2 -> tree(T491, T492, void),\nT3 -> T492", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 216 [arrowhead = none ];
216 -> 125;

217 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 217 [arrowhead = none ];
217 -> 126;

218 [label="EVAL with clause\ndelete(X10, tree(X10, X11, void), X11).\nand substitutionT1 -> T10,\nX10 -> T10,\nX11 -> T11,\nT2 -> tree(T10, T11, void),\nT7 -> T11", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 218 [arrowhead = none ];
218 -> 6;

219 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 219 [arrowhead = none ];
219 -> 7;

220 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 220 [arrowhead = none ];
220 -> 8;

221 [label="EVAL with clause\ndelete(X272, tree(X272, X273, X274), tree(X275, X273, X276)) :- delmin(X274, X275, X276).\nand substitutionT1 -> T304,\nX272 -> T304,\nX273 -> T305,\nX274 -> T309,\nT2 -> tree(T304, T305, T309),\nX275 -> T307,\nX276 -> T308,\nT7 -> tree(T307, T305, T308),\nT306 -> T309", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 221 [arrowhead = none ];
221 -> 83;

222 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
7 -> 222 [arrowhead = none ];
222 -> 84;

223 [label="EVAL with clause\ndelete(X17, tree(X17, X18, X19), tree(X20, X18, X21)) :- delmin(X19, X20, X21).\nand substitutionT1 -> T17,\nX17 -> T17,\nX18 -> T18,\nX19 -> T22,\nT2 -> tree(T17, T18, T22),\nX20 -> T20,\nX21 -> T21,\nT11 -> tree(T20, T18, T21),\nT19 -> T22", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 223 [arrowhead = none ];
223 -> 9;

224 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
8 -> 224 [arrowhead = none ];
224 -> 10;

225 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 225 [arrowhead = none ];
225 -> 11;

226 [label="EVAL with clause\ndelete(X185, tree(X186, X187, X188), tree(X186, X189, X188)) :- ','(less(X185, X186), delete(X185, X187, X189)).\nand substitutionT1 -> T203,\nX185 -> T203,\nX186 -> T199,\nX187 -> T204,\nX188 -> T201,\nT2 -> tree(T199, T204, T201),\nX189 -> T202,\nT11 -> tree(T199, T202, T201),\nT198 -> T203,\nT200 -> T204", fontsize=14, style = filled, fillcolor = lightblue];
10 -> 226 [arrowhead = none ];
226 -> 56;

227 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 227 [arrowhead = none ];
227 -> 57;

228 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 228 [arrowhead = none ];
228 -> 12;

229 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
11 -> 229 [arrowhead = none ];
229 -> 13;

230 [label="EVAL with clause\ndelmin(tree(X30, void, X31), X30, X31).\nand substitutionX30 -> T31,\nX31 -> T32,\nT22 -> tree(T31, void, T32),\nT20 -> T31,\nT21 -> T32", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 230 [arrowhead = none ];
230 -> 14;

231 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 231 [arrowhead = none ];
231 -> 15;

232 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 232 [arrowhead = none ];
232 -> 17;

233 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
13 -> 233 [arrowhead = none ];
233 -> 18;

234 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
14 -> 234 [arrowhead = none ];
234 -> 16;

235 [label="EVAL with clause\ndelmin(tree(X56, X57, X58), X59, tree(X56, X60, X61)) :- delmin(X57, X59, X60).\nand substitutionX56 -> T57,\nX57 -> T63,\nX58 -> T59,\nT22 -> tree(T57, T63, T59),\nT20 -> T60,\nX59 -> T60,\nX60 -> T61,\nX61 -> T62,\nT21 -> tree(T57, T61, T62),\nT58 -> T63", fontsize=14, style = filled, fillcolor = lightblue];
17 -> 235 [arrowhead = none ];
235 -> 19;

236 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 236 [arrowhead = none ];
236 -> 20;

237 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
18 -> 237 [arrowhead = none ];
237 -> 29;

238 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
19 -> 238 [arrowhead = none ];
238 -> 21;

239 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 239 [arrowhead = none ];
239 -> 22;

240 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
21 -> 240 [arrowhead = none ];
240 -> 23;

241 [label="EVAL with clause\ndelmin(tree(X74, void, X75), X74, X75).\nand substitutionX74 -> T76,\nX75 -> T77,\nT63 -> tree(T76, void, T77),\nT60 -> T76,\nT61 -> T77", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 241 [arrowhead = none ];
241 -> 24;

242 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 242 [arrowhead = none ];
242 -> 25;

243 [label="EVAL with clause\ndelmin(tree(X88, X89, X90), X91, tree(X88, X92, X93)) :- delmin(X89, X91, X92).\nand substitutionX88 -> T90,\nX89 -> T96,\nX90 -> T92,\nT63 -> tree(T90, T96, T92),\nT60 -> T93,\nX91 -> T93,\nX92 -> T94,\nX93 -> T95,\nT61 -> tree(T90, T94, T95),\nT91 -> T96", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 243 [arrowhead = none ];
243 -> 27;

244 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 244 [arrowhead = none ];
244 -> 28;

245 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 245 [arrowhead = none ];
245 -> 26;

246 [label="INSTANCE with matching:\nT63 -> T96\nT60 -> T93\nT61 -> T94", fontsize=14, style = filled, fillcolor = lightgrey];
27 -> 246 [arrowhead = none , style=dashed];
246 -> 19[style=dashed];

247 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
29 -> 247 [arrowhead = none ];
247 -> 30;

248 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
29 -> 248 [arrowhead = none ];
248 -> 31;

249 [label="EVAL with clause\ndelete(X118, tree(X119, X120, X121), tree(X119, X122, X121)) :- ','(less(X118, X119), delete(X118, X120, X122)).\nand substitutionT1 -> T126,\nX118 -> T126,\nX119 -> T122,\nX120 -> T127,\nX121 -> T124,\nT2 -> tree(T122, T127, T124),\nT20 -> T122,\nT18 -> T125,\nX122 -> T125,\nT21 -> T124,\nT121 -> T126,\nT123 -> T127", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 249 [arrowhead = none ];
249 -> 32;

250 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
30 -> 250 [arrowhead = none ];
250 -> 33;

251 [label="EVAL with clause\ndelete(X154, tree(X155, X156, X157), tree(X155, X156, X158)) :- ','(less(X155, X154), delete(X154, X157, X158)).\nand substitutionT1 -> T167,\nX154 -> T167,\nX155 -> T163,\nX156 -> T164,\nX157 -> T168,\nT2 -> tree(T163, T164, T168),\nT20 -> T163,\nT18 -> T164,\nT21 -> T166,\nX158 -> T166,\nT162 -> T167,\nT165 -> T168", fontsize=14, style = filled, fillcolor = lightblue];
31 -> 251 [arrowhead = none ];
251 -> 44;

252 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 252 [arrowhead = none ];
252 -> 45;

253 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
32 -> 253 [arrowhead = none ];
253 -> 34;

254 [label="SPLIT 2\nnew knowledge:\nT130 is ground\nT122 is ground\nreplacements:T126 -> T130,\nT127 -> T131", fontsize=14, style = filled, fillcolor = violet];
32 -> 254 [arrowhead = none ];
254 -> 35;

255 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
34 -> 255 [arrowhead = none ];
255 -> 36;

256 [label="INSTANCE with matching:\nT1 -> T130\nT2 -> T131\nT3 -> T125", fontsize=14, style = filled, fillcolor = lightgrey];
35 -> 256 [arrowhead = none , style=dashed];
256 -> 1[style=dashed];

257 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
36 -> 257 [arrowhead = none ];
257 -> 37;

258 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
36 -> 258 [arrowhead = none ];
258 -> 38;

259 [label="EVAL with clause\nless(0, s(X131)).\nand substitutionT126 -> 0,\nX131 -> T138,\nT122 -> s(T138)", fontsize=14, style = filled, fillcolor = lightblue];
37 -> 259 [arrowhead = none ];
259 -> 39;

260 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
37 -> 260 [arrowhead = none ];
260 -> 40;

261 [label="EVAL with clause\nless(s(X136), s(X137)) :- less(X136, X137).\nand substitutionX136 -> T145,\nT126 -> s(T145),\nX137 -> T144,\nT122 -> s(T144),\nT143 -> T145", fontsize=14, style = filled, fillcolor = lightblue];
38 -> 261 [arrowhead = none ];
261 -> 42;

262 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
38 -> 262 [arrowhead = none ];
262 -> 43;

263 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
39 -> 263 [arrowhead = none ];
263 -> 41;

264 [label="INSTANCE with matching:\nT126 -> T145\nT122 -> T144", fontsize=14, style = filled, fillcolor = lightgrey];
42 -> 264 [arrowhead = none , style=dashed];
264 -> 34[style=dashed];

265 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
44 -> 265 [arrowhead = none ];
265 -> 46;

266 [label="SPLIT 2\nnew knowledge:\nT163 is ground\nreplacements:T167 -> T171,\nT168 -> T172", fontsize=14, style = filled, fillcolor = violet];
44 -> 266 [arrowhead = none ];
266 -> 47;

267 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
46 -> 267 [arrowhead = none ];
267 -> 48;

268 [label="INSTANCE with matching:\nT1 -> T171\nT2 -> T172\nT3 -> T166", fontsize=14, style = filled, fillcolor = lightgrey];
47 -> 268 [arrowhead = none , style=dashed];
268 -> 1[style=dashed];

269 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
48 -> 269 [arrowhead = none ];
269 -> 49;

270 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
48 -> 270 [arrowhead = none ];
270 -> 50;

271 [label="EVAL with clause\nless(0, s(X167)).\nand substitutionT163 -> 0,\nX167 -> T179,\nT167 -> s(T179)", fontsize=14, style = filled, fillcolor = lightblue];
49 -> 271 [arrowhead = none ];
271 -> 51;

272 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
49 -> 272 [arrowhead = none ];
272 -> 52;

273 [label="EVAL with clause\nless(s(X172), s(X173)) :- less(X172, X173).\nand substitutionX172 -> T184,\nT163 -> s(T184),\nX173 -> T186,\nT167 -> s(T186),\nT185 -> T186", fontsize=14, style = filled, fillcolor = lightblue];
50 -> 273 [arrowhead = none ];
273 -> 54;

274 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
50 -> 274 [arrowhead = none ];
274 -> 55;

275 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
51 -> 275 [arrowhead = none ];
275 -> 53;

276 [label="INSTANCE with matching:\nT163 -> T184\nT167 -> T186", fontsize=14, style = filled, fillcolor = lightgrey];
54 -> 276 [arrowhead = none , style=dashed];
276 -> 46[style=dashed];

277 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
56 -> 277 [arrowhead = none ];
277 -> 58;

278 [label="EVAL with clause\ndelete(X239, tree(X240, X241, X242), tree(X240, X241, X243)) :- ','(less(X240, X239), delete(X239, X242, X243)).\nand substitutionT1 -> T266,\nX239 -> T266,\nX240 -> T262,\nX241 -> T263,\nX242 -> T267,\nT2 -> tree(T262, T263, T267),\nX243 -> T265,\nT11 -> tree(T262, T263, T265),\nT261 -> T266,\nT264 -> T267", fontsize=14, style = filled, fillcolor = lightblue];
57 -> 278 [arrowhead = none ];
278 -> 72;

279 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
57 -> 279 [arrowhead = none ];
279 -> 73;

280 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 280 [arrowhead = none ];
280 -> 59;

281 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
58 -> 281 [arrowhead = none ];
281 -> 60;

282 [label="EVAL with clause\nless(0, s(X194)).\nand substitutionT203 -> 0,\nX194 -> T209,\nT199 -> s(T209),\nT204 -> T210", fontsize=14, style = filled, fillcolor = lightblue];
59 -> 282 [arrowhead = none ];
282 -> 61;

283 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
59 -> 283 [arrowhead = none ];
283 -> 62;

284 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
60 -> 284 [arrowhead = none ];
284 -> 63;

285 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
60 -> 285 [arrowhead = none ];
285 -> 64;

286 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T210\nT3 -> T202", fontsize=14, style = filled, fillcolor = lightgrey];
61 -> 286 [arrowhead = none , style=dashed];
286 -> 1[style=dashed];

287 [label="EVAL with clause\nless(s(X207), s(X208)) :- less(X207, X208).\nand substitutionX207 -> T223,\nT203 -> s(T223),\nX208 -> T222,\nT199 -> s(T222),\nT221 -> T223,\nT204 -> T224", fontsize=14, style = filled, fillcolor = lightblue];
63 -> 287 [arrowhead = none ];
287 -> 65;

288 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
63 -> 288 [arrowhead = none ];
288 -> 66;

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

290 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
65 -> 290 [arrowhead = none ];
290 -> 67;

291 [label="SPLIT 2\nnew knowledge:\nT227 is ground\nT222 is ground\nreplacements:T223 -> T227,\nT224 -> T228,\nT1 -> T229,\nT2 -> T230", fontsize=14, style = filled, fillcolor = violet];
65 -> 291 [arrowhead = none ];
291 -> 68;

292 [label="INSTANCE with matching:\nT126 -> T223\nT122 -> T222", fontsize=14, style = filled, fillcolor = lightgrey];
67 -> 292 [arrowhead = none , style=dashed];
292 -> 34[style=dashed];

293 [label="INSTANCE with matching:\nT1 -> s(T227)\nT2 -> T228\nT3 -> T202", fontsize=14, style = filled, fillcolor = lightgrey];
68 -> 293 [arrowhead = none , style=dashed];
293 -> 1[style=dashed];

294 [label="EVAL with clause\ndelete(X227, tree(X228, X229, X230), tree(X228, X229, X231)) :- ','(less(X228, X227), delete(X227, X230, X231)).\nand substitutionT1 -> T252,\nX227 -> T252,\nX228 -> T248,\nX229 -> T249,\nX230 -> T253,\nT2 -> tree(T248, T249, T253),\nT199 -> T248,\nT202 -> T249,\nT201 -> T251,\nX231 -> T251,\nT247 -> T252,\nT250 -> T253", fontsize=14, style = filled, fillcolor = lightblue];
69 -> 294 [arrowhead = none ];
294 -> 70;

295 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
69 -> 295 [arrowhead = none ];
295 -> 71;

296 [label="INSTANCE with matching:\nT163 -> T248\nT167 -> T252\nT168 -> T253\nT166 -> T251", fontsize=14, style = filled, fillcolor = lightgrey];
70 -> 296 [arrowhead = none , style=dashed];
296 -> 44[style=dashed];

297 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
72 -> 297 [arrowhead = none ];
297 -> 74;

298 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 298 [arrowhead = none ];
298 -> 75;

299 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
74 -> 299 [arrowhead = none ];
299 -> 76;

300 [label="EVAL with clause\nless(0, s(X248)).\nand substitutionT262 -> 0,\nX248 -> T274,\nT266 -> s(T274),\nT267 -> T273,\nT272 -> T274", fontsize=14, style = filled, fillcolor = lightblue];
75 -> 300 [arrowhead = none ];
300 -> 77;

301 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
75 -> 301 [arrowhead = none ];
301 -> 78;

302 [label="EVAL with clause\nless(s(X257), s(X258)) :- less(X257, X258).\nand substitutionX257 -> T283,\nT262 -> s(T283),\nX258 -> T285,\nT266 -> s(T285),\nT284 -> T285,\nT267 -> T286", fontsize=14, style = filled, fillcolor = lightblue];
76 -> 302 [arrowhead = none ];
302 -> 79;

303 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
76 -> 303 [arrowhead = none ];
303 -> 80;

304 [label="INSTANCE with matching:\nT1 -> s(T274)\nT2 -> T273\nT3 -> T265", fontsize=14, style = filled, fillcolor = lightgrey];
77 -> 304 [arrowhead = none , style=dashed];
304 -> 1[style=dashed];

305 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
79 -> 305 [arrowhead = none ];
305 -> 81;

306 [label="SPLIT 2\nnew knowledge:\nT283 is ground\nreplacements:T285 -> T289,\nT286 -> T290,\nT1 -> T291,\nT2 -> T292", fontsize=14, style = filled, fillcolor = violet];
79 -> 306 [arrowhead = none ];
306 -> 82;

307 [label="INSTANCE with matching:\nT163 -> T283\nT167 -> T285", fontsize=14, style = filled, fillcolor = lightgrey];
81 -> 307 [arrowhead = none , style=dashed];
307 -> 46[style=dashed];

308 [label="INSTANCE with matching:\nT1 -> s(T289)\nT2 -> T290\nT3 -> T265", fontsize=14, style = filled, fillcolor = lightgrey];
82 -> 308 [arrowhead = none , style=dashed];
308 -> 1[style=dashed];

309 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
83 -> 309 [arrowhead = none ];
309 -> 85;

310 [label="EVAL with clause\ndelete(X370, tree(X371, X372, X373), tree(X371, X374, X373)) :- ','(less(X370, X371), delete(X370, X372, X374)).\nand substitutionT1 -> T413,\nX370 -> T413,\nX371 -> T409,\nX372 -> T414,\nX373 -> T411,\nT2 -> tree(T409, T414, T411),\nX374 -> T412,\nT7 -> tree(T409, T412, T411),\nT408 -> T413,\nT410 -> T414", fontsize=14, style = filled, fillcolor = lightblue];
84 -> 310 [arrowhead = none ];
310 -> 102;

311 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
84 -> 311 [arrowhead = none ];
311 -> 103;

312 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
85 -> 312 [arrowhead = none ];
312 -> 86;

313 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
85 -> 313 [arrowhead = none ];
313 -> 87;

314 [label="EVAL with clause\ndelmin(tree(X285, void, X286), X285, X286).\nand substitutionX285 -> T318,\nX286 -> T319,\nT309 -> tree(T318, void, T319),\nT307 -> T318,\nT308 -> T319", fontsize=14, style = filled, fillcolor = lightblue];
86 -> 314 [arrowhead = none ];
314 -> 88;

315 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
86 -> 315 [arrowhead = none ];
315 -> 89;

316 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 316 [arrowhead = none ];
316 -> 91;

317 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
87 -> 317 [arrowhead = none ];
317 -> 92;

318 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
88 -> 318 [arrowhead = none ];
318 -> 90;

319 [label="EVAL with clause\ndelmin(tree(X311, X312, X313), X314, tree(X311, X315, X316)) :- delmin(X312, X314, X315).\nand substitutionX311 -> T344,\nX312 -> T350,\nX313 -> T346,\nT309 -> tree(T344, T350, T346),\nT307 -> T347,\nX314 -> T347,\nX315 -> T348,\nX316 -> T349,\nT308 -> tree(T344, T348, T349),\nT345 -> T350", fontsize=14, style = filled, fillcolor = lightblue];
91 -> 319 [arrowhead = none ];
319 -> 93;

320 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
91 -> 320 [arrowhead = none ];
320 -> 94;

321 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
92 -> 321 [arrowhead = none ];
321 -> 95;

322 [label="INSTANCE with matching:\nT63 -> T350\nT60 -> T347\nT61 -> T348", fontsize=14, style = filled, fillcolor = lightgrey];
93 -> 322 [arrowhead = none , style=dashed];
322 -> 19[style=dashed];

323 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
95 -> 323 [arrowhead = none ];
323 -> 96;

324 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
95 -> 324 [arrowhead = none ];
324 -> 97;

325 [label="EVAL with clause\ndelete(X341, tree(X342, X343, X344), tree(X342, X345, X344)) :- ','(less(X341, X342), delete(X341, X343, X345)).\nand substitutionT1 -> T380,\nX341 -> T380,\nX342 -> T376,\nX343 -> T381,\nX344 -> T378,\nT2 -> tree(T376, T381, T378),\nT307 -> T376,\nT305 -> T379,\nX345 -> T379,\nT308 -> T378,\nT375 -> T380,\nT377 -> T381", fontsize=14, style = filled, fillcolor = lightblue];
96 -> 325 [arrowhead = none ];
325 -> 98;

326 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
96 -> 326 [arrowhead = none ];
326 -> 99;

327 [label="EVAL with clause\ndelete(X358, tree(X359, X360, X361), tree(X359, X360, X362)) :- ','(less(X359, X358), delete(X358, X361, X362)).\nand substitutionT1 -> T399,\nX358 -> T399,\nX359 -> T395,\nX360 -> T396,\nX361 -> T400,\nT2 -> tree(T395, T396, T400),\nT307 -> T395,\nT305 -> T396,\nT308 -> T398,\nX362 -> T398,\nT394 -> T399,\nT397 -> T400", fontsize=14, style = filled, fillcolor = lightblue];
97 -> 327 [arrowhead = none ];
327 -> 100;

328 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
97 -> 328 [arrowhead = none ];
328 -> 101;

329 [label="INSTANCE with matching:\nT126 -> T380\nT122 -> T376\nT127 -> T381\nT125 -> T379", fontsize=14, style = filled, fillcolor = lightgrey];
98 -> 329 [arrowhead = none , style=dashed];
329 -> 32[style=dashed];

330 [label="INSTANCE with matching:\nT163 -> T395\nT167 -> T399\nT168 -> T400\nT166 -> T398", fontsize=14, style = filled, fillcolor = lightgrey];
100 -> 330 [arrowhead = none , style=dashed];
330 -> 44[style=dashed];

331 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
102 -> 331 [arrowhead = none ];
331 -> 104;

332 [label="EVAL with clause\ndelete(X418, tree(X419, X420, X421), tree(X419, X420, X422)) :- ','(less(X419, X418), delete(X418, X421, X422)).\nand substitutionT1 -> T466,\nX418 -> T466,\nX419 -> T462,\nX420 -> T463,\nX421 -> T467,\nT2 -> tree(T462, T463, T467),\nX422 -> T465,\nT7 -> tree(T462, T463, T465),\nT461 -> T466,\nT464 -> T467", fontsize=14, style = filled, fillcolor = lightblue];
103 -> 332 [arrowhead = none ];
332 -> 116;

333 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
103 -> 333 [arrowhead = none ];
333 -> 117;

334 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 334 [arrowhead = none ];
334 -> 105;

335 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
104 -> 335 [arrowhead = none ];
335 -> 106;

336 [label="EVAL with clause\nless(0, s(X379)).\nand substitutionT413 -> 0,\nX379 -> T419,\nT409 -> s(T419),\nT414 -> T420", fontsize=14, style = filled, fillcolor = lightblue];
105 -> 336 [arrowhead = none ];
336 -> 107;

337 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
105 -> 337 [arrowhead = none ];
337 -> 108;

338 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 338 [arrowhead = none ];
338 -> 109;

339 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
106 -> 339 [arrowhead = none ];
339 -> 110;

340 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T420\nT3 -> T412", fontsize=14, style = filled, fillcolor = lightgrey];
107 -> 340 [arrowhead = none , style=dashed];
340 -> 1[style=dashed];

341 [label="EVAL with clause\nless(s(X392), s(X393)) :- less(X392, X393).\nand substitutionX392 -> T433,\nT413 -> s(T433),\nX393 -> T432,\nT409 -> s(T432),\nT431 -> T433,\nT414 -> T434", fontsize=14, style = filled, fillcolor = lightblue];
109 -> 341 [arrowhead = none ];
341 -> 111;

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

343 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
110 -> 343 [arrowhead = none ];
343 -> 113;

344 [label="INSTANCE with matching:\nT223 -> T433\nT222 -> T432\nT224 -> T434\nT202 -> T412\nT201 -> T411\nX17 -> X272\nX18 -> X273\nX19 -> X274\nX20 -> X275\nX21 -> X276", fontsize=14, style = filled, fillcolor = lightgrey];
111 -> 344 [arrowhead = none , style=dashed];
344 -> 65[style=dashed];

345 [label="EVAL with clause\ndelete(X406, tree(X407, X408, X409), tree(X407, X408, X410)) :- ','(less(X407, X406), delete(X406, X409, X410)).\nand substitutionT1 -> T452,\nX406 -> T452,\nX407 -> T448,\nX408 -> T449,\nX409 -> T453,\nT2 -> tree(T448, T449, T453),\nT409 -> T448,\nT412 -> T449,\nT411 -> T451,\nX410 -> T451,\nT447 -> T452,\nT450 -> T453", fontsize=14, style = filled, fillcolor = lightblue];
113 -> 345 [arrowhead = none ];
345 -> 114;

346 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
113 -> 346 [arrowhead = none ];
346 -> 115;

347 [label="INSTANCE with matching:\nT163 -> T448\nT167 -> T452\nT168 -> T453\nT166 -> T451", fontsize=14, style = filled, fillcolor = lightgrey];
114 -> 347 [arrowhead = none , style=dashed];
347 -> 44[style=dashed];

348 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
116 -> 348 [arrowhead = none ];
348 -> 118;

349 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
118 -> 349 [arrowhead = none ];
349 -> 119;

350 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
118 -> 350 [arrowhead = none ];
350 -> 120;

351 [label="EVAL with clause\nless(0, s(X427)).\nand substitutionT462 -> 0,\nX427 -> T474,\nT466 -> s(T474),\nT467 -> T473,\nT472 -> T474", fontsize=14, style = filled, fillcolor = lightblue];
119 -> 351 [arrowhead = none ];
351 -> 121;

352 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
119 -> 352 [arrowhead = none ];
352 -> 122;

353 [label="EVAL with clause\nless(s(X436), s(X437)) :- less(X436, X437).\nand substitutionX436 -> T483,\nT462 -> s(T483),\nX437 -> T485,\nT466 -> s(T485),\nT484 -> T485,\nT467 -> T486", fontsize=14, style = filled, fillcolor = lightblue];
120 -> 353 [arrowhead = none ];
353 -> 123;

354 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
120 -> 354 [arrowhead = none ];
354 -> 124;

355 [label="INSTANCE with matching:\nT1 -> s(T474)\nT2 -> T473\nT3 -> T465", fontsize=14, style = filled, fillcolor = lightgrey];
121 -> 355 [arrowhead = none , style=dashed];
355 -> 1[style=dashed];

356 [label="INSTANCE with matching:\nT283 -> T483\nT285 -> T485\nT286 -> T486\nT265 -> T465\nT263 -> T463\nX17 -> X272\nX18 -> X273\nX19 -> X274\nX20 -> X275\nX21 -> X276\nX185 -> X370\nX186 -> X371\nX187 -> X372\nX188 -> X373\nX189 -> X374", fontsize=14, style = filled, fillcolor = lightgrey];
123 -> 356 [arrowhead = none , style=dashed];
356 -> 79[style=dashed];

357 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
125 -> 357 [arrowhead = none ];
357 -> 127;

358 [label="EVAL with clause\ndelete(X622, tree(X622, X623, X624), tree(X625, X623, X626)) :- delmin(X624, X625, X626).\nand substitutionT1 -> T688,\nX622 -> T688,\nX623 -> T689,\nX624 -> T693,\nT2 -> tree(T688, T689, T693),\nX625 -> T691,\nX626 -> T692,\nT3 -> tree(T691, T689, T692),\nT690 -> T693", fontsize=14, style = filled, fillcolor = lightblue];
126 -> 358 [arrowhead = none ];
358 -> 170;

359 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
126 -> 359 [arrowhead = none ];
359 -> 171;

360 [label="EVAL with clause\ndelete(X449, tree(X449, X450, X451), tree(X452, X450, X453)) :- delmin(X451, X452, X453).\nand substitutionT1 -> T498,\nX449 -> T498,\nX450 -> T499,\nX451 -> T503,\nT2 -> tree(T498, T499, T503),\nX452 -> T501,\nX453 -> T502,\nT492 -> tree(T501, T499, T502),\nT500 -> T503", fontsize=14, style = filled, fillcolor = lightblue];
127 -> 360 [arrowhead = none ];
360 -> 128;

361 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
127 -> 361 [arrowhead = none ];
361 -> 129;

362 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
128 -> 362 [arrowhead = none ];
362 -> 130;

363 [label="EVAL with clause\ndelete(X547, tree(X548, X549, X550), tree(X548, X551, X550)) :- ','(less(X547, X548), delete(X547, X549, X551)).\nand substitutionT1 -> T607,\nX547 -> T607,\nX548 -> T603,\nX549 -> T608,\nX550 -> T605,\nT2 -> tree(T603, T608, T605),\nX551 -> T606,\nT492 -> tree(T603, T606, T605),\nT602 -> T607,\nT604 -> T608", fontsize=14, style = filled, fillcolor = lightblue];
129 -> 363 [arrowhead = none ];
363 -> 147;

364 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
129 -> 364 [arrowhead = none ];
364 -> 148;

365 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
130 -> 365 [arrowhead = none ];
365 -> 131;

366 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
130 -> 366 [arrowhead = none ];
366 -> 132;

367 [label="EVAL with clause\ndelmin(tree(X462, void, X463), X462, X463).\nand substitutionX462 -> T512,\nX463 -> T513,\nT503 -> tree(T512, void, T513),\nT501 -> T512,\nT502 -> T513", fontsize=14, style = filled, fillcolor = lightblue];
131 -> 367 [arrowhead = none ];
367 -> 133;

368 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
131 -> 368 [arrowhead = none ];
368 -> 134;

369 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 369 [arrowhead = none ];
369 -> 136;

370 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
132 -> 370 [arrowhead = none ];
370 -> 137;

371 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
133 -> 371 [arrowhead = none ];
371 -> 135;

372 [label="EVAL with clause\ndelmin(tree(X488, X489, X490), X491, tree(X488, X492, X493)) :- delmin(X489, X491, X492).\nand substitutionX488 -> T538,\nX489 -> T544,\nX490 -> T540,\nT503 -> tree(T538, T544, T540),\nT501 -> T541,\nX491 -> T541,\nX492 -> T542,\nX493 -> T543,\nT502 -> tree(T538, T542, T543),\nT539 -> T544", fontsize=14, style = filled, fillcolor = lightblue];
136 -> 372 [arrowhead = none ];
372 -> 138;

373 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
136 -> 373 [arrowhead = none ];
373 -> 139;

374 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
137 -> 374 [arrowhead = none ];
374 -> 140;

375 [label="INSTANCE with matching:\nT63 -> T544\nT60 -> T541\nT61 -> T542", fontsize=14, style = filled, fillcolor = lightgrey];
138 -> 375 [arrowhead = none , style=dashed];
375 -> 19[style=dashed];

376 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
140 -> 376 [arrowhead = none ];
376 -> 141;

377 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
140 -> 377 [arrowhead = none ];
377 -> 142;

378 [label="EVAL with clause\ndelete(X518, tree(X519, X520, X521), tree(X519, X522, X521)) :- ','(less(X518, X519), delete(X518, X520, X522)).\nand substitutionT1 -> T574,\nX518 -> T574,\nX519 -> T570,\nX520 -> T575,\nX521 -> T572,\nT2 -> tree(T570, T575, T572),\nT501 -> T570,\nT499 -> T573,\nX522 -> T573,\nT502 -> T572,\nT569 -> T574,\nT571 -> T575", fontsize=14, style = filled, fillcolor = lightblue];
141 -> 378 [arrowhead = none ];
378 -> 143;

379 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
141 -> 379 [arrowhead = none ];
379 -> 144;

380 [label="EVAL with clause\ndelete(X535, tree(X536, X537, X538), tree(X536, X537, X539)) :- ','(less(X536, X535), delete(X535, X538, X539)).\nand substitutionT1 -> T593,\nX535 -> T593,\nX536 -> T589,\nX537 -> T590,\nX538 -> T594,\nT2 -> tree(T589, T590, T594),\nT501 -> T589,\nT499 -> T590,\nT502 -> T592,\nX539 -> T592,\nT588 -> T593,\nT591 -> T594", fontsize=14, style = filled, fillcolor = lightblue];
142 -> 380 [arrowhead = none ];
380 -> 145;

381 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
142 -> 381 [arrowhead = none ];
381 -> 146;

382 [label="INSTANCE with matching:\nT126 -> T574\nT122 -> T570\nT127 -> T575\nT125 -> T573", fontsize=14, style = filled, fillcolor = lightgrey];
143 -> 382 [arrowhead = none , style=dashed];
382 -> 32[style=dashed];

383 [label="INSTANCE with matching:\nT163 -> T589\nT167 -> T593\nT168 -> T594\nT166 -> T592", fontsize=14, style = filled, fillcolor = lightgrey];
145 -> 383 [arrowhead = none , style=dashed];
383 -> 44[style=dashed];

384 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
147 -> 384 [arrowhead = none ];
384 -> 149;

385 [label="EVAL with clause\ndelete(X595, tree(X596, X597, X598), tree(X596, X597, X599)) :- ','(less(X596, X595), delete(X595, X598, X599)).\nand substitutionT1 -> T660,\nX595 -> T660,\nX596 -> T656,\nX597 -> T657,\nX598 -> T661,\nT2 -> tree(T656, T657, T661),\nX599 -> T659,\nT492 -> tree(T656, T657, T659),\nT655 -> T660,\nT658 -> T661", fontsize=14, style = filled, fillcolor = lightblue];
148 -> 385 [arrowhead = none ];
385 -> 161;

386 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
148 -> 386 [arrowhead = none ];
386 -> 162;

387 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
149 -> 387 [arrowhead = none ];
387 -> 150;

388 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
149 -> 388 [arrowhead = none ];
388 -> 151;

389 [label="EVAL with clause\nless(0, s(X556)).\nand substitutionT607 -> 0,\nX556 -> T613,\nT603 -> s(T613),\nT608 -> T614", fontsize=14, style = filled, fillcolor = lightblue];
150 -> 389 [arrowhead = none ];
389 -> 152;

390 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
150 -> 390 [arrowhead = none ];
390 -> 153;

391 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
151 -> 391 [arrowhead = none ];
391 -> 154;

392 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
151 -> 392 [arrowhead = none ];
392 -> 155;

393 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T614\nT3 -> T606", fontsize=14, style = filled, fillcolor = lightgrey];
152 -> 393 [arrowhead = none , style=dashed];
393 -> 1[style=dashed];

394 [label="EVAL with clause\nless(s(X569), s(X570)) :- less(X569, X570).\nand substitutionX569 -> T627,\nT607 -> s(T627),\nX570 -> T626,\nT603 -> s(T626),\nT625 -> T627,\nT608 -> T628", fontsize=14, style = filled, fillcolor = lightblue];
154 -> 394 [arrowhead = none ];
394 -> 156;

395 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
154 -> 395 [arrowhead = none ];
395 -> 157;

396 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
155 -> 396 [arrowhead = none ];
396 -> 158;

397 [label="INSTANCE with matching:\nT223 -> T627\nT222 -> T626\nT224 -> T628\nT202 -> T606\nT201 -> T605\nX17 -> X449\nX18 -> X450\nX19 -> X451\nX20 -> X452\nX21 -> X453", fontsize=14, style = filled, fillcolor = lightgrey];
156 -> 397 [arrowhead = none , style=dashed];
397 -> 65[style=dashed];

398 [label="EVAL with clause\ndelete(X583, tree(X584, X585, X586), tree(X584, X585, X587)) :- ','(less(X584, X583), delete(X583, X586, X587)).\nand substitutionT1 -> T646,\nX583 -> T646,\nX584 -> T642,\nX585 -> T643,\nX586 -> T647,\nT2 -> tree(T642, T643, T647),\nT603 -> T642,\nT606 -> T643,\nT605 -> T645,\nX587 -> T645,\nT641 -> T646,\nT644 -> T647", fontsize=14, style = filled, fillcolor = lightblue];
158 -> 398 [arrowhead = none ];
398 -> 159;

399 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
158 -> 399 [arrowhead = none ];
399 -> 160;

400 [label="INSTANCE with matching:\nT163 -> T642\nT167 -> T646\nT168 -> T647\nT166 -> T645", fontsize=14, style = filled, fillcolor = lightgrey];
159 -> 400 [arrowhead = none , style=dashed];
400 -> 44[style=dashed];

401 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
161 -> 401 [arrowhead = none ];
401 -> 163;

402 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
163 -> 402 [arrowhead = none ];
402 -> 164;

403 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
163 -> 403 [arrowhead = none ];
403 -> 165;

404 [label="EVAL with clause\nless(0, s(X604)).\nand substitutionT656 -> 0,\nX604 -> T668,\nT660 -> s(T668),\nT661 -> T667,\nT666 -> T668", fontsize=14, style = filled, fillcolor = lightblue];
164 -> 404 [arrowhead = none ];
404 -> 166;

405 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
164 -> 405 [arrowhead = none ];
405 -> 167;

406 [label="EVAL with clause\nless(s(X613), s(X614)) :- less(X613, X614).\nand substitutionX613 -> T677,\nT656 -> s(T677),\nX614 -> T679,\nT660 -> s(T679),\nT678 -> T679,\nT661 -> T680", fontsize=14, style = filled, fillcolor = lightblue];
165 -> 406 [arrowhead = none ];
406 -> 168;

407 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
165 -> 407 [arrowhead = none ];
407 -> 169;

408 [label="INSTANCE with matching:\nT1 -> s(T668)\nT2 -> T667\nT3 -> T659", fontsize=14, style = filled, fillcolor = lightgrey];
166 -> 408 [arrowhead = none , style=dashed];
408 -> 1[style=dashed];

409 [label="INSTANCE with matching:\nT283 -> T677\nT285 -> T679\nT286 -> T680\nT265 -> T659\nT263 -> T657\nX17 -> X449\nX18 -> X450\nX19 -> X451\nX20 -> X452\nX21 -> X453\nX185 -> X547\nX186 -> X548\nX187 -> X549\nX188 -> X550\nX189 -> X551", fontsize=14, style = filled, fillcolor = lightgrey];
168 -> 409 [arrowhead = none , style=dashed];
409 -> 79[style=dashed];

410 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
170 -> 410 [arrowhead = none ];
410 -> 172;

411 [label="EVAL with clause\ndelete(X720, tree(X721, X722, X723), tree(X721, X724, X723)) :- ','(less(X720, X721), delete(X720, X722, X724)).\nand substitutionT1 -> T797,\nX720 -> T797,\nX721 -> T793,\nX722 -> T798,\nX723 -> T795,\nT2 -> tree(T793, T798, T795),\nX724 -> T796,\nT3 -> tree(T793, T796, T795),\nT792 -> T797,\nT794 -> T798", fontsize=14, style = filled, fillcolor = lightblue];
171 -> 411 [arrowhead = none ];
411 -> 189;

412 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
171 -> 412 [arrowhead = none ];
412 -> 190;

413 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
172 -> 413 [arrowhead = none ];
413 -> 173;

414 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
172 -> 414 [arrowhead = none ];
414 -> 174;

415 [label="EVAL with clause\ndelmin(tree(X635, void, X636), X635, X636).\nand substitutionX635 -> T702,\nX636 -> T703,\nT693 -> tree(T702, void, T703),\nT691 -> T702,\nT692 -> T703", fontsize=14, style = filled, fillcolor = lightblue];
173 -> 415 [arrowhead = none ];
415 -> 175;

416 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
173 -> 416 [arrowhead = none ];
416 -> 176;

417 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
174 -> 417 [arrowhead = none ];
417 -> 178;

418 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
174 -> 418 [arrowhead = none ];
418 -> 179;

419 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
175 -> 419 [arrowhead = none ];
419 -> 177;

420 [label="EVAL with clause\ndelmin(tree(X661, X662, X663), X664, tree(X661, X665, X666)) :- delmin(X662, X664, X665).\nand substitutionX661 -> T728,\nX662 -> T734,\nX663 -> T730,\nT693 -> tree(T728, T734, T730),\nT691 -> T731,\nX664 -> T731,\nX665 -> T732,\nX666 -> T733,\nT692 -> tree(T728, T732, T733),\nT729 -> T734", fontsize=14, style = filled, fillcolor = lightblue];
178 -> 420 [arrowhead = none ];
420 -> 180;

421 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
178 -> 421 [arrowhead = none ];
421 -> 181;

422 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
179 -> 422 [arrowhead = none ];
422 -> 182;

423 [label="INSTANCE with matching:\nT63 -> T734\nT60 -> T731\nT61 -> T732", fontsize=14, style = filled, fillcolor = lightgrey];
180 -> 423 [arrowhead = none , style=dashed];
423 -> 19[style=dashed];

424 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
182 -> 424 [arrowhead = none ];
424 -> 183;

425 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
182 -> 425 [arrowhead = none ];
425 -> 184;

426 [label="EVAL with clause\ndelete(X691, tree(X692, X693, X694), tree(X692, X695, X694)) :- ','(less(X691, X692), delete(X691, X693, X695)).\nand substitutionT1 -> T764,\nX691 -> T764,\nX692 -> T760,\nX693 -> T765,\nX694 -> T762,\nT2 -> tree(T760, T765, T762),\nT691 -> T760,\nT689 -> T763,\nX695 -> T763,\nT692 -> T762,\nT759 -> T764,\nT761 -> T765", fontsize=14, style = filled, fillcolor = lightblue];
183 -> 426 [arrowhead = none ];
426 -> 185;

427 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
183 -> 427 [arrowhead = none ];
427 -> 186;

428 [label="EVAL with clause\ndelete(X708, tree(X709, X710, X711), tree(X709, X710, X712)) :- ','(less(X709, X708), delete(X708, X711, X712)).\nand substitutionT1 -> T783,\nX708 -> T783,\nX709 -> T779,\nX710 -> T780,\nX711 -> T784,\nT2 -> tree(T779, T780, T784),\nT691 -> T779,\nT689 -> T780,\nT692 -> T782,\nX712 -> T782,\nT778 -> T783,\nT781 -> T784", fontsize=14, style = filled, fillcolor = lightblue];
184 -> 428 [arrowhead = none ];
428 -> 187;

429 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
184 -> 429 [arrowhead = none ];
429 -> 188;

430 [label="INSTANCE with matching:\nT126 -> T764\nT122 -> T760\nT127 -> T765\nT125 -> T763", fontsize=14, style = filled, fillcolor = lightgrey];
185 -> 430 [arrowhead = none , style=dashed];
430 -> 32[style=dashed];

431 [label="INSTANCE with matching:\nT163 -> T779\nT167 -> T783\nT168 -> T784\nT166 -> T782", fontsize=14, style = filled, fillcolor = lightgrey];
187 -> 431 [arrowhead = none , style=dashed];
431 -> 44[style=dashed];

432 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
189 -> 432 [arrowhead = none ];
432 -> 191;

433 [label="EVAL with clause\ndelete(X768, tree(X769, X770, X771), tree(X769, X770, X772)) :- ','(less(X769, X768), delete(X768, X771, X772)).\nand substitutionT1 -> T850,\nX768 -> T850,\nX769 -> T846,\nX770 -> T847,\nX771 -> T851,\nT2 -> tree(T846, T847, T851),\nX772 -> T849,\nT3 -> tree(T846, T847, T849),\nT845 -> T850,\nT848 -> T851", fontsize=14, style = filled, fillcolor = lightblue];
190 -> 433 [arrowhead = none ];
433 -> 203;

434 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
190 -> 434 [arrowhead = none ];
434 -> 204;

435 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
191 -> 435 [arrowhead = none ];
435 -> 192;

436 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
191 -> 436 [arrowhead = none ];
436 -> 193;

437 [label="EVAL with clause\nless(0, s(X729)).\nand substitutionT797 -> 0,\nX729 -> T803,\nT793 -> s(T803),\nT798 -> T804", fontsize=14, style = filled, fillcolor = lightblue];
192 -> 437 [arrowhead = none ];
437 -> 194;

438 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
192 -> 438 [arrowhead = none ];
438 -> 195;

439 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 439 [arrowhead = none ];
439 -> 196;

440 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
193 -> 440 [arrowhead = none ];
440 -> 197;

441 [label="INSTANCE with matching:\nT1 -> 0\nT2 -> T804\nT3 -> T796", fontsize=14, style = filled, fillcolor = lightgrey];
194 -> 441 [arrowhead = none , style=dashed];
441 -> 1[style=dashed];

442 [label="EVAL with clause\nless(s(X742), s(X743)) :- less(X742, X743).\nand substitutionX742 -> T817,\nT797 -> s(T817),\nX743 -> T816,\nT793 -> s(T816),\nT815 -> T817,\nT798 -> T818", fontsize=14, style = filled, fillcolor = lightblue];
196 -> 442 [arrowhead = none ];
442 -> 198;

443 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
196 -> 443 [arrowhead = none ];
443 -> 199;

444 [label="FAILURE", fontsize=14, style = filled, fillcolor = lightgreen];
197 -> 444 [arrowhead = none ];
444 -> 200;

445 [label="INSTANCE with matching:\nT223 -> T817\nT222 -> T816\nT224 -> T818\nT202 -> T796\nT201 -> T795\nX17 -> X622\nX18 -> X623\nX19 -> X624\nX20 -> X625\nX21 -> X626", fontsize=14, style = filled, fillcolor = lightgrey];
198 -> 445 [arrowhead = none , style=dashed];
445 -> 65[style=dashed];

446 [label="EVAL with clause\ndelete(X756, tree(X757, X758, X759), tree(X757, X758, X760)) :- ','(less(X757, X756), delete(X756, X759, X760)).\nand substitutionT1 -> T836,\nX756 -> T836,\nX757 -> T832,\nX758 -> T833,\nX759 -> T837,\nT2 -> tree(T832, T833, T837),\nT793 -> T832,\nT796 -> T833,\nT795 -> T835,\nX760 -> T835,\nT831 -> T836,\nT834 -> T837", fontsize=14, style = filled, fillcolor = lightblue];
200 -> 446 [arrowhead = none ];
446 -> 201;

447 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
200 -> 447 [arrowhead = none ];
447 -> 202;

448 [label="INSTANCE with matching:\nT163 -> T832\nT167 -> T836\nT168 -> T837\nT166 -> T835", fontsize=14, style = filled, fillcolor = lightgrey];
201 -> 448 [arrowhead = none , style=dashed];
448 -> 44[style=dashed];

449 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
203 -> 449 [arrowhead = none ];
449 -> 205;

450 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 450 [arrowhead = none ];
450 -> 206;

451 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
205 -> 451 [arrowhead = none ];
451 -> 207;

452 [label="EVAL with clause\nless(0, s(X777)).\nand substitutionT846 -> 0,\nX777 -> T858,\nT850 -> s(T858),\nT851 -> T857,\nT856 -> T858", fontsize=14, style = filled, fillcolor = lightblue];
206 -> 452 [arrowhead = none ];
452 -> 208;

453 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
206 -> 453 [arrowhead = none ];
453 -> 209;

454 [label="EVAL with clause\nless(s(X786), s(X787)) :- less(X786, X787).\nand substitutionX786 -> T867,\nT846 -> s(T867),\nX787 -> T869,\nT850 -> s(T869),\nT868 -> T869,\nT851 -> T870", fontsize=14, style = filled, fillcolor = lightblue];
207 -> 454 [arrowhead = none ];
454 -> 210;

455 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
207 -> 455 [arrowhead = none ];
455 -> 211;

456 [label="INSTANCE with matching:\nT1 -> s(T858)\nT2 -> T857\nT3 -> T849", fontsize=14, style = filled, fillcolor = lightgrey];
208 -> 456 [arrowhead = none , style=dashed];
456 -> 1[style=dashed];

457 [label="INSTANCE with matching:\nT283 -> T867\nT285 -> T869\nT286 -> T870\nT265 -> T849\nT263 -> T847\nX17 -> X622\nX18 -> X623\nX19 -> X624\nX20 -> X625\nX21 -> X626\nX185 -> X720\nX186 -> X721\nX187 -> X722\nX188 -> X723\nX189 -> X724", fontsize=14, style = filled, fillcolor = lightgrey];
210 -> 457 [arrowhead = none , style=dashed];
457 -> 79[style=dashed];

}

(2) Obligation:

Clauses:

delminA(tree(T76, void, T77), T76, T77).
delminA(tree(T90, T96, T92), T93, tree(T90, T94, T95)) :- delminA(T96, T93, T94).
lessB(0, s(T138)).
lessB(s(T145), s(T144)) :- lessB(T145, T144).
lessC(0, s(T179)).
lessC(s(T184), s(T186)) :- lessC(T184, T186).
pD(T163, T167, T168, T166) :- lessC(T163, T167).
pD(T163, T171, T172, T166) :- ','(lessC(T163, T171), deleteE(T171, T172, T166)).
pF(T126, T122, T127, T125) :- lessB(T126, T122).
pF(T130, T122, T131, T125) :- ','(lessB(T130, T122), deleteE(T130, T131, T125)).
pG(T223, T222, T224, T202) :- lessB(T223, T222).
pG(T227, T222, T228, T202) :- ','(lessB(T227, T222), deleteE(s(T227), T228, T202)).
pH(T283, T285, T286, T265) :- lessC(T283, T285).
pH(T283, T289, T290, T265) :- ','(lessC(T283, T289), deleteE(s(T289), T290, T265)).
deleteE(T6, tree(T6, void, T7), T7).
deleteE(T10, tree(T10, T11, void), T11).
deleteE(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)).
deleteE(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) :- delminA(T63, T60, T61).
deleteE(T126, tree(T122, T127, T124), tree(T122, T125, T124)) :- pF(T126, T122, T127, T125).
deleteE(T167, tree(T163, T164, T168), tree(T163, T164, T166)) :- pD(T163, T167, T168, T166).
deleteE(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) :- deleteE(0, T210, T202).
deleteE(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) :- pG(T223, T222, T224, T202).
deleteE(T252, tree(T248, T249, T253), tree(T248, T249, T251)) :- pD(T248, T252, T253, T251).
deleteE(s(T274), tree(0, T263, T273), tree(0, T263, T265)) :- deleteE(s(T274), T273, T265).
deleteE(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) :- pH(T283, T285, T286, T265).
deleteE(T304, tree(T304, T305, tree(T318, void, T319)), tree(T318, T305, T319)).
deleteE(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) :- delminA(T350, T347, T348).
deleteE(T380, tree(T376, T381, T378), tree(T376, T379, T378)) :- pF(T380, T376, T381, T379).
deleteE(T399, tree(T395, T396, T400), tree(T395, T396, T398)) :- pD(T395, T399, T400, T398).
deleteE(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) :- deleteE(0, T420, T412).
deleteE(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) :- pG(T433, T432, T434, T412).
deleteE(T452, tree(T448, T449, T453), tree(T448, T449, T451)) :- pD(T448, T452, T453, T451).
deleteE(s(T474), tree(0, T463, T473), tree(0, T463, T465)) :- deleteE(s(T474), T473, T465).
deleteE(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) :- pH(T483, T485, T486, T465).
deleteE(T491, tree(T491, T492, void), T492).
deleteE(T498, tree(T498, T499, tree(T512, void, T513)), tree(T512, T499, T513)).
deleteE(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) :- delminA(T544, T541, T542).
deleteE(T574, tree(T570, T575, T572), tree(T570, T573, T572)) :- pF(T574, T570, T575, T573).
deleteE(T593, tree(T589, T590, T594), tree(T589, T590, T592)) :- pD(T589, T593, T594, T592).
deleteE(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) :- deleteE(0, T614, T606).
deleteE(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) :- pG(T627, T626, T628, T606).
deleteE(T646, tree(T642, T643, T647), tree(T642, T643, T645)) :- pD(T642, T646, T647, T645).
deleteE(s(T668), tree(0, T657, T667), tree(0, T657, T659)) :- deleteE(s(T668), T667, T659).
deleteE(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) :- pH(T677, T679, T680, T659).
deleteE(T688, tree(T688, T689, tree(T702, void, T703)), tree(T702, T689, T703)).
deleteE(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) :- delminA(T734, T731, T732).
deleteE(T764, tree(T760, T765, T762), tree(T760, T763, T762)) :- pF(T764, T760, T765, T763).
deleteE(T783, tree(T779, T780, T784), tree(T779, T780, T782)) :- pD(T779, T783, T784, T782).
deleteE(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) :- deleteE(0, T804, T796).
deleteE(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) :- pG(T817, T816, T818, T796).
deleteE(T836, tree(T832, T833, T837), tree(T832, T833, T835)) :- pD(T832, T836, T837, T835).
deleteE(s(T858), tree(0, T847, T857), tree(0, T847, T849)) :- deleteE(s(T858), T857, T849).
deleteE(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) :- pH(T867, T869, T870, T849).

Query: deleteE(a,a,g)

(3) PrologToPiTRSProof (SOUND transformation)

We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
deleteE_in: (f,f,b) (b,f,b)
delminA_in: (f,b,b)
pF_in: (f,b,f,b) (b,b,f,b)
lessB_in: (f,b) (b,b)
pD_in: (b,b,f,b) (b,f,f,b)
lessC_in: (b,b) (b,f)
pG_in: (b,b,f,b) (f,b,f,b)
pH_in: (b,b,f,b) (b,f,f,b)
Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

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

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(5) DependencyPairsProof (EQUIVALENT transformation)

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

DELETEE_IN_AAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_AAG(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
DELETEE_IN_AAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → DELMINA_IN_AGG(T63, T60, T61)
DELMINA_IN_AGG(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_AGG(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
DELMINA_IN_AGG(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → DELMINA_IN_AGG(T96, T93, T94)
DELETEE_IN_AAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_AAG(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
DELETEE_IN_AAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → PF_IN_AGAG(T126, T122, T127, T125)
PF_IN_AGAG(T126, T122, T127, T125) → U7_AGAG(T126, T122, T127, T125, lessB_in_ag(T126, T122))
PF_IN_AGAG(T126, T122, T127, T125) → LESSB_IN_AG(T126, T122)
LESSB_IN_AG(s(T145), s(T144)) → U2_AG(T145, T144, lessB_in_ag(T145, T144))
LESSB_IN_AG(s(T145), s(T144)) → LESSB_IN_AG(T145, T144)
PF_IN_AGAG(T130, T122, T131, T125) → U8_AGAG(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_AGAG(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_AGAG(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
U8_AGAG(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → DELETEE_IN_GAG(T130, T131, T125)
DELETEE_IN_GAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_GAG(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
DELETEE_IN_GAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → DELMINA_IN_AGG(T63, T60, T61)
DELETEE_IN_GAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_GAG(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
DELETEE_IN_GAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → PF_IN_GGAG(T126, T122, T127, T125)
PF_IN_GGAG(T126, T122, T127, T125) → U7_GGAG(T126, T122, T127, T125, lessB_in_gg(T126, T122))
PF_IN_GGAG(T126, T122, T127, T125) → LESSB_IN_GG(T126, T122)
LESSB_IN_GG(s(T145), s(T144)) → U2_GG(T145, T144, lessB_in_gg(T145, T144))
LESSB_IN_GG(s(T145), s(T144)) → LESSB_IN_GG(T145, T144)
PF_IN_GGAG(T130, T122, T131, T125) → U8_GGAG(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_GGAG(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_GGAG(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
U8_GGAG(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → DELETEE_IN_GAG(T130, T131, T125)
DELETEE_IN_GAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_GAG(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
DELETEE_IN_GAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → PD_IN_GGAG(T163, T167, T168, T166)
PD_IN_GGAG(T163, T167, T168, T166) → U4_GGAG(T163, T167, T168, T166, lessC_in_gg(T163, T167))
PD_IN_GGAG(T163, T167, T168, T166) → LESSC_IN_GG(T163, T167)
LESSC_IN_GG(s(T184), s(T186)) → U3_GG(T184, T186, lessC_in_gg(T184, T186))
LESSC_IN_GG(s(T184), s(T186)) → LESSC_IN_GG(T184, T186)
PD_IN_GGAG(T163, T171, T172, T166) → U5_GGAG(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_GGAG(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_GGAG(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
U5_GGAG(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → DELETEE_IN_GAG(T171, T172, T166)
DELETEE_IN_GAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_GAG(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
DELETEE_IN_GAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → DELETEE_IN_GAG(0, T210, T202)
DELETEE_IN_GAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_GAG(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
DELETEE_IN_GAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → PG_IN_GGAG(T223, T222, T224, T202)
PG_IN_GGAG(T223, T222, T224, T202) → U10_GGAG(T223, T222, T224, T202, lessB_in_gg(T223, T222))
PG_IN_GGAG(T223, T222, T224, T202) → LESSB_IN_GG(T223, T222)
PG_IN_GGAG(T227, T222, T228, T202) → U11_GGAG(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_GGAG(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_GGAG(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U11_GGAG(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → DELETEE_IN_GAG(s(T227), T228, T202)
DELETEE_IN_GAG(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_GAG(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
DELETEE_IN_GAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_GAG(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
DELETEE_IN_GAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → DELETEE_IN_GAG(s(T274), T273, T265)
DELETEE_IN_GAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_GAG(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
DELETEE_IN_GAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → PH_IN_GGAG(T283, T285, T286, T265)
PH_IN_GGAG(T283, T285, T286, T265) → U13_GGAG(T283, T285, T286, T265, lessC_in_gg(T283, T285))
PH_IN_GGAG(T283, T285, T286, T265) → LESSC_IN_GG(T283, T285)
PH_IN_GGAG(T283, T289, T290, T265) → U14_GGAG(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_GGAG(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_GGAG(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
U14_GGAG(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → DELETEE_IN_GAG(s(T289), T290, T265)
DELETEE_IN_GAG(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_GAG(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
DELETEE_IN_GAG(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_GAG(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
DELETEE_IN_GAG(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_GAG(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
DELETEE_IN_GAG(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_GAG(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
DELETEE_IN_GAG(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_GAG(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
DELETEE_IN_GAG(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_GAG(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
DELETEE_IN_GAG(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_GAG(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
DELETEE_IN_GAG(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_GAG(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
DELETEE_IN_GAG(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_GAG(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
DELETEE_IN_GAG(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_GAG(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
DELETEE_IN_GAG(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_GAG(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
DELETEE_IN_GAG(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_GAG(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
DELETEE_IN_GAG(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_GAG(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
DELETEE_IN_GAG(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_GAG(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
DELETEE_IN_GAG(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_GAG(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
DELETEE_IN_GAG(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_GAG(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
DELETEE_IN_GAG(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_GAG(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
DELETEE_IN_GAG(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_GAG(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
DELETEE_IN_GAG(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_GAG(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
DELETEE_IN_GAG(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_GAG(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
DELETEE_IN_GAG(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_GAG(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
DELETEE_IN_GAG(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_GAG(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
DELETEE_IN_GAG(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_GAG(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
DELETEE_IN_GAG(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_GAG(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
DELETEE_IN_AAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_AAG(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
DELETEE_IN_AAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → PD_IN_GAAG(T163, T167, T168, T166)
PD_IN_GAAG(T163, T167, T168, T166) → U4_GAAG(T163, T167, T168, T166, lessC_in_ga(T163, T167))
PD_IN_GAAG(T163, T167, T168, T166) → LESSC_IN_GA(T163, T167)
LESSC_IN_GA(s(T184), s(T186)) → U3_GA(T184, T186, lessC_in_ga(T184, T186))
LESSC_IN_GA(s(T184), s(T186)) → LESSC_IN_GA(T184, T186)
PD_IN_GAAG(T163, T171, T172, T166) → U5_GAAG(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_GAAG(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_GAAG(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
U5_GAAG(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → DELETEE_IN_AAG(T171, T172, T166)
DELETEE_IN_AAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_AAG(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
DELETEE_IN_AAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → DELETEE_IN_GAG(0, T210, T202)
DELETEE_IN_AAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_AAG(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
DELETEE_IN_AAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → PG_IN_AGAG(T223, T222, T224, T202)
PG_IN_AGAG(T223, T222, T224, T202) → U10_AGAG(T223, T222, T224, T202, lessB_in_ag(T223, T222))
PG_IN_AGAG(T223, T222, T224, T202) → LESSB_IN_AG(T223, T222)
PG_IN_AGAG(T227, T222, T228, T202) → U11_AGAG(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_AGAG(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_AGAG(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U11_AGAG(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → DELETEE_IN_GAG(s(T227), T228, T202)
DELETEE_IN_AAG(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_AAG(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
DELETEE_IN_AAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_AAG(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
DELETEE_IN_AAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → DELETEE_IN_AAG(s(T274), T273, T265)
DELETEE_IN_AAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_AAG(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
DELETEE_IN_AAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → PH_IN_GAAG(T283, T285, T286, T265)
PH_IN_GAAG(T283, T285, T286, T265) → U13_GAAG(T283, T285, T286, T265, lessC_in_ga(T283, T285))
PH_IN_GAAG(T283, T285, T286, T265) → LESSC_IN_GA(T283, T285)
PH_IN_GAAG(T283, T289, T290, T265) → U14_GAAG(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_GAAG(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_GAAG(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
U14_GAAG(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → DELETEE_IN_AAG(s(T289), T290, T265)
DELETEE_IN_AAG(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_AAG(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
DELETEE_IN_AAG(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_AAG(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
DELETEE_IN_AAG(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_AAG(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
DELETEE_IN_AAG(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_AAG(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
DELETEE_IN_AAG(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_AAG(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
DELETEE_IN_AAG(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_AAG(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
DELETEE_IN_AAG(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_AAG(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
DELETEE_IN_AAG(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_AAG(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
DELETEE_IN_AAG(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_AAG(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
DELETEE_IN_AAG(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_AAG(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
DELETEE_IN_AAG(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_AAG(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
DELETEE_IN_AAG(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_AAG(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
DELETEE_IN_AAG(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_AAG(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
DELETEE_IN_AAG(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_AAG(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
DELETEE_IN_AAG(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_AAG(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
DELETEE_IN_AAG(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_AAG(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
DELETEE_IN_AAG(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_AAG(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
DELETEE_IN_AAG(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_AAG(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
DELETEE_IN_AAG(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_AAG(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
DELETEE_IN_AAG(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_AAG(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
DELETEE_IN_AAG(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_AAG(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
DELETEE_IN_AAG(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_AAG(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
DELETEE_IN_AAG(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_AAG(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
DELETEE_IN_AAG(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_AAG(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

The argument filtering Pi contains the following mapping:
deleteE_in_aag(x1, x2, x3) = deleteE_in_aag(x3)
deleteE_out_aag(x1, x2, x3) = deleteE_out_aag
tree(x1, x2, x3) = tree(x1, x2, x3)
U16_aag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U16_aag(x9)
delminA_in_agg(x1, x2, x3) = delminA_in_agg(x2, x3)
delminA_out_agg(x1, x2, x3) = delminA_out_agg
U1_agg(x1, x2, x3, x4, x5, x6, x7) = U1_agg(x7)
U17_aag(x1, x2, x3, x4, x5, x6) = U17_aag(x6)
pF_in_agag(x1, x2, x3, x4) = pF_in_agag(x2, x4)
U7_agag(x1, x2, x3, x4, x5) = U7_agag(x5)
lessB_in_ag(x1, x2) = lessB_in_ag(x2)
s(x1) = s(x1)
lessB_out_ag(x1, x2) = lessB_out_ag(x1)
U2_ag(x1, x2, x3) = U2_ag(x3)
pF_out_agag(x1, x2, x3, x4) = pF_out_agag(x1)
U8_agag(x1, x2, x3, x4, x5) = U8_agag(x4, x5)
U9_agag(x1, x2, x3, x4, x5) = U9_agag(x1, x5)
deleteE_in_gag(x1, x2, x3) = deleteE_in_gag(x1, x3)
deleteE_out_gag(x1, x2, x3) = deleteE_out_gag
U16_gag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U16_gag(x9)
U17_gag(x1, x2, x3, x4, x5, x6) = U17_gag(x6)
pF_in_ggag(x1, x2, x3, x4) = pF_in_ggag(x1, x2, x4)
U7_ggag(x1, x2, x3, x4, x5) = U7_ggag(x5)
lessB_in_gg(x1, x2) = lessB_in_gg(x1, x2)
0 = 0
lessB_out_gg(x1, x2) = lessB_out_gg
U2_gg(x1, x2, x3) = U2_gg(x3)
pF_out_ggag(x1, x2, x3, x4) = pF_out_ggag
U8_ggag(x1, x2, x3, x4, x5) = U8_ggag(x1, x4, x5)
U9_ggag(x1, x2, x3, x4, x5) = U9_ggag(x5)
U18_gag(x1, x2, x3, x4, x5, x6) = U18_gag(x6)
pD_in_ggag(x1, x2, x3, x4) = pD_in_ggag(x1, x2, x4)
U4_ggag(x1, x2, x3, x4, x5) = U4_ggag(x5)
lessC_in_gg(x1, x2) = lessC_in_gg(x1, x2)
lessC_out_gg(x1, x2) = lessC_out_gg
U3_gg(x1, x2, x3) = U3_gg(x3)
pD_out_ggag(x1, x2, x3, x4) = pD_out_ggag
U5_ggag(x1, x2, x3, x4, x5) = U5_ggag(x2, x4, x5)
U6_ggag(x1, x2, x3, x4, x5) = U6_ggag(x5)
U19_gag(x1, x2, x3, x4, x5) = U19_gag(x5)
U20_gag(x1, x2, x3, x4, x5, x6) = U20_gag(x6)
pG_in_ggag(x1, x2, x3, x4) = pG_in_ggag(x1, x2, x4)
U10_ggag(x1, x2, x3, x4, x5) = U10_ggag(x5)
pG_out_ggag(x1, x2, x3, x4) = pG_out_ggag
U11_ggag(x1, x2, x3, x4, x5) = U11_ggag(x1, x4, x5)
U12_ggag(x1, x2, x3, x4, x5) = U12_ggag(x5)
U21_gag(x1, x2, x3, x4, x5, x6) = U21_gag(x6)
U22_gag(x1, x2, x3, x4, x5) = U22_gag(x5)
U23_gag(x1, x2, x3, x4, x5, x6) = U23_gag(x6)
pH_in_ggag(x1, x2, x3, x4) = pH_in_ggag(x1, x2, x4)
U13_ggag(x1, x2, x3, x4, x5) = U13_ggag(x5)
pH_out_ggag(x1, x2, x3, x4) = pH_out_ggag
U14_ggag(x1, x2, x3, x4, x5) = U14_ggag(x2, x4, x5)
U15_ggag(x1, x2, x3, x4, x5) = U15_ggag(x5)
U24_gag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U24_gag(x9)
U25_gag(x1, x2, x3, x4, x5, x6) = U25_gag(x6)
U26_gag(x1, x2, x3, x4, x5, x6) = U26_gag(x6)
U27_gag(x1, x2, x3, x4, x5) = U27_gag(x5)
U28_gag(x1, x2, x3, x4, x5, x6) = U28_gag(x6)
U29_gag(x1, x2, x3, x4, x5, x6) = U29_gag(x6)
U30_gag(x1, x2, x3, x4, x5) = U30_gag(x5)
U31_gag(x1, x2, x3, x4, x5, x6) = U31_gag(x6)
U32_gag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U32_gag(x9)
U33_gag(x1, x2, x3, x4, x5, x6) = U33_gag(x6)
U34_gag(x1, x2, x3, x4, x5, x6) = U34_gag(x6)
U35_gag(x1, x2, x3, x4, x5) = U35_gag(x5)
U36_gag(x1, x2, x3, x4, x5, x6) = U36_gag(x6)
U37_gag(x1, x2, x3, x4, x5, x6) = U37_gag(x6)
U38_gag(x1, x2, x3, x4, x5) = U38_gag(x5)
U39_gag(x1, x2, x3, x4, x5, x6) = U39_gag(x6)
U40_gag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U40_gag(x9)
U41_gag(x1, x2, x3, x4, x5, x6) = U41_gag(x6)
U42_gag(x1, x2, x3, x4, x5, x6) = U42_gag(x6)
U43_gag(x1, x2, x3, x4, x5) = U43_gag(x5)
U44_gag(x1, x2, x3, x4, x5, x6) = U44_gag(x6)
U45_gag(x1, x2, x3, x4, x5, x6) = U45_gag(x6)
U46_gag(x1, x2, x3, x4, x5) = U46_gag(x5)
U47_gag(x1, x2, x3, x4, x5, x6) = U47_gag(x6)
U18_aag(x1, x2, x3, x4, x5, x6) = U18_aag(x6)
pD_in_gaag(x1, x2, x3, x4) = pD_in_gaag(x1, x4)
U4_gaag(x1, x2, x3, x4, x5) = U4_gaag(x5)
lessC_in_ga(x1, x2) = lessC_in_ga(x1)
lessC_out_ga(x1, x2) = lessC_out_ga
U3_ga(x1, x2, x3) = U3_ga(x3)
pD_out_gaag(x1, x2, x3, x4) = pD_out_gaag
U5_gaag(x1, x2, x3, x4, x5) = U5_gaag(x4, x5)
U6_gaag(x1, x2, x3, x4, x5) = U6_gaag(x5)
U19_aag(x1, x2, x3, x4, x5) = U19_aag(x5)
U20_aag(x1, x2, x3, x4, x5, x6) = U20_aag(x6)
pG_in_agag(x1, x2, x3, x4) = pG_in_agag(x2, x4)
U10_agag(x1, x2, x3, x4, x5) = U10_agag(x5)
pG_out_agag(x1, x2, x3, x4) = pG_out_agag(x1)
U11_agag(x1, x2, x3, x4, x5) = U11_agag(x4, x5)
U12_agag(x1, x2, x3, x4, x5) = U12_agag(x1, x5)
U21_aag(x1, x2, x3, x4, x5, x6) = U21_aag(x6)
U22_aag(x1, x2, x3, x4, x5) = U22_aag(x5)
U23_aag(x1, x2, x3, x4, x5, x6) = U23_aag(x6)
pH_in_gaag(x1, x2, x3, x4) = pH_in_gaag(x1, x4)
U13_gaag(x1, x2, x3, x4, x5) = U13_gaag(x5)
pH_out_gaag(x1, x2, x3, x4) = pH_out_gaag
U14_gaag(x1, x2, x3, x4, x5) = U14_gaag(x4, x5)
U15_gaag(x1, x2, x3, x4, x5) = U15_gaag(x5)
U24_aag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U24_aag(x9)
U25_aag(x1, x2, x3, x4, x5, x6) = U25_aag(x6)
U26_aag(x1, x2, x3, x4, x5, x6) = U26_aag(x6)
U27_aag(x1, x2, x3, x4, x5) = U27_aag(x5)
U28_aag(x1, x2, x3, x4, x5, x6) = U28_aag(x6)
U29_aag(x1, x2, x3, x4, x5, x6) = U29_aag(x6)
U30_aag(x1, x2, x3, x4, x5) = U30_aag(x5)
U31_aag(x1, x2, x3, x4, x5, x6) = U31_aag(x6)
U32_aag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U32_aag(x9)
U33_aag(x1, x2, x3, x4, x5, x6) = U33_aag(x6)
U34_aag(x1, x2, x3, x4, x5, x6) = U34_aag(x6)
U35_aag(x1, x2, x3, x4, x5) = U35_aag(x5)
U36_aag(x1, x2, x3, x4, x5, x6) = U36_aag(x6)
U37_aag(x1, x2, x3, x4, x5, x6) = U37_aag(x6)
U38_aag(x1, x2, x3, x4, x5) = U38_aag(x5)
U39_aag(x1, x2, x3, x4, x5, x6) = U39_aag(x6)
U40_aag(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U40_aag(x9)
U41_aag(x1, x2, x3, x4, x5, x6) = U41_aag(x6)
U42_aag(x1, x2, x3, x4, x5, x6) = U42_aag(x6)
U43_aag(x1, x2, x3, x4, x5) = U43_aag(x5)
U44_aag(x1, x2, x3, x4, x5, x6) = U44_aag(x6)
U45_aag(x1, x2, x3, x4, x5, x6) = U45_aag(x6)
U46_aag(x1, x2, x3, x4, x5) = U46_aag(x5)
U47_aag(x1, x2, x3, x4, x5, x6) = U47_aag(x6)
DELETEE_IN_AAG(x1, x2, x3) = DELETEE_IN_AAG(x3)
U16_AAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U16_AAG(x9)
DELMINA_IN_AGG(x1, x2, x3) = DELMINA_IN_AGG(x2, x3)
U1_AGG(x1, x2, x3, x4, x5, x6, x7) = U1_AGG(x7)
U17_AAG(x1, x2, x3, x4, x5, x6) = U17_AAG(x6)
PF_IN_AGAG(x1, x2, x3, x4) = PF_IN_AGAG(x2, x4)
U7_AGAG(x1, x2, x3, x4, x5) = U7_AGAG(x5)
LESSB_IN_AG(x1, x2) = LESSB_IN_AG(x2)
U2_AG(x1, x2, x3) = U2_AG(x3)
U8_AGAG(x1, x2, x3, x4, x5) = U8_AGAG(x4, x5)
U9_AGAG(x1, x2, x3, x4, x5) = U9_AGAG(x1, x5)
DELETEE_IN_GAG(x1, x2, x3) = DELETEE_IN_GAG(x1, x3)
U16_GAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U16_GAG(x9)
U17_GAG(x1, x2, x3, x4, x5, x6) = U17_GAG(x6)
PF_IN_GGAG(x1, x2, x3, x4) = PF_IN_GGAG(x1, x2, x4)
U7_GGAG(x1, x2, x3, x4, x5) = U7_GGAG(x5)
LESSB_IN_GG(x1, x2) = LESSB_IN_GG(x1, x2)
U2_GG(x1, x2, x3) = U2_GG(x3)
U8_GGAG(x1, x2, x3, x4, x5) = U8_GGAG(x1, x4, x5)
U9_GGAG(x1, x2, x3, x4, x5) = U9_GGAG(x5)
U18_GAG(x1, x2, x3, x4, x5, x6) = U18_GAG(x6)
PD_IN_GGAG(x1, x2, x3, x4) = PD_IN_GGAG(x1, x2, x4)
U4_GGAG(x1, x2, x3, x4, x5) = U4_GGAG(x5)
LESSC_IN_GG(x1, x2) = LESSC_IN_GG(x1, x2)
U3_GG(x1, x2, x3) = U3_GG(x3)
U5_GGAG(x1, x2, x3, x4, x5) = U5_GGAG(x2, x4, x5)
U6_GGAG(x1, x2, x3, x4, x5) = U6_GGAG(x5)
U19_GAG(x1, x2, x3, x4, x5) = U19_GAG(x5)
U20_GAG(x1, x2, x3, x4, x5, x6) = U20_GAG(x6)
PG_IN_GGAG(x1, x2, x3, x4) = PG_IN_GGAG(x1, x2, x4)
U10_GGAG(x1, x2, x3, x4, x5) = U10_GGAG(x5)
U11_GGAG(x1, x2, x3, x4, x5) = U11_GGAG(x1, x4, x5)
U12_GGAG(x1, x2, x3, x4, x5) = U12_GGAG(x5)
U21_GAG(x1, x2, x3, x4, x5, x6) = U21_GAG(x6)
U22_GAG(x1, x2, x3, x4, x5) = U22_GAG(x5)
U23_GAG(x1, x2, x3, x4, x5, x6) = U23_GAG(x6)
PH_IN_GGAG(x1, x2, x3, x4) = PH_IN_GGAG(x1, x2, x4)
U13_GGAG(x1, x2, x3, x4, x5) = U13_GGAG(x5)
U14_GGAG(x1, x2, x3, x4, x5) = U14_GGAG(x2, x4, x5)
U15_GGAG(x1, x2, x3, x4, x5) = U15_GGAG(x5)
U24_GAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U24_GAG(x9)
U25_GAG(x1, x2, x3, x4, x5, x6) = U25_GAG(x6)
U26_GAG(x1, x2, x3, x4, x5, x6) = U26_GAG(x6)
U27_GAG(x1, x2, x3, x4, x5) = U27_GAG(x5)
U28_GAG(x1, x2, x3, x4, x5, x6) = U28_GAG(x6)
U29_GAG(x1, x2, x3, x4, x5, x6) = U29_GAG(x6)
U30_GAG(x1, x2, x3, x4, x5) = U30_GAG(x5)
U31_GAG(x1, x2, x3, x4, x5, x6) = U31_GAG(x6)
U32_GAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U32_GAG(x9)
U33_GAG(x1, x2, x3, x4, x5, x6) = U33_GAG(x6)
U34_GAG(x1, x2, x3, x4, x5, x6) = U34_GAG(x6)
U35_GAG(x1, x2, x3, x4, x5) = U35_GAG(x5)
U36_GAG(x1, x2, x3, x4, x5, x6) = U36_GAG(x6)
U37_GAG(x1, x2, x3, x4, x5, x6) = U37_GAG(x6)
U38_GAG(x1, x2, x3, x4, x5) = U38_GAG(x5)
U39_GAG(x1, x2, x3, x4, x5, x6) = U39_GAG(x6)
U40_GAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U40_GAG(x9)
U41_GAG(x1, x2, x3, x4, x5, x6) = U41_GAG(x6)
U42_GAG(x1, x2, x3, x4, x5, x6) = U42_GAG(x6)
U43_GAG(x1, x2, x3, x4, x5) = U43_GAG(x5)
U44_GAG(x1, x2, x3, x4, x5, x6) = U44_GAG(x6)
U45_GAG(x1, x2, x3, x4, x5, x6) = U45_GAG(x6)
U46_GAG(x1, x2, x3, x4, x5) = U46_GAG(x5)
U47_GAG(x1, x2, x3, x4, x5, x6) = U47_GAG(x6)
U18_AAG(x1, x2, x3, x4, x5, x6) = U18_AAG(x6)
PD_IN_GAAG(x1, x2, x3, x4) = PD_IN_GAAG(x1, x4)
U4_GAAG(x1, x2, x3, x4, x5) = U4_GAAG(x5)
LESSC_IN_GA(x1, x2) = LESSC_IN_GA(x1)
U3_GA(x1, x2, x3) = U3_GA(x3)
U5_GAAG(x1, x2, x3, x4, x5) = U5_GAAG(x4, x5)
U6_GAAG(x1, x2, x3, x4, x5) = U6_GAAG(x5)
U19_AAG(x1, x2, x3, x4, x5) = U19_AAG(x5)
U20_AAG(x1, x2, x3, x4, x5, x6) = U20_AAG(x6)
PG_IN_AGAG(x1, x2, x3, x4) = PG_IN_AGAG(x2, x4)
U10_AGAG(x1, x2, x3, x4, x5) = U10_AGAG(x5)
U11_AGAG(x1, x2, x3, x4, x5) = U11_AGAG(x4, x5)
U12_AGAG(x1, x2, x3, x4, x5) = U12_AGAG(x1, x5)
U21_AAG(x1, x2, x3, x4, x5, x6) = U21_AAG(x6)
U22_AAG(x1, x2, x3, x4, x5) = U22_AAG(x5)
U23_AAG(x1, x2, x3, x4, x5, x6) = U23_AAG(x6)
PH_IN_GAAG(x1, x2, x3, x4) = PH_IN_GAAG(x1, x4)
U13_GAAG(x1, x2, x3, x4, x5) = U13_GAAG(x5)
U14_GAAG(x1, x2, x3, x4, x5) = U14_GAAG(x4, x5)
U15_GAAG(x1, x2, x3, x4, x5) = U15_GAAG(x5)
U24_AAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U24_AAG(x9)
U25_AAG(x1, x2, x3, x4, x5, x6) = U25_AAG(x6)
U26_AAG(x1, x2, x3, x4, x5, x6) = U26_AAG(x6)
U27_AAG(x1, x2, x3, x4, x5) = U27_AAG(x5)
U28_AAG(x1, x2, x3, x4, x5, x6) = U28_AAG(x6)
U29_AAG(x1, x2, x3, x4, x5, x6) = U29_AAG(x6)
U30_AAG(x1, x2, x3, x4, x5) = U30_AAG(x5)
U31_AAG(x1, x2, x3, x4, x5, x6) = U31_AAG(x6)
U32_AAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U32_AAG(x9)
U33_AAG(x1, x2, x3, x4, x5, x6) = U33_AAG(x6)
U34_AAG(x1, x2, x3, x4, x5, x6) = U34_AAG(x6)
U35_AAG(x1, x2, x3, x4, x5) = U35_AAG(x5)
U36_AAG(x1, x2, x3, x4, x5, x6) = U36_AAG(x6)
U37_AAG(x1, x2, x3, x4, x5, x6) = U37_AAG(x6)
U38_AAG(x1, x2, x3, x4, x5) = U38_AAG(x5)
U39_AAG(x1, x2, x3, x4, x5, x6) = U39_AAG(x6)
U40_AAG(x1, x2, x3, x4, x5, x6, x7, x8, x9) = U40_AAG(x9)
U41_AAG(x1, x2, x3, x4, x5, x6) = U41_AAG(x6)
U42_AAG(x1, x2, x3, x4, x5, x6) = U42_AAG(x6)
U43_AAG(x1, x2, x3, x4, x5) = U43_AAG(x5)
U44_AAG(x1, x2, x3, x4, x5, x6) = U44_AAG(x6)
U45_AAG(x1, x2, x3, x4, x5, x6) = U45_AAG(x6)
U46_AAG(x1, x2, x3, x4, x5) = U46_AAG(x5)
U47_AAG(x1, x2, x3, x4, x5, x6) = U47_AAG(x6)

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

(6) Obligation:

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

DELETEE_IN_AAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_AAG(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
DELETEE_IN_AAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → DELMINA_IN_AGG(T63, T60, T61)
DELMINA_IN_AGG(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_AGG(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
DELMINA_IN_AGG(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → DELMINA_IN_AGG(T96, T93, T94)
DELETEE_IN_AAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_AAG(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
DELETEE_IN_AAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → PF_IN_AGAG(T126, T122, T127, T125)
PF_IN_AGAG(T126, T122, T127, T125) → U7_AGAG(T126, T122, T127, T125, lessB_in_ag(T126, T122))
PF_IN_AGAG(T126, T122, T127, T125) → LESSB_IN_AG(T126, T122)
LESSB_IN_AG(s(T145), s(T144)) → U2_AG(T145, T144, lessB_in_ag(T145, T144))
LESSB_IN_AG(s(T145), s(T144)) → LESSB_IN_AG(T145, T144)
PF_IN_AGAG(T130, T122, T131, T125) → U8_AGAG(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_AGAG(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_AGAG(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
U8_AGAG(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → DELETEE_IN_GAG(T130, T131, T125)
DELETEE_IN_GAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_GAG(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
DELETEE_IN_GAG(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → DELMINA_IN_AGG(T63, T60, T61)
DELETEE_IN_GAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_GAG(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
DELETEE_IN_GAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → PF_IN_GGAG(T126, T122, T127, T125)
PF_IN_GGAG(T126, T122, T127, T125) → U7_GGAG(T126, T122, T127, T125, lessB_in_gg(T126, T122))
PF_IN_GGAG(T126, T122, T127, T125) → LESSB_IN_GG(T126, T122)
LESSB_IN_GG(s(T145), s(T144)) → U2_GG(T145, T144, lessB_in_gg(T145, T144))
LESSB_IN_GG(s(T145), s(T144)) → LESSB_IN_GG(T145, T144)
PF_IN_GGAG(T130, T122, T131, T125) → U8_GGAG(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_GGAG(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_GGAG(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
U8_GGAG(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → DELETEE_IN_GAG(T130, T131, T125)
DELETEE_IN_GAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_GAG(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
DELETEE_IN_GAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → PD_IN_GGAG(T163, T167, T168, T166)
PD_IN_GGAG(T163, T167, T168, T166) → U4_GGAG(T163, T167, T168, T166, lessC_in_gg(T163, T167))
PD_IN_GGAG(T163, T167, T168, T166) → LESSC_IN_GG(T163, T167)
LESSC_IN_GG(s(T184), s(T186)) → U3_GG(T184, T186, lessC_in_gg(T184, T186))
LESSC_IN_GG(s(T184), s(T186)) → LESSC_IN_GG(T184, T186)
PD_IN_GGAG(T163, T171, T172, T166) → U5_GGAG(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_GGAG(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_GGAG(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
U5_GGAG(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → DELETEE_IN_GAG(T171, T172, T166)
DELETEE_IN_GAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_GAG(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
DELETEE_IN_GAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → DELETEE_IN_GAG(0, T210, T202)
DELETEE_IN_GAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_GAG(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
DELETEE_IN_GAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → PG_IN_GGAG(T223, T222, T224, T202)
PG_IN_GGAG(T223, T222, T224, T202) → U10_GGAG(T223, T222, T224, T202, lessB_in_gg(T223, T222))
PG_IN_GGAG(T223, T222, T224, T202) → LESSB_IN_GG(T223, T222)
PG_IN_GGAG(T227, T222, T228, T202) → U11_GGAG(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_GGAG(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_GGAG(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U11_GGAG(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → DELETEE_IN_GAG(s(T227), T228, T202)
DELETEE_IN_GAG(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_GAG(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
DELETEE_IN_GAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_GAG(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
DELETEE_IN_GAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → DELETEE_IN_GAG(s(T274), T273, T265)
DELETEE_IN_GAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_GAG(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
DELETEE_IN_GAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → PH_IN_GGAG(T283, T285, T286, T265)
PH_IN_GGAG(T283, T285, T286, T265) → U13_GGAG(T283, T285, T286, T265, lessC_in_gg(T283, T285))
PH_IN_GGAG(T283, T285, T286, T265) → LESSC_IN_GG(T283, T285)
PH_IN_GGAG(T283, T289, T290, T265) → U14_GGAG(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_GGAG(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_GGAG(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
U14_GGAG(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → DELETEE_IN_GAG(s(T289), T290, T265)
DELETEE_IN_GAG(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_GAG(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
DELETEE_IN_GAG(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_GAG(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
DELETEE_IN_GAG(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_GAG(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
DELETEE_IN_GAG(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_GAG(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
DELETEE_IN_GAG(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_GAG(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
DELETEE_IN_GAG(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_GAG(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
DELETEE_IN_GAG(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_GAG(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
DELETEE_IN_GAG(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_GAG(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
DELETEE_IN_GAG(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_GAG(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
DELETEE_IN_GAG(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_GAG(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
DELETEE_IN_GAG(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_GAG(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
DELETEE_IN_GAG(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_GAG(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
DELETEE_IN_GAG(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_GAG(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
DELETEE_IN_GAG(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_GAG(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
DELETEE_IN_GAG(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_GAG(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
DELETEE_IN_GAG(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_GAG(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
DELETEE_IN_GAG(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_GAG(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
DELETEE_IN_GAG(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_GAG(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
DELETEE_IN_GAG(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_GAG(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
DELETEE_IN_GAG(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_GAG(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
DELETEE_IN_GAG(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_GAG(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
DELETEE_IN_GAG(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_GAG(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
DELETEE_IN_GAG(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_GAG(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
DELETEE_IN_GAG(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_GAG(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
DELETEE_IN_AAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_AAG(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
DELETEE_IN_AAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → PD_IN_GAAG(T163, T167, T168, T166)
PD_IN_GAAG(T163, T167, T168, T166) → U4_GAAG(T163, T167, T168, T166, lessC_in_ga(T163, T167))
PD_IN_GAAG(T163, T167, T168, T166) → LESSC_IN_GA(T163, T167)
LESSC_IN_GA(s(T184), s(T186)) → U3_GA(T184, T186, lessC_in_ga(T184, T186))
LESSC_IN_GA(s(T184), s(T186)) → LESSC_IN_GA(T184, T186)
PD_IN_GAAG(T163, T171, T172, T166) → U5_GAAG(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_GAAG(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_GAAG(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
U5_GAAG(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → DELETEE_IN_AAG(T171, T172, T166)
DELETEE_IN_AAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_AAG(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
DELETEE_IN_AAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → DELETEE_IN_GAG(0, T210, T202)
DELETEE_IN_AAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_AAG(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
DELETEE_IN_AAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → PG_IN_AGAG(T223, T222, T224, T202)
PG_IN_AGAG(T223, T222, T224, T202) → U10_AGAG(T223, T222, T224, T202, lessB_in_ag(T223, T222))
PG_IN_AGAG(T223, T222, T224, T202) → LESSB_IN_AG(T223, T222)
PG_IN_AGAG(T227, T222, T228, T202) → U11_AGAG(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_AGAG(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_AGAG(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U11_AGAG(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → DELETEE_IN_GAG(s(T227), T228, T202)
DELETEE_IN_AAG(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_AAG(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
DELETEE_IN_AAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_AAG(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
DELETEE_IN_AAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → DELETEE_IN_AAG(s(T274), T273, T265)
DELETEE_IN_AAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_AAG(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
DELETEE_IN_AAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → PH_IN_GAAG(T283, T285, T286, T265)
PH_IN_GAAG(T283, T285, T286, T265) → U13_GAAG(T283, T285, T286, T265, lessC_in_ga(T283, T285))
PH_IN_GAAG(T283, T285, T286, T265) → LESSC_IN_GA(T283, T285)
PH_IN_GAAG(T283, T289, T290, T265) → U14_GAAG(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_GAAG(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_GAAG(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
U14_GAAG(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → DELETEE_IN_AAG(s(T289), T290, T265)
DELETEE_IN_AAG(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_AAG(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
DELETEE_IN_AAG(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_AAG(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
DELETEE_IN_AAG(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_AAG(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
DELETEE_IN_AAG(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_AAG(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
DELETEE_IN_AAG(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_AAG(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
DELETEE_IN_AAG(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_AAG(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
DELETEE_IN_AAG(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_AAG(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
DELETEE_IN_AAG(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_AAG(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
DELETEE_IN_AAG(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_AAG(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
DELETEE_IN_AAG(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_AAG(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
DELETEE_IN_AAG(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_AAG(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
DELETEE_IN_AAG(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_AAG(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
DELETEE_IN_AAG(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_AAG(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
DELETEE_IN_AAG(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_AAG(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
DELETEE_IN_AAG(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_AAG(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
DELETEE_IN_AAG(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_AAG(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
DELETEE_IN_AAG(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_AAG(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
DELETEE_IN_AAG(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_AAG(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
DELETEE_IN_AAG(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_AAG(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
DELETEE_IN_AAG(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_AAG(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
DELETEE_IN_AAG(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_AAG(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
DELETEE_IN_AAG(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_AAG(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
DELETEE_IN_AAG(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_AAG(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
DELETEE_IN_AAG(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_AAG(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(7) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LOPSTR] contains 7 SCCs with 102 less nodes.

(8) Complex Obligation (AND)

(9) Obligation:

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

LESSC_IN_GA(s(T184), s(T186)) → LESSC_IN_GA(T184, T186)

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(10) UsableRulesProof (EQUIVALENT transformation)

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

(11) Obligation:

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

LESSC_IN_GA(s(T184), s(T186)) → LESSC_IN_GA(T184, T186)

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

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

(12) PiDPToQDPProof (SOUND transformation)

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

(13) Obligation:

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

LESSC_IN_GA(s(T184)) → LESSC_IN_GA(T184)

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

(14) 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:

LESSC_IN_GA(s(T184)) → LESSC_IN_GA(T184)
The graph contains the following edges 1 > 1

(15) YES

(16) Obligation:

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

LESSC_IN_GG(s(T184), s(T186)) → LESSC_IN_GG(T184, T186)

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(17) UsableRulesProof (EQUIVALENT transformation)

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

(18) Obligation:

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

LESSC_IN_GG(s(T184), s(T186)) → LESSC_IN_GG(T184, T186)

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

(19) PiDPToQDPProof (EQUIVALENT transformation)

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

(20) Obligation:

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

LESSC_IN_GG(s(T184), s(T186)) → LESSC_IN_GG(T184, T186)

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

(21) 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:

LESSC_IN_GG(s(T184), s(T186)) → LESSC_IN_GG(T184, T186)
The graph contains the following edges 1 > 1, 2 > 2

(22) YES

(23) Obligation:

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

LESSB_IN_GG(s(T145), s(T144)) → LESSB_IN_GG(T145, T144)

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(24) UsableRulesProof (EQUIVALENT transformation)

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

(25) Obligation:

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

LESSB_IN_GG(s(T145), s(T144)) → LESSB_IN_GG(T145, T144)

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

(26) PiDPToQDPProof (EQUIVALENT transformation)

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

(27) Obligation:

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

LESSB_IN_GG(s(T145), s(T144)) → LESSB_IN_GG(T145, T144)

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

(28) 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:

LESSB_IN_GG(s(T145), s(T144)) → LESSB_IN_GG(T145, T144)
The graph contains the following edges 1 > 1, 2 > 2

(29) YES

(30) Obligation:

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

LESSB_IN_AG(s(T145), s(T144)) → LESSB_IN_AG(T145, T144)

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(31) UsableRulesProof (EQUIVALENT transformation)

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

(32) Obligation:

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

LESSB_IN_AG(s(T145), s(T144)) → LESSB_IN_AG(T145, T144)

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

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

(33) PiDPToQDPProof (SOUND transformation)

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

(34) Obligation:

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

LESSB_IN_AG(s(T144)) → LESSB_IN_AG(T144)

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

(35) 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:

LESSB_IN_AG(s(T144)) → LESSB_IN_AG(T144)
The graph contains the following edges 1 > 1

(36) YES

(37) Obligation:

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

DELMINA_IN_AGG(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → DELMINA_IN_AGG(T96, T93, T94)

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(38) UsableRulesProof (EQUIVALENT transformation)

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

(39) Obligation:

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

DELMINA_IN_AGG(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → DELMINA_IN_AGG(T96, T93, T94)

R is empty.
The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
DELMINA_IN_AGG(x1, x2, x3) = DELMINA_IN_AGG(x2, x3)

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

(40) PiDPToQDPProof (SOUND transformation)

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

(41) Obligation:

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

DELMINA_IN_AGG(T93, tree(T90, T94, T95)) → DELMINA_IN_AGG(T93, T94)

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

(42) 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:

DELMINA_IN_AGG(T93, tree(T90, T94, T95)) → DELMINA_IN_AGG(T93, T94)
The graph contains the following edges 1 >= 1, 2 > 2

(43) YES

(44) Obligation:

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

DELETEE_IN_GAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → PF_IN_GGAG(T126, T122, T127, T125)
PF_IN_GGAG(T130, T122, T131, T125) → U8_GGAG(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_GGAG(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → DELETEE_IN_GAG(T130, T131, T125)
DELETEE_IN_GAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → PD_IN_GGAG(T163, T167, T168, T166)
PD_IN_GGAG(T163, T171, T172, T166) → U5_GGAG(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_GGAG(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → DELETEE_IN_GAG(T171, T172, T166)
DELETEE_IN_GAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → DELETEE_IN_GAG(0, T210, T202)
DELETEE_IN_GAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → PG_IN_GGAG(T223, T222, T224, T202)
PG_IN_GGAG(T227, T222, T228, T202) → U11_GGAG(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_GGAG(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → DELETEE_IN_GAG(s(T227), T228, T202)
DELETEE_IN_GAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → DELETEE_IN_GAG(s(T274), T273, T265)
DELETEE_IN_GAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → PH_IN_GGAG(T283, T285, T286, T265)
PH_IN_GGAG(T283, T289, T290, T265) → U14_GGAG(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_GGAG(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → DELETEE_IN_GAG(s(T289), T290, T265)

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(45) UsableRulesProof (EQUIVALENT transformation)

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

(46) Obligation:

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

DELETEE_IN_GAG(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → PF_IN_GGAG(T126, T122, T127, T125)
PF_IN_GGAG(T130, T122, T131, T125) → U8_GGAG(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_GGAG(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → DELETEE_IN_GAG(T130, T131, T125)
DELETEE_IN_GAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → PD_IN_GGAG(T163, T167, T168, T166)
PD_IN_GGAG(T163, T171, T172, T166) → U5_GGAG(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_GGAG(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → DELETEE_IN_GAG(T171, T172, T166)
DELETEE_IN_GAG(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → DELETEE_IN_GAG(0, T210, T202)
DELETEE_IN_GAG(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → PG_IN_GGAG(T223, T222, T224, T202)
PG_IN_GGAG(T227, T222, T228, T202) → U11_GGAG(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_GGAG(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → DELETEE_IN_GAG(s(T227), T228, T202)
DELETEE_IN_GAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → DELETEE_IN_GAG(s(T274), T273, T265)
DELETEE_IN_GAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → PH_IN_GGAG(T283, T285, T286, T265)
PH_IN_GGAG(T283, T289, T290, T265) → U14_GGAG(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_GGAG(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → DELETEE_IN_GAG(s(T289), T290, T265)

The TRS R consists of the following rules:

lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
lessB_in_gg(x1, x2) = lessB_in_gg(x1, x2)
0 = 0
lessB_out_gg(x1, x2) = lessB_out_gg
U2_gg(x1, x2, x3) = U2_gg(x3)
lessC_in_gg(x1, x2) = lessC_in_gg(x1, x2)
lessC_out_gg(x1, x2) = lessC_out_gg
U3_gg(x1, x2, x3) = U3_gg(x3)
DELETEE_IN_GAG(x1, x2, x3) = DELETEE_IN_GAG(x1, x3)
PF_IN_GGAG(x1, x2, x3, x4) = PF_IN_GGAG(x1, x2, x4)
U8_GGAG(x1, x2, x3, x4, x5) = U8_GGAG(x1, x4, x5)
PD_IN_GGAG(x1, x2, x3, x4) = PD_IN_GGAG(x1, x2, x4)
U5_GGAG(x1, x2, x3, x4, x5) = U5_GGAG(x2, x4, x5)
PG_IN_GGAG(x1, x2, x3, x4) = PG_IN_GGAG(x1, x2, x4)
U11_GGAG(x1, x2, x3, x4, x5) = U11_GGAG(x1, x4, x5)
PH_IN_GGAG(x1, x2, x3, x4) = PH_IN_GGAG(x1, x2, x4)
U14_GGAG(x1, x2, x3, x4, x5) = U14_GGAG(x2, x4, x5)

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

(47) PiDPToQDPProof (SOUND transformation)

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

(48) Obligation:

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

DELETEE_IN_GAG(T126, tree(T122, T125, T124)) → PF_IN_GGAG(T126, T122, T125)
PF_IN_GGAG(T130, T122, T125) → U8_GGAG(T130, T125, lessB_in_gg(T130, T122))
U8_GGAG(T130, T125, lessB_out_gg) → DELETEE_IN_GAG(T130, T125)
DELETEE_IN_GAG(T167, tree(T163, T164, T166)) → PD_IN_GGAG(T163, T167, T166)
PD_IN_GGAG(T163, T171, T166) → U5_GGAG(T171, T166, lessC_in_gg(T163, T171))
U5_GGAG(T171, T166, lessC_out_gg) → DELETEE_IN_GAG(T171, T166)
DELETEE_IN_GAG(0, tree(s(T209), T202, T201)) → DELETEE_IN_GAG(0, T202)
DELETEE_IN_GAG(s(T223), tree(s(T222), T202, T201)) → PG_IN_GGAG(T223, T222, T202)
PG_IN_GGAG(T227, T222, T202) → U11_GGAG(T227, T202, lessB_in_gg(T227, T222))
U11_GGAG(T227, T202, lessB_out_gg) → DELETEE_IN_GAG(s(T227), T202)
DELETEE_IN_GAG(s(T274), tree(0, T263, T265)) → DELETEE_IN_GAG(s(T274), T265)
DELETEE_IN_GAG(s(T285), tree(s(T283), T263, T265)) → PH_IN_GGAG(T283, T285, T265)
PH_IN_GGAG(T283, T289, T265) → U14_GGAG(T289, T265, lessC_in_gg(T283, T289))
U14_GGAG(T289, T265, lessC_out_gg) → DELETEE_IN_GAG(s(T289), T265)

The TRS R consists of the following rules:

lessB_in_gg(0, s(T138)) → lessB_out_gg
lessB_in_gg(s(T145), s(T144)) → U2_gg(lessB_in_gg(T145, T144))
lessC_in_gg(0, s(T179)) → lessC_out_gg
lessC_in_gg(s(T184), s(T186)) → U3_gg(lessC_in_gg(T184, T186))
U2_gg(lessB_out_gg) → lessB_out_gg
U3_gg(lessC_out_gg) → lessC_out_gg

The set Q consists of the following terms:

lessB_in_gg(x0, x1)
lessC_in_gg(x0, x1)
U2_gg(x0)
U3_gg(x0)

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

(49) 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:

PF_IN_GGAG(T130, T122, T125) → U8_GGAG(T130, T125, lessB_in_gg(T130, T122))
The graph contains the following edges 1 >= 1, 3 >= 2
U8_GGAG(T130, T125, lessB_out_gg) → DELETEE_IN_GAG(T130, T125)
The graph contains the following edges 1 >= 1, 2 >= 2
DELETEE_IN_GAG(T126, tree(T122, T125, T124)) → PF_IN_GGAG(T126, T122, T125)
The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3
PD_IN_GGAG(T163, T171, T166) → U5_GGAG(T171, T166, lessC_in_gg(T163, T171))
The graph contains the following edges 2 >= 1, 3 >= 2
U5_GGAG(T171, T166, lessC_out_gg) → DELETEE_IN_GAG(T171, T166)
The graph contains the following edges 1 >= 1, 2 >= 2
DELETEE_IN_GAG(T167, tree(T163, T164, T166)) → PD_IN_GGAG(T163, T167, T166)
The graph contains the following edges 2 > 1, 1 >= 2, 2 > 3
DELETEE_IN_GAG(0, tree(s(T209), T202, T201)) → DELETEE_IN_GAG(0, T202)
The graph contains the following edges 1 >= 1, 2 > 2
DELETEE_IN_GAG(s(T274), tree(0, T263, T265)) → DELETEE_IN_GAG(s(T274), T265)
The graph contains the following edges 1 >= 1, 2 > 2
PG_IN_GGAG(T227, T222, T202) → U11_GGAG(T227, T202, lessB_in_gg(T227, T222))
The graph contains the following edges 1 >= 1, 3 >= 2
PH_IN_GGAG(T283, T289, T265) → U14_GGAG(T289, T265, lessC_in_gg(T283, T289))
The graph contains the following edges 2 >= 1, 3 >= 2
U11_GGAG(T227, T202, lessB_out_gg) → DELETEE_IN_GAG(s(T227), T202)
The graph contains the following edges 2 >= 2
U14_GGAG(T289, T265, lessC_out_gg) → DELETEE_IN_GAG(s(T289), T265)
The graph contains the following edges 2 >= 2
DELETEE_IN_GAG(s(T223), tree(s(T222), T202, T201)) → PG_IN_GGAG(T223, T222, T202)
The graph contains the following edges 1 > 1, 2 > 2, 2 > 3
DELETEE_IN_GAG(s(T285), tree(s(T283), T263, T265)) → PH_IN_GGAG(T283, T285, T265)
The graph contains the following edges 2 > 1, 1 > 2, 2 > 3

(50) YES

(51) Obligation:

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

DELETEE_IN_AAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → PD_IN_GAAG(T163, T167, T168, T166)
PD_IN_GAAG(T163, T171, T172, T166) → U5_GAAG(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_GAAG(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → DELETEE_IN_AAG(T171, T172, T166)
DELETEE_IN_AAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → DELETEE_IN_AAG(s(T274), T273, T265)
DELETEE_IN_AAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → PH_IN_GAAG(T283, T285, T286, T265)
PH_IN_GAAG(T283, T289, T290, T265) → U14_GAAG(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_GAAG(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → DELETEE_IN_AAG(s(T289), T290, T265)

The TRS R consists of the following rules:

deleteE_in_aag(T6, tree(T6, void, T7), T7) → deleteE_out_aag(T6, tree(T6, void, T7), T7)
deleteE_in_aag(T10, tree(T10, T11, void), T11) → deleteE_out_aag(T10, tree(T10, T11, void), T11)
deleteE_in_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_aag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
delminA_in_agg(tree(T76, void, T77), T76, T77) → delminA_out_agg(tree(T76, void, T77), T76, T77)
delminA_in_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95)) → U1_agg(T90, T96, T92, T93, T94, T95, delminA_in_agg(T96, T93, T94))
U1_agg(T90, T96, T92, T93, T94, T95, delminA_out_agg(T96, T93, T94)) → delminA_out_agg(tree(T90, T96, T92), T93, tree(T90, T94, T95))
U16_aag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_aag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_aag(T126, T122, T127, T124, T125, pF_in_agag(T126, T122, T127, T125))
pF_in_agag(T126, T122, T127, T125) → U7_agag(T126, T122, T127, T125, lessB_in_ag(T126, T122))
lessB_in_ag(0, s(T138)) → lessB_out_ag(0, s(T138))
lessB_in_ag(s(T145), s(T144)) → U2_ag(T145, T144, lessB_in_ag(T145, T144))
U2_ag(T145, T144, lessB_out_ag(T145, T144)) → lessB_out_ag(s(T145), s(T144))
U7_agag(T126, T122, T127, T125, lessB_out_ag(T126, T122)) → pF_out_agag(T126, T122, T127, T125)
pF_in_agag(T130, T122, T131, T125) → U8_agag(T130, T122, T131, T125, lessB_in_ag(T130, T122))
U8_agag(T130, T122, T131, T125, lessB_out_ag(T130, T122)) → U9_agag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T6, tree(T6, void, T7), T7) → deleteE_out_gag(T6, tree(T6, void, T7), T7)
deleteE_in_gag(T10, tree(T10, T11, void), T11) → deleteE_out_gag(T10, tree(T10, T11, void), T11)
deleteE_in_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32)) → deleteE_out_gag(T17, tree(T17, T18, tree(T31, void, T32)), tree(T31, T18, T32))
deleteE_in_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62))) → U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_in_agg(T63, T60, T61))
U16_gag(T17, T18, T57, T63, T59, T60, T61, T62, delminA_out_agg(T63, T60, T61)) → deleteE_out_gag(T17, tree(T17, T18, tree(T57, T63, T59)), tree(T60, T18, tree(T57, T61, T62)))
deleteE_in_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124)) → U17_gag(T126, T122, T127, T124, T125, pF_in_ggag(T126, T122, T127, T125))
pF_in_ggag(T126, T122, T127, T125) → U7_ggag(T126, T122, T127, T125, lessB_in_gg(T126, T122))
lessB_in_gg(0, s(T138)) → lessB_out_gg(0, s(T138))
lessB_in_gg(s(T145), s(T144)) → U2_gg(T145, T144, lessB_in_gg(T145, T144))
U2_gg(T145, T144, lessB_out_gg(T145, T144)) → lessB_out_gg(s(T145), s(T144))
U7_ggag(T126, T122, T127, T125, lessB_out_gg(T126, T122)) → pF_out_ggag(T126, T122, T127, T125)
pF_in_ggag(T130, T122, T131, T125) → U8_ggag(T130, T122, T131, T125, lessB_in_gg(T130, T122))
U8_ggag(T130, T122, T131, T125, lessB_out_gg(T130, T122)) → U9_ggag(T130, T122, T131, T125, deleteE_in_gag(T130, T131, T125))
deleteE_in_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_gag(T167, T163, T164, T168, T166, pD_in_ggag(T163, T167, T168, T166))
pD_in_ggag(T163, T167, T168, T166) → U4_ggag(T163, T167, T168, T166, lessC_in_gg(T163, T167))
lessC_in_gg(0, s(T179)) → lessC_out_gg(0, s(T179))
lessC_in_gg(s(T184), s(T186)) → U3_gg(T184, T186, lessC_in_gg(T184, T186))
U3_gg(T184, T186, lessC_out_gg(T184, T186)) → lessC_out_gg(s(T184), s(T186))
U4_ggag(T163, T167, T168, T166, lessC_out_gg(T163, T167)) → pD_out_ggag(T163, T167, T168, T166)
pD_in_ggag(T163, T171, T172, T166) → U5_ggag(T163, T171, T172, T166, lessC_in_gg(T163, T171))
U5_ggag(T163, T171, T172, T166, lessC_out_gg(T163, T171)) → U6_ggag(T163, T171, T172, T166, deleteE_in_gag(T171, T172, T166))
deleteE_in_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_gag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
deleteE_in_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_gag(T223, T222, T224, T201, T202, pG_in_ggag(T223, T222, T224, T202))
pG_in_ggag(T223, T222, T224, T202) → U10_ggag(T223, T222, T224, T202, lessB_in_gg(T223, T222))
U10_ggag(T223, T222, T224, T202, lessB_out_gg(T223, T222)) → pG_out_ggag(T223, T222, T224, T202)
pG_in_ggag(T227, T222, T228, T202) → U11_ggag(T227, T222, T228, T202, lessB_in_gg(T227, T222))
U11_ggag(T227, T222, T228, T202, lessB_out_gg(T227, T222)) → U12_ggag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
deleteE_in_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_gag(T252, T248, T249, T253, T251, pD_in_ggag(T248, T252, T253, T251))
U21_gag(T252, T248, T249, T253, T251, pD_out_ggag(T248, T252, T253, T251)) → deleteE_out_gag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_gag(T274, T263, T273, T265, deleteE_in_gag(s(T274), T273, T265))
deleteE_in_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_gag(T285, T283, T263, T286, T265, pH_in_ggag(T283, T285, T286, T265))
pH_in_ggag(T283, T285, T286, T265) → U13_ggag(T283, T285, T286, T265, lessC_in_gg(T283, T285))
U13_ggag(T283, T285, T286, T265, lessC_out_gg(T283, T285)) → pH_out_ggag(T283, T285, T286, T265)
pH_in_ggag(T283, T289, T290, T265) → U14_ggag(T283, T289, T290, T265, lessC_in_gg(T283, T289))
U14_ggag(T283, T289, T290, T265, lessC_out_gg(T283, T289)) → U15_ggag(T283, T289, T290, T265, deleteE_in_gag(s(T289), T290, T265))
deleteE_in_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_gag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_gag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_gag(T380, T376, T381, T378, T379, pF_in_ggag(T380, T376, T381, T379))
U25_gag(T380, T376, T381, T378, T379, pF_out_ggag(T380, T376, T381, T379)) → deleteE_out_gag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_gag(T399, T395, T396, T400, T398, pD_in_ggag(T395, T399, T400, T398))
U26_gag(T399, T395, T396, T400, T398, pD_out_ggag(T395, T399, T400, T398)) → deleteE_out_gag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_gag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
deleteE_in_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_gag(T433, T432, T434, T411, T412, pG_in_ggag(T433, T432, T434, T412))
U28_gag(T433, T432, T434, T411, T412, pG_out_ggag(T433, T432, T434, T412)) → deleteE_out_gag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_gag(T452, T448, T449, T453, T451, pD_in_ggag(T448, T452, T453, T451))
U29_gag(T452, T448, T449, T453, T451, pD_out_ggag(T448, T452, T453, T451)) → deleteE_out_gag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_gag(T474, T463, T473, T465, deleteE_in_gag(s(T474), T473, T465))
deleteE_in_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_gag(T485, T483, T463, T486, T465, pH_in_ggag(T483, T485, T486, T465))
U31_gag(T485, T483, T463, T486, T465, pH_out_ggag(T483, T485, T486, T465)) → deleteE_out_gag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_gag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_gag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_gag(T574, T570, T575, T572, T573, pF_in_ggag(T574, T570, T575, T573))
U33_gag(T574, T570, T575, T572, T573, pF_out_ggag(T574, T570, T575, T573)) → deleteE_out_gag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_gag(T593, T589, T590, T594, T592, pD_in_ggag(T589, T593, T594, T592))
U34_gag(T593, T589, T590, T594, T592, pD_out_ggag(T589, T593, T594, T592)) → deleteE_out_gag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_gag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
deleteE_in_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_gag(T627, T626, T628, T605, T606, pG_in_ggag(T627, T626, T628, T606))
U36_gag(T627, T626, T628, T605, T606, pG_out_ggag(T627, T626, T628, T606)) → deleteE_out_gag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_gag(T646, T642, T643, T647, T645, pD_in_ggag(T642, T646, T647, T645))
U37_gag(T646, T642, T643, T647, T645, pD_out_ggag(T642, T646, T647, T645)) → deleteE_out_gag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_gag(T668, T657, T667, T659, deleteE_in_gag(s(T668), T667, T659))
deleteE_in_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_gag(T679, T677, T657, T680, T659, pH_in_ggag(T677, T679, T680, T659))
U39_gag(T679, T677, T657, T680, T659, pH_out_ggag(T677, T679, T680, T659)) → deleteE_out_gag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_gag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_gag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_gag(T764, T760, T765, T762, T763, pF_in_ggag(T764, T760, T765, T763))
U41_gag(T764, T760, T765, T762, T763, pF_out_ggag(T764, T760, T765, T763)) → deleteE_out_gag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_gag(T783, T779, T780, T784, T782, pD_in_ggag(T779, T783, T784, T782))
U42_gag(T783, T779, T780, T784, T782, pD_out_ggag(T779, T783, T784, T782)) → deleteE_out_gag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_gag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
deleteE_in_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_gag(T817, T816, T818, T795, T796, pG_in_ggag(T817, T816, T818, T796))
U44_gag(T817, T816, T818, T795, T796, pG_out_ggag(T817, T816, T818, T796)) → deleteE_out_gag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_gag(T836, T832, T833, T837, T835, pD_in_ggag(T832, T836, T837, T835))
U45_gag(T836, T832, T833, T837, T835, pD_out_ggag(T832, T836, T837, T835)) → deleteE_out_gag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_gag(T858, T847, T857, T849, deleteE_in_gag(s(T858), T857, T849))
deleteE_in_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_gag(T869, T867, T847, T870, T849, pH_in_ggag(T867, T869, T870, T849))
U47_gag(T869, T867, T847, T870, T849, pH_out_ggag(T867, T869, T870, T849)) → deleteE_out_gag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_gag(T858, T847, T857, T849, deleteE_out_gag(s(T858), T857, T849)) → deleteE_out_gag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U43_gag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_gag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
U38_gag(T668, T657, T667, T659, deleteE_out_gag(s(T668), T667, T659)) → deleteE_out_gag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U35_gag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_gag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
U30_gag(T474, T463, T473, T465, deleteE_out_gag(s(T474), T473, T465)) → deleteE_out_gag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U27_gag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_gag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
U15_ggag(T283, T289, T290, T265, deleteE_out_gag(s(T289), T290, T265)) → pH_out_ggag(T283, T289, T290, T265)
U23_gag(T285, T283, T263, T286, T265, pH_out_ggag(T283, T285, T286, T265)) → deleteE_out_gag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_gag(T274, T263, T273, T265, deleteE_out_gag(s(T274), T273, T265)) → deleteE_out_gag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U12_ggag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_ggag(T227, T222, T228, T202)
U20_gag(T223, T222, T224, T201, T202, pG_out_ggag(T223, T222, T224, T202)) → deleteE_out_gag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
U19_gag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_gag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
U6_ggag(T163, T171, T172, T166, deleteE_out_gag(T171, T172, T166)) → pD_out_ggag(T163, T171, T172, T166)
U18_gag(T167, T163, T164, T168, T166, pD_out_ggag(T163, T167, T168, T166)) → deleteE_out_gag(T167, tree(T163, T164, T168), tree(T163, T164, T166))
U9_ggag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_ggag(T130, T122, T131, T125)
U17_gag(T126, T122, T127, T124, T125, pF_out_ggag(T126, T122, T127, T125)) → deleteE_out_gag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
U9_agag(T130, T122, T131, T125, deleteE_out_gag(T130, T131, T125)) → pF_out_agag(T130, T122, T131, T125)
U17_aag(T126, T122, T127, T124, T125, pF_out_agag(T126, T122, T127, T125)) → deleteE_out_aag(T126, tree(T122, T127, T124), tree(T122, T125, T124))
deleteE_in_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → U18_aag(T167, T163, T164, T168, T166, pD_in_gaag(T163, T167, T168, T166))
pD_in_gaag(T163, T167, T168, T166) → U4_gaag(T163, T167, T168, T166, lessC_in_ga(T163, T167))
lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))
U4_gaag(T163, T167, T168, T166, lessC_out_ga(T163, T167)) → pD_out_gaag(T163, T167, T168, T166)
pD_in_gaag(T163, T171, T172, T166) → U5_gaag(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_gaag(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → U6_gaag(T163, T171, T172, T166, deleteE_in_aag(T171, T172, T166))
deleteE_in_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201)) → U19_aag(T209, T210, T201, T202, deleteE_in_gag(0, T210, T202))
U19_aag(T209, T210, T201, T202, deleteE_out_gag(0, T210, T202)) → deleteE_out_aag(0, tree(s(T209), T210, T201), tree(s(T209), T202, T201))
deleteE_in_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201)) → U20_aag(T223, T222, T224, T201, T202, pG_in_agag(T223, T222, T224, T202))
pG_in_agag(T223, T222, T224, T202) → U10_agag(T223, T222, T224, T202, lessB_in_ag(T223, T222))
U10_agag(T223, T222, T224, T202, lessB_out_ag(T223, T222)) → pG_out_agag(T223, T222, T224, T202)
pG_in_agag(T227, T222, T228, T202) → U11_agag(T227, T222, T228, T202, lessB_in_ag(T227, T222))
U11_agag(T227, T222, T228, T202, lessB_out_ag(T227, T222)) → U12_agag(T227, T222, T228, T202, deleteE_in_gag(s(T227), T228, T202))
U12_agag(T227, T222, T228, T202, deleteE_out_gag(s(T227), T228, T202)) → pG_out_agag(T227, T222, T228, T202)
U20_aag(T223, T222, T224, T201, T202, pG_out_agag(T223, T222, T224, T202)) → deleteE_out_aag(s(T223), tree(s(T222), T224, T201), tree(s(T222), T202, T201))
deleteE_in_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251)) → U21_aag(T252, T248, T249, T253, T251, pD_in_gaag(T248, T252, T253, T251))
U21_aag(T252, T248, T249, T253, T251, pD_out_gaag(T248, T252, T253, T251)) → deleteE_out_aag(T252, tree(T248, T249, T253), tree(T248, T249, T251))
deleteE_in_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → U22_aag(T274, T263, T273, T265, deleteE_in_aag(s(T274), T273, T265))
deleteE_in_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → U23_aag(T285, T283, T263, T286, T265, pH_in_gaag(T283, T285, T286, T265))
pH_in_gaag(T283, T285, T286, T265) → U13_gaag(T283, T285, T286, T265, lessC_in_ga(T283, T285))
U13_gaag(T283, T285, T286, T265, lessC_out_ga(T283, T285)) → pH_out_gaag(T283, T285, T286, T265)
pH_in_gaag(T283, T289, T290, T265) → U14_gaag(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_gaag(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → U15_gaag(T283, T289, T290, T265, deleteE_in_aag(s(T289), T290, T265))
deleteE_in_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349))) → U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_in_agg(T350, T347, T348))
U24_aag(T304, T305, T344, T350, T346, T347, T348, T349, delminA_out_agg(T350, T347, T348)) → deleteE_out_aag(T304, tree(T304, T305, tree(T344, T350, T346)), tree(T347, T305, tree(T344, T348, T349)))
deleteE_in_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378)) → U25_aag(T380, T376, T381, T378, T379, pF_in_agag(T380, T376, T381, T379))
U25_aag(T380, T376, T381, T378, T379, pF_out_agag(T380, T376, T381, T379)) → deleteE_out_aag(T380, tree(T376, T381, T378), tree(T376, T379, T378))
deleteE_in_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398)) → U26_aag(T399, T395, T396, T400, T398, pD_in_gaag(T395, T399, T400, T398))
U26_aag(T399, T395, T396, T400, T398, pD_out_gaag(T395, T399, T400, T398)) → deleteE_out_aag(T399, tree(T395, T396, T400), tree(T395, T396, T398))
deleteE_in_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411)) → U27_aag(T419, T420, T411, T412, deleteE_in_gag(0, T420, T412))
U27_aag(T419, T420, T411, T412, deleteE_out_gag(0, T420, T412)) → deleteE_out_aag(0, tree(s(T419), T420, T411), tree(s(T419), T412, T411))
deleteE_in_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411)) → U28_aag(T433, T432, T434, T411, T412, pG_in_agag(T433, T432, T434, T412))
U28_aag(T433, T432, T434, T411, T412, pG_out_agag(T433, T432, T434, T412)) → deleteE_out_aag(s(T433), tree(s(T432), T434, T411), tree(s(T432), T412, T411))
deleteE_in_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451)) → U29_aag(T452, T448, T449, T453, T451, pD_in_gaag(T448, T452, T453, T451))
U29_aag(T452, T448, T449, T453, T451, pD_out_gaag(T448, T452, T453, T451)) → deleteE_out_aag(T452, tree(T448, T449, T453), tree(T448, T449, T451))
deleteE_in_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465)) → U30_aag(T474, T463, T473, T465, deleteE_in_aag(s(T474), T473, T465))
deleteE_in_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465)) → U31_aag(T485, T483, T463, T486, T465, pH_in_gaag(T483, T485, T486, T465))
U31_aag(T485, T483, T463, T486, T465, pH_out_gaag(T483, T485, T486, T465)) → deleteE_out_aag(s(T485), tree(s(T483), T463, T486), tree(s(T483), T463, T465))
deleteE_in_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543))) → U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_in_agg(T544, T541, T542))
U32_aag(T498, T499, T538, T544, T540, T541, T542, T543, delminA_out_agg(T544, T541, T542)) → deleteE_out_aag(T498, tree(T498, T499, tree(T538, T544, T540)), tree(T541, T499, tree(T538, T542, T543)))
deleteE_in_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572)) → U33_aag(T574, T570, T575, T572, T573, pF_in_agag(T574, T570, T575, T573))
U33_aag(T574, T570, T575, T572, T573, pF_out_agag(T574, T570, T575, T573)) → deleteE_out_aag(T574, tree(T570, T575, T572), tree(T570, T573, T572))
deleteE_in_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592)) → U34_aag(T593, T589, T590, T594, T592, pD_in_gaag(T589, T593, T594, T592))
U34_aag(T593, T589, T590, T594, T592, pD_out_gaag(T589, T593, T594, T592)) → deleteE_out_aag(T593, tree(T589, T590, T594), tree(T589, T590, T592))
deleteE_in_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605)) → U35_aag(T613, T614, T605, T606, deleteE_in_gag(0, T614, T606))
U35_aag(T613, T614, T605, T606, deleteE_out_gag(0, T614, T606)) → deleteE_out_aag(0, tree(s(T613), T614, T605), tree(s(T613), T606, T605))
deleteE_in_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605)) → U36_aag(T627, T626, T628, T605, T606, pG_in_agag(T627, T626, T628, T606))
U36_aag(T627, T626, T628, T605, T606, pG_out_agag(T627, T626, T628, T606)) → deleteE_out_aag(s(T627), tree(s(T626), T628, T605), tree(s(T626), T606, T605))
deleteE_in_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645)) → U37_aag(T646, T642, T643, T647, T645, pD_in_gaag(T642, T646, T647, T645))
U37_aag(T646, T642, T643, T647, T645, pD_out_gaag(T642, T646, T647, T645)) → deleteE_out_aag(T646, tree(T642, T643, T647), tree(T642, T643, T645))
deleteE_in_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659)) → U38_aag(T668, T657, T667, T659, deleteE_in_aag(s(T668), T667, T659))
deleteE_in_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659)) → U39_aag(T679, T677, T657, T680, T659, pH_in_gaag(T677, T679, T680, T659))
U39_aag(T679, T677, T657, T680, T659, pH_out_gaag(T677, T679, T680, T659)) → deleteE_out_aag(s(T679), tree(s(T677), T657, T680), tree(s(T677), T657, T659))
deleteE_in_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733))) → U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_in_agg(T734, T731, T732))
U40_aag(T688, T689, T728, T734, T730, T731, T732, T733, delminA_out_agg(T734, T731, T732)) → deleteE_out_aag(T688, tree(T688, T689, tree(T728, T734, T730)), tree(T731, T689, tree(T728, T732, T733)))
deleteE_in_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762)) → U41_aag(T764, T760, T765, T762, T763, pF_in_agag(T764, T760, T765, T763))
U41_aag(T764, T760, T765, T762, T763, pF_out_agag(T764, T760, T765, T763)) → deleteE_out_aag(T764, tree(T760, T765, T762), tree(T760, T763, T762))
deleteE_in_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782)) → U42_aag(T783, T779, T780, T784, T782, pD_in_gaag(T779, T783, T784, T782))
U42_aag(T783, T779, T780, T784, T782, pD_out_gaag(T779, T783, T784, T782)) → deleteE_out_aag(T783, tree(T779, T780, T784), tree(T779, T780, T782))
deleteE_in_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795)) → U43_aag(T803, T804, T795, T796, deleteE_in_gag(0, T804, T796))
U43_aag(T803, T804, T795, T796, deleteE_out_gag(0, T804, T796)) → deleteE_out_aag(0, tree(s(T803), T804, T795), tree(s(T803), T796, T795))
deleteE_in_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795)) → U44_aag(T817, T816, T818, T795, T796, pG_in_agag(T817, T816, T818, T796))
U44_aag(T817, T816, T818, T795, T796, pG_out_agag(T817, T816, T818, T796)) → deleteE_out_aag(s(T817), tree(s(T816), T818, T795), tree(s(T816), T796, T795))
deleteE_in_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835)) → U45_aag(T836, T832, T833, T837, T835, pD_in_gaag(T832, T836, T837, T835))
U45_aag(T836, T832, T833, T837, T835, pD_out_gaag(T832, T836, T837, T835)) → deleteE_out_aag(T836, tree(T832, T833, T837), tree(T832, T833, T835))
deleteE_in_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849)) → U46_aag(T858, T847, T857, T849, deleteE_in_aag(s(T858), T857, T849))
deleteE_in_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849)) → U47_aag(T869, T867, T847, T870, T849, pH_in_gaag(T867, T869, T870, T849))
U47_aag(T869, T867, T847, T870, T849, pH_out_gaag(T867, T869, T870, T849)) → deleteE_out_aag(s(T869), tree(s(T867), T847, T870), tree(s(T867), T847, T849))
U46_aag(T858, T847, T857, T849, deleteE_out_aag(s(T858), T857, T849)) → deleteE_out_aag(s(T858), tree(0, T847, T857), tree(0, T847, T849))
U38_aag(T668, T657, T667, T659, deleteE_out_aag(s(T668), T667, T659)) → deleteE_out_aag(s(T668), tree(0, T657, T667), tree(0, T657, T659))
U30_aag(T474, T463, T473, T465, deleteE_out_aag(s(T474), T473, T465)) → deleteE_out_aag(s(T474), tree(0, T463, T473), tree(0, T463, T465))
U15_gaag(T283, T289, T290, T265, deleteE_out_aag(s(T289), T290, T265)) → pH_out_gaag(T283, T289, T290, T265)
U23_aag(T285, T283, T263, T286, T265, pH_out_gaag(T283, T285, T286, T265)) → deleteE_out_aag(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265))
U22_aag(T274, T263, T273, T265, deleteE_out_aag(s(T274), T273, T265)) → deleteE_out_aag(s(T274), tree(0, T263, T273), tree(0, T263, T265))
U6_gaag(T163, T171, T172, T166, deleteE_out_aag(T171, T172, T166)) → pD_out_gaag(T163, T171, T172, T166)
U18_aag(T167, T163, T164, T168, T166, pD_out_gaag(T163, T167, T168, T166)) → deleteE_out_aag(T167, tree(T163, T164, T168), tree(T163, T164, T166))

(52) UsableRulesProof (EQUIVALENT transformation)

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

(53) Obligation:

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

DELETEE_IN_AAG(T167, tree(T163, T164, T168), tree(T163, T164, T166)) → PD_IN_GAAG(T163, T167, T168, T166)
PD_IN_GAAG(T163, T171, T172, T166) → U5_GAAG(T163, T171, T172, T166, lessC_in_ga(T163, T171))
U5_GAAG(T163, T171, T172, T166, lessC_out_ga(T163, T171)) → DELETEE_IN_AAG(T171, T172, T166)
DELETEE_IN_AAG(s(T274), tree(0, T263, T273), tree(0, T263, T265)) → DELETEE_IN_AAG(s(T274), T273, T265)
DELETEE_IN_AAG(s(T285), tree(s(T283), T263, T286), tree(s(T283), T263, T265)) → PH_IN_GAAG(T283, T285, T286, T265)
PH_IN_GAAG(T283, T289, T290, T265) → U14_GAAG(T283, T289, T290, T265, lessC_in_ga(T283, T289))
U14_GAAG(T283, T289, T290, T265, lessC_out_ga(T283, T289)) → DELETEE_IN_AAG(s(T289), T290, T265)

The TRS R consists of the following rules:

lessC_in_ga(0, s(T179)) → lessC_out_ga(0, s(T179))
lessC_in_ga(s(T184), s(T186)) → U3_ga(T184, T186, lessC_in_ga(T184, T186))
U3_ga(T184, T186, lessC_out_ga(T184, T186)) → lessC_out_ga(s(T184), s(T186))

The argument filtering Pi contains the following mapping:
tree(x1, x2, x3) = tree(x1, x2, x3)
s(x1) = s(x1)
0 = 0
lessC_in_ga(x1, x2) = lessC_in_ga(x1)
lessC_out_ga(x1, x2) = lessC_out_ga
U3_ga(x1, x2, x3) = U3_ga(x3)
DELETEE_IN_AAG(x1, x2, x3) = DELETEE_IN_AAG(x3)
PD_IN_GAAG(x1, x2, x3, x4) = PD_IN_GAAG(x1, x4)
U5_GAAG(x1, x2, x3, x4, x5) = U5_GAAG(x4, x5)
PH_IN_GAAG(x1, x2, x3, x4) = PH_IN_GAAG(x1, x4)
U14_GAAG(x1, x2, x3, x4, x5) = U14_GAAG(x4, x5)

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

(54) PiDPToQDPProof (SOUND transformation)

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

(55) Obligation:

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

DELETEE_IN_AAG(tree(T163, T164, T166)) → PD_IN_GAAG(T163, T166)
PD_IN_GAAG(T163, T166) → U5_GAAG(T166, lessC_in_ga(T163))
U5_GAAG(T166, lessC_out_ga) → DELETEE_IN_AAG(T166)
DELETEE_IN_AAG(tree(0, T263, T265)) → DELETEE_IN_AAG(T265)
DELETEE_IN_AAG(tree(s(T283), T263, T265)) → PH_IN_GAAG(T283, T265)
PH_IN_GAAG(T283, T265) → U14_GAAG(T265, lessC_in_ga(T283))
U14_GAAG(T265, lessC_out_ga) → DELETEE_IN_AAG(T265)

The TRS R consists of the following rules:

lessC_in_ga(0) → lessC_out_ga
lessC_in_ga(s(T184)) → U3_ga(lessC_in_ga(T184))
U3_ga(lessC_out_ga) → lessC_out_ga

The set Q consists of the following terms:

lessC_in_ga(x0)
U3_ga(x0)

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

(56) 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:

PD_IN_GAAG(T163, T166) → U5_GAAG(T166, lessC_in_ga(T163))
The graph contains the following edges 2 >= 1
U5_GAAG(T166, lessC_out_ga) → DELETEE_IN_AAG(T166)
The graph contains the following edges 1 >= 1
DELETEE_IN_AAG(tree(T163, T164, T166)) → PD_IN_GAAG(T163, T166)
The graph contains the following edges 1 > 1, 1 > 2
DELETEE_IN_AAG(tree(0, T263, T265)) → DELETEE_IN_AAG(T265)
The graph contains the following edges 1 > 1
U14_GAAG(T265, lessC_out_ga) → DELETEE_IN_AAG(T265)
The graph contains the following edges 1 >= 1
DELETEE_IN_AAG(tree(s(T283), T263, T265)) → PH_IN_GAAG(T283, T265)
The graph contains the following edges 1 > 1, 1 > 2
PH_IN_GAAG(T283, T265) → U14_GAAG(T265, lessC_in_ga(T283))
The graph contains the following edges 2 >= 1

(0) Obligation:

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

(2) Obligation:

(3) PrologToPiTRSProof (SOUND transformation)

(4) Obligation:

(5) DependencyPairsProof (EQUIVALENT transformation)

(6) Obligation:

(7) DependencyGraphProof (EQUIVALENT transformation)

(8) Complex Obligation (AND)

(9) Obligation:

(10) UsableRulesProof (EQUIVALENT transformation)

(11) Obligation:

(12) PiDPToQDPProof (SOUND transformation)

(13) Obligation:

(14) QDPSizeChangeProof (EQUIVALENT transformation)

(15) YES

(16) Obligation:

(17) UsableRulesProof (EQUIVALENT transformation)

(18) Obligation:

(19) PiDPToQDPProof (EQUIVALENT transformation)

(20) Obligation:

(21) QDPSizeChangeProof (EQUIVALENT transformation)

(22) YES

(23) Obligation:

(24) UsableRulesProof (EQUIVALENT transformation)

(25) Obligation:

(26) PiDPToQDPProof (EQUIVALENT transformation)

(27) Obligation:

(28) QDPSizeChangeProof (EQUIVALENT transformation)

(29) YES

(30) Obligation:

(31) UsableRulesProof (EQUIVALENT transformation)

(32) Obligation:

(33) PiDPToQDPProof (SOUND transformation)

(34) Obligation:

(35) QDPSizeChangeProof (EQUIVALENT transformation)

(36) YES

(37) Obligation:

(38) UsableRulesProof (EQUIVALENT transformation)

(39) Obligation:

(40) PiDPToQDPProof (SOUND transformation)

(41) Obligation:

(42) QDPSizeChangeProof (EQUIVALENT transformation)

(43) YES

(44) Obligation:

(45) UsableRulesProof (EQUIVALENT transformation)

(46) Obligation:

(47) PiDPToQDPProof (SOUND transformation)

(48) Obligation:

(49) QDPSizeChangeProof (EQUIVALENT transformation)

(50) YES

(51) Obligation:

(52) UsableRulesProof (EQUIVALENT transformation)

(53) Obligation:

(54) PiDPToQDPProof (SOUND transformation)

(55) Obligation:

(56) QDPSizeChangeProof (EQUIVALENT transformation)

(57) YES